ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW299+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 : n006.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 09:05:15 AM UTC 2026

% Result   : Theorem 107.35s 107.65s
% Output   : Proof 107.57s
% 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_empty,axiom,
    ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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_triple_Oinject,axiom,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
      ( c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2) = c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_H_2,V_com_H_2,V_fun2_H_2)
    <=> ( V_fun2_2 = V_fun2_H_2
        & V_com_2 = V_com_H_2
        & V_fun1_2 = V_fun1_H_2 ) ),
    file('theBenchmark.p',fact_triple_Oinject) ).

fof(fact_cut,axiom,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
    file('theBenchmark.p',fact_cut) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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_Ga_2,V_ts_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ),
    file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_triple_Orecs,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    file('theBenchmark.p',fact_triple_Orecs) ).

fof(fact_triple_Osimps_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    file('theBenchmark.p',fact_triple_Osimps_I2_J) ).

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__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_doubleton__eq__iff,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_ca_2 ) ) ),
    file('theBenchmark.p',fact_doubleton__eq__iff) ).

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_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_hoare__derivs_OSkip,axiom,
    ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSKIP,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_OSkip) ).

fof(fact_hoare__derivs_Oequations_I7_J,axiom,
    ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_a2_2,c_Com_Ocom_OSKIP,V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

fof(fact_Comp,axiom,
    ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Qa_2,V_d_2,V_R_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSemi(V_ca_2,V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_Comp) ).

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_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_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_com_Osimps_I12_J,axiom,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
    file('theBenchmark.p',fact_com_Osimps_I12_J) ).

fof(fact_com_Osimps_I13_J,axiom,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I13_J) ).

fof(fact_com_Osimps_I3_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
      ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
    <=> ( V_com2_2 = V_com2_H_2
        & V_com1_2 = V_com1_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_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_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_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_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_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_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_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_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_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_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_equalityCE,axiom,
    ! [V_ca_2,T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
       => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_equalityCE) ).

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_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_ca_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_ca_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subsetD) ).

fof(fact_UnE,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_UnE) ).

fof(fact_UnCI,axiom,
    ! [V_A_2,V_B_2,V_ca_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_DiffI,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_DiffE) ).

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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_Diff__iff,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Diff__iff) ).

fof(fact_Un__iff,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Un__iff) ).

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_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_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_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_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_bex__Un,axiom,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x)) )
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
           => hBOOL(hAPP(V_Pa_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_ball__Un) ).

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_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_UnI1,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_DiffD1,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    file('theBenchmark.p',fact_DiffD1) ).

fof(fact_DiffD2,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2)) ),
    file('theBenchmark.p',fact_DiffD2) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_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_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_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_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_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_asm,axiom,
    ! [V_Ga_2,V_ts_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ),
    file('theBenchmark.p',fact_asm) ).

fof(fact_weaken,axiom,
    ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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_ts_2),V_ts_H_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
    file('theBenchmark.p',fact_weaken) ).

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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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__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__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_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__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__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_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__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__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_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__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__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_rev__predicate1D,axiom,
    ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
       => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_predicate1D,axiom,
    ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
     => ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_predicate1D) ).

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_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_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__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_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_diff__eq__diff__less__eq,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

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_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_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_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_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_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__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_nonempty__iff,axiom,
    ! [T_b,V_A_2] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ? [B_x,B_B] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
          & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) ) ),
    file('theBenchmark.p',fact_nonempty__iff) ).

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_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_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_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__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_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_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_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__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_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_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_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_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_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__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__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__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_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_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_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_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_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_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_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_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__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_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_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_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_diff__eq__diff__less,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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_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__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_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__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_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_psubsetD,axiom,
    ! [V_ca_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_ca_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubsetD) ).

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_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__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_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_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__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_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_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_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__UnI,axiom,
    ! [V_Ga_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_Ga_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_Ga_2))) ) ),
    file('theBenchmark.p',fact_finite__UnI) ).

fof(fact_finite__Un,axiom,
    ! [V_Ga_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_Ga_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__Un) ).

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_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_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_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_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_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_diff__eq__diff__eq,axiom,
    ! [V_d_2,V_ca_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_ca_2),V_d_2)
       => ( V_a_2 = V_b_2
        <=> V_ca_2 = V_d_2 ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__eq) ).

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_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_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_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_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_finite__empty__induct,axiom,
    ! [V_Pa_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(V_Pa_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_Pa_2,B_A))
                 => hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,B_F))
                     => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
           => hBOOL(hAPP(V_Pa_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_IntI,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_IntE) ).

fof(fact_finite__Int,axiom,
    ! [V_Ga_2,V_F_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_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_Ga_2))) ),
    file('theBenchmark.p',fact_finite__Int) ).

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_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_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_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_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__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_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_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_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__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_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_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__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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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_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_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_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__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__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_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_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__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_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_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_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_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__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__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__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_Int__iff,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__iff) ).

fof(fact_IntD1,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    file('theBenchmark.p',fact_IntD1) ).

fof(fact_IntD2,axiom,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2)) ),
    file('theBenchmark.p',fact_IntD2) ).

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_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_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_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__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__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_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_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_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_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_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_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__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__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,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,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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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__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_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_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_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_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_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__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__right__cancel,axiom,
    ! [V_ca_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_ca_2),V_a_2)
      <=> V_b_2 = V_ca_2 ) ),
    file('theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__left__cancel,axiom,
    ! [V_ca_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_ca_2)
      <=> V_b_2 = V_ca_2 ) ),
    file('theBenchmark.p',fact_add__left__cancel) ).

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_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_add__le__cancel__right,axiom,
    ! [V_b_2,V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_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_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_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_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_less__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_less__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

fof(fact_le__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2) = V_d_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

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_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_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_ca_2,V_b_2,V_a_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( ( V_ca_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_ca_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_ca_2)) ) ),
    file('theBenchmark.p',fact_crossproduct__noteq) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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__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__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__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__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_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__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_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_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_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_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_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_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_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_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_Pa_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_Pa_2,V_n_2),V_m_2)) )
     => ( ( V_m_2 = V_n_2
         => hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2)) )
         => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_nat__less__cases) ).

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_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_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_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_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__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_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__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__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_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_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_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_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_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_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__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_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_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_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__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__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__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_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__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_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_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__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_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__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_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_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__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_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__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_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_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__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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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__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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__n__not__n,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    file('theBenchmark.p',fact_Suc__n__not__n) ).

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_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_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__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__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_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__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_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__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_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_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_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_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__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_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_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_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_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_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__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__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__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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_inf__le__fold__inf,axiom,
    ! [V_ca_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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_inf__le__fold__inf) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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__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__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_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_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_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__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__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_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_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_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_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_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__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__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__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_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_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_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_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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_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_ca_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_ca_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_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_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_ca_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_ca_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_ca_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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__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_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_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__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__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__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__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_mult__le__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_ca_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_ca_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_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_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_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_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_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_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_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__asm,axiom,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_Pa_2,B_d))
              & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          | ( ~ hBOOL(hAPP(V_Pa_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_nat__diff__split,axiom,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_d)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
         => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split) ).

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_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_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_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_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_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_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_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_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_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_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_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_triple_Osize_I1_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_triple_Osize_I1_J) ).

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_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_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__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_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__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_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_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_triple_Osize_I2_J,axiom,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_triple_Osize_I2_J) ).

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_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_com_Osize_I4_J,axiom,
    ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I4_J) ).

fof(fact_com_Osize_I12_J,axiom,
    ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I12_J) ).

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_ex__least__nat__less,axiom,
    ! [V_n_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_Pa_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_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_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_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_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_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_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_nonzero__divide__eq__eq,axiom,
    ! [V_a_2,V_b_2,V_ca_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
        <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ),
    file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ),
    file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).

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_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_com_Osize_I9_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I9_J) ).

fof(fact_com_Osize_I1_J,axiom,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I1_J) ).

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_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_le__divide__eq,axiom,
    ! [V_ca_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_ca_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq) ).

fof(fact_divide__le__eq,axiom,
    ! [V_a_2,V_ca_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_ca_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__le__eq) ).

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_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_neg__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2))) ) ) ),
    file('theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [V_a_2,V_b_2,V_ca_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__le__eq) ).

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_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__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__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_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_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_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_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__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__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__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__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__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_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_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_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_divide__eq__eq,axiom,
    ! [V_a_2,V_ca_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_ca_2) = V_a_2
      <=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [V_ca_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_ca_2)
      <=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq) ).

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__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_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_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__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_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_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__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_ca_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_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_ca_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_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_ca_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_ca_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_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_ca_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_ca_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_ca_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_ca_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [V_a_2,V_ca_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_ca_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [V_ca_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_ca_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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__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_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__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_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_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_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_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_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_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_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_com_Osize_I5_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I5_J) ).

fof(fact_com_Osize_I13_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I13_J) ).

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_com_Osimps_I4_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
      ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
    <=> ( V_com2_2 = V_com2_H_2
        & V_com1_2 = V_com1_H_2
        & V_fun_2 = V_fun_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I4_J) ).

fof(fact_com_Osimps_I44_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I44_J) ).

fof(fact_com_Osimps_I45_J,axiom,
    ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I45_J) ).

fof(fact_com_Osimps_I14_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I14_J) ).

fof(fact_com_Osimps_I15_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I15_J) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [V_ca_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_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_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_com_Osize_I11_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I11_J) ).

fof(fact_com_Osize_I3_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I3_J) ).

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_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_com_Osimps_I2_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
      ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
    <=> ( V_com_2 = V_com_H_2
        & V_fun_2 = V_fun_H_2
        & V_loc_2 = V_loc_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I2_J) ).

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_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_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_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_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_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_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_com_Osimps_I37_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I37_J) ).

fof(fact_com_Osimps_I36_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I36_J) ).

fof(fact_com_Osimps_I34_J,axiom,
    ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    file('theBenchmark.p',fact_com_Osimps_I34_J) ).

fof(fact_com_Osimps_I35_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I35_J) ).

fof(fact_com_Osimps_I11_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I11_J) ).

fof(fact_com_Osimps_I10_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I10_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__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_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_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_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_ca_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_ca_2)
      <=> ( ( V_ca_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_ca_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_ca_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_ca_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_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
      <=> ( ( V_ca_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_ca_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_ca_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_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_less__divide__eq__number__of,axiom,
    ! [V_ca_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_ca_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [V_w_2,V_ca_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_ca_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_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of) ).

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__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_divide__le__eq__number__of,axiom,
    ! [V_w_2,V_ca_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_ca_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_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [V_ca_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_ca_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of) ).

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_finite__induct,axiom,
    ! [V_Pa_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(V_Pa_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_Pa_2,B_F))
                 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
         => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ),
    file('theBenchmark.p',fact_finite__induct) ).

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_com_Osize_I6_J,axiom,
    ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I6_J) ).

fof(fact_com_Osize_I14_J,axiom,
    ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I14_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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__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_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_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_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_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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_com_Osimps_I5_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
      ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
    <=> ( V_com_2 = V_com_H_2
        & V_fun_2 = V_fun_H_2 ) ),
    file('theBenchmark.p',fact_com_Osimps_I5_J) ).

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__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_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_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_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__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__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_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_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_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__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_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_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__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__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_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__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_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_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__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_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_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_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_com_Osimps_I52_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I52_J) ).

fof(fact_com_Osimps_I53_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I53_J) ).

fof(fact_com_Osimps_I46_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I46_J) ).

fof(fact_com_Osimps_I47_J,axiom,
    ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I47_J) ).

fof(fact_com_Osimps_I38_J,axiom,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I38_J) ).

fof(fact_com_Osimps_I39_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I39_J) ).

fof(fact_com_Osimps_I16_J,axiom,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    file('theBenchmark.p',fact_com_Osimps_I16_J) ).

fof(fact_com_Osimps_I17_J,axiom,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    file('theBenchmark.p',fact_com_Osimps_I17_J) ).

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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [V_Pa_2] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [V_Pa_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_Pa_2,B_x)) )
    <=> ! [B_x] : hBOOL(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_zdiff__int__split,axiom,
    ! [V_y_2,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_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_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_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_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_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_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_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_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__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_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_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_succ__pred,axiom,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    file('theBenchmark.p',fact_succ__pred) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_decr__mult__lemma,axiom,
    ! [V_k_2,V_Pa_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_Pa_2,B_x))
           => hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x))
           => hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Pa_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_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_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_min__max_Oinf__le__fold__inf,axiom,
    ! [V_ca_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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

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_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__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_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__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__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__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__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__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__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__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__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__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__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__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__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_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__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__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__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__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__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_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_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_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_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_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_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_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_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_split__zmod,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_j)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_Pa_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__zmod) ).

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_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_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__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_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__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__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__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__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__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_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_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_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_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_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__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__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__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_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_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_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_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_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_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__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_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_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__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__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_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_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_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_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_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_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_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_succ__Pls) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_pred__Min,axiom,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    file('theBenchmark.p',fact_pred__Min) ).

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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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__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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_split__mod,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_j)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_ComplI,axiom,
    ! [V_A_2,V_ca_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_ComplI) ).

fof(fact_ComplE,axiom,
    ! [V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplE) ).

fof(fact_ComplD,axiom,
    ! [V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplD) ).

fof(fact_Compl__iff,axiom,
    ! [V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__iff) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_all__nat,axiom,
    ! [V_Pa_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Int_Onat,B_x))) ) ),
    file('theBenchmark.p',fact_all__nat) ).

fof(fact_ex__nat,axiom,
    ! [V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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__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__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__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__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_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_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_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_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_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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_split__nat,axiom,
    ! [V_i_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_n)) ) ) ),
    file('theBenchmark.p',fact_split__nat) ).

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__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_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_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__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_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_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_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_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_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_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_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_split__zdiv) ).

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__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_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_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__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_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_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_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_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_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_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_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_split__neg__lemma,axiom,
    ! [V_n_2,V_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_split__pos__lemma,axiom,
    ! [V_n_2,V_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__pos__lemma) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_split__div,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

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_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_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_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_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_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_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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_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_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__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__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_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_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_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_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_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_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_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_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__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__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_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_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__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_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_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_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__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__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__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_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__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_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_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__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__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__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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Pa_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_Pa_2,B_i))
           => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
     => ( hBOOL(hAPP(V_Pa_2,V_i_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
         => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_mod__induct__0) ).

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_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_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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_ca_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_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_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_ca_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_ca_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_predicate2D,axiom,
    ! [V_y_2,V_x_2,V_Qa_2,V_Pa_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_Pa_2),V_Qa_2))
     => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2),V_Qa_2))
       => hBOOL(hAPP(hAPP(V_Qa_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_split__paired__All,axiom,
    ! [T_c,T_b,V_Pa_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
    <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_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_ca_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_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ),
    file('theBenchmark.p',fact_split__weak__cong) ).

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_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_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_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_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_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_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_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opinduct) ).

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_mem__splitI,axiom,
    ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_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_ca_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_H,axiom,
    ! [V_ca_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_ca_2))
     => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ),
    file('theBenchmark.p',fact_splitD_H) ).

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_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_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_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_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_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__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_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_posDivAlg_Opinduct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opinduct) ).

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_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_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__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_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__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_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_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_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_norm__frac_Opinduct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Opinduct) ).

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_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_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_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_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__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_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_split__beta,axiom,
    ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_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_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_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_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_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
     => hBOOL(hAPP(hAPP(V_Pa_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_Qa_2,V_p_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_p_2))
     => ( hBOOL(hAPP(V_Qa_2,V_q_2))
       => ( hBOOL(hAPP(V_Qa_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_Pa_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_nat__gcd_Opinduct,axiom,
    ! [V_Pa_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_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
             => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opinduct) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_same__fstI,axiom,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_same__fstI) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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_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_sum__diff__distrib,axiom,
    ! [V_n_2,V_Pa_2,V_Qa_2] :
      ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_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_Pa_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_Qa_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_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ),
    file('theBenchmark.p',fact_sum__diff__distrib) ).

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__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_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__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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_INF2__E,axiom,
    ! [V_a_2,V_ca_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_ca_2))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
       => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF2__E) ).

fof(fact_INF2__D,axiom,
    ! [V_a_2,V_ca_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_ca_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_ca_2)) ) ),
    file('theBenchmark.p',fact_INF2__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_INT__constant,axiom,
    ! [V_ca_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_ca_2)) = V_ca_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_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__constant) ).

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__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_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_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_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_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_atLeastatMost__subset__iff,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_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_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_atLeastAtMost__singleton__iff,axiom,
    ! [V_ca_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_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      <=> ( V_b_2 = V_ca_2
          & V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

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_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_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_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_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_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_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_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_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_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_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_Int__atLeastAtMost,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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_ca_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_ca_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_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_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_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_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_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_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_ex__nat__less,axiom,
    ! [V_Pa_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less) ).

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_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_INF2__iff,axiom,
    ! [V_ca_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_ca_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_ca_2)) ) ),
    file('theBenchmark.p',fact_INF2__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_Pa_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_Pa_2,B_x))
          <=> hBOOL(hAPP(V_Pa_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_Pa_2,B_x1))
        <=> ? [B_x] :
              ( hBOOL(hAPP(V_Pa_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_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_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_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_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_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__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_Int__greaterThanLessThan,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanLessThan) ).

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__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_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_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_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_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_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_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_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_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_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_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_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_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_Int__greaterThanAtMost,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanAtMost) ).

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_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_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_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_setsum__head,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head) ).

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_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_rp__inv__image__rp,axiom,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
     => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ),
    file('theBenchmark.p',fact_rp__inv__image__rp) ).

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_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_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_SUP2__I,axiom,
    ! [T_d,T_c,V_ca_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_ca_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_ca_2)) ) ),
    file('theBenchmark.p',fact_SUP2__I) ).

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_ca_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_ca_2)) = V_ca_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_ca_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_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_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_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__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_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__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_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_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__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__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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_ball__UN,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_xa)) ) ) ),
    file('theBenchmark.p',fact_ball__UN) ).

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_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__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_SUP2__iff,axiom,
    ! [V_ca_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_ca_2))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP2__iff) ).

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_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_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_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_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_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__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_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_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_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_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_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_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_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__atLeastAtMostR1,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).

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_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_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_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_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_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_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_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_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__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_atLeastLessThan__eq__iff,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2)
          <=> ( V_b_2 = V_d_2
              & V_a_2 = V_ca_2 ) ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2))
           => V_a_2 = V_ca_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2))
           => V_b_2 = V_d_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [V_Pa_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_Pa_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_all__nat__less__eq,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less__eq) ).

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_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_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_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_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_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_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_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__subset__iff,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Int__atLeastLessThan,axiom,
    ! [V_d_2,V_ca_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_ca_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_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastLessThan) ).

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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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__onE,axiom,
    ! [V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_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_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
    file('theBenchmark.p',fact_Id__onE) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [V_x_2,V_y_2,V_ca_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) ),
    file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

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_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_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_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__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__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_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_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_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__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_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_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__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_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__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_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__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_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_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_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_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_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_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_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__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_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__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_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_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__constant__conv,axiom,
    ! [V_ca_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_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_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_ca_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_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_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__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_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_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_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_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_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__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__constant,axiom,
    ! [V_ca_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_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_image__constant) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__twist,axiom,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
      ( V_a_2 != V_ca_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_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ),
    file('theBenchmark.p',fact_fun__upd__twist) ).

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__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__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_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__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_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__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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_Int__atLeastAtMostR2,axiom,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [V_ca_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_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).

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_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_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_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_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_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_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_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_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_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_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__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__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_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,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_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__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_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_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__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_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_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_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_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__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_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__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_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_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_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__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_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_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__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_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_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_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_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__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_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_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_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__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_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__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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_split__paired__The,axiom,
    ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__The) ).

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_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_Pa_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_Pa_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_Pa_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_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_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_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_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_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__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__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__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__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__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__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__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__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_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_ca_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_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_ca_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_Pa_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_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
       => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ),
    file('theBenchmark.p',fact_Rep__Integ__induct) ).

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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_ca_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_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_ca_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__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__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_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_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_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_ca_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_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_ca_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_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_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_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_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_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__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__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_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_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_CollectI,axiom,
    ! [T_b,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    file('theBenchmark.p',fact_CollectI) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [V_Qa_2,V_Pa_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),V_Qa_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_CollectE,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
     => hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectE) ).

fof(fact_CollectD,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
     => hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectD) ).

fof(fact_mem__Collect__eq,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
    <=> hBOOL(hAPP(V_Pa_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_Collect__conj__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_Collect__disj__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_insert__Collect,axiom,
    ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),
    file('theBenchmark.p',fact_insert__Collect) ).

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_finite__Collect__disjI,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    file('theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_empty__Collect__eq,axiom,
    ! [V_Pa_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
    file('theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [V_Pa_2,T_b] :
      ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
    file('theBenchmark.p',fact_Collect__empty__eq) ).

fof(fact_Collect__def,axiom,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
    file('theBenchmark.p',fact_Collect__def) ).

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_vimage__Collect__eq,axiom,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)),
    file('theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_Collect__neg__eq,axiom,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),
    file('theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_Collect__split,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))),
    file('theBenchmark.p',fact_Collect__split) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_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_Qa_2)),
    file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).

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_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_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_Pa_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_Pa_2))))
    <=> ( hBOOL(hAPP(V_Pa_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_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_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_Collect__conv__if2,axiom,
    ! [T_b,V_a_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_Pa_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_Pa_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_Collect__conv__if,axiom,
    ! [T_b,V_a_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_Pa_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_Pa_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_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_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_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_Qa_2,V_Pa_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_Pa_2)),V_Qa_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_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [V_i_2,V_Pa_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_Pa_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_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_Pa_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_Pa_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_Pa_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_Pa_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_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_Pa_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_Pa_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_Pa_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_Pa_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_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_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_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_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_Qa_2,T_c,V_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2))),V_Qa_2)))))
      <=> ! [B_y] :
            ( hBOOL(hAPP(V_Pa_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_Qa_2),B_y)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_finite__image__set,axiom,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Pa_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_Pa_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_Pa_2))),
    file('theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_rel__compI,axiom,
    ! [V_s_2,V_ca_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_ca_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_ca_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__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_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_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_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__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__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_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_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_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_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_ca_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_ca_2))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_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_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_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_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_Pa_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_Pa_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_Pa_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_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_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__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__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_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__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_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_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__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__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__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_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__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__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__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_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2)) ) ),
    file('theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [V_S_2,V_R_2,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_Pa_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_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_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_Collect__ball__eq,axiom,
    ! [V_Pa_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_Pa_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_Pa_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__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_Abs__Integ__induct,axiom,
    ! [V_x_2,V_Pa_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_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
     => hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    file('theBenchmark.p',fact_Abs__Integ__induct) ).

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_ca_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_ca_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_ca_2),V_p_2))) ),
    file('theBenchmark.p',fact_mem__splitI2) ).

fof(fact_mem__splitE,axiom,
    ! [V_p_2,V_ca_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_ca_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_ca_2,B_x),B_y))) ) ),
    file('theBenchmark.p',fact_mem__splitE) ).

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_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_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_o__eq__id__dest,axiom,
    ! [V_v_2,V_ca_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_ca_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__id__dest) ).

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_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_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_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_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__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__eq__dest,axiom,
    ! [V_v_2,V_d_2,V_ca_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_ca_2),V_d_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ),
    file('theBenchmark.p',fact_o__eq__dest) ).

fof(fact_o__eq__elim,axiom,
    ! [V_d_2,V_ca_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_ca_2),V_d_2)
     => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ),
    file('theBenchmark.p',fact_o__eq__elim) ).

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_K__record__comp,axiom,
    ! [V_x_2,V_f_2,V_ca_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_ca_2)),V_f_2),V_x_2) = V_ca_2,
    file('theBenchmark.p',fact_K__record__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_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_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_o__eq__dest__lhs,axiom,
    ! [V_v_2,V_ca_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_ca_2
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__dest__lhs) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_hoare__derivs_OIf,axiom,
    ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Qa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)),V_d_2,V_Qa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_Loop,axiom,
    ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Pa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OWhile(V_b_2,V_ca_2),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop) ).

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_peek__and__def,axiom,
    ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
    <=> ( hBOOL(hAPP(V_p_2,V_s_2))
        & hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_peek__and__def) ).

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_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_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_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_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_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_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_Eps__split,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_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_exE__some,axiom,
    ! [T_b,V_ca_2,V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
     => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
       => hBOOL(hAPP(V_Pa_2,V_ca_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
    <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
    file('theBenchmark.p',fact_some__eq__ex) ).

fof(fact_someI__ex,axiom,
    ! [T_b,V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
     => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
     => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ),
    file('theBenchmark.p',fact_someI) ).

fof(fact_split__paired__Eps,axiom,
    ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_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_Pa_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_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_min__max_Ofold__sup__le__sup,axiom,
    ! [V_ca_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_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

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_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__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_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__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_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_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_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_setsum__ivl__cong,axiom,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
      ( ( class_Orderings_Oord(T_b)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( V_a_2 = V_ca_2
       => ( V_b_2 = V_d_2
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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_ca_2),V_d_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__ivl__cong) ).

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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_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_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_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_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_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_ca_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_ca_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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__into__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_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_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__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_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__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__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__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__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__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__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__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__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_ca_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_ca_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_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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__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_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_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_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__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__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_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__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__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__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__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__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__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_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_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_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_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_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_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_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_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__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__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__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_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_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__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_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_rtrancl__Un__separator__converseE,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2),V_Qa_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_Pa_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_Qa_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_Pa_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2),V_Qa_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_Pa_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_Qa_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_Pa_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).

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_Ha_2,V_Pa_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_Pa_2,B_x))
          <=> hBOOL(hAPP(V_P_Ha_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_Pa_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_Ha_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_Int__Collect__mono,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Qa_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_Pa_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_Qa_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_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_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_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_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_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_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_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_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__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_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__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_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__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_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__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_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_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__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_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_Pa_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_Pa_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_Pa_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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,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_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_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__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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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__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_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__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_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_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_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_ts_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_ts_2)
    <=> ? [B_us] :
          ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_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_ts_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_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_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__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__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__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__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_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_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__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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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__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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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_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__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_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_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__mult__const,axiom,
    ! [V_xs_2,V_ca_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_ca_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_ca_2) ),
    file('theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_listsum__const__mult,axiom,
    ! [V_xs_2,V_f_2,V_ca_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_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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__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__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_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_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__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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_Pa_2,T_b] :
      ( c_List_Opartition(T_b,V_Pa_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_Pa_2,T_b] :
      ( c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_partition__P) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_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_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_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_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__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_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_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_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_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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__map2,axiom,
    ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2)),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map2) ).

fof(fact_list__all2__map1,axiom,
    ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map1) ).

fof(fact_list__all2__Nil,axiom,
    ! [V_ys_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_list__all2__Nil2,axiom,
    ! [V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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__lengthD,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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__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__takeI,axiom,
    ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
     => c_List_Olist__all2(T_b,T_c,V_Pa_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__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,V_ys_2)
        & hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_list__all2__append,axiom,
    ! [V_vs_2,V_us_2,V_Pa_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_Pa_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_Pa_2,V_us_2,V_vs_2)
          & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ),
    file('theBenchmark.p',fact_list__all2__append) ).

fof(fact_list__all2__appendI,axiom,
    ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
     => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
       => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_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__dropI,axiom,
    ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
     => c_List_Olist__all2(T_b,T_c,V_Pa_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_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_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_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_Pa_2,V_xs_2,V_ys_2)
       => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
         => c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_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__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_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_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_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_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_Pa_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)) ),
    file('theBenchmark.p',fact_filter__sort) ).

fof(fact_distinct__filter,axiom,
    ! [V_Pa_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_Pa_2),V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__filter) ).

fof(fact_length__filter__le,axiom,
    ! [V_xs_2,V_Pa_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_Pa_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_sum__length__filter__compl,axiom,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_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_filter__id__conv,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__id__conv) ).

fof(fact_filter__is__subset,axiom,
    ! [V_xs_2,V_Pa_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_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_filter__is__subset) ).

fof(fact_filter__remove1,axiom,
    ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2),V_xs_2)),
    file('theBenchmark.p',fact_filter__remove1) ).

fof(fact_remove1__filter__not,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
     => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ),
    file('theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_filter__filter,axiom,
    ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2)),V_Pa_2)),V_xs_2),
    file('theBenchmark.p',fact_filter__filter) ).

fof(fact_filter__insort__triv,axiom,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_partition__filter1,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2),
    file('theBenchmark.p',fact_partition__filter1) ).

fof(fact_filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__map) ).

fof(fact_filter__append,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)),
    file('theBenchmark.p',fact_filter__append) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_filter_Osimps_I1_J) ).

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__empty__conv,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_remdups__filter,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)),
    file('theBenchmark.p',fact_remdups__filter) ).

fof(fact_removeAll__filter__not,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
     => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ),
    file('theBenchmark.p',fact_removeAll__filter__not) ).

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_partition__filter2,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_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_Pa_2)),V_xs_2),
    file('theBenchmark.p',fact_partition__filter2) ).

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_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2)),
    file('theBenchmark.p',fact_set__filter) ).

fof(fact_length__filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_length__filter__map) ).

fof(fact_length__filter__less,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_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_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_Pa_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_Pa_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_Pa_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_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_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_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__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_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_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__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,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_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_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__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_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__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__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__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__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__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__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_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_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_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_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_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_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_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_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__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__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__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__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__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__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__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_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__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__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_Pa_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_Pa_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_Pa_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_Pa_2,V_x_2))
         => hAPP(c_List_Ofilter(T_c,V_Pa_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_Pa_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__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_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__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_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_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_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_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_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_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__rev,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__rev) ).

fof(fact_list__all2__rev1,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
    <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ),
    file('theBenchmark.p',fact_list__all2__rev1) ).

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_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__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_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_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_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_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_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_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_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_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_Pa_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_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_length__takeWhile__le,axiom,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_set__takeWhileD,axiom,
    ! [V_xs_2,V_Pa_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_Pa_2,V_xs_2))))
     => ( hBOOL(hAPP(V_Pa_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__fst,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_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_Pa_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_zip__takeWhile__snd,axiom,
    ! [V_ys_2,V_Pa_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_Pa_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_Pa_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_takeWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_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_Pa_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_takeWhile__map) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_takeWhile__tail,axiom,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
     => c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_distinct__takeWhile,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_takeWhile__nth,axiom,
    ! [V_xs_2,V_Pa_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_Pa_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_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_Pa_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_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2,
    file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_hd__dropWhile,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
     => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_sorted__dropWhile,axiom,
    ! [V_Pa_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_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_length__dropWhile__le,axiom,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_distinct__dropWhile,axiom,
    ! [V_Pa_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_Pa_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_dropWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_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_Pa_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_dropWhile__map) ).

fof(fact_dropWhile__append1,axiom,
    ! [V_ys_2,V_Pa_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_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_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_Pa_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_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
    <=> ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
        & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_dropWhile__nth,axiom,
    ! [V_xs_2,V_Pa_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_Pa_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_listsum__map__filter,axiom,
    ! [V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,V_xs_2))))
         => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
     => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
       => c_List_OtakeWhile(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_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_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_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_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_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__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_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_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_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_Pa_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_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
    file('theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_enum__ex,axiom,
    ! [V_Pa_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
      <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__ex) ).

fof(fact_exists__code,axiom,
    ! [V_Pa_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ),
    file('theBenchmark.p',fact_exists__code) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,B_x)) )
     => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ),
    file('theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,B_x)) )
     => c_List_OtakeWhile(T_b,V_Pa_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_Pa_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_Cons__eq__filter__iff,axiom,
    ! [V_ys_2,V_Pa_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_Pa_2),V_ys_2)
    <=> ? [B_us,B_vs] :
          ( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs)
          & hBOOL(hAPP(V_Pa_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_Pa_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_filter__eq__Cons__iff,axiom,
    ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),B_vs)
          & hBOOL(hAPP(V_Pa_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_Pa_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_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_all__code,axiom,
    ! [V_Pa_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ),
    file('theBenchmark.p',fact_all__code) ).

fof(fact_enum__all,axiom,
    ! [V_Pa_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
      <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__all) ).

fof(fact_enum__all__prod__def,axiom,
    ! [V_Pa_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_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
    file('theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_list__ball__nth,axiom,
    ! [V_Pa_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_Pa_2,B_x)) )
       => hBOOL(hAPP(V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
    <=> ? [B_n] :
          ( hBOOL(hAPP(V_Pa_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,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_list__ex__simps_I2_J,axiom,
    ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_ys_2)
        | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_list__ex__append) ).

fof(fact_list__ex__iff,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
    <=> c_List_Olist__ex(T_b,V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__ex__simps_I1_J) ).

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_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_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_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_Pa_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_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__all(T_b,V_Pa_2,V_ys_2)
        & c_List_Olist__all(T_b,V_Pa_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_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_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_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_list__all__iff,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_list__all__iff) ).

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_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_list__all__rev,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
    <=> c_List_Olist__all(T_b,V_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_Ball__set__list__all,axiom,
    ! [V_Pa_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_Pa_2,B_x)) )
    <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ),
    file('theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__all(T_b,V_Pa_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_Pa_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_Pa_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
         => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) )
        & ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_list__ex1__simps_I1_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_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_list__ex1__iff,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
    <=> ? [B_x] :
          ( ! [B_y] :
              ( ( hBOOL(hAPP(V_Pa_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_Pa_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_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__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__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__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__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_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_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_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_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_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__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_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_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_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_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_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_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__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__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__eq,axiom,
    ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
    file('theBenchmark.p',fact_conversep__eq) ).

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__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_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_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_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_Pa_2,V_a_2,V_n_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_Bex__set__replicate) ).

fof(fact_Ball__set__replicate,axiom,
    ! [V_Pa_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_Pa_2,B_x)) )
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_Pa_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_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_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_Pa_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_Pa_2,B_d),B_i)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_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_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_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_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_list__ex1__iff__raw,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
    <=> ? [B_x] :
          ( ! [B_y] :
              ( ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2] :
      ( ( ~ ? [B_x] :
              ( ! [B_y] :
                  ( hBOOL(hAPP(V_Pa_2,B_y))
                 => B_y = B_x )
              & hBOOL(hAPP(V_Pa_2,B_x)) )
       => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 )
      & ( ? [B_x] :
            ( ! [B_y] :
                ( hBOOL(hAPP(V_Pa_2,B_y))
               => B_y = B_x )
            & hBOOL(hAPP(V_Pa_2,B_x)) )
       => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) ),
    file('theBenchmark.p',fact_THE__default__def) ).

fof(fact_SUP2__E,axiom,
    ! [V_ca_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_ca_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_ca_2)) ) ),
    file('theBenchmark.p',fact_SUP2__E) ).

fof(fact_INF2__I,axiom,
    ! [T_d,T_c,V_ca_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_ca_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_ca_2)) ),
    file('theBenchmark.p',fact_INF2__I) ).

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_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_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_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_Pa_2] :
      ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
    <=> c_List_Oall__interval__int(V_Pa_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_Pa_2] :
      ( c_List_Olist__ex(tc_Int_Oint,V_Pa_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_Pa_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_Pa_2] :
      ( c_List_Oall__interval__int(V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__interval__int__def) ).

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_exE__realizer,axiom,
    ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,B_y),B_x))
           => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
       => hBOOL(hAPP(V_Qa_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_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_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_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_Image__Collect__split,axiom,
    ! [V_A_2,V_Pa_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_Pa_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_Pa_2)))),
    file('theBenchmark.p',fact_Image__Collect__split) ).

fof(fact_list__ex__iff__raw,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Bex__set__list__ex,axiom,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2) ),
    file('theBenchmark.p',fact_Bex__set__list__ex) ).

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_bex__empty,axiom,
    ! [V_Pa_2,T_b] :
      ~ ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_finite__Collect__bex,axiom,
    ! [V_Qa_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_Qa_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_Qa_2),B_x)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bex) ).

fof(fact_bex__UNIV,axiom,
    ! [V_Pa_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x1)) ),
    file('theBenchmark.p',fact_bex__UNIV) ).

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_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__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_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_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_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_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_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_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_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_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_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__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_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_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_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__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_transD,axiom,
    ! [V_ca_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_ca_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_ca_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_transD) ).

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_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_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_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_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_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_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_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__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__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_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__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_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_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__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__Id,axiom,
    ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_sym__Id) ).

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_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_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_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_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_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_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__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__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_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_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__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_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_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_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_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__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__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_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_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_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_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_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__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_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
       => hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
     => hBOOL(hAPP(V_Pa_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_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_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_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_bij__image__Collect__eq,axiom,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_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_curry__def,axiom,
    ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_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_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_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_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__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_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_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_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__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_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__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__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__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_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__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,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__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__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_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__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_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_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_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_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_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_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__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_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_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_bex__reg__eqv,axiom,
    ! [V_Pa_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x1)) ) ),
    file('theBenchmark.p',fact_bex__reg__eqv) ).

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_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_bex__reg__right,axiom,
    ! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_Qa_2,B_x))
           => hBOOL(hAPP(V_Pa_2,B_x)) )
       => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1))
         => ? [B_x] :
              ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2) = V_Pa_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_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_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_rtrancl__induct2,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b))
                   => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
         => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ),
    file('theBenchmark.p',fact_rtrancl__induct2) ).

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_Pa_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_Pa_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_Pa_2,B_aa),B_ba))
                 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
         => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ),
    file('theBenchmark.p',fact_converse__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_list__all__iff__all__interval__nat,axiom,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
    <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__all__iff__all__interval__nat) ).

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_all__interval__nat__def,axiom,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( c_List_Oall__interval__nat(V_Pa_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_Pa_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_Pa_2] :
      ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_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_Pa_2),V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).

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_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__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_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_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_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__setprod,axiom,
    ! [V_f_2,V_i_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))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_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_dvd__setprod) ).

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_dvd_OatLeastAtMost__singleton__iff,axiom,
    ! [V_ca_2,V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    <=> ( V_b_2 = V_ca_2
        & V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).

fof(fact_dvd_OatLeastAtMost__singleton,axiom,
    ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).

fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
    ! [V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).

fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Obot__class_Obot(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)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).

fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).

fof(fact_dvd_OatLeastatMost__empty,axiom,
    ! [V_a_2,V_b_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_a_2)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).

fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
     => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).

fof(fact_dvd_OatLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
     => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).

fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_OatLeastLessThan__empty__iff) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).

fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_OatLeastLessThan__empty__iff2) ).

fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
    ! [V_k_2,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
     => c_SetInterval_Oord_OgreaterThanLessThan(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).

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__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_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_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__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_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__reduce,axiom,
    ! [V_n_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ),
    file('theBenchmark.p',fact_dvd__reduce) ).

fof(fact_dvd__add,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_a),V_c))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_dvd__add) ).

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_div__dvd__div,axiom,
    ! [V_ca_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_ca_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_ca_2),V_a_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) ) ) ) ),
    file('theBenchmark.p',fact_div__dvd__div) ).

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_nat__dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_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__dvd__1__iff__1) ).

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_one__dvd,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ),
    file('theBenchmark.p',fact_one__dvd) ).

fof(fact_dvd_Oeq__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd_Oeq__iff) ).

fof(fact_dvd_Ole__less,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
    <=> ( V_x_2 = V_y_2
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less) ).

fof(fact_dvd_Oless__le,axiom,
    ! [V_y_2,V_x_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
    <=> ( V_x_2 != V_y_2
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le) ).

fof(fact_dvd_Oneq__le__trans,axiom,
    ! [V_b,V_a] :
      ( 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))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).

fof(fact_dvd_Oeq__refl,axiom,
    ! [V_y,V_x] :
      ( V_x = V_y
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_dvd_Oeq__refl) ).

fof(fact_dvd_Oantisym__conv,axiom,
    ! [V_x_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_dvd_Oantisym__conv) ).

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(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_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_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__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_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_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_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_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_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_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__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__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__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__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_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__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_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__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,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__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__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__if__abs__eq,axiom,
    ! [V_k,V_l,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ),
    file('theBenchmark.p',fact_dvd__if__abs__eq) ).

fof(fact_abs__dvd__iff,axiom,
    ! [V_k_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_abs__dvd__iff) ).

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_Com__Ocom__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ocom),
    file('theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).

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_Com__Ostate__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ostate),
    file('theBenchmark.p',arity_Com__Ostate__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_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBB__1) ).

fof(help_c__COMBC__1,axiom,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2),
    file('theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBS__1,axiom,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_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_Pa_2] :
      ( ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
    file('theBenchmark.p',help_c__fNot__1) ).

fof(help_c__fNot__2,axiom,
    ! [V_Pa_2] :
      ( hBOOL(hAPP(c_fNot,V_Pa_2))
      | ~ ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fNot__2) ).

fof(help_c__fconj__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fconj__1) ).

fof(help_c__fconj__2,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fconj__3) ).

fof(help_c__fdisj__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    file('theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fdisj__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fimplies__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fimplies__1) ).

fof(help_c__fimplies__2,axiom,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    file('theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fimplies__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fimplies__3) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    ! [B_Z,B_s] :
      ( v_P(B_Z,B_s)
     => ! [B_s_H] :
          ( ! [B_Z_H] :
              ( hBOOL(hAPP(hAPP(v_P_H,B_Z_H),B_s))
             => hBOOL(hAPP(hAPP(v_Q_H,B_Z_H),B_s_H)) )
         => v_Q(B_Z,B_s_H) ) ),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,conjecture,
    ! [B_Z,B_s] :
      ( v_P(B_Z,B_s)
     => ? [B_P_H,B_Q_H] :
          ( ! [B_s_H] :
              ( ! [B_Z_H] :
                  ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
                 => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
             => v_Q(B_Z,B_s_H) )
          & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,B_P_H,v_c,B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',conj_2) ).

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_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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_2_2,plain,
    ! [U_4,U_3] : c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_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_3_2,plain,
    ! [U_6,U_5] : c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2) = c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_H_2,V_com_H_2,V_fun2_H_2)
        | V_fun2_2 != V_fun2_H_2
        | V_com_2 != V_com_H_2
        | V_fun1_2 != V_fun1_H_2 )
      & ( ( V_fun2_2 = V_fun2_H_2
          & V_com_2 = V_com_H_2
          & V_fun1_2 = V_fun1_H_2 )
        | c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2) != c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_H_2,V_com_H_2,V_fun2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple_Oinject]) ).

fof(f_4_2,plain,
    ! [U_13,U_12,U_11,U_10,U_9,U_8,U_7] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple(U_7,U_8,U_9,U_10) = c_Hoare__Mirabelle_Otriple_Otriple(U_7,U_11,U_12,U_13)
        | U_10 != U_13
        | U_9 != U_12
        | U_8 != U_11 )
      & ( ( U_10 = U_13
          & U_9 = U_12
          & U_8 = U_11 )
        | c_Hoare__Mirabelle_Otriple_Otriple(U_7,U_8,U_9,U_10) != c_Hoare__Mirabelle_Otriple_Otriple(U_7,U_11,U_12,U_13) ) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ( ! [U_27,U_25,U_23,U_21,U_19,U_17] :
        ( ! [U_15] : c_Hoare__Mirabelle_Otriple_Otriple(U_15,U_17,U_19,U_21) = c_Hoare__Mirabelle_Otriple_Otriple(U_15,U_23,U_25,U_27)
        | U_21 != U_27
        | U_19 != U_25
        | U_17 != U_23 )
    & ! [U_26,U_24,U_22,U_20,U_18,U_16] :
        ( ! [U_14] : c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_16,U_18,U_20) != c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_22,U_24,U_26)
        | ( U_20 = U_26
          & U_18 = U_24
          & U_16 = U_22 ) ) ),
    inference(miniscope,[status(thm)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( U_16 = U_22
    | c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_16,U_18,U_20) != c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_22,U_24,U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_5,plain,
    ( U_18 = U_24
    | c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_16,U_18,U_20) != c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_22,U_24,U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_6,plain,
    ( U_20 = U_26
    | c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_16,U_18,U_20) != c_Hoare__Mirabelle_Otriple_Otriple(U_14,U_22,U_24,U_26) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

cnf(f_4_7,plain,
    ( c_Hoare__Mirabelle_Otriple_Otriple(U_15,U_17,U_19,U_21) = c_Hoare__Mirabelle_Otriple_Otriple(U_15,U_23,U_25,U_27)
    | U_21 != U_27
    | U_19 != U_25
    | U_17 != U_23 ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_1,plain,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_cut]) ).

fof(f_5_2,plain,
    ! [U_31,U_30,U_29,U_28] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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_6_2,plain,
    ! [U_35,U_34,U_33,U_32] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    inference(fof_nnf,[status(thm)],[fact_triple_Orecs]) ).

fof(f_7_2,plain,
    ! [U_41,U_40,U_39,U_38,U_37,U_36] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_36,U_37,U_38,c_Hoare__Mirabelle_Otriple_Otriple(U_36,U_39,U_40,U_41)) = hAPP(hAPP(hAPP(U_38,U_39),U_40),U_41),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(U_36,U_37,U_38,c_Hoare__Mirabelle_Otriple_Otriple(U_36,U_39,U_40,U_41)) = hAPP(hAPP(hAPP(U_38,U_39),U_40),U_41),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
    inference(fof_nnf,[status(thm)],[fact_triple_Osimps_I2_J]) ).

fof(f_8_2,plain,
    ! [U_47,U_46,U_45,U_44,U_43,U_42] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_42,U_43,U_44,c_Hoare__Mirabelle_Otriple_Otriple(U_42,U_45,U_46,U_47)) = hAPP(hAPP(hAPP(U_44,U_45),U_46),U_47),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(U_42,U_43,U_44,c_Hoare__Mirabelle_Otriple_Otriple(U_42,U_45,U_46,U_47)) = hAPP(hAPP(hAPP(U_44,U_45),U_46),U_47),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_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_9_2,plain,
    ! [U_50,U_49,U_48] : c_Orderings_Obot__class_Obot(tc_fun(U_48,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_48),U_49),U_50),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

cnf(f_9_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_48,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_48),U_49),U_50),
    inference(clausify,[status(thm)],[f_9_2]) ).

fof(f_10_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_10_2,plain,
    ! [U_53,U_52,U_51] : hAPP(hAPP(c_Set_Oinsert(U_51),U_52),U_53) != c_Orderings_Obot__class_Obot(tc_fun(U_51,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_51),U_52),U_53) != c_Orderings_Obot__class_Obot(tc_fun(U_51,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_2
            | V_a_2 != V_d_2 )
          & ( V_b_2 != V_d_2
            | V_a_2 != V_ca_2 ) ) )
      & ( ( V_b_2 = V_ca_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_ca_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_ca_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_11_2,plain,
    ! [U_58,U_57,U_56,U_55,U_54] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_54),U_55),hAPP(hAPP(c_Set_Oinsert(U_54),U_56),c_Orderings_Obot__class_Obot(tc_fun(U_54,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_54),U_57),hAPP(hAPP(c_Set_Oinsert(U_54),U_58),c_Orderings_Obot__class_Obot(tc_fun(U_54,tc_HOL_Obool))))
        | ( ( U_56 != U_57
            | U_55 != U_58 )
          & ( U_56 != U_58
            | U_55 != U_57 ) ) )
      & ( ( U_56 = U_57
          & U_55 = U_58 )
        | ( U_56 = U_58
          & U_55 = U_57 )
        | hAPP(hAPP(c_Set_Oinsert(U_54),U_55),hAPP(hAPP(c_Set_Oinsert(U_54),U_56),c_Orderings_Obot__class_Obot(tc_fun(U_54,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_54),U_57),hAPP(hAPP(c_Set_Oinsert(U_54),U_58),c_Orderings_Obot__class_Obot(tc_fun(U_54,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ( ! [U_68,U_66,U_64,U_62] :
        ( ! [U_60] : hAPP(hAPP(c_Set_Oinsert(U_60),U_62),hAPP(hAPP(c_Set_Oinsert(U_60),U_64),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_60),U_66),hAPP(hAPP(c_Set_Oinsert(U_60),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool))))
        | ( ( U_64 != U_66
            | U_62 != U_68 )
          & ( U_64 != U_68
            | U_62 != U_66 ) ) )
    & ! [U_67,U_65,U_63,U_61] :
        ( ! [U_59] : hAPP(hAPP(c_Set_Oinsert(U_59),U_61),hAPP(hAPP(c_Set_Oinsert(U_59),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_59),U_65),hAPP(hAPP(c_Set_Oinsert(U_59),U_67),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool))))
        | ( U_63 = U_65
          & U_61 = U_67 )
        | ( U_63 = U_67
          & U_61 = U_65 ) ) ),
    inference(miniscope,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( U_61 = U_67
    | U_61 = U_65
    | hAPP(hAPP(c_Set_Oinsert(U_59),U_61),hAPP(hAPP(c_Set_Oinsert(U_59),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_59),U_65),hAPP(hAPP(c_Set_Oinsert(U_59),U_67),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_5,plain,
    ( U_63 = U_65
    | U_61 = U_65
    | hAPP(hAPP(c_Set_Oinsert(U_59),U_61),hAPP(hAPP(c_Set_Oinsert(U_59),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_59),U_65),hAPP(hAPP(c_Set_Oinsert(U_59),U_67),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_6,plain,
    ( U_61 = U_67
    | U_63 = U_67
    | hAPP(hAPP(c_Set_Oinsert(U_59),U_61),hAPP(hAPP(c_Set_Oinsert(U_59),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_59),U_65),hAPP(hAPP(c_Set_Oinsert(U_59),U_67),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_7,plain,
    ( U_63 = U_65
    | U_63 = U_67
    | hAPP(hAPP(c_Set_Oinsert(U_59),U_61),hAPP(hAPP(c_Set_Oinsert(U_59),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_59),U_65),hAPP(hAPP(c_Set_Oinsert(U_59),U_67),c_Orderings_Obot__class_Obot(tc_fun(U_59,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_8,plain,
    ( U_64 != U_68
    | U_62 != U_66
    | hAPP(hAPP(c_Set_Oinsert(U_60),U_62),hAPP(hAPP(c_Set_Oinsert(U_60),U_64),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_60),U_66),hAPP(hAPP(c_Set_Oinsert(U_60),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_9,plain,
    ( U_64 != U_66
    | U_62 != U_68
    | hAPP(hAPP(c_Set_Oinsert(U_60),U_62),hAPP(hAPP(c_Set_Oinsert(U_60),U_64),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_60),U_66),hAPP(hAPP(c_Set_Oinsert(U_60),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_60,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_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_12_2,plain,
    ! [U_71,U_70,U_69] :
      ( U_70 = U_71
      | hAPP(hAPP(c_Set_Oinsert(U_69),U_70),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_69),U_71),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_71,U_70] :
      ( ! [U_69] : hAPP(hAPP(c_Set_Oinsert(U_69),U_70),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_69),U_71),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool)))
      | U_70 = U_71 ),
    inference(miniscope,[status(thm)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_69),U_70),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_69),U_71),c_Orderings_Obot__class_Obot(tc_fun(U_69,tc_HOL_Obool)))
    | U_70 = U_71 ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_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_13_2,plain,
    ! [U_74,U_73,U_72] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_73,U_72)),U_74) = c_Orderings_Obot__class_Obot(U_72)
      | ~ class_Orderings_Obot(U_72) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_73,U_72)),U_74) = c_Orderings_Obot__class_Obot(U_72)
    | ~ class_Orderings_Obot(U_72) ),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSKIP,V_Pa_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_OSkip]) ).

fof(f_14_2,plain,
    ! [U_77,U_76,U_75] : c_Hoare__Mirabelle_Ohoare__derivs(U_75,U_76,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_75)),c_Hoare__Mirabelle_Otriple_Otriple(U_75,U_77,c_Com_Ocom_OSKIP,U_77)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_75),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

cnf(f_14_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_75,U_76,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_75)),c_Hoare__Mirabelle_Otriple_Otriple(U_75,U_77,c_Com_Ocom_OSKIP,U_77)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_75),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_14_2]) ).

fof(f_15_1,plain,
    ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_a2_2,c_Com_Ocom_OSKIP,V_a2_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_I7_J]) ).

fof(f_15_2,plain,
    ! [U_80,U_79,U_78] : c_Hoare__Mirabelle_Ohoare__derivs(U_78,U_79,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_78)),c_Hoare__Mirabelle_Otriple_Otriple(U_78,U_80,c_Com_Ocom_OSKIP,U_80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_78),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

cnf(f_15_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_78,U_79,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_78)),c_Hoare__Mirabelle_Otriple_Otriple(U_78,U_80,c_Com_Ocom_OSKIP,U_80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_78),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_15_2]) ).

fof(f_16_1,plain,
    ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSemi(V_ca_2,V_d_2),V_R_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Qa_2,V_d_2,V_R_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Comp]) ).

fof(f_16_2,plain,
    ! [U_87,U_86,U_85,U_84,U_83,U_82,U_81] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_83,c_Com_Ocom_OSemi(U_84,U_86),U_87)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_85,U_86,U_87)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_83,U_84,U_85)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

cnf(f_16_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_83,c_Com_Ocom_OSemi(U_84,U_86),U_87)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_85,U_86,U_87)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_81,U_82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_81)),c_Hoare__Mirabelle_Otriple_Otriple(U_81,U_83,U_84,U_85)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_81),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_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_17_2,plain,
    ! [U_89,U_88] : c_Set_Othe__elem(U_88,hAPP(hAPP(c_Set_Oinsert(U_88),U_89),c_Orderings_Obot__class_Obot(tc_fun(U_88,tc_HOL_Obool)))) = U_89,
    inference(variable_rename,[status(thm)],[f_17_1]) ).

cnf(f_17_3,plain,
    c_Set_Othe__elem(U_88,hAPP(hAPP(c_Set_Oinsert(U_88),U_89),c_Orderings_Obot__class_Obot(tc_fun(U_88,tc_HOL_Obool)))) = U_89,
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_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_18_2,plain,
    ! [U_92,U_91,U_90] : hAPP(hAPP(c_Set_Oinsert(U_90),U_91),hAPP(hAPP(c_Set_Oinsert(U_90),U_91),U_92)) = hAPP(hAPP(c_Set_Oinsert(U_90),U_91),U_92),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

cnf(f_18_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_90),U_91),hAPP(hAPP(c_Set_Oinsert(U_90),U_91),U_92)) = hAPP(hAPP(c_Set_Oinsert(U_90),U_91),U_92),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_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_19_2,plain,
    ! [U_96,U_95,U_94,U_93] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_93),U_94),U_95),U_96))
        | ( ~ hBOOL(hAPP(U_95,U_96))
          & U_94 != U_96 ) )
      & ( hBOOL(hAPP(U_95,U_96))
        | U_94 = U_96
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_93),U_94),U_95),U_96)) ) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ( ! [U_104,U_102,U_100] :
        ( ! [U_98] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_98),U_100),U_102),U_104))
        | ( ~ hBOOL(hAPP(U_102,U_104))
          & U_100 != U_104 ) )
    & ! [U_103,U_101,U_99] :
        ( ! [U_97] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_97),U_99),U_101),U_103))
        | hBOOL(hAPP(U_101,U_103))
        | U_99 = U_103 ) ),
    inference(miniscope,[status(thm)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_97),U_99),U_101),U_103))
    | hBOOL(hAPP(U_101,U_103))
    | U_99 = U_103 ),
    inference(clausify,[status(thm)],[f_19_3]) ).

cnf(f_19_5,plain,
    ( U_100 != U_104
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_98),U_100),U_102),U_104)) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

cnf(f_19_6,plain,
    ( ~ hBOOL(hAPP(U_102,U_104))
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_98),U_100),U_102),U_104)) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_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_20_2,plain,
    ! [U_108,U_107,U_106,U_105] : hAPP(hAPP(c_Set_Oinsert(U_105),U_106),hAPP(hAPP(c_Set_Oinsert(U_105),U_107),U_108)) = hAPP(hAPP(c_Set_Oinsert(U_105),U_107),hAPP(hAPP(c_Set_Oinsert(U_105),U_106),U_108)),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_105),U_106),hAPP(hAPP(c_Set_Oinsert(U_105),U_107),U_108)) = hAPP(hAPP(c_Set_Oinsert(U_105),U_107),hAPP(hAPP(c_Set_Oinsert(U_105),U_106),U_108)),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I12_J]) ).

fof(f_21_2,plain,
    ! [U_110,U_109] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_109,U_110),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_109,U_110),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I13_J]) ).

fof(f_22_2,plain,
    ! [U_112,U_111] : c_Com_Ocom_OSemi(U_111,U_112) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    c_Com_Ocom_OSemi(U_111,U_112) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
      ( ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
        | V_com2_2 != V_com2_H_2
        | V_com1_2 != V_com1_H_2 )
      & ( ( V_com2_2 = V_com2_H_2
          & V_com1_2 = V_com1_H_2 )
        | c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J]) ).

fof(f_23_2,plain,
    ! [U_116,U_115,U_114,U_113] :
      ( ( c_Com_Ocom_OSemi(U_113,U_114) = c_Com_Ocom_OSemi(U_115,U_116)
        | U_114 != U_116
        | U_113 != U_115 )
      & ( ( U_114 = U_116
          & U_113 = U_115 )
        | c_Com_Ocom_OSemi(U_113,U_114) != c_Com_Ocom_OSemi(U_115,U_116) ) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ( ! [U_124,U_122,U_120,U_118] :
        ( c_Com_Ocom_OSemi(U_118,U_120) = c_Com_Ocom_OSemi(U_122,U_124)
        | U_120 != U_124
        | U_118 != U_122 )
    & ! [U_123,U_121,U_119,U_117] :
        ( ( U_119 = U_123
          & U_117 = U_121 )
        | c_Com_Ocom_OSemi(U_117,U_119) != c_Com_Ocom_OSemi(U_121,U_123) ) ),
    inference(miniscope,[status(thm)],[f_23_2]) ).

cnf(f_23_4,plain,
    ( U_117 = U_121
    | c_Com_Ocom_OSemi(U_117,U_119) != c_Com_Ocom_OSemi(U_121,U_123) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_5,plain,
    ( U_119 = U_123
    | c_Com_Ocom_OSemi(U_117,U_119) != c_Com_Ocom_OSemi(U_121,U_123) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_6,plain,
    ( c_Com_Ocom_OSemi(U_118,U_120) = c_Com_Ocom_OSemi(U_122,U_124)
    | U_120 != U_124
    | U_118 != U_122 ),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_24_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_24_2,plain,
    ! [U_127,U_126,U_125] :
      ( U_126 = hAPP(hAPP(c_Set_Oinsert(U_125),U_127),c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool)))
      | U_126 = c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),U_126),hAPP(hAPP(c_Set_Oinsert(U_125),U_127),c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ( U_126 = hAPP(hAPP(c_Set_Oinsert(U_125),U_127),c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool)))
    | U_126 = c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),U_126),hAPP(hAPP(c_Set_Oinsert(U_125),U_127),c_Orderings_Obot__class_Obot(tc_fun(U_125,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_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_25_2,plain,
    ! [U_130,U_129,U_128] :
      ( U_129 = U_130
      | ~ hBOOL(hAPP(hAPP(c_member(U_128),U_129),hAPP(hAPP(c_Set_Oinsert(U_128),U_130),c_Orderings_Obot__class_Obot(tc_fun(U_128,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_130,U_129] :
      ( ! [U_128] : ~ hBOOL(hAPP(hAPP(c_member(U_128),U_129),hAPP(hAPP(c_Set_Oinsert(U_128),U_130),c_Orderings_Obot__class_Obot(tc_fun(U_128,tc_HOL_Obool)))))
      | U_129 = U_130 ),
    inference(miniscope,[status(thm)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_128),U_129),hAPP(hAPP(c_Set_Oinsert(U_128),U_130),c_Orderings_Obot__class_Obot(tc_fun(U_128,tc_HOL_Obool)))))
    | U_129 = U_130 ),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_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_26_2,plain,
    ! [U_133,U_132,U_131] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_131),U_132),hAPP(hAPP(c_Set_Oinsert(U_131),U_133),c_Orderings_Obot__class_Obot(tc_fun(U_131,tc_HOL_Obool)))))
        | U_132 != U_133 )
      & ( U_132 = U_133
        | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_132),hAPP(hAPP(c_Set_Oinsert(U_131),U_133),c_Orderings_Obot__class_Obot(tc_fun(U_131,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ( ! [U_139,U_137] :
        ( ! [U_135] : hBOOL(hAPP(hAPP(c_member(U_135),U_137),hAPP(hAPP(c_Set_Oinsert(U_135),U_139),c_Orderings_Obot__class_Obot(tc_fun(U_135,tc_HOL_Obool)))))
        | U_137 != U_139 )
    & ! [U_138,U_136] :
        ( ! [U_134] : ~ hBOOL(hAPP(hAPP(c_member(U_134),U_136),hAPP(hAPP(c_Set_Oinsert(U_134),U_138),c_Orderings_Obot__class_Obot(tc_fun(U_134,tc_HOL_Obool)))))
        | U_136 = U_138 ) ),
    inference(miniscope,[status(thm)],[f_26_2]) ).

cnf(f_26_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_134),U_136),hAPP(hAPP(c_Set_Oinsert(U_134),U_138),c_Orderings_Obot__class_Obot(tc_fun(U_134,tc_HOL_Obool)))))
    | U_136 = U_138 ),
    inference(clausify,[status(thm)],[f_26_3]) ).

cnf(f_26_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_135),U_137),hAPP(hAPP(c_Set_Oinsert(U_135),U_139),c_Orderings_Obot__class_Obot(tc_fun(U_135,tc_HOL_Obool)))))
    | U_137 != U_139 ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_143,U_142,U_141,U_140] :
      ( hAPP(U_142,hAPP(hAPP(c_Set_Oinsert(U_140),U_143),c_Orderings_Obot__class_Obot(tc_fun(U_140,tc_HOL_Obool)))) = U_143
      | ~ c_Finite__Set_Ofolding__one(U_140,U_141,U_142) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    ( hAPP(U_142,hAPP(hAPP(c_Set_Oinsert(U_140),U_143),c_Orderings_Obot__class_Obot(tc_fun(U_140,tc_HOL_Obool)))) = U_143
    | ~ c_Finite__Set_Ofolding__one(U_140,U_141,U_142) ),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_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_28_2,plain,
    ! [U_147,U_146,U_145,U_144] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_144,U_145,hAPP(hAPP(c_Set_Oinsert(U_144),U_146),c_Orderings_Obot__class_Obot(tc_fun(U_144,tc_HOL_Obool)))),U_147))
        | U_146 != U_147 )
      & ( U_146 = U_147
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_144,U_145,hAPP(hAPP(c_Set_Oinsert(U_144),U_146),c_Orderings_Obot__class_Obot(tc_fun(U_144,tc_HOL_Obool)))),U_147)) ) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ( ! [U_155,U_153] :
        ( ! [U_151,U_149] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_149,U_151,hAPP(hAPP(c_Set_Oinsert(U_149),U_153),c_Orderings_Obot__class_Obot(tc_fun(U_149,tc_HOL_Obool)))),U_155))
        | U_153 != U_155 )
    & ! [U_154,U_152] :
        ( ! [U_150,U_148] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_148,U_150,hAPP(hAPP(c_Set_Oinsert(U_148),U_152),c_Orderings_Obot__class_Obot(tc_fun(U_148,tc_HOL_Obool)))),U_154))
        | U_152 = U_154 ) ),
    inference(miniscope,[status(thm)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_148,U_150,hAPP(hAPP(c_Set_Oinsert(U_148),U_152),c_Orderings_Obot__class_Obot(tc_fun(U_148,tc_HOL_Obool)))),U_154))
    | U_152 = U_154 ),
    inference(clausify,[status(thm)],[f_28_3]) ).

cnf(f_28_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_149,U_151,hAPP(hAPP(c_Set_Oinsert(U_149),U_153),c_Orderings_Obot__class_Obot(tc_fun(U_149,tc_HOL_Obool)))),U_155))
    | U_153 != U_155 ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_158,U_157,U_156] : hAPP(hAPP(c_Set_Oinsert(U_156),U_157),U_158) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_156,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_156),U_157),c_Orderings_Obot__class_Obot(tc_fun(U_156,tc_HOL_Obool)))),U_158),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_156),U_157),U_158) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_156,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_156),U_157),c_Orderings_Obot__class_Obot(tc_fun(U_156,tc_HOL_Obool)))),U_158),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_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_30_2,plain,
    ! [U_161,U_160,U_159] : hAPP(hAPP(c_Set_Oinsert(U_159),U_160),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_159,tc_HOL_Obool)),U_161),hAPP(hAPP(c_Set_Oinsert(U_159),U_160),c_Orderings_Obot__class_Obot(tc_fun(U_159,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_159),U_160),U_161),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_159),U_160),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_159,tc_HOL_Obool)),U_161),hAPP(hAPP(c_Set_Oinsert(U_159),U_160),c_Orderings_Obot__class_Obot(tc_fun(U_159,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_159),U_160),U_161),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_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_31_2,plain,
    ! [U_165,U_164,U_163,U_162] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),U_163),hAPP(hAPP(c_Set_Oinsert(U_162),U_164),U_165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),U_163),hAPP(hAPP(c_Set_Oinsert(U_162),U_164),c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool))))),U_165),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),U_163),hAPP(hAPP(c_Set_Oinsert(U_162),U_164),U_165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_162,tc_HOL_Obool)),U_163),hAPP(hAPP(c_Set_Oinsert(U_162),U_164),c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool))))),U_165),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_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_32_2,plain,
    ! [U_169,U_168,U_167,U_166] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),U_167),hAPP(hAPP(c_Set_Oinsert(U_166),U_168),U_169)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),U_167),U_169)),hAPP(hAPP(c_Set_Oinsert(U_166),U_168),c_Orderings_Obot__class_Obot(tc_fun(U_166,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),U_167),hAPP(hAPP(c_Set_Oinsert(U_166),U_168),U_169)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_166,tc_HOL_Obool)),U_167),U_169)),hAPP(hAPP(c_Set_Oinsert(U_166),U_168),c_Orderings_Obot__class_Obot(tc_fun(U_166,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_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_33_2,plain,
    ! [U_171,U_170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_170),U_171),U_171))
      | ~ class_Orderings_Opreorder(U_170) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_170),U_171),U_171))
    | ~ class_Orderings_Opreorder(U_170) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [V_ca_2,T_b,V_B_2,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      | ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).

fof(f_34_2,plain,
    ! [U_175,U_174,U_173,U_172] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
        & ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
        & hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172)) )
      | U_172 != U_173 ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172))
    | hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172))
    | U_172 != U_173 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
    | hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172))
    | U_172 != U_173 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

cnf(f_34_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_172))
    | hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
    | U_172 != U_173 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

cnf(f_34_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
    | hBOOL(hAPP(hAPP(c_member(U_174),U_175),U_173))
    | U_172 != U_173 ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_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_35_2,plain,
    ! [U_178,U_177,U_176] :
      ( U_177 = U_178
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,tc_HOL_Obool)),U_178),U_177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,tc_HOL_Obool)),U_177),U_178)) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( U_177 = U_178
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,tc_HOL_Obool)),U_178),U_177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,tc_HOL_Obool)),U_177),U_178)) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_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_36_2,plain,
    ! [U_180,U_179] : ~ hBOOL(hAPP(hAPP(c_member(U_179),U_180),c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_179),U_180),c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_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_37_2,plain,
    ! [U_184,U_183,U_182,U_181] :
      ( hBOOL(hAPP(hAPP(c_member(U_181),U_182),U_184))
      | U_182 = U_183
      | ~ hBOOL(hAPP(hAPP(c_member(U_181),U_182),hAPP(hAPP(c_Set_Oinsert(U_181),U_183),U_184))) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_181),U_182),U_184))
    | U_182 = U_183
    | ~ hBOOL(hAPP(hAPP(c_member(U_181),U_182),hAPP(hAPP(c_Set_Oinsert(U_181),U_183),U_184))) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_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_38_2,plain,
    ! [U_188,U_187,U_186,U_185] :
      ( hBOOL(hAPP(hAPP(c_member(U_185),U_186),hAPP(hAPP(c_Set_Oinsert(U_185),U_188),U_187)))
      | ( U_186 != U_188
        & ~ hBOOL(hAPP(hAPP(c_member(U_185),U_186),U_187)) ) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_185),U_186),U_187))
    | hBOOL(hAPP(hAPP(c_member(U_185),U_186),hAPP(hAPP(c_Set_Oinsert(U_185),U_188),U_187))) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( U_186 != U_188
    | hBOOL(hAPP(hAPP(c_member(U_185),U_186),hAPP(hAPP(c_Set_Oinsert(U_185),U_188),U_187))) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [V_ca_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_39_2,plain,
    ! [U_192,U_191,U_190,U_189] :
      ( hBOOL(hAPP(hAPP(c_member(U_189),U_192),U_191))
      | ~ hBOOL(hAPP(hAPP(c_member(U_189),U_192),U_190))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_189,tc_HOL_Obool)),U_190),U_191)) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_189),U_192),U_191))
    | ~ hBOOL(hAPP(hAPP(c_member(U_189),U_192),U_190))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_189,tc_HOL_Obool)),U_190),U_191)) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_40_2,plain,
    ! [U_196,U_195,U_194,U_193] :
      ( hBOOL(hAPP(hAPP(c_member(U_193),U_194),U_196))
      | hBOOL(hAPP(hAPP(c_member(U_193),U_194),U_195))
      | ~ hBOOL(hAPP(hAPP(c_member(U_193),U_194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_193,tc_HOL_Obool)),U_195),U_196))) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_193),U_194),U_196))
    | hBOOL(hAPP(hAPP(c_member(U_193),U_194),U_195))
    | ~ hBOOL(hAPP(hAPP(c_member(U_193),U_194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_193,tc_HOL_Obool)),U_195),U_196))) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [V_A_2,V_B_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UnCI]) ).

fof(f_41_2,plain,
    ! [U_200,U_199,U_198,U_197] :
      ( hBOOL(hAPP(hAPP(c_member(U_197),U_198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_197,tc_HOL_Obool)),U_200),U_199)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_197),U_198),U_200))
        & ~ hBOOL(hAPP(hAPP(c_member(U_197),U_198),U_199)) ) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_197),U_198),U_199))
    | hBOOL(hAPP(hAPP(c_member(U_197),U_198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_197,tc_HOL_Obool)),U_200),U_199))) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

cnf(f_41_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_197),U_198),U_200))
    | hBOOL(hAPP(hAPP(c_member(U_197),U_198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_197,tc_HOL_Obool)),U_200),U_199))) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DiffI]) ).

fof(f_42_2,plain,
    ! [U_204,U_203,U_202,U_201] :
      ( hBOOL(hAPP(hAPP(c_member(U_201),U_202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_201,tc_HOL_Obool)),U_203),U_204)))
      | hBOOL(hAPP(hAPP(c_member(U_201),U_202),U_204))
      | ~ hBOOL(hAPP(hAPP(c_member(U_201),U_202),U_203)) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_201),U_202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_201,tc_HOL_Obool)),U_203),U_204)))
    | hBOOL(hAPP(hAPP(c_member(U_201),U_202),U_204))
    | ~ hBOOL(hAPP(hAPP(c_member(U_201),U_202),U_203)) ),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_43_2,plain,
    ! [U_208,U_207,U_206,U_205] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_208))
        & hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_205,tc_HOL_Obool)),U_207),U_208))) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207))
    | ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_205,tc_HOL_Obool)),U_207),U_208))) ),
    inference(clausify,[status(thm)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_208))
    | ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_205,tc_HOL_Obool)),U_207),U_208))) ),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_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_44_2,plain,
    ! [U_210,U_209] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_209,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_209,tc_HOL_Obool))),U_210)),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_209,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_209,tc_HOL_Obool))),U_210)),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_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_45_2,plain,
    ! [U_212,U_211] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_211,tc_HOL_Obool)),U_212),U_212)),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_211,tc_HOL_Obool)),U_212),U_212)),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_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_46_2,plain,
    ! [U_215,U_214,U_213] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_213,tc_HOL_Obool)),U_214),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_213,tc_HOL_Obool)),U_214),U_215))),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_213,tc_HOL_Obool)),U_214),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_213,tc_HOL_Obool)),U_214),U_215))),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_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_47_2,plain,
    ! [U_218,U_217,U_216] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_216,tc_HOL_Obool)),U_217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_216,tc_HOL_Obool)),U_218),U_217))),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

cnf(f_47_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_216,tc_HOL_Obool)),U_217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_216,tc_HOL_Obool)),U_218),U_217))),
    inference(clausify,[status(thm)],[f_47_2]) ).

fof(f_48_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_48_2,plain,
    ! [U_220,U_219] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_219,tc_HOL_Obool)),U_220),U_220) = U_220,
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_219,tc_HOL_Obool)),U_220),U_220) = U_220,
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_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_49_2,plain,
    ! [U_223,U_222,U_221] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_221,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_221,tc_HOL_Obool)),U_222),U_223)),U_222)),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_221,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_221,tc_HOL_Obool)),U_222),U_223)),U_222)),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_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_50_2,plain,
    ! [U_229,U_228,U_227,U_226] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229))
          | ? [U_225] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,U_225)),hAPP(U_229,U_225))) )
        & ( ! [U_224] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,U_224)),hAPP(U_229,U_224)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229)) ) )
      | ~ class_Orderings_Oord(U_226) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_229,U_228,U_227,U_226] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,sK2(U_229,U_228,U_227,U_226))),hAPP(U_229,sK2(U_229,U_228,U_227,U_226)))) )
        & ( ! [U_224] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,U_224)),hAPP(U_229,U_224)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229)) ) )
      | ~ class_Orderings_Oord(U_226) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_225,sK2(U_229,U_228,U_227,U_226))],[f_50_2]) ).

cnf(f_50_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,U_224)),hAPP(U_229,U_224)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229))
    | ~ class_Orderings_Oord(U_226) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

cnf(f_50_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_227,U_226)),U_228),U_229))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),hAPP(U_228,sK2(U_229,U_228,U_227,U_226))),hAPP(U_229,sK2(U_229,U_228,U_227,U_226))))
    | ~ class_Orderings_Oord(U_226) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_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_51_2,plain,
    ! [U_232,U_231,U_230] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_230),U_231),U_232))
        | ~ hBOOL(hAPP(U_232,U_231)) )
      & ( hBOOL(hAPP(U_232,U_231))
        | ~ hBOOL(hAPP(hAPP(c_member(U_230),U_231),U_232)) ) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ( ! [U_238,U_236] :
        ( ! [U_234] : hBOOL(hAPP(hAPP(c_member(U_234),U_236),U_238))
        | ~ hBOOL(hAPP(U_238,U_236)) )
    & ! [U_237,U_235] :
        ( ! [U_233] : ~ hBOOL(hAPP(hAPP(c_member(U_233),U_235),U_237))
        | hBOOL(hAPP(U_237,U_235)) ) ),
    inference(miniscope,[status(thm)],[f_51_2]) ).

cnf(f_51_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_233),U_235),U_237))
    | hBOOL(hAPP(U_237,U_235)) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_234),U_236),U_238))
    | ~ hBOOL(hAPP(U_238,U_236)) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_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_52_2,plain,
    ! [U_241,U_240,U_239] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_239,tc_HOL_Obool)),U_240),U_241) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_239,tc_HOL_Obool)),U_241),U_240),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_239,tc_HOL_Obool)),U_240),U_241) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_239,tc_HOL_Obool)),U_241),U_240),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_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_53_2,plain,
    ! [U_244,U_243,U_242] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),U_244),U_243))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),U_243),U_244))
      | ~ class_Orderings_Olinorder(U_242) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),U_244),U_243))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),U_243),U_244))
    | ~ class_Orderings_Olinorder(U_242) ),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_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_54_2,plain,
    ! [U_247,U_246,U_245] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_245,tc_HOL_Obool)),U_246),U_247))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_245,tc_HOL_Obool)),U_246),U_247) != U_247 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_245,tc_HOL_Obool)),U_246),U_247) = U_247
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_245,tc_HOL_Obool)),U_246),U_247)) ) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ( ! [U_253,U_251,U_249] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_249,tc_HOL_Obool)),U_251),U_253))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_249,tc_HOL_Obool)),U_251),U_253) != U_253 )
    & ! [U_252,U_250,U_248] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_248,tc_HOL_Obool)),U_250),U_252) = U_252
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_248,tc_HOL_Obool)),U_250),U_252)) ) ),
    inference(miniscope,[status(thm)],[f_54_2]) ).

cnf(f_54_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_248,tc_HOL_Obool)),U_250),U_252) = U_252
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_248,tc_HOL_Obool)),U_250),U_252)) ),
    inference(clausify,[status(thm)],[f_54_3]) ).

cnf(f_54_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_249,tc_HOL_Obool)),U_251),U_253))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_249,tc_HOL_Obool)),U_251),U_253) != U_253 ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_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_55_2,plain,
    ! [U_256,U_255,U_254] :
      ( ( U_254 = U_255
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_256,tc_HOL_Obool)),U_255),U_254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_256,tc_HOL_Obool)),U_254),U_255)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_256,tc_HOL_Obool)),U_255),U_254))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_256,tc_HOL_Obool)),U_254),U_255)) )
        | U_254 != U_255 ) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ( ! [U_262,U_260,U_258] :
        ( U_258 = U_260
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_262,tc_HOL_Obool)),U_260),U_258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_262,tc_HOL_Obool)),U_258),U_260)) )
    & ! [U_261,U_259,U_257] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_261,tc_HOL_Obool)),U_259),U_257))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_261,tc_HOL_Obool)),U_257),U_259)) )
        | U_257 != U_259 ) ),
    inference(miniscope,[status(thm)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_261,tc_HOL_Obool)),U_257),U_259))
    | U_257 != U_259 ),
    inference(clausify,[status(thm)],[f_55_3]) ).

cnf(f_55_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_261,tc_HOL_Obool)),U_259),U_257))
    | U_257 != U_259 ),
    inference(clausify,[status(thm)],[f_55_3]) ).

cnf(f_55_6,plain,
    ( U_258 = U_260
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_262,tc_HOL_Obool)),U_260),U_258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_262,tc_HOL_Obool)),U_258),U_260)) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_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_56_2,plain,
    ! [U_265,U_264,U_263] :
      ( ( ( U_264 = U_265
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_265),U_264))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_264),U_265)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_265),U_264))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_264),U_265)) )
          | U_264 != U_265 ) )
      | ~ class_Orderings_Oorder(U_263) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_264),U_265))
    | U_264 != U_265
    | ~ class_Orderings_Oorder(U_263) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_265),U_264))
    | U_264 != U_265
    | ~ class_Orderings_Oorder(U_263) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

cnf(f_56_5,plain,
    ( U_264 = U_265
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_265),U_264))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_263),U_264),U_265))
    | ~ class_Orderings_Oorder(U_263) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_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_57_2,plain,
    ! [U_268,U_267,U_266] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_266,tc_HOL_Obool)),U_267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_266,tc_HOL_Obool)),U_268),U_267)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_266,tc_HOL_Obool)),U_267),U_268),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_266,tc_HOL_Obool)),U_267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_266,tc_HOL_Obool)),U_268),U_267)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_266,tc_HOL_Obool)),U_267),U_268),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_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_58_2,plain,
    ! [U_271,U_270,U_269] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),U_271)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),U_271),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),U_271)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_269,tc_HOL_Obool)),U_270),U_271),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_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_59_2,plain,
    ! [U_275,U_274,U_273,U_272] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_273),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_274),U_275)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_274),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_273),U_275)),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_273),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_274),U_275)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_274),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_272,tc_HOL_Obool)),U_273),U_275)),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_60_2,plain,
    ! [U_279,U_278,U_277,U_276] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_276),U_277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_276,tc_HOL_Obool)),U_278),U_279)))
        | hBOOL(hAPP(hAPP(c_member(U_276),U_277),U_279))
        | ~ hBOOL(hAPP(hAPP(c_member(U_276),U_277),U_278)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_276),U_277),U_279))
          & hBOOL(hAPP(hAPP(c_member(U_276),U_277),U_278)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_276),U_277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_276,tc_HOL_Obool)),U_278),U_279))) ) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ( ! [U_287,U_285,U_283,U_281] :
        ( hBOOL(hAPP(hAPP(c_member(U_281),U_283),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_281,tc_HOL_Obool)),U_285),U_287)))
        | hBOOL(hAPP(hAPP(c_member(U_281),U_283),U_287))
        | ~ hBOOL(hAPP(hAPP(c_member(U_281),U_283),U_285)) )
    & ! [U_286,U_284,U_282,U_280] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_280),U_282),U_286))
          & hBOOL(hAPP(hAPP(c_member(U_280),U_282),U_284)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_280),U_282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_280,tc_HOL_Obool)),U_284),U_286))) ) ),
    inference(miniscope,[status(thm)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_280),U_282),U_284))
    | ~ hBOOL(hAPP(hAPP(c_member(U_280),U_282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_280,tc_HOL_Obool)),U_284),U_286))) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

cnf(f_60_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_280),U_282),U_286))
    | ~ hBOOL(hAPP(hAPP(c_member(U_280),U_282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_280,tc_HOL_Obool)),U_284),U_286))) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

cnf(f_60_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_281),U_283),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_281,tc_HOL_Obool)),U_285),U_287)))
    | hBOOL(hAPP(hAPP(c_member(U_281),U_283),U_287))
    | ~ hBOOL(hAPP(hAPP(c_member(U_281),U_283),U_285)) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_61_2,plain,
    ! [U_291,U_290,U_289,U_288] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_288),U_289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_288,tc_HOL_Obool)),U_290),U_291)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_288),U_289),U_291))
          & ~ hBOOL(hAPP(hAPP(c_member(U_288),U_289),U_290)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_288),U_289),U_291))
        | hBOOL(hAPP(hAPP(c_member(U_288),U_289),U_290))
        | ~ hBOOL(hAPP(hAPP(c_member(U_288),U_289),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_288,tc_HOL_Obool)),U_290),U_291))) ) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ( ! [U_299,U_297,U_295,U_293] :
        ( hBOOL(hAPP(hAPP(c_member(U_293),U_295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_293,tc_HOL_Obool)),U_297),U_299)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_293),U_295),U_299))
          & ~ hBOOL(hAPP(hAPP(c_member(U_293),U_295),U_297)) ) )
    & ! [U_298,U_296,U_294,U_292] :
        ( hBOOL(hAPP(hAPP(c_member(U_292),U_294),U_298))
        | hBOOL(hAPP(hAPP(c_member(U_292),U_294),U_296))
        | ~ hBOOL(hAPP(hAPP(c_member(U_292),U_294),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_292,tc_HOL_Obool)),U_296),U_298))) ) ),
    inference(miniscope,[status(thm)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_292),U_294),U_298))
    | hBOOL(hAPP(hAPP(c_member(U_292),U_294),U_296))
    | ~ hBOOL(hAPP(hAPP(c_member(U_292),U_294),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_292,tc_HOL_Obool)),U_296),U_298))) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_293),U_295),U_297))
    | hBOOL(hAPP(hAPP(c_member(U_293),U_295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_293,tc_HOL_Obool)),U_297),U_299))) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_293),U_295),U_299))
    | hBOOL(hAPP(hAPP(c_member(U_293),U_295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_293,tc_HOL_Obool)),U_297),U_299))) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_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_62_2,plain,
    ! [U_302,U_301,U_300] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302)),U_302) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302)),U_302) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_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_63_2,plain,
    ! [U_305,U_304,U_303] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_303,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_303,tc_HOL_Obool)),U_304),U_305)),U_305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_303,tc_HOL_Obool)),U_304),U_305),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_303,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_303,tc_HOL_Obool)),U_304),U_305)),U_305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_303,tc_HOL_Obool)),U_304),U_305),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_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_64_2,plain,
    ! [U_309,U_308,U_307,U_306] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308)),U_309))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_306,tc_HOL_Obool)),U_308),U_309))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),U_307),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_306,tc_HOL_Obool)),U_308),U_309)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_306,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_306,tc_HOL_Obool)),U_307),U_308)),U_309)) ) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ( ! [U_317,U_315,U_313,U_311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_311,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_311,tc_HOL_Obool)),U_313),U_315)),U_317))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_311,tc_HOL_Obool)),U_313),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_311,tc_HOL_Obool)),U_315),U_317))) )
    & ! [U_316,U_314,U_312,U_310] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_310,tc_HOL_Obool)),U_312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_310,tc_HOL_Obool)),U_314),U_316)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_310,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_310,tc_HOL_Obool)),U_312),U_314)),U_316)) ) ),
    inference(miniscope,[status(thm)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_310,tc_HOL_Obool)),U_312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_310,tc_HOL_Obool)),U_314),U_316)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_310,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_310,tc_HOL_Obool)),U_312),U_314)),U_316)) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

cnf(f_64_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_311,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_311,tc_HOL_Obool)),U_313),U_315)),U_317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_311,tc_HOL_Obool)),U_313),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_311,tc_HOL_Obool)),U_315),U_317))) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_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_65_2,plain,
    ! [U_321,U_320,U_319,U_318] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_319),U_320)),U_321) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_319),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_320),U_321)),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_319),U_320)),U_321) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_319),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_318,tc_HOL_Obool)),U_320),U_321)),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_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_66_2,plain,
    ! [U_325,U_324,U_323,U_322] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),U_323),U_324)),U_325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),U_323),U_325)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),U_324),U_325)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),U_323),U_324)),U_325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),U_323),U_325)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_322,tc_HOL_Obool)),U_324),U_325)),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_67_2,plain,
    ! [U_335,U_334,U_333,U_332] :
      ( ( ? [U_331] :
            ( hBOOL(hAPP(U_335,U_331))
            & hBOOL(hAPP(hAPP(c_member(U_332),U_331),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_332,tc_HOL_Obool)),U_333),U_334))) )
        | ( ! [U_330] :
              ( ~ hBOOL(hAPP(U_335,U_330))
              | ~ hBOOL(hAPP(hAPP(c_member(U_332),U_330),U_334)) )
          & ! [U_329] :
              ( ~ hBOOL(hAPP(U_335,U_329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_332),U_329),U_333)) ) ) )
      & ( ? [U_328] :
            ( hBOOL(hAPP(U_335,U_328))
            & hBOOL(hAPP(hAPP(c_member(U_332),U_328),U_334)) )
        | ? [U_327] :
            ( hBOOL(hAPP(U_335,U_327))
            & hBOOL(hAPP(hAPP(c_member(U_332),U_327),U_333)) )
        | ! [U_326] :
            ( ~ hBOOL(hAPP(U_335,U_326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_332),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_332,tc_HOL_Obool)),U_333),U_334))) ) ) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ( ! [U_343,U_341,U_339,U_337] :
        ( ? [U_331] :
            ( hBOOL(hAPP(U_343,U_331))
            & hBOOL(hAPP(hAPP(c_member(U_337),U_331),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341))) )
        | ( ! [U_330] :
              ( ~ hBOOL(hAPP(U_343,U_330))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) )
          & ! [U_329] :
              ( ~ hBOOL(hAPP(U_343,U_329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ) ) )
    & ! [U_342,U_340,U_338,U_336] :
        ( ? [U_328] :
            ( hBOOL(hAPP(U_342,U_328))
            & hBOOL(hAPP(hAPP(c_member(U_336),U_328),U_340)) )
        | ? [U_327] :
            ( hBOOL(hAPP(U_342,U_327))
            & hBOOL(hAPP(hAPP(c_member(U_336),U_327),U_338)) )
        | ! [U_326] :
            ( ~ hBOOL(hAPP(U_342,U_326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ) ) ),
    inference(miniscope,[status(thm)],[f_67_2]) ).

fof(f_67_4,plain,
    ( ! [U_343,U_341,U_339,U_337] :
        ( ? [U_331] :
            ( hBOOL(hAPP(U_343,U_331))
            & hBOOL(hAPP(hAPP(c_member(U_337),U_331),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341))) )
        | ( ! [U_330] :
              ( ~ hBOOL(hAPP(U_343,U_330))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) )
          & ! [U_329] :
              ( ~ hBOOL(hAPP(U_343,U_329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ) ) )
    & ! [U_342,U_340,U_338,U_336] :
        ( ? [U_328] :
            ( hBOOL(hAPP(U_342,U_328))
            & hBOOL(hAPP(hAPP(c_member(U_336),U_328),U_340)) )
        | ( hBOOL(hAPP(U_342,sK3(U_342,U_340,U_338,U_336)))
          & hBOOL(hAPP(hAPP(c_member(U_336),sK3(U_342,U_340,U_338,U_336)),U_338)) )
        | ! [U_326] :
            ( ~ hBOOL(hAPP(U_342,U_326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_327,sK3(U_342,U_340,U_338,U_336))],[f_67_3]) ).

fof(f_67_5,plain,
    ( ! [U_343,U_341,U_339,U_337] :
        ( ? [U_331] :
            ( hBOOL(hAPP(U_343,U_331))
            & hBOOL(hAPP(hAPP(c_member(U_337),U_331),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341))) )
        | ( ! [U_330] :
              ( ~ hBOOL(hAPP(U_343,U_330))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) )
          & ! [U_329] :
              ( ~ hBOOL(hAPP(U_343,U_329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ) ) )
    & ! [U_342,U_340,U_338,U_336] :
        ( ( hBOOL(hAPP(U_342,sK4(U_342,U_340,U_338,U_336)))
          & hBOOL(hAPP(hAPP(c_member(U_336),sK4(U_342,U_340,U_338,U_336)),U_340)) )
        | ( hBOOL(hAPP(U_342,sK3(U_342,U_340,U_338,U_336)))
          & hBOOL(hAPP(hAPP(c_member(U_336),sK3(U_342,U_340,U_338,U_336)),U_338)) )
        | ! [U_326] :
            ( ~ hBOOL(hAPP(U_342,U_326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_328,sK4(U_342,U_340,U_338,U_336))],[f_67_4]) ).

fof(f_67_6,plain,
    ( ! [U_343,U_341,U_339,U_337] :
        ( ( hBOOL(hAPP(U_343,sK5(U_343,U_341,U_339,U_337)))
          & hBOOL(hAPP(hAPP(c_member(U_337),sK5(U_343,U_341,U_339,U_337)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341))) )
        | ( ! [U_330] :
              ( ~ hBOOL(hAPP(U_343,U_330))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) )
          & ! [U_329] :
              ( ~ hBOOL(hAPP(U_343,U_329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ) ) )
    & ! [U_342,U_340,U_338,U_336] :
        ( ( hBOOL(hAPP(U_342,sK4(U_342,U_340,U_338,U_336)))
          & hBOOL(hAPP(hAPP(c_member(U_336),sK4(U_342,U_340,U_338,U_336)),U_340)) )
        | ( hBOOL(hAPP(U_342,sK3(U_342,U_340,U_338,U_336)))
          & hBOOL(hAPP(hAPP(c_member(U_336),sK3(U_342,U_340,U_338,U_336)),U_338)) )
        | ! [U_326] :
            ( ~ hBOOL(hAPP(U_342,U_326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_331,sK5(U_343,U_341,U_339,U_337))],[f_67_5]) ).

cnf(f_67_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_336),sK4(U_342,U_340,U_338,U_336)),U_340))
    | hBOOL(hAPP(hAPP(c_member(U_336),sK3(U_342,U_340,U_338,U_336)),U_338))
    | ~ hBOOL(hAPP(U_342,U_326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_8,plain,
    ( hBOOL(hAPP(U_342,sK4(U_342,U_340,U_338,U_336)))
    | hBOOL(hAPP(hAPP(c_member(U_336),sK3(U_342,U_340,U_338,U_336)),U_338))
    | ~ hBOOL(hAPP(U_342,U_326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_336),sK4(U_342,U_340,U_338,U_336)),U_340))
    | hBOOL(hAPP(U_342,sK3(U_342,U_340,U_338,U_336)))
    | ~ hBOOL(hAPP(U_342,U_326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_10,plain,
    ( hBOOL(hAPP(U_342,sK4(U_342,U_340,U_338,U_336)))
    | hBOOL(hAPP(U_342,sK3(U_342,U_340,U_338,U_336)))
    | ~ hBOOL(hAPP(U_342,U_326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_336),U_326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_336,tc_HOL_Obool)),U_338),U_340))) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_337),sK5(U_343,U_341,U_339,U_337)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341)))
    | ~ hBOOL(hAPP(U_343,U_329))
    | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_12,plain,
    ( hBOOL(hAPP(U_343,sK5(U_343,U_341,U_339,U_337)))
    | ~ hBOOL(hAPP(U_343,U_329))
    | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_329),U_339)) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_337),sK5(U_343,U_341,U_339,U_337)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_337,tc_HOL_Obool)),U_339),U_341)))
    | ~ hBOOL(hAPP(U_343,U_330))
    | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

cnf(f_67_14,plain,
    ( hBOOL(hAPP(U_343,sK5(U_343,U_341,U_339,U_337)))
    | ~ hBOOL(hAPP(U_343,U_330))
    | ~ hBOOL(hAPP(hAPP(c_member(U_337),U_330),U_341)) ),
    inference(clausify,[status(thm)],[f_67_6]) ).

fof(f_68_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_68_2,plain,
    ! [U_353,U_352,U_351,U_350] :
      ( ( ! [U_349] :
            ( hBOOL(hAPP(U_353,U_349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_350),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_350,tc_HOL_Obool)),U_351),U_352))) )
        | ? [U_348] :
            ( ~ hBOOL(hAPP(U_353,U_348))
            & hBOOL(hAPP(hAPP(c_member(U_350),U_348),U_352)) )
        | ? [U_347] :
            ( ~ hBOOL(hAPP(U_353,U_347))
            & hBOOL(hAPP(hAPP(c_member(U_350),U_347),U_351)) ) )
      & ( ( ! [U_346] :
              ( hBOOL(hAPP(U_353,U_346))
              | ~ hBOOL(hAPP(hAPP(c_member(U_350),U_346),U_352)) )
          & ! [U_345] :
              ( hBOOL(hAPP(U_353,U_345))
              | ~ hBOOL(hAPP(hAPP(c_member(U_350),U_345),U_351)) ) )
        | ? [U_344] :
            ( ~ hBOOL(hAPP(U_353,U_344))
            & hBOOL(hAPP(hAPP(c_member(U_350),U_344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_350,tc_HOL_Obool)),U_351),U_352))) ) ) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ( ! [U_361,U_359,U_357,U_355] :
        ( ! [U_349] :
            ( hBOOL(hAPP(U_361,U_349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) )
        | ? [U_348] :
            ( ~ hBOOL(hAPP(U_361,U_348))
            & hBOOL(hAPP(hAPP(c_member(U_355),U_348),U_359)) )
        | ? [U_347] :
            ( ~ hBOOL(hAPP(U_361,U_347))
            & hBOOL(hAPP(hAPP(c_member(U_355),U_347),U_357)) ) )
    & ! [U_360,U_358,U_356,U_354] :
        ( ( ! [U_346] :
              ( hBOOL(hAPP(U_360,U_346))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358)) )
          & ! [U_345] :
              ( hBOOL(hAPP(U_360,U_345))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356)) ) )
        | ? [U_344] :
            ( ~ hBOOL(hAPP(U_360,U_344))
            & hBOOL(hAPP(hAPP(c_member(U_354),U_344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ) ) ),
    inference(miniscope,[status(thm)],[f_68_2]) ).

fof(f_68_4,plain,
    ( ! [U_361,U_359,U_357,U_355] :
        ( ! [U_349] :
            ( hBOOL(hAPP(U_361,U_349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) )
        | ? [U_348] :
            ( ~ hBOOL(hAPP(U_361,U_348))
            & hBOOL(hAPP(hAPP(c_member(U_355),U_348),U_359)) )
        | ? [U_347] :
            ( ~ hBOOL(hAPP(U_361,U_347))
            & hBOOL(hAPP(hAPP(c_member(U_355),U_347),U_357)) ) )
    & ! [U_360,U_358,U_356,U_354] :
        ( ( ! [U_346] :
              ( hBOOL(hAPP(U_360,U_346))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358)) )
          & ! [U_345] :
              ( hBOOL(hAPP(U_360,U_345))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356)) ) )
        | ( ~ hBOOL(hAPP(U_360,sK6(U_360,U_358,U_356,U_354)))
          & hBOOL(hAPP(hAPP(c_member(U_354),sK6(U_360,U_358,U_356,U_354)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_344,sK6(U_360,U_358,U_356,U_354))],[f_68_3]) ).

fof(f_68_5,plain,
    ( ! [U_361,U_359,U_357,U_355] :
        ( ! [U_349] :
            ( hBOOL(hAPP(U_361,U_349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) )
        | ? [U_348] :
            ( ~ hBOOL(hAPP(U_361,U_348))
            & hBOOL(hAPP(hAPP(c_member(U_355),U_348),U_359)) )
        | ( ~ hBOOL(hAPP(U_361,sK7(U_361,U_359,U_357,U_355)))
          & hBOOL(hAPP(hAPP(c_member(U_355),sK7(U_361,U_359,U_357,U_355)),U_357)) ) )
    & ! [U_360,U_358,U_356,U_354] :
        ( ( ! [U_346] :
              ( hBOOL(hAPP(U_360,U_346))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358)) )
          & ! [U_345] :
              ( hBOOL(hAPP(U_360,U_345))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356)) ) )
        | ( ~ hBOOL(hAPP(U_360,sK6(U_360,U_358,U_356,U_354)))
          & hBOOL(hAPP(hAPP(c_member(U_354),sK6(U_360,U_358,U_356,U_354)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_347,sK7(U_361,U_359,U_357,U_355))],[f_68_4]) ).

fof(f_68_6,plain,
    ( ! [U_361,U_359,U_357,U_355] :
        ( ! [U_349] :
            ( hBOOL(hAPP(U_361,U_349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) )
        | ( ~ hBOOL(hAPP(U_361,sK8(U_361,U_359,U_357,U_355)))
          & hBOOL(hAPP(hAPP(c_member(U_355),sK8(U_361,U_359,U_357,U_355)),U_359)) )
        | ( ~ hBOOL(hAPP(U_361,sK7(U_361,U_359,U_357,U_355)))
          & hBOOL(hAPP(hAPP(c_member(U_355),sK7(U_361,U_359,U_357,U_355)),U_357)) ) )
    & ! [U_360,U_358,U_356,U_354] :
        ( ( ! [U_346] :
              ( hBOOL(hAPP(U_360,U_346))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358)) )
          & ! [U_345] :
              ( hBOOL(hAPP(U_360,U_345))
              | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356)) ) )
        | ( ~ hBOOL(hAPP(U_360,sK6(U_360,U_358,U_356,U_354)))
          & hBOOL(hAPP(hAPP(c_member(U_354),sK6(U_360,U_358,U_356,U_354)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_348,sK8(U_361,U_359,U_357,U_355))],[f_68_5]) ).

cnf(f_68_7,plain,
    ( hBOOL(hAPP(U_360,U_345))
    | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356))
    | hBOOL(hAPP(hAPP(c_member(U_354),sK6(U_360,U_358,U_356,U_354)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_8,plain,
    ( hBOOL(hAPP(U_360,U_346))
    | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358))
    | hBOOL(hAPP(hAPP(c_member(U_354),sK6(U_360,U_358,U_356,U_354)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_358))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_9,plain,
    ( hBOOL(hAPP(U_360,U_345))
    | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_345),U_356))
    | ~ hBOOL(hAPP(U_360,sK6(U_360,U_358,U_356,U_354))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_10,plain,
    ( hBOOL(hAPP(U_360,U_346))
    | ~ hBOOL(hAPP(hAPP(c_member(U_354),U_346),U_358))
    | ~ hBOOL(hAPP(U_360,sK6(U_360,U_358,U_356,U_354))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_355),sK8(U_361,U_359,U_357,U_355)),U_359))
    | hBOOL(hAPP(hAPP(c_member(U_355),sK7(U_361,U_359,U_357,U_355)),U_357))
    | hBOOL(hAPP(U_361,U_349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_12,plain,
    ( ~ hBOOL(hAPP(U_361,sK8(U_361,U_359,U_357,U_355)))
    | hBOOL(hAPP(hAPP(c_member(U_355),sK7(U_361,U_359,U_357,U_355)),U_357))
    | hBOOL(hAPP(U_361,U_349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_355),sK8(U_361,U_359,U_357,U_355)),U_359))
    | ~ hBOOL(hAPP(U_361,sK7(U_361,U_359,U_357,U_355)))
    | hBOOL(hAPP(U_361,U_349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

cnf(f_68_14,plain,
    ( ~ hBOOL(hAPP(U_361,sK8(U_361,U_359,U_357,U_355)))
    | ~ hBOOL(hAPP(U_361,sK7(U_361,U_359,U_357,U_355)))
    | hBOOL(hAPP(U_361,U_349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_355),U_349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_355,tc_HOL_Obool)),U_357),U_359))) ),
    inference(clausify,[status(thm)],[f_68_6]) ).

fof(f_69_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_69_2,plain,
    ! [U_364,U_363,U_362] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_364,tc_HOL_Obool)),U_362),U_363))
      | U_362 != U_363 ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_364,tc_HOL_Obool)),U_362),U_363))
    | U_362 != U_363 ),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_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_70_2,plain,
    ! [U_367,U_366,U_365] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_367,tc_HOL_Obool)),U_366),U_365))
      | U_365 != U_366 ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_367,tc_HOL_Obool)),U_366),U_365))
    | U_365 != U_366 ),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_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_71_2,plain,
    ! [U_370,U_369,U_368] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_368),U_369),U_370))
      | U_369 != U_370
      | ~ class_Orderings_Opreorder(U_368) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_368),U_369),U_370))
    | U_369 != U_370
    | ~ class_Orderings_Opreorder(U_368) ),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI1]) ).

fof(f_72_2,plain,
    ! [U_374,U_373,U_372,U_371] :
      ( hBOOL(hAPP(hAPP(c_member(U_371),U_372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),U_373),U_374)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_371),U_372),U_373)) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_371),U_372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),U_373),U_374)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_371),U_372),U_373)) ),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [V_A_2,V_B_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI2]) ).

fof(f_73_2,plain,
    ! [U_378,U_377,U_376,U_375] :
      ( hBOOL(hAPP(hAPP(c_member(U_375),U_376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_378),U_377)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_375),U_376),U_377)) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_375),U_376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_378),U_377)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_375),U_376),U_377)) ),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_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_74_2,plain,
    ! [U_383,U_382,U_381,U_380,U_379] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_379),hAPP(U_381,U_383)),hAPP(U_382,U_383)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_380,U_379)),U_381),U_382))
      | ~ class_Orderings_Oord(U_379) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_379),hAPP(U_381,U_383)),hAPP(U_382,U_383)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_380,U_379)),U_381),U_382))
    | ~ class_Orderings_Oord(U_379) ),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_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_75_2,plain,
    ! [U_386,U_385,U_384] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_384,tc_HOL_Obool)),U_385),U_386) = U_386
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_384,tc_HOL_Obool)),U_385),U_386)) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_384,tc_HOL_Obool)),U_385),U_386) = U_386
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_384,tc_HOL_Obool)),U_385),U_386)) ),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_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_76_2,plain,
    ! [U_389,U_388,U_387] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),U_389),U_388) = U_389
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_387,tc_HOL_Obool)),U_388),U_389)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),U_389),U_388) = U_389
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_387,tc_HOL_Obool)),U_388),U_389)) ),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_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_77_2,plain,
    ! [U_393,U_392,U_391,U_390] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_390))
          | ~ hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_391)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_391))
          | ~ hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_390)) ) )
      | U_390 != U_391 ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

cnf(f_77_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_391))
    | ~ hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_390))
    | U_390 != U_391 ),
    inference(clausify,[status(thm)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_390))
    | ~ hBOOL(hAPP(hAPP(c_member(U_392),U_393),U_391))
    | U_390 != U_391 ),
    inference(clausify,[status(thm)],[f_77_2]) ).

fof(f_78_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_78_2,plain,
    ! [U_397,U_396,U_395,U_394] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_396),U_394),U_397))
          | ~ hBOOL(hAPP(hAPP(c_member(U_396),U_395),U_397)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_396),U_395),U_397))
          | ~ hBOOL(hAPP(hAPP(c_member(U_396),U_394),U_397)) ) )
      | U_394 != U_395 ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

cnf(f_78_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_396),U_395),U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_396),U_394),U_397))
    | U_394 != U_395 ),
    inference(clausify,[status(thm)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_396),U_394),U_397))
    | ~ hBOOL(hAPP(hAPP(c_member(U_396),U_395),U_397))
    | U_394 != U_395 ),
    inference(clausify,[status(thm)],[f_78_2]) ).

fof(f_79_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_79_2,plain,
    ! [U_401,U_400,U_399,U_398] :
      ( hBOOL(hAPP(hAPP(c_member(U_398),U_401),U_400))
      | ~ hBOOL(hAPP(hAPP(c_member(U_398),U_401),U_399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_398,tc_HOL_Obool)),U_399),U_400)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_398),U_401),U_400))
    | ~ hBOOL(hAPP(hAPP(c_member(U_398),U_401),U_399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_398,tc_HOL_Obool)),U_399),U_400)) ),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_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_80_2,plain,
    ! [U_404,U_403,U_402] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_404),U_403))
          | U_404 != U_403 )
        & ( U_404 = U_403
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_404),U_403)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_403),U_404))
      | ~ class_Orderings_Oorder(U_402) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

cnf(f_80_3,plain,
    ( U_404 = U_403
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_404),U_403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_403),U_404))
    | ~ class_Orderings_Oorder(U_402) ),
    inference(clausify,[status(thm)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_404),U_403))
    | U_404 != U_403
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_402),U_403),U_404))
    | ~ class_Orderings_Oorder(U_402) ),
    inference(clausify,[status(thm)],[f_80_2]) ).

fof(f_81_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_81_2,plain,
    ! [U_407,U_406,U_405] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_405,tc_HOL_Obool)),U_407),U_406)) = U_407
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_405,tc_HOL_Obool)),U_406),U_407)) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_405,tc_HOL_Obool)),U_407),U_406)) = U_407
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_405,tc_HOL_Obool)),U_406),U_407)) ),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_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_82_2,plain,
    ! [U_411,U_410,U_409,U_408] :
      ( hBOOL(hAPP(hAPP(c_member(U_410),U_408),U_411))
      | ~ hBOOL(hAPP(hAPP(c_member(U_410),U_409),U_411))
      | U_408 != U_409 ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_410),U_408),U_411))
    | ~ hBOOL(hAPP(hAPP(c_member(U_410),U_409),U_411))
    | U_408 != U_409 ),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_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_83_2,plain,
    ! [U_415,U_414,U_413,U_412] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_412),U_413),U_415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_412),U_414),U_415))
      | U_413 != U_414
      | ~ class_Orderings_Oord(U_412) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_412),U_413),U_415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_412),U_414),U_415))
    | U_413 != U_414
    | ~ class_Orderings_Oord(U_412) ),
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_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_84_2,plain,
    ! [U_419,U_418,U_417,U_416] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_416),U_419),U_417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_416),U_419),U_418))
      | U_417 != U_418
      | ~ class_Orderings_Oorder(U_416) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_416),U_419),U_417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_416),U_419),U_418))
    | U_417 != U_418
    | ~ class_Orderings_Oorder(U_416) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_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_85_2,plain,
    ! [U_423,U_422,U_421,U_420] :
      ( hBOOL(hAPP(hAPP(c_member(U_420),U_421),U_423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_420,tc_HOL_Obool)),U_422),U_423))
      | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_421),U_422)) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_420),U_421),U_423))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_420,tc_HOL_Obool)),U_422),U_423))
    | ~ hBOOL(hAPP(hAPP(c_member(U_420),U_421),U_422)) ),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_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_86_2,plain,
    ! [U_427,U_426,U_425,U_424] :
      ( hBOOL(hAPP(hAPP(c_member(U_424),U_427),U_426))
      | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_427),U_425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_424,tc_HOL_Obool)),U_425),U_426)) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

cnf(f_86_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_424),U_427),U_426))
    | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_427),U_425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_424,tc_HOL_Obool)),U_425),U_426)) ),
    inference(clausify,[status(thm)],[f_86_2]) ).

fof(f_87_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_87_2,plain,
    ! [U_431,U_430,U_429,U_428] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_428,tc_HOL_Obool)),U_429),U_431))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_428,tc_HOL_Obool)),U_430),U_431))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_428,tc_HOL_Obool)),U_429),U_430)) ),
    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_428,tc_HOL_Obool)),U_429),U_431))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_428,tc_HOL_Obool)),U_430),U_431))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_428,tc_HOL_Obool)),U_429),U_430)) ),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_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_88_2,plain,
    ! [U_435,U_434,U_433,U_432] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_435))
      | U_434 != U_435
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_434))
      | ~ class_Orderings_Oord(U_432) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_435))
    | U_434 != U_435
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_432),U_433),U_434))
    | ~ class_Orderings_Oord(U_432) ),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_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_89_2,plain,
    ! [U_439,U_438,U_437,U_436] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_436),U_439),U_438))
      | U_437 != U_439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_436),U_437),U_438))
      | ~ class_Orderings_Oorder(U_436) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_436),U_439),U_438))
    | U_437 != U_439
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_436),U_437),U_438))
    | ~ class_Orderings_Oorder(U_436) ),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_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_90_2,plain,
    ! [U_442,U_441,U_440] :
      ( U_441 = U_442
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_440),U_442),U_441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_440),U_441),U_442))
      | ~ class_Orderings_Oorder(U_440) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

cnf(f_90_3,plain,
    ( U_441 = U_442
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_440),U_442),U_441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_440),U_441),U_442))
    | ~ class_Orderings_Oorder(U_440) ),
    inference(clausify,[status(thm)],[f_90_2]) ).

fof(f_91_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_91_2,plain,
    ! [U_446,U_445,U_444,U_443] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_444),U_446))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_445),U_446))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_444),U_445))
      | ~ class_Orderings_Opreorder(U_443) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_444),U_446))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_445),U_446))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_443),U_444),U_445))
    | ~ class_Orderings_Opreorder(U_443) ),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_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_92_2,plain,
    ! [U_449,U_448,U_447] :
      ( U_449 = U_448
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_447),U_449),U_448))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_447),U_448),U_449))
      | ~ class_Orderings_Oorder(U_447) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    ( U_449 = U_448
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_447),U_449),U_448))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_447),U_448),U_449))
    | ~ class_Orderings_Oorder(U_447) ),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_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_93_2,plain,
    ! [U_453,U_452,U_451,U_450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_453),U_452))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_453),U_451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_451),U_452))
      | ~ class_Orderings_Oorder(U_450) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_453),U_452))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_453),U_451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_450),U_451),U_452))
    | ~ class_Orderings_Oorder(U_450) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_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_94_2,plain,
    ! [U_457,U_456,U_455,U_454] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_455),U_457)),U_456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),U_457),U_456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),U_455),U_456)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_455),U_457)),U_456))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),U_457),U_456))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_454,tc_HOL_Obool)),U_455),U_456)) ),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_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_95_2,plain,
    ! [U_462,U_461,U_460,U_459,U_458] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_458,tc_HOL_Obool)),U_459),U_461)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_458,tc_HOL_Obool)),U_460),U_462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),U_461),U_462))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),U_459),U_460)) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_458,tc_HOL_Obool)),U_459),U_461)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_458,tc_HOL_Obool)),U_460),U_462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),U_461),U_462))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_458,tc_HOL_Obool)),U_459),U_460)) ),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_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_96_2,plain,
    ! [U_467,U_466,U_465,U_464,U_463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_467)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_465),U_466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),U_466),U_467))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465)) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

cnf(f_96_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_467)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_465),U_466)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),U_466),U_467))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465)) ),
    inference(clausify,[status(thm)],[f_96_2]) ).

fof(f_97_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_97_2,plain,
    ! [U_471,U_470,U_469,U_468] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_468,tc_HOL_Obool)),U_470),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_468,tc_HOL_Obool)),U_471),U_469)) = U_469
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_468,tc_HOL_Obool)),U_470),U_471))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_468,tc_HOL_Obool)),U_469),U_470)) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_468,tc_HOL_Obool)),U_470),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_468,tc_HOL_Obool)),U_471),U_469)) = U_469
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_468,tc_HOL_Obool)),U_470),U_471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_468,tc_HOL_Obool)),U_469),U_470)) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_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_98_2,plain,
    ! [U_474,U_473,U_472] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_474,tc_HOL_Obool)),U_473),U_472))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_474,tc_HOL_Obool)),U_472),U_473)) )
      | U_472 != U_473 ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_474,tc_HOL_Obool)),U_472),U_473))
    | U_472 != U_473 ),
    inference(clausify,[status(thm)],[f_98_2]) ).

cnf(f_98_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_474,tc_HOL_Obool)),U_473),U_472))
    | U_472 != U_473 ),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_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_99_2,plain,
    ! [U_479,U_478,U_477,U_476,U_475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_475),hAPP(U_477,U_479)),hAPP(U_478,U_479)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_476,U_475)),U_477),U_478))
      | ~ class_Orderings_Oord(U_475) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_475),hAPP(U_477,U_479)),hAPP(U_478,U_479)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_476,U_475)),U_477),U_478))
    | ~ class_Orderings_Oord(U_475) ),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_100_2,plain,
    ! [U_483,U_482,U_481,U_480] :
      ( hBOOL(hAPP(hAPP(c_member(U_480),U_481),U_482))
      | ~ hBOOL(hAPP(hAPP(c_member(U_480),U_481),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_480,tc_HOL_Obool)),U_482),U_483))) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_480),U_481),U_482))
    | ~ hBOOL(hAPP(hAPP(c_member(U_480),U_481),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_480,tc_HOL_Obool)),U_482),U_483))) ),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_101_2,plain,
    ! [U_487,U_486,U_485,U_484] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_484),U_485),U_487))
      | ~ hBOOL(hAPP(hAPP(c_member(U_484),U_485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_484,tc_HOL_Obool)),U_486),U_487))) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_484),U_485),U_487))
    | ~ hBOOL(hAPP(hAPP(c_member(U_484),U_485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_484,tc_HOL_Obool)),U_486),U_487))) ),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_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_102_2,plain,
    ! [U_490,U_489,U_488] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_490),U_489))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_489),U_490))
      | ~ class_Orderings_Olinorder(U_488) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_490),U_489))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_488),U_489),U_490))
    | ~ class_Orderings_Olinorder(U_488) ),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_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_103_2,plain,
    ! [U_494,U_493,U_492,U_491] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_491,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_491),U_492),U_494)),U_493) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_491,tc_HOL_Obool)),U_494),U_493)
      | ~ hBOOL(hAPP(hAPP(c_member(U_491),U_492),U_493)) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_491,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_491),U_492),U_494)),U_493) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_491,tc_HOL_Obool)),U_494),U_493)
    | ~ hBOOL(hAPP(hAPP(c_member(U_491),U_492),U_493)) ),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_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_104_2,plain,
    ! [U_498,U_497,U_496,U_495] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_495),U_496),U_498)),U_497) = hAPP(hAPP(c_Set_Oinsert(U_495),U_496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),U_498),U_497))
        | hBOOL(hAPP(hAPP(c_member(U_495),U_496),U_497)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_495),U_496),U_498)),U_497) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),U_498),U_497)
        | ~ hBOOL(hAPP(hAPP(c_member(U_495),U_496),U_497)) ) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ( ! [U_506,U_504,U_502,U_500] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_500),U_502),U_506)),U_504) = hAPP(hAPP(c_Set_Oinsert(U_500),U_502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_500,tc_HOL_Obool)),U_506),U_504))
        | hBOOL(hAPP(hAPP(c_member(U_500),U_502),U_504)) )
    & ! [U_505,U_503,U_501,U_499] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_499),U_501),U_505)),U_503) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_505),U_503)
        | ~ hBOOL(hAPP(hAPP(c_member(U_499),U_501),U_503)) ) ),
    inference(miniscope,[status(thm)],[f_104_2]) ).

cnf(f_104_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_499),U_501),U_505)),U_503) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_505),U_503)
    | ~ hBOOL(hAPP(hAPP(c_member(U_499),U_501),U_503)) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

cnf(f_104_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_500),U_502),U_506)),U_504) = hAPP(hAPP(c_Set_Oinsert(U_500),U_502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_500,tc_HOL_Obool)),U_506),U_504))
    | hBOOL(hAPP(hAPP(c_member(U_500),U_502),U_504)) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_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_105_2,plain,
    ! [U_510,U_509,U_508,U_507] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),hAPP(hAPP(c_Set_Oinsert(U_507),U_508),U_510)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),U_510)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),U_510))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),hAPP(hAPP(c_Set_Oinsert(U_507),U_508),U_510))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_507),U_508),U_509)) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),U_510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),hAPP(hAPP(c_Set_Oinsert(U_507),U_508),U_510)))
    | hBOOL(hAPP(hAPP(c_member(U_507),U_508),U_509)) ),
    inference(clausify,[status(thm)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),hAPP(hAPP(c_Set_Oinsert(U_507),U_508),U_510)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_507,tc_HOL_Obool)),U_509),U_510))
    | hBOOL(hAPP(hAPP(c_member(U_507),U_508),U_509)) ),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_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_106_2,plain,
    ! [U_514,U_513,U_512,U_511] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_511,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_511),U_512),U_513)),U_514))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_511,tc_HOL_Obool)),U_513),U_514))
        | ~ hBOOL(hAPP(hAPP(c_member(U_511),U_512),U_514)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_511,tc_HOL_Obool)),U_513),U_514))
          & hBOOL(hAPP(hAPP(c_member(U_511),U_512),U_514)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_511,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_511),U_512),U_513)),U_514)) ) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ( ! [U_522,U_520,U_518,U_516] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_516,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_516),U_518),U_520)),U_522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_516,tc_HOL_Obool)),U_520),U_522))
        | ~ hBOOL(hAPP(hAPP(c_member(U_516),U_518),U_522)) )
    & ! [U_521,U_519,U_517,U_515] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_515,tc_HOL_Obool)),U_519),U_521))
          & hBOOL(hAPP(hAPP(c_member(U_515),U_517),U_521)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_515,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_515),U_517),U_519)),U_521)) ) ),
    inference(miniscope,[status(thm)],[f_106_2]) ).

cnf(f_106_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_515),U_517),U_521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_515,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_515),U_517),U_519)),U_521)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_515,tc_HOL_Obool)),U_519),U_521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_515,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_515),U_517),U_519)),U_521)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_516,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_516),U_518),U_520)),U_522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_516,tc_HOL_Obool)),U_520),U_522))
    | ~ hBOOL(hAPP(hAPP(c_member(U_516),U_518),U_522)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_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_107_2,plain,
    ! [U_526,U_525,U_524,U_523] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),U_524),hAPP(hAPP(c_Set_Oinsert(U_523),U_525),U_526)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),U_524),U_526))
          & ~ hBOOL(hAPP(hAPP(c_member(U_523),U_525),U_524)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_523,tc_HOL_Obool)),U_524),hAPP(hAPP(c_Set_Oinsert(U_523),U_525),c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))))),U_526))
          & hBOOL(hAPP(hAPP(c_member(U_523),U_525),U_524)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),U_524),U_526))
            | hBOOL(hAPP(hAPP(c_member(U_523),U_525),U_524)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_523,tc_HOL_Obool)),U_524),hAPP(hAPP(c_Set_Oinsert(U_523),U_525),c_Orderings_Obot__class_Obot(tc_fun(U_523,tc_HOL_Obool))))),U_526))
            | ~ hBOOL(hAPP(hAPP(c_member(U_523),U_525),U_524)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,tc_HOL_Obool)),U_524),hAPP(hAPP(c_Set_Oinsert(U_523),U_525),U_526))) ) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ( ! [U_534,U_532,U_530,U_528] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),U_534)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),U_534))
          & ~ hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),c_Orderings_Obot__class_Obot(tc_fun(U_528,tc_HOL_Obool))))),U_534))
          & hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530)) ) )
    & ! [U_533,U_531,U_529,U_527] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_529),U_533))
            | hBOOL(hAPP(hAPP(c_member(U_527),U_531),U_529)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_527,tc_HOL_Obool)),U_529),hAPP(hAPP(c_Set_Oinsert(U_527),U_531),c_Orderings_Obot__class_Obot(tc_fun(U_527,tc_HOL_Obool))))),U_533))
            | ~ hBOOL(hAPP(hAPP(c_member(U_527),U_531),U_529)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_529),hAPP(hAPP(c_Set_Oinsert(U_527),U_531),U_533))) ) ),
    inference(miniscope,[status(thm)],[f_107_2]) ).

cnf(f_107_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_527,tc_HOL_Obool)),U_529),hAPP(hAPP(c_Set_Oinsert(U_527),U_531),c_Orderings_Obot__class_Obot(tc_fun(U_527,tc_HOL_Obool))))),U_533))
    | ~ hBOOL(hAPP(hAPP(c_member(U_527),U_531),U_529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_529),hAPP(hAPP(c_Set_Oinsert(U_527),U_531),U_533))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_529),U_533))
    | hBOOL(hAPP(hAPP(c_member(U_527),U_531),U_529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_527,tc_HOL_Obool)),U_529),hAPP(hAPP(c_Set_Oinsert(U_527),U_531),U_533))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530))
    | hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),U_534))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),U_534))
    | hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),U_534))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_528),U_532),U_530))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),c_Orderings_Obot__class_Obot(tc_fun(U_528,tc_HOL_Obool))))),U_534))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),U_534))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),U_534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),c_Orderings_Obot__class_Obot(tc_fun(U_528,tc_HOL_Obool))))),U_534))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_528),U_532),U_534))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_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_108_2,plain,
    ! [U_538,U_537,U_536,U_535] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_535,tc_HOL_Obool)),U_536),hAPP(hAPP(c_Set_Oinsert(U_535),U_537),U_538)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_535),U_537),U_536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_535,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_535,tc_HOL_Obool)),U_536),hAPP(hAPP(c_Set_Oinsert(U_535),U_537),c_Orderings_Obot__class_Obot(tc_fun(U_535,tc_HOL_Obool))))),U_538)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_535,tc_HOL_Obool)),U_536),hAPP(hAPP(c_Set_Oinsert(U_535),U_537),U_538)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_535),U_537),U_536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_535,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_535,tc_HOL_Obool)),U_536),hAPP(hAPP(c_Set_Oinsert(U_535),U_537),c_Orderings_Obot__class_Obot(tc_fun(U_535,tc_HOL_Obool))))),U_538)) ),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_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_109_2,plain,
    ! [U_541,U_540,U_539] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_539,U_540,c_Orderings_Obot__class_Obot(tc_fun(U_539,tc_HOL_Obool))),U_541)),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_539,U_540,c_Orderings_Obot__class_Obot(tc_fun(U_539,tc_HOL_Obool))),U_541)),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_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_110_2,plain,
    ! [U_545,U_544,U_543,U_542] :
      ( U_544 != c_Orderings_Obot__class_Obot(tc_fun(U_542,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_542,U_543,U_544),U_545)) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    ( U_544 != c_Orderings_Obot__class_Obot(tc_fun(U_542,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_542,U_543,U_544),U_545)) ),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_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_111_2,plain,
    ! [U_548,U_547,U_546] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_546,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_546),U_547),U_548)),hAPP(hAPP(c_Set_Oinsert(U_546),U_547),c_Orderings_Obot__class_Obot(tc_fun(U_546,tc_HOL_Obool)))) = U_548
      | hBOOL(hAPP(hAPP(c_member(U_546),U_547),U_548)) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_546,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_546),U_547),U_548)),hAPP(hAPP(c_Set_Oinsert(U_546),U_547),c_Orderings_Obot__class_Obot(tc_fun(U_546,tc_HOL_Obool)))) = U_548
    | hBOOL(hAPP(hAPP(c_member(U_546),U_547),U_548)) ),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_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_112_2,plain,
    ! [U_551,U_550,U_549] :
      ( hAPP(hAPP(c_Set_Oinsert(U_549),U_550),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_549,tc_HOL_Obool)),U_551),hAPP(hAPP(c_Set_Oinsert(U_549),U_550),c_Orderings_Obot__class_Obot(tc_fun(U_549,tc_HOL_Obool))))) = U_551
      | ~ hBOOL(hAPP(hAPP(c_member(U_549),U_550),U_551)) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_549),U_550),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_549,tc_HOL_Obool)),U_551),hAPP(hAPP(c_Set_Oinsert(U_549),U_550),c_Orderings_Obot__class_Obot(tc_fun(U_549,tc_HOL_Obool))))) = U_551
    | ~ hBOOL(hAPP(hAPP(c_member(U_549),U_550),U_551)) ),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_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_113_2,plain,
    ! [U_553,U_552] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_552,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_552,tc_HOL_Obool))),U_553) = c_Orderings_Obot__class_Obot(tc_fun(U_552,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_552,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_552,tc_HOL_Obool))),U_553) = c_Orderings_Obot__class_Obot(tc_fun(U_552,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_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_114_2,plain,
    ! [U_555,U_554] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_554,tc_HOL_Obool)),U_555),c_Orderings_Obot__class_Obot(tc_fun(U_554,tc_HOL_Obool))) = U_555,
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_554,tc_HOL_Obool)),U_555),c_Orderings_Obot__class_Obot(tc_fun(U_554,tc_HOL_Obool))) = U_555,
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_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_115_2,plain,
    ! [U_557,U_556] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_557),U_557) = c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_557),U_557) = c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_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_116_2,plain,
    ! [U_559,U_558] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_558,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_558,tc_HOL_Obool))),U_559) = U_559,
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_558,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_558,tc_HOL_Obool))),U_559) = U_559,
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_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_117_2,plain,
    ! [U_561,U_560] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_560,tc_HOL_Obool)),U_561),c_Orderings_Obot__class_Obot(tc_fun(U_560,tc_HOL_Obool))) = U_561,
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_560,tc_HOL_Obool)),U_561),c_Orderings_Obot__class_Obot(tc_fun(U_560,tc_HOL_Obool))) = U_561,
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_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_118_2,plain,
    ! [U_564,U_563,U_562] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_562,tc_HOL_Obool)),U_563),U_564) = c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool))
        | U_564 != c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool))
        | U_563 != c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool)) )
      & ( ( U_564 = c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool))
          & U_563 = c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_562,tc_HOL_Obool)),U_563),U_564) != c_Orderings_Obot__class_Obot(tc_fun(U_562,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ( ! [U_570,U_568,U_566] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_566,tc_HOL_Obool)),U_568),U_570) = c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool))
        | U_570 != c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool))
        | U_568 != c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool)) )
    & ! [U_569,U_567,U_565] :
        ( ( U_569 = c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool))
          & U_567 = c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_565,tc_HOL_Obool)),U_567),U_569) != c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( U_567 = c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_565,tc_HOL_Obool)),U_567),U_569) != c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

cnf(f_118_5,plain,
    ( U_569 = c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_565,tc_HOL_Obool)),U_567),U_569) != c_Orderings_Obot__class_Obot(tc_fun(U_565,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

cnf(f_118_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_566,tc_HOL_Obool)),U_568),U_570) = c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool))
    | U_570 != c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool))
    | U_568 != c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_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_119_2,plain,
    ! [U_574,U_573,U_572,U_571] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_571,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_571),U_573),U_574)) = hAPP(hAPP(c_Set_Oinsert(U_571),U_573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_571,tc_HOL_Obool)),U_572),U_574)),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_571,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_571),U_573),U_574)) = hAPP(hAPP(c_Set_Oinsert(U_571),U_573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_571,tc_HOL_Obool)),U_572),U_574)),
    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__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_120_2,plain,
    ! [U_578,U_577,U_576,U_575] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_575,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_575),U_576),U_577)),U_578) = hAPP(hAPP(c_Set_Oinsert(U_575),U_576),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_575,tc_HOL_Obool)),U_577),U_578)),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_575,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_575),U_576),U_577)),U_578) = hAPP(hAPP(c_Set_Oinsert(U_575),U_576),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_575,tc_HOL_Obool)),U_577),U_578)),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_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_121_2,plain,
    ! [U_580,U_579] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_579),c_Orderings_Obot__class_Obot(U_579)),U_580))
      | ~ class_Orderings_Obot(U_579) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_579),c_Orderings_Obot__class_Obot(U_579)),U_580))
    | ~ class_Orderings_Obot(U_579) ),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_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_122_2,plain,
    ! [U_584,U_583] :
      ( ( ! [U_582] : ~ hBOOL(hAPP(hAPP(c_member(U_583),U_582),U_584))
        | U_584 != c_Orderings_Obot__class_Obot(tc_fun(U_583,tc_HOL_Obool)) )
      & ( U_584 = c_Orderings_Obot__class_Obot(tc_fun(U_583,tc_HOL_Obool))
        | ? [U_581] : hBOOL(hAPP(hAPP(c_member(U_583),U_581),U_584)) ) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ( ! [U_588,U_586] :
        ( ! [U_582] : ~ hBOOL(hAPP(hAPP(c_member(U_586),U_582),U_588))
        | U_588 != c_Orderings_Obot__class_Obot(tc_fun(U_586,tc_HOL_Obool)) )
    & ! [U_587,U_585] :
        ( U_587 = c_Orderings_Obot__class_Obot(tc_fun(U_585,tc_HOL_Obool))
        | ? [U_581] : hBOOL(hAPP(hAPP(c_member(U_585),U_581),U_587)) ) ),
    inference(miniscope,[status(thm)],[f_122_2]) ).

fof(f_122_4,plain,
    ( ! [U_588,U_586] :
        ( ! [U_582] : ~ hBOOL(hAPP(hAPP(c_member(U_586),U_582),U_588))
        | U_588 != c_Orderings_Obot__class_Obot(tc_fun(U_586,tc_HOL_Obool)) )
    & ! [U_587,U_585] :
        ( U_587 = c_Orderings_Obot__class_Obot(tc_fun(U_585,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_585),sK9(U_587,U_585)),U_587)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_581,sK9(U_587,U_585))],[f_122_3]) ).

cnf(f_122_5,plain,
    ( U_587 = c_Orderings_Obot__class_Obot(tc_fun(U_585,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_585),sK9(U_587,U_585)),U_587)) ),
    inference(clausify,[status(thm)],[f_122_4]) ).

cnf(f_122_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_586),U_582),U_588))
    | U_588 != c_Orderings_Obot__class_Obot(tc_fun(U_586,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_122_4]) ).

fof(f_123_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_123_2,plain,
    ! [U_592,U_591] :
      ( ( ? [U_590] : hBOOL(hAPP(hAPP(c_member(U_591),U_590),U_592))
        | U_592 = c_Orderings_Obot__class_Obot(tc_fun(U_591,tc_HOL_Obool)) )
      & ( U_592 != c_Orderings_Obot__class_Obot(tc_fun(U_591,tc_HOL_Obool))
        | ! [U_589] : ~ hBOOL(hAPP(hAPP(c_member(U_591),U_589),U_592)) ) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ( ! [U_596,U_594] :
        ( ? [U_590] : hBOOL(hAPP(hAPP(c_member(U_594),U_590),U_596))
        | U_596 = c_Orderings_Obot__class_Obot(tc_fun(U_594,tc_HOL_Obool)) )
    & ! [U_595,U_593] :
        ( U_595 != c_Orderings_Obot__class_Obot(tc_fun(U_593,tc_HOL_Obool))
        | ! [U_589] : ~ hBOOL(hAPP(hAPP(c_member(U_593),U_589),U_595)) ) ),
    inference(miniscope,[status(thm)],[f_123_2]) ).

fof(f_123_4,plain,
    ( ! [U_596,U_594] :
        ( hBOOL(hAPP(hAPP(c_member(U_594),sK10(U_596,U_594)),U_596))
        | U_596 = c_Orderings_Obot__class_Obot(tc_fun(U_594,tc_HOL_Obool)) )
    & ! [U_595,U_593] :
        ( U_595 != c_Orderings_Obot__class_Obot(tc_fun(U_593,tc_HOL_Obool))
        | ! [U_589] : ~ hBOOL(hAPP(hAPP(c_member(U_593),U_589),U_595)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_590,sK10(U_596,U_594))],[f_123_3]) ).

cnf(f_123_5,plain,
    ( U_595 != c_Orderings_Obot__class_Obot(tc_fun(U_593,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_593),U_589),U_595)) ),
    inference(clausify,[status(thm)],[f_123_4]) ).

cnf(f_123_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_594),sK10(U_596,U_594)),U_596))
    | U_596 = c_Orderings_Obot__class_Obot(tc_fun(U_594,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_123_4]) ).

fof(f_124_1,plain,
    ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).

fof(f_124_2,plain,
    ! [U_598,U_597] : ~ hBOOL(hAPP(hAPP(c_member(U_597),U_598),c_Orderings_Obot__class_Obot(tc_fun(U_597,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

cnf(f_124_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_597),U_598),c_Orderings_Obot__class_Obot(tc_fun(U_597,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_124_2]) ).

fof(f_125_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_125_2,plain,
    ! [U_601,U_600,U_599] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_600),U_601),U_599))
      | U_599 != c_Orderings_Obot__class_Obot(tc_fun(U_600,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

cnf(f_125_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_600),U_601),U_599))
    | U_599 != c_Orderings_Obot__class_Obot(tc_fun(U_600,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_125_2]) ).

fof(f_126_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_126_2,plain,
    ! [U_603,U_602] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_602,tc_HOL_Obool)),U_603),c_Orderings_Obot__class_Obot(tc_fun(U_602,tc_HOL_Obool))))
        | U_603 != c_Orderings_Obot__class_Obot(tc_fun(U_602,tc_HOL_Obool)) )
      & ( U_603 = c_Orderings_Obot__class_Obot(tc_fun(U_602,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_602,tc_HOL_Obool)),U_603),c_Orderings_Obot__class_Obot(tc_fun(U_602,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ( ! [U_607,U_605] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_605,tc_HOL_Obool)),U_607),c_Orderings_Obot__class_Obot(tc_fun(U_605,tc_HOL_Obool))))
        | U_607 != c_Orderings_Obot__class_Obot(tc_fun(U_605,tc_HOL_Obool)) )
    & ! [U_606,U_604] :
        ( U_606 = c_Orderings_Obot__class_Obot(tc_fun(U_604,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_604,tc_HOL_Obool)),U_606),c_Orderings_Obot__class_Obot(tc_fun(U_604,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( U_606 = c_Orderings_Obot__class_Obot(tc_fun(U_604,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_604,tc_HOL_Obool)),U_606),c_Orderings_Obot__class_Obot(tc_fun(U_604,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_605,tc_HOL_Obool)),U_607),c_Orderings_Obot__class_Obot(tc_fun(U_605,tc_HOL_Obool))))
    | U_607 != c_Orderings_Obot__class_Obot(tc_fun(U_605,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_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_127_2,plain,
    ! [U_610,U_609,U_608] : hBOOL(hAPP(hAPP(c_member(U_608),U_609),hAPP(hAPP(c_Set_Oinsert(U_608),U_609),U_610))),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_608),U_609),hAPP(hAPP(c_Set_Oinsert(U_608),U_609),U_610))),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_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_128_2,plain,
    ! [U_614,U_613,U_612,U_611] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_611),U_612),hAPP(hAPP(c_Set_Oinsert(U_611),U_613),U_614)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_611),U_612),U_614))
          & U_612 != U_613 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_611),U_612),U_614))
        | U_612 = U_613
        | ~ hBOOL(hAPP(hAPP(c_member(U_611),U_612),hAPP(hAPP(c_Set_Oinsert(U_611),U_613),U_614))) ) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ( ! [U_622,U_620,U_618,U_616] :
        ( hBOOL(hAPP(hAPP(c_member(U_616),U_618),hAPP(hAPP(c_Set_Oinsert(U_616),U_620),U_622)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_616),U_618),U_622))
          & U_618 != U_620 ) )
    & ! [U_621,U_619,U_617,U_615] :
        ( hBOOL(hAPP(hAPP(c_member(U_615),U_617),U_621))
        | U_617 = U_619
        | ~ hBOOL(hAPP(hAPP(c_member(U_615),U_617),hAPP(hAPP(c_Set_Oinsert(U_615),U_619),U_621))) ) ),
    inference(miniscope,[status(thm)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_615),U_617),U_621))
    | U_617 = U_619
    | ~ hBOOL(hAPP(hAPP(c_member(U_615),U_617),hAPP(hAPP(c_Set_Oinsert(U_615),U_619),U_621))) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

cnf(f_128_5,plain,
    ( U_618 != U_620
    | hBOOL(hAPP(hAPP(c_member(U_616),U_618),hAPP(hAPP(c_Set_Oinsert(U_616),U_620),U_622))) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

cnf(f_128_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_616),U_618),U_622))
    | hBOOL(hAPP(hAPP(c_member(U_616),U_618),hAPP(hAPP(c_Set_Oinsert(U_616),U_620),U_622))) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_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_129_2,plain,
    ! [U_626,U_625,U_624,U_623] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_625) = hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_626)
          | U_625 != U_626 )
        & ( U_625 = U_626
          | hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_625) != hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_626) ) )
      | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_626))
      | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_625)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

cnf(f_129_3,plain,
    ( U_625 = U_626
    | hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_625) != hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_626)
    | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_626))
    | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_625)) ),
    inference(clausify,[status(thm)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_625) = hAPP(hAPP(c_Set_Oinsert(U_623),U_624),U_626)
    | U_625 != U_626
    | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_626))
    | hBOOL(hAPP(hAPP(c_member(U_623),U_624),U_625)) ),
    inference(clausify,[status(thm)],[f_129_2]) ).

fof(f_130_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_130_2,plain,
    ! [U_630,U_629,U_628,U_627] :
      ( hBOOL(hAPP(hAPP(c_member(U_627),U_628),hAPP(hAPP(c_Set_Oinsert(U_627),U_630),U_629)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_627),U_628),U_629)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

cnf(f_130_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_627),U_628),hAPP(hAPP(c_Set_Oinsert(U_627),U_630),U_629)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_627),U_628),U_629)) ),
    inference(clausify,[status(thm)],[f_130_2]) ).

fof(f_131_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_131_2,plain,
    ! [U_633,U_632,U_631] :
      ( hAPP(hAPP(c_Set_Oinsert(U_631),U_632),U_633) = U_633
      | ~ hBOOL(hAPP(hAPP(c_member(U_631),U_632),U_633)) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

cnf(f_131_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_631),U_632),U_633) = U_633
    | ~ hBOOL(hAPP(hAPP(c_member(U_631),U_632),U_633)) ),
    inference(clausify,[status(thm)],[f_131_2]) ).

fof(f_132_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_132_2,plain,
    ! [U_636,U_635,U_634] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_634,tc_HOL_Obool)),U_635),hAPP(hAPP(c_Set_Oinsert(U_634),U_636),U_635))),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_634,tc_HOL_Obool)),U_635),hAPP(hAPP(c_Set_Oinsert(U_634),U_636),U_635))),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_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_133_2,plain,
    ! [U_640,U_639,U_638,U_637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_637,tc_HOL_Obool)),U_638),hAPP(hAPP(c_Set_Oinsert(U_637),U_640),U_639)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_637,tc_HOL_Obool)),U_638),U_639)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

cnf(f_133_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_637,tc_HOL_Obool)),U_638),hAPP(hAPP(c_Set_Oinsert(U_637),U_640),U_639)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_637,tc_HOL_Obool)),U_638),U_639)) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

fof(f_134_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_134_2,plain,
    ! [U_644,U_643,U_642,U_641] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_641,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_641),U_644),U_642)),hAPP(hAPP(c_Set_Oinsert(U_641),U_644),U_643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_641,tc_HOL_Obool)),U_642),U_643)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

cnf(f_134_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_641,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_641),U_644),U_642)),hAPP(hAPP(c_Set_Oinsert(U_641),U_644),U_643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_641,tc_HOL_Obool)),U_642),U_643)) ),
    inference(clausify,[status(thm)],[f_134_2]) ).

fof(f_135_1,plain,
    ! [V_Ga_2,V_ts_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) ),
    inference(fof_nnf,[status(thm)],[fact_asm]) ).

fof(f_135_2,plain,
    ! [U_647,U_646,U_645] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_645,U_647,U_646)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_645),tc_HOL_Obool)),U_646),U_647)) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

cnf(f_135_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_645,U_647,U_646)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_645),tc_HOL_Obool)),U_646),U_647)) ),
    inference(clausify,[status(thm)],[f_135_2]) ).

fof(f_136_1,plain,
    ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_weaken]) ).

fof(f_136_2,plain,
    ! [U_651,U_650,U_649,U_648] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_648,U_649,U_651)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_648),tc_HOL_Obool)),U_651),U_650))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_648,U_649,U_650) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

cnf(f_136_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_648,U_649,U_651)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_648),tc_HOL_Obool)),U_651),U_650))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_648,U_649,U_650) ),
    inference(clausify,[status(thm)],[f_136_2]) ).

fof(f_137_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_137_2,plain,
    ! [U_655,U_654,U_653,U_652] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_655,tc_HOL_Obool)),U_654),U_652),U_653))
      | ( ~ hBOOL(hAPP(U_654,U_653))
        & ~ hBOOL(hAPP(U_652,U_653)) ) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    ( ~ hBOOL(hAPP(U_652,U_653))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_655,tc_HOL_Obool)),U_654),U_652),U_653)) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( ~ hBOOL(hAPP(U_654,U_653))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_655,tc_HOL_Obool)),U_654),U_652),U_653)) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_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_138_2,plain,
    ! [U_659,U_658,U_657,U_656] :
      ( hBOOL(hAPP(U_658,U_659))
      | hBOOL(hAPP(U_657,U_659))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_656,tc_HOL_Obool)),U_657),U_658),U_659)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_659,U_658,U_657] :
      ( ! [U_656] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_656,tc_HOL_Obool)),U_657),U_658),U_659))
      | hBOOL(hAPP(U_658,U_659))
      | hBOOL(hAPP(U_657,U_659)) ),
    inference(miniscope,[status(thm)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_656,tc_HOL_Obool)),U_657),U_658),U_659))
    | hBOOL(hAPP(U_658,U_659))
    | hBOOL(hAPP(U_657,U_659)) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_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_139_2,plain,
    ! [U_664,U_663,U_662,U_661,U_660] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_661,U_660)),U_662),U_663),U_664) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_660),hAPP(U_662,U_664)),hAPP(U_663,U_664))
      | ~ class_Groups_Ominus(U_660) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

cnf(f_139_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_661,U_660)),U_662),U_663),U_664) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_660),hAPP(U_662,U_664)),hAPP(U_663,U_664))
    | ~ class_Groups_Ominus(U_660) ),
    inference(clausify,[status(thm)],[f_139_2]) ).

fof(f_140_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_140_2,plain,
    ! [U_669,U_668,U_667,U_666,U_665] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_666,U_665)),U_667),U_668),U_669) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_665),hAPP(U_667,U_669)),hAPP(U_668,U_669))
      | ~ class_Lattices_Olattice(U_665) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

cnf(f_140_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_666,U_665)),U_667),U_668),U_669) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_665),hAPP(U_667,U_669)),hAPP(U_668,U_669))
    | ~ class_Lattices_Olattice(U_665) ),
    inference(clausify,[status(thm)],[f_140_2]) ).

fof(f_141_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_141_2,plain,
    ! [U_671,U_670] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_670),c_Orderings_Obot__class_Obot(U_670)),U_671) = U_671
      | ~ class_Lattices_Obounded__lattice__bot(U_670) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_670),c_Orderings_Obot__class_Obot(U_670)),U_671) = U_671
    | ~ class_Lattices_Obounded__lattice__bot(U_670) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_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_142_2,plain,
    ! [U_673,U_672] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_672),U_673),c_Orderings_Obot__class_Obot(U_672)) = U_673
      | ~ class_Lattices_Obounded__lattice__bot(U_672) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_672),U_673),c_Orderings_Obot__class_Obot(U_672)) = U_673
    | ~ class_Lattices_Obounded__lattice__bot(U_672) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_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_143_2,plain,
    ! [U_676,U_675,U_674] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_674),U_675),U_676) = c_Orderings_Obot__class_Obot(U_674)
          | U_676 != c_Orderings_Obot__class_Obot(U_674)
          | U_675 != c_Orderings_Obot__class_Obot(U_674) )
        & ( ( U_676 = c_Orderings_Obot__class_Obot(U_674)
            & U_675 = c_Orderings_Obot__class_Obot(U_674) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_674),U_675),U_676) != c_Orderings_Obot__class_Obot(U_674) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_674) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    ( U_675 = c_Orderings_Obot__class_Obot(U_674)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_674),U_675),U_676) != c_Orderings_Obot__class_Obot(U_674)
    | ~ class_Lattices_Obounded__lattice__bot(U_674) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( U_676 = c_Orderings_Obot__class_Obot(U_674)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_674),U_675),U_676) != c_Orderings_Obot__class_Obot(U_674)
    | ~ class_Lattices_Obounded__lattice__bot(U_674) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

cnf(f_143_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_674),U_675),U_676) = c_Orderings_Obot__class_Obot(U_674)
    | U_676 != c_Orderings_Obot__class_Obot(U_674)
    | U_675 != c_Orderings_Obot__class_Obot(U_674)
    | ~ class_Lattices_Obounded__lattice__bot(U_674) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_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_144_2,plain,
    ! [U_680,U_679,U_678,U_677] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_679),U_680))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_678),U_680)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_677),U_678),U_679)),U_680))
      | ~ class_Lattices_Osemilattice__sup(U_677) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

cnf(f_144_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_678),U_680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_677),U_678),U_679)),U_680))
    | ~ class_Lattices_Osemilattice__sup(U_677) ),
    inference(clausify,[status(thm)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_679),U_680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_677),U_678),U_679)),U_680))
    | ~ class_Lattices_Osemilattice__sup(U_677) ),
    inference(clausify,[status(thm)],[f_144_2]) ).

fof(f_145_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_145_2,plain,
    ! [U_685,U_684,U_683,U_682,U_681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_681),U_682),U_684)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_681),U_683),U_685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),U_684),U_685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),U_682),U_683))
      | ~ class_Lattices_Osemilattice__sup(U_681) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

cnf(f_145_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_681),U_682),U_684)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_681),U_683),U_685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),U_684),U_685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_681),U_682),U_683))
    | ~ class_Lattices_Osemilattice__sup(U_681) ),
    inference(clausify,[status(thm)],[f_145_2]) ).

fof(f_146_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_146_2,plain,
    ! [U_689,U_688,U_687,U_686] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_686),U_687),U_689)),U_688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),U_689),U_688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),U_687),U_688))
      | ~ class_Lattices_Osemilattice__sup(U_686) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

cnf(f_146_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_686),U_687),U_689)),U_688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),U_689),U_688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_686),U_687),U_688))
    | ~ class_Lattices_Osemilattice__sup(U_686) ),
    inference(clausify,[status(thm)],[f_146_2]) ).

fof(f_147_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_147_2,plain,
    ! [U_693,U_692,U_691,U_690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_690),U_691),U_693)),U_692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_693),U_692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_692))
      | ~ class_Lattices_Osemilattice__sup(U_690) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

cnf(f_147_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_690),U_691),U_693)),U_692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_693),U_692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_692))
    | ~ class_Lattices_Osemilattice__sup(U_690) ),
    inference(clausify,[status(thm)],[f_147_2]) ).

fof(f_148_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_148_2,plain,
    ! [U_696,U_695,U_694] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_694),U_696),U_695) = U_696
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_695),U_696))
      | ~ class_Lattices_Osemilattice__sup(U_694) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_694),U_696),U_695) = U_696
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_695),U_696))
    | ~ class_Lattices_Osemilattice__sup(U_694) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_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_149_2,plain,
    ! [U_699,U_698,U_697] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_697),U_698),hAPP(c_fequal,U_699)))
        | U_698 != U_699 )
      & ( U_698 = U_699
        | ~ hBOOL(hAPP(hAPP(c_member(U_697),U_698),hAPP(c_fequal,U_699))) ) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ( ! [U_705,U_703] :
        ( ! [U_701] : hBOOL(hAPP(hAPP(c_member(U_701),U_703),hAPP(c_fequal,U_705)))
        | U_703 != U_705 )
    & ! [U_704,U_702] :
        ( ! [U_700] : ~ hBOOL(hAPP(hAPP(c_member(U_700),U_702),hAPP(c_fequal,U_704)))
        | U_702 = U_704 ) ),
    inference(miniscope,[status(thm)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_700),U_702),hAPP(c_fequal,U_704)))
    | U_702 = U_704 ),
    inference(clausify,[status(thm)],[f_149_3]) ).

cnf(f_149_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_701),U_703),hAPP(c_fequal,U_705)))
    | U_703 != U_705 ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_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_150_2,plain,
    ! [U_707,U_706] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_706),U_707),U_707) = U_707
      | ~ class_Lattices_Osemilattice__sup(U_706) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_706),U_707),U_707) = U_707
    | ~ class_Lattices_Osemilattice__sup(U_706) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_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_151_2,plain,
    ! [U_709,U_708] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_708),U_709),U_709) = U_709
      | ~ class_Lattices_Osemilattice__sup(U_708) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_708),U_709),U_709) = U_709
    | ~ class_Lattices_Osemilattice__sup(U_708) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_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_152_2,plain,
    ! [U_712,U_711,U_710] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_710),U_711),U_712) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_710),U_712),U_711)
      | ~ class_Lattices_Osemilattice__sup(U_710) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

cnf(f_152_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_710),U_711),U_712) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_710),U_712),U_711)
    | ~ class_Lattices_Osemilattice__sup(U_710) ),
    inference(clausify,[status(thm)],[f_152_2]) ).

fof(f_153_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_153_2,plain,
    ! [U_715,U_714,U_713] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_713),U_714),U_715) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_713),U_715),U_714)
      | ~ class_Lattices_Olattice(U_713) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_713),U_714),U_715) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_713),U_715),U_714)
    | ~ class_Lattices_Olattice(U_713) ),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_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_154_2,plain,
    ! [U_718,U_717,U_716] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_716),U_717),U_718) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_716),U_718),U_717)
      | ~ class_Lattices_Osemilattice__sup(U_716) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_716),U_717),U_718) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_716),U_718),U_717)
    | ~ class_Lattices_Osemilattice__sup(U_716) ),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_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_155_2,plain,
    ! [U_721,U_720,U_719] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),U_721)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),U_721)
      | ~ class_Lattices_Osemilattice__sup(U_719) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

cnf(f_155_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),U_721)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_719),U_720),U_721)
    | ~ class_Lattices_Osemilattice__sup(U_719) ),
    inference(clausify,[status(thm)],[f_155_2]) ).

fof(f_156_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_156_2,plain,
    ! [U_724,U_723,U_722] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),U_724)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),U_724)
      | ~ class_Lattices_Olattice(U_722) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),U_724)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_722),U_723),U_724)
    | ~ class_Lattices_Olattice(U_722) ),
    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),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_157_2,plain,
    ! [U_727,U_726,U_725] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),U_727)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),U_727)
      | ~ class_Lattices_Osemilattice__sup(U_725) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

cnf(f_157_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),U_727)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_725),U_726),U_727)
    | ~ class_Lattices_Osemilattice__sup(U_725) ),
    inference(clausify,[status(thm)],[f_157_2]) ).

fof(f_158_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_158_2,plain,
    ! [U_731,U_730,U_729,U_728] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_729),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_730),U_731)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_729),U_731))
      | ~ class_Lattices_Osemilattice__sup(U_728) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_729),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_730),U_731)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_728),U_729),U_731))
    | ~ class_Lattices_Osemilattice__sup(U_728) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_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_159_2,plain,
    ! [U_735,U_734,U_733,U_732] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_734),U_735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_734),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),U_735))
      | ~ class_Lattices_Olattice(U_732) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_734),U_735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_734),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),U_735))
    | ~ class_Lattices_Olattice(U_732) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_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_160_2,plain,
    ! [U_739,U_738,U_737,U_736] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_737),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_738),U_739)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_737),U_739))
      | ~ class_Lattices_Osemilattice__sup(U_736) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_737),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_738),U_739)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_736),U_737),U_739))
    | ~ class_Lattices_Osemilattice__sup(U_736) ),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_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_161_2,plain,
    ! [U_743,U_742,U_741,U_740] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_741),U_742)),U_743) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_741),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_742),U_743))
      | ~ class_Lattices_Osemilattice__sup(U_740) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_741),U_742)),U_743) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_741),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_740),U_742),U_743))
    | ~ class_Lattices_Osemilattice__sup(U_740) ),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_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_162_2,plain,
    ! [U_747,U_746,U_745,U_744] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_745),U_746)),U_747) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_746),U_747))
      | ~ class_Lattices_Olattice(U_744) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_745),U_746)),U_747) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_744),U_746),U_747))
    | ~ class_Lattices_Olattice(U_744) ),
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_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_163_2,plain,
    ! [U_751,U_750,U_749,U_748] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_749),U_750)),U_751) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_749),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_750),U_751))
      | ~ class_Lattices_Osemilattice__sup(U_748) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_749),U_750)),U_751) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_749),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_748),U_750),U_751))
    | ~ class_Lattices_Osemilattice__sup(U_748) ),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Qa_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).

fof(f_164_2,plain,
    ! [U_755,U_754,U_753,U_752] :
      ( hBOOL(hAPP(U_755,U_753))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_754,tc_HOL_Obool)),U_752),U_755))
      | ~ hBOOL(hAPP(U_752,U_753)) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    ( hBOOL(hAPP(U_755,U_753))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_754,tc_HOL_Obool)),U_752),U_755))
    | ~ hBOOL(hAPP(U_752,U_753)) ),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(V_Qa_2,V_x_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).

fof(f_165_2,plain,
    ! [U_759,U_758,U_757,U_756] :
      ( hBOOL(hAPP(U_758,U_759))
      | ~ hBOOL(hAPP(U_757,U_759))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_756,tc_HOL_Obool)),U_757),U_758)) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_759,U_758,U_757] :
      ( ! [U_756] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_756,tc_HOL_Obool)),U_757),U_758))
      | hBOOL(hAPP(U_758,U_759))
      | ~ hBOOL(hAPP(U_757,U_759)) ),
    inference(miniscope,[status(thm)],[f_165_2]) ).

cnf(f_165_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_756,tc_HOL_Obool)),U_757),U_758))
    | hBOOL(hAPP(U_758,U_759))
    | ~ hBOOL(hAPP(U_757,U_759)) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_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_166_2,plain,
    ! [U_763,U_762,U_761,U_760] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_762,tc_HOL_Obool)),U_760),U_763),U_761))
      | ~ hBOOL(hAPP(U_760,U_761)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

cnf(f_166_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_762,tc_HOL_Obool)),U_760),U_763),U_761))
    | ~ hBOOL(hAPP(U_760,U_761)) ),
    inference(clausify,[status(thm)],[f_166_2]) ).

fof(f_167_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_167_2,plain,
    ! [U_767,U_766,U_765,U_764] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_766,tc_HOL_Obool)),U_767),U_764),U_765))
      | ~ hBOOL(hAPP(U_764,U_765)) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_766,tc_HOL_Obool)),U_767),U_764),U_765))
    | ~ hBOOL(hAPP(U_764,U_765)) ),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_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_168_2,plain,
    ! [U_770,U_769,U_768] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_768),U_769),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_768),U_769),U_770)))
      | ~ class_Lattices_Olattice(U_768) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_768),U_769),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_768),U_769),U_770)))
    | ~ class_Lattices_Olattice(U_768) ),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_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_169_2,plain,
    ! [U_773,U_772,U_771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_771),U_772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_771),U_772),U_773)))
      | ~ class_Lattices_Osemilattice__sup(U_771) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

cnf(f_169_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_771),U_772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_771),U_772),U_773)))
    | ~ class_Lattices_Osemilattice__sup(U_771) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

fof(f_170_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_170_2,plain,
    ! [U_776,U_775,U_774] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_774),U_775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_774),U_776),U_775)))
      | ~ class_Lattices_Olattice(U_774) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_774),U_775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_774),U_776),U_775)))
    | ~ class_Lattices_Olattice(U_774) ),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_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_171_2,plain,
    ! [U_779,U_778,U_777] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_777),U_779),U_778)))
      | ~ class_Lattices_Osemilattice__sup(U_777) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_777),U_779),U_778)))
    | ~ class_Lattices_Osemilattice__sup(U_777) ),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_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_172_2,plain,
    ! [U_782,U_781,U_780] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_780),U_781),U_782) != U_782 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_780),U_781),U_782) = U_782
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_780) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

cnf(f_172_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_780),U_781),U_782) = U_782
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
    | ~ class_Lattices_Osemilattice__sup(U_780) ),
    inference(clausify,[status(thm)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_780),U_781),U_782) != U_782
    | ~ class_Lattices_Osemilattice__sup(U_780) ),
    inference(clausify,[status(thm)],[f_172_2]) ).

fof(f_173_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_173_2,plain,
    ! [U_786,U_785,U_784,U_783] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_783),U_784),U_785)),U_786))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_785),U_786))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_784),U_786)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_785),U_786))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_784),U_786)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_783),U_784),U_785)),U_786)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_783) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_784),U_786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_783),U_784),U_785)),U_786))
    | ~ class_Lattices_Osemilattice__sup(U_783) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

cnf(f_173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_785),U_786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_783),U_784),U_785)),U_786))
    | ~ class_Lattices_Osemilattice__sup(U_783) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

cnf(f_173_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_783),U_784),U_785)),U_786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_785),U_786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_783),U_784),U_786))
    | ~ class_Lattices_Osemilattice__sup(U_783) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_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_174_2,plain,
    ! [U_790,U_789,U_788,U_787] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_787),U_788),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_787),U_789),U_790)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_787),U_788),U_789))
      | ~ class_Lattices_Osemilattice__sup(U_787) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

cnf(f_174_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_787),U_788),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_787),U_789),U_790)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_787),U_788),U_789))
    | ~ class_Lattices_Osemilattice__sup(U_787) ),
    inference(clausify,[status(thm)],[f_174_2]) ).

fof(f_175_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_175_2,plain,
    ! [U_794,U_793,U_792,U_791] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_791),U_792),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_791),U_794),U_793)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_791),U_792),U_793))
      | ~ class_Lattices_Osemilattice__sup(U_791) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_791),U_792),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_791),U_794),U_793)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_791),U_792),U_793))
    | ~ class_Lattices_Osemilattice__sup(U_791) ),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_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_176_2,plain,
    ! [U_797,U_796,U_795] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_795),U_796),U_797) = U_797
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_795),U_796),U_797))
      | ~ class_Lattices_Osemilattice__sup(U_795) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

cnf(f_176_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_795),U_796),U_797) = U_797
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_795),U_796),U_797))
    | ~ class_Lattices_Osemilattice__sup(U_795) ),
    inference(clausify,[status(thm)],[f_176_2]) ).

fof(f_177_1,plain,
    ! [V_d_2,V_ca_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_ca_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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_ca_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_177_2,plain,
    ! [U_802,U_801,U_800,U_799,U_798] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_801),U_802)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_801),U_802))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_799),U_800) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_801),U_802)
      | ~ class_Groups_Oordered__ab__group__add(U_798) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

cnf(f_177_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_801),U_802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_799),U_800) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_801),U_802)
    | ~ class_Groups_Oordered__ab__group__add(U_798) ),
    inference(clausify,[status(thm)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_801),U_802))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_799),U_800) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_798),U_801),U_802)
    | ~ class_Groups_Oordered__ab__group__add(U_798) ),
    inference(clausify,[status(thm)],[f_177_2]) ).

fof(f_178_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_178_2,plain,
    ! [U_807,U_806,U_805,U_804,U_803] :
      ( ( ( hAPP(U_805,U_806) = hAPP(hAPP(U_804,U_807),hAPP(U_805,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)) )
        & ( hAPP(U_805,U_806) = U_807
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_803),U_807),U_806))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_803),U_806))
      | ~ c_Finite__Set_Ofolding__one(U_803,U_804,U_805) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

cnf(f_178_3,plain,
    ( hAPP(U_805,U_806) = U_807
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_803),U_807),U_806))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_803),U_806))
    | ~ c_Finite__Set_Ofolding__one(U_803,U_804,U_805) ),
    inference(clausify,[status(thm)],[f_178_2]) ).

cnf(f_178_4,plain,
    ( hAPP(U_805,U_806) = hAPP(hAPP(U_804,U_807),hAPP(U_805,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_803,tc_HOL_Obool)),U_806),hAPP(hAPP(c_Set_Oinsert(U_803),U_807),c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_803,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_803),U_807),U_806))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_803),U_806))
    | ~ c_Finite__Set_Ofolding__one(U_803,U_804,U_805) ),
    inference(clausify,[status(thm)],[f_178_2]) ).

fof(f_179_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_179_2,plain,
    ! [U_812,U_811,U_810,U_809,U_808] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_808,U_809,hAPP(hAPP(c_Set_Oinsert(U_808),U_810),U_811)),U_812))
      | hBOOL(hAPP(hAPP(c_member(U_808),U_810),U_811))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_808,U_808,U_809,U_810,U_811),U_812)) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

cnf(f_179_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_808,U_809,hAPP(hAPP(c_Set_Oinsert(U_808),U_810),U_811)),U_812))
    | hBOOL(hAPP(hAPP(c_member(U_808),U_810),U_811))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_808,U_808,U_809,U_810,U_811),U_812)) ),
    inference(clausify,[status(thm)],[f_179_2]) ).

fof(f_180_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_180_2,plain,
    ! [U_816,U_815,U_814,U_813] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),U_814),hAPP(hAPP(c_Set_Oinsert(U_813),U_815),U_816)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_813,tc_HOL_Obool)),U_814),U_816))
              & ~ hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_814)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_813,tc_HOL_Obool)),U_814),hAPP(hAPP(c_Set_Oinsert(U_813),U_815),c_Orderings_Obot__class_Obot(tc_fun(U_813,tc_HOL_Obool))))),U_816))
              & hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_814)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_816)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),U_814),U_816))
          & hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_816)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_813,tc_HOL_Obool)),U_814),U_816))
                | hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_814)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_813,tc_HOL_Obool)),U_814),hAPP(hAPP(c_Set_Oinsert(U_813),U_815),c_Orderings_Obot__class_Obot(tc_fun(U_813,tc_HOL_Obool))))),U_816))
                | ~ hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_814)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_816)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),U_814),U_816))
            | ~ hBOOL(hAPP(hAPP(c_member(U_813),U_815),U_816)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_813,tc_HOL_Obool)),U_814),hAPP(hAPP(c_Set_Oinsert(U_813),U_815),U_816))) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ! [U_824,U_822,U_820,U_818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
              & ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),c_Orderings_Obot__class_Obot(tc_fun(U_818,tc_HOL_Obool))))),U_824))
              & hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
          & hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824)) ) )
    & ! [U_823,U_821,U_819,U_817] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_817,tc_HOL_Obool)),U_819),U_823))
                | hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_819)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),c_Orderings_Obot__class_Obot(tc_fun(U_817,tc_HOL_Obool))))),U_823))
                | ~ hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_819)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_823)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),U_823))
            | ~ hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_823)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),U_823))) ) ),
    inference(miniscope,[status(thm)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),U_823))
    | ~ hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),U_823))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),c_Orderings_Obot__class_Obot(tc_fun(U_817,tc_HOL_Obool))))),U_823))
    | ~ hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_819))
    | hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),U_823))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_817,tc_HOL_Obool)),U_819),U_823))
    | hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_819))
    | hBOOL(hAPP(hAPP(c_member(U_817),U_821),U_823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_817,tc_HOL_Obool)),U_819),hAPP(hAPP(c_Set_Oinsert(U_817),U_821),U_823))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),c_Orderings_Obot__class_Obot(tc_fun(U_818,tc_HOL_Obool))))),U_824))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),c_Orderings_Obot__class_Obot(tc_fun(U_818,tc_HOL_Obool))))),U_824))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_818),U_822),U_820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),c_Orderings_Obot__class_Obot(tc_fun(U_818,tc_HOL_Obool))))),U_824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),c_Orderings_Obot__class_Obot(tc_fun(U_818,tc_HOL_Obool))))),U_824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),U_824))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_818,tc_HOL_Obool)),U_820),hAPP(hAPP(c_Set_Oinsert(U_818),U_822),U_824))) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_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_181_2,plain,
    ! [U_831,U_830,U_829,U_828,U_827,U_826,U_825] :
      ( c_Nitpick_Ofold__graph_H(U_825,U_828,U_829,U_830,U_827,hAPP(hAPP(U_829,U_826),U_831))
      | ~ c_Nitpick_Ofold__graph_H(U_825,U_828,U_829,U_830,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_825,tc_HOL_Obool)),U_827),hAPP(hAPP(c_Set_Oinsert(U_825),U_826),c_Orderings_Obot__class_Obot(tc_fun(U_825,tc_HOL_Obool)))),U_831)
      | ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_827)) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    ( c_Nitpick_Ofold__graph_H(U_825,U_828,U_829,U_830,U_827,hAPP(hAPP(U_829,U_826),U_831))
    | ~ c_Nitpick_Ofold__graph_H(U_825,U_828,U_829,U_830,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_825,tc_HOL_Obool)),U_827),hAPP(hAPP(c_Set_Oinsert(U_825),U_826),c_Orderings_Obot__class_Obot(tc_fun(U_825,tc_HOL_Obool)))),U_831)
    | ~ hBOOL(hAPP(hAPP(c_member(U_825),U_826),U_827)) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_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_182_2,plain,
    ! [U_838,U_837,U_836,U_835,U_834,U_833,U_832] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_832,U_833,U_834,U_835,U_836),hAPP(hAPP(U_834,U_837),U_838)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_832),U_837),U_836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_832,U_833,U_834,U_835,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_832,tc_HOL_Obool)),U_836),hAPP(hAPP(c_Set_Oinsert(U_832),U_837),c_Orderings_Obot__class_Obot(tc_fun(U_832,tc_HOL_Obool))))),U_838)) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_832,U_833,U_834,U_835,U_836),hAPP(hAPP(U_834,U_837),U_838)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_832),U_837),U_836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_832,U_833,U_834,U_835,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_832,tc_HOL_Obool)),U_836),hAPP(hAPP(c_Set_Oinsert(U_832),U_837),c_Orderings_Obot__class_Obot(tc_fun(U_832,tc_HOL_Obool))))),U_838)) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_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_183_2,plain,
    ! [U_843,U_842,U_841,U_840,U_839] :
      ( ( ( hAPP(U_841,hAPP(hAPP(c_Set_Oinsert(U_839),U_843),U_842)) = hAPP(hAPP(U_840,U_843),hAPP(U_841,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)) )
        & ( hAPP(U_841,hAPP(hAPP(c_Set_Oinsert(U_839),U_843),U_842)) = U_843
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_839),U_842))
      | ~ c_Finite__Set_Ofolding__one(U_839,U_840,U_841) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    ( hAPP(U_841,hAPP(hAPP(c_Set_Oinsert(U_839),U_843),U_842)) = U_843
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_839),U_842))
    | ~ c_Finite__Set_Ofolding__one(U_839,U_840,U_841) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( hAPP(U_841,hAPP(hAPP(c_Set_Oinsert(U_839),U_843),U_842)) = hAPP(hAPP(U_840,U_843),hAPP(U_841,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_839,tc_HOL_Obool)),U_842),hAPP(hAPP(c_Set_Oinsert(U_839),U_843),c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_839,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_839),U_842))
    | ~ c_Finite__Set_Ofolding__one(U_839,U_840,U_841) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_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_184_2,plain,
    ! [U_848,U_847,U_846,U_845,U_844] :
      ( hAPP(U_846,hAPP(hAPP(c_Set_Oinsert(U_844),U_848),U_847)) = hAPP(hAPP(U_845,U_848),hAPP(U_846,U_847))
      | U_847 = c_Orderings_Obot__class_Obot(tc_fun(U_844,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_844),U_848),U_847))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_844),U_847))
      | ~ c_Finite__Set_Ofolding__one(U_844,U_845,U_846) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

cnf(f_184_3,plain,
    ( hAPP(U_846,hAPP(hAPP(c_Set_Oinsert(U_844),U_848),U_847)) = hAPP(hAPP(U_845,U_848),hAPP(U_846,U_847))
    | U_847 = c_Orderings_Obot__class_Obot(tc_fun(U_844,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_844),U_848),U_847))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_844),U_847))
    | ~ c_Finite__Set_Ofolding__one(U_844,U_845,U_846) ),
    inference(clausify,[status(thm)],[f_184_2]) ).

fof(f_185_1,plain,
    ! [T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ! [B_x,B_B] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
            | V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) ) )
      & ( ? [B_x,B_B] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B))
            & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) )
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nonempty__iff]) ).

fof(f_185_2,plain,
    ! [U_854,U_853] :
      ( ( U_853 != c_Orderings_Obot__class_Obot(tc_fun(U_854,tc_HOL_Obool))
        | ! [U_852,U_851] :
            ( hBOOL(hAPP(hAPP(c_member(U_854),U_852),U_851))
            | U_853 != hAPP(hAPP(c_Set_Oinsert(U_854),U_852),U_851) ) )
      & ( ? [U_850,U_849] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_854),U_850),U_849))
            & U_853 = hAPP(hAPP(c_Set_Oinsert(U_854),U_850),U_849) )
        | U_853 = c_Orderings_Obot__class_Obot(tc_fun(U_854,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ( ! [U_858,U_856] :
        ( U_856 != c_Orderings_Obot__class_Obot(tc_fun(U_858,tc_HOL_Obool))
        | ! [U_852,U_851] :
            ( hBOOL(hAPP(hAPP(c_member(U_858),U_852),U_851))
            | U_856 != hAPP(hAPP(c_Set_Oinsert(U_858),U_852),U_851) ) )
    & ! [U_857,U_855] :
        ( ? [U_850,U_849] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_857),U_850),U_849))
            & U_855 = hAPP(hAPP(c_Set_Oinsert(U_857),U_850),U_849) )
        | U_855 = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_185_2]) ).

fof(f_185_4,plain,
    ( ! [U_858,U_856] :
        ( U_856 != c_Orderings_Obot__class_Obot(tc_fun(U_858,tc_HOL_Obool))
        | ! [U_852,U_851] :
            ( hBOOL(hAPP(hAPP(c_member(U_858),U_852),U_851))
            | U_856 != hAPP(hAPP(c_Set_Oinsert(U_858),U_852),U_851) ) )
    & ! [U_857,U_855] :
        ( ? [U_849] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_857),sK11(U_857,U_855)),U_849))
            & U_855 = hAPP(hAPP(c_Set_Oinsert(U_857),sK11(U_857,U_855)),U_849) )
        | U_855 = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_850,sK11(U_857,U_855))],[f_185_3]) ).

fof(f_185_5,plain,
    ( ! [U_858,U_856] :
        ( U_856 != c_Orderings_Obot__class_Obot(tc_fun(U_858,tc_HOL_Obool))
        | ! [U_852,U_851] :
            ( hBOOL(hAPP(hAPP(c_member(U_858),U_852),U_851))
            | U_856 != hAPP(hAPP(c_Set_Oinsert(U_858),U_852),U_851) ) )
    & ! [U_857,U_855] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_857),sK11(U_857,U_855)),sK12(U_857,U_855)))
          & U_855 = hAPP(hAPP(c_Set_Oinsert(U_857),sK11(U_857,U_855)),sK12(U_857,U_855)) )
        | U_855 = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_849,sK12(U_857,U_855))],[f_185_4]) ).

cnf(f_185_6,plain,
    ( U_855 = hAPP(hAPP(c_Set_Oinsert(U_857),sK11(U_857,U_855)),sK12(U_857,U_855))
    | U_855 = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_857),sK11(U_857,U_855)),sK12(U_857,U_855)))
    | U_855 = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_8,plain,
    ( U_856 != c_Orderings_Obot__class_Obot(tc_fun(U_858,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_858),U_852),U_851))
    | U_856 != hAPP(hAPP(c_Set_Oinsert(U_858),U_852),U_851) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

fof(f_186_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_186_2,plain,
    ! [U_860,U_859] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_859),U_860),U_860) = U_860
      | ~ class_Lattices_Olattice(U_859) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

cnf(f_186_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_859),U_860),U_860) = U_860
    | ~ class_Lattices_Olattice(U_859) ),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_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_187_2,plain,
    ! [U_863,U_862,U_861] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_861,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_861,U_862)),c_Predicate_OPowp(U_861,U_863)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_861,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_861,U_862)),c_Predicate_OPowp(U_861,U_863)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_861,tc_HOL_Obool)),U_862),U_863)) ),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_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_188_2,plain,
    ! [U_864] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_864),c_Orderings_Obot__class_Obot(tc_fun(U_864,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_864),c_Orderings_Obot__class_Obot(tc_fun(U_864,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_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_189_2,plain,
    ! [U_867,U_866,U_865] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_865),hAPP(hAPP(c_Set_Oinsert(U_865),U_867),U_866)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_865),U_866)) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_865),hAPP(hAPP(c_Set_Oinsert(U_865),U_867),U_866)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_865),U_866)) ),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_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_190_2,plain,
    ! [U_870,U_869,U_868] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_868),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_868,tc_HOL_Obool)),U_869),U_870)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_868),U_869)) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_868),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_868,tc_HOL_Obool)),U_869),U_870)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_868),U_869)) ),
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_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_191_2,plain,
    ! [U_872,U_871] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_871),U_872),U_872))
      | ~ class_Orderings_Opreorder(U_871) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_871),U_872),U_872))
    | ~ class_Orderings_Opreorder(U_871) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_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_192_2,plain,
    ! [U_875,U_874,U_873] :
      ( ( ( U_874 != U_875
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_875),U_874))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),U_875)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_875),U_874))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),U_875))
          | U_874 = U_875 ) )
      | ~ class_Orderings_Olinorder(U_873) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_875),U_874))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),U_875))
    | U_874 = U_875
    | ~ class_Orderings_Olinorder(U_873) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),U_875))
    | U_874 != U_875
    | ~ class_Orderings_Olinorder(U_873) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

cnf(f_192_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_875),U_874))
    | U_874 != U_875
    | ~ class_Orderings_Olinorder(U_873) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_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_193_2,plain,
    ! [U_878,U_877,U_876] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_877),U_878))
          | ( U_877 != U_878
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_878),U_877)) ) )
        & ( U_877 = U_878
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_878),U_877))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_877),U_878)) ) )
      | ~ class_Orderings_Olinorder(U_876) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( U_877 = U_878
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_878),U_877))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_877),U_878))
    | ~ class_Orderings_Olinorder(U_876) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_878),U_877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_877),U_878))
    | ~ class_Orderings_Olinorder(U_876) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

cnf(f_193_5,plain,
    ( U_877 != U_878
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_876),U_877),U_878))
    | ~ class_Orderings_Olinorder(U_876) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_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_194_2,plain,
    ! [U_881,U_880,U_879] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_881),U_880))
      | U_880 = U_881
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),U_881))
      | ~ class_Orderings_Olinorder(U_879) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

cnf(f_194_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_881),U_880))
    | U_880 = U_881
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),U_881))
    | ~ class_Orderings_Olinorder(U_879) ),
    inference(clausify,[status(thm)],[f_194_2]) ).

fof(f_195_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_195_2,plain,
    ! [U_884,U_883,U_882] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_884),U_883))
          | U_884 != U_883 )
        & ( U_884 = U_883
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_884),U_883)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_883),U_884))
      | ~ class_Orderings_Olinorder(U_882) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ( U_884 = U_883
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_884),U_883))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_883),U_884))
    | ~ class_Orderings_Olinorder(U_882) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_884),U_883))
    | U_884 != U_883
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_882),U_883),U_884))
    | ~ class_Orderings_Olinorder(U_882) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_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_196_2,plain,
    ! [U_887,U_886,U_885] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_885),U_887),U_886))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_885),U_886),U_887))
      | U_886 = U_887
      | ~ class_Orderings_Olinorder(U_885) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_885),U_887),U_886))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_885),U_886),U_887))
    | U_886 = U_887
    | ~ class_Orderings_Olinorder(U_885) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_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_197_2,plain,
    ! [U_890,U_889,U_888] :
      ( U_889 != U_890
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_888),U_889),U_890))
      | ~ class_Orderings_Oorder(U_888) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ( U_889 != U_890
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_888),U_889),U_890))
    | ~ class_Orderings_Oorder(U_888) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_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_198_2,plain,
    ! [U_893,U_892,U_891] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_891),U_893),U_892))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_891),U_892),U_893))
      | ~ class_Orderings_Opreorder(U_891) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

cnf(f_198_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_891),U_893),U_892))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_891),U_892),U_893))
    | ~ class_Orderings_Opreorder(U_891) ),
    inference(clausify,[status(thm)],[f_198_2]) ).

fof(f_199_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_199_2,plain,
    ! [U_896,U_895,U_894] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_894),U_896),U_895))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_894),U_895),U_896))
      | ~ class_Orderings_Opreorder(U_894) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_894),U_896),U_895))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_894),U_895),U_896))
    | ~ class_Orderings_Opreorder(U_894) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_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_200_2,plain,
    ! [U_899,U_898,U_897] :
      ( U_898 != U_899
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_897),U_898),U_899))
      | ~ class_Orderings_Oorder(U_897) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

cnf(f_200_3,plain,
    ( U_898 != U_899
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_897),U_898),U_899))
    | ~ class_Orderings_Oorder(U_897) ),
    inference(clausify,[status(thm)],[f_200_2]) ).

fof(f_201_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_201_2,plain,
    ! [U_902,U_901,U_900] :
      ( U_902 != U_901
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_900),U_901),U_902))
      | ~ class_Orderings_Oorder(U_900) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

cnf(f_201_3,plain,
    ( U_902 != U_901
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_900),U_901),U_902))
    | ~ class_Orderings_Oorder(U_900) ),
    inference(clausify,[status(thm)],[f_201_2]) ).

fof(f_202_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_202_2,plain,
    ! [U_905,U_904,U_903] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_903),U_905),U_904))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_903),U_904),U_905))
      | ~ class_Orderings_Opreorder(U_903) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

cnf(f_202_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_903),U_905),U_904))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_903),U_904),U_905))
    | ~ class_Orderings_Opreorder(U_903) ),
    inference(clausify,[status(thm)],[f_202_2]) ).

fof(f_203_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_203_2,plain,
    ! [U_908,U_907,U_906] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_906),U_908),U_907))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_906),U_907),U_908))
      | ~ class_Orderings_Oorder(U_906) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

cnf(f_203_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_906),U_908),U_907))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_906),U_907),U_908))
    | ~ class_Orderings_Oorder(U_906) ),
    inference(clausify,[status(thm)],[f_203_2]) ).

fof(f_204_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_204_2,plain,
    ! [U_912,U_911,U_910,U_909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_909),U_910),U_912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_909),U_911),U_912))
      | U_910 != U_911
      | ~ class_Orderings_Oord(U_909) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

cnf(f_204_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_909),U_910),U_912))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_909),U_911),U_912))
    | U_910 != U_911
    | ~ class_Orderings_Oord(U_909) ),
    inference(clausify,[status(thm)],[f_204_2]) ).

fof(f_205_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_205_2,plain,
    ! [U_916,U_915,U_914,U_913] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_913),U_916),U_914))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_913),U_916),U_915))
      | U_914 != U_915
      | ~ class_Orderings_Oorder(U_913) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

cnf(f_205_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_913),U_916),U_914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_913),U_916),U_915))
    | U_914 != U_915
    | ~ class_Orderings_Oorder(U_913) ),
    inference(clausify,[status(thm)],[f_205_2]) ).

fof(f_206_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_206_2,plain,
    ! [U_920,U_919,U_918,U_917] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_918),U_920))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_919),U_920))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_918),U_919)) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

cnf(f_206_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_918),U_920))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_919),U_920))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_917,tc_HOL_Obool)),U_918),U_919)) ),
    inference(clausify,[status(thm)],[f_206_2]) ).

fof(f_207_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_207_2,plain,
    ! [U_924,U_923,U_922,U_921] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_921),U_922),U_924))
      | U_923 != U_924
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_921),U_922),U_923))
      | ~ class_Orderings_Oord(U_921) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_921),U_922),U_924))
    | U_923 != U_924
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_921),U_922),U_923))
    | ~ class_Orderings_Oord(U_921) ),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_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_208_2,plain,
    ! [U_928,U_927,U_926,U_925] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_925),U_928),U_927))
      | U_926 != U_928
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_925),U_926),U_927))
      | ~ class_Orderings_Oorder(U_925) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_925),U_928),U_927))
    | U_926 != U_928
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_925),U_926),U_927))
    | ~ class_Orderings_Oorder(U_925) ),
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_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_209_2,plain,
    ! [U_932,U_931,U_930,U_929] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_930),U_932))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_931),U_932))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_930),U_931))
      | ~ class_Orderings_Opreorder(U_929) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_930),U_932))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_931),U_932))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_929),U_930),U_931))
    | ~ class_Orderings_Opreorder(U_929) ),
    inference(clausify,[status(thm)],[f_209_2]) ).

fof(f_210_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_210_2,plain,
    ! [U_936,U_935,U_934,U_933] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_936),U_935))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_936),U_934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_934),U_935))
      | ~ class_Orderings_Oorder(U_933) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

cnf(f_210_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_936),U_935))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_936),U_934))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_933),U_934),U_935))
    | ~ class_Orderings_Oorder(U_933) ),
    inference(clausify,[status(thm)],[f_210_2]) ).

fof(f_211_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_211_2,plain,
    ! [U_939,U_938,U_937] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_937),U_939),U_938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_937),U_938),U_939))
      | ~ class_Orderings_Opreorder(U_937) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

cnf(f_211_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_937),U_939),U_938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_937),U_938),U_939))
    | ~ class_Orderings_Opreorder(U_937) ),
    inference(clausify,[status(thm)],[f_211_2]) ).

fof(f_212_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_212_2,plain,
    ! [U_942,U_941,U_940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_940),U_942),U_941))
      | U_941 = U_942
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_940),U_941),U_942))
      | ~ class_Orderings_Olinorder(U_940) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

cnf(f_212_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_940),U_942),U_941))
    | U_941 = U_942
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_940),U_941),U_942))
    | ~ class_Orderings_Olinorder(U_940) ),
    inference(clausify,[status(thm)],[f_212_2]) ).

fof(f_213_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_213_2,plain,
    ! [U_944,U_943] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_943),U_944))
      | ~ class_Finite__Set_Ofinite(U_943) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

cnf(f_213_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_943),U_944))
    | ~ class_Finite__Set_Ofinite(U_943) ),
    inference(clausify,[status(thm)],[f_213_2]) ).

fof(f_214_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_214_2,plain,
    ! [U_946,U_945] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_945),U_946))
      | ~ class_Finite__Set_Ofinite(U_945) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

cnf(f_214_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_945),U_946))
    | ~ class_Finite__Set_Ofinite(U_945) ),
    inference(clausify,[status(thm)],[f_214_2]) ).

fof(f_215_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_215_2,plain,
    ! [U_952,U_951,U_950,U_949,U_948,U_947] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_947),U_951))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_947,U_948,U_949,U_950,U_951),U_952)) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

cnf(f_215_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_947),U_951))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_947,U_948,U_949,U_950,U_951),U_952)) ),
    inference(clausify,[status(thm)],[f_215_2]) ).

fof(f_216_1,plain,
    ! [V_d_2,V_ca_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_ca_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_216_2,plain,
    ! [U_957,U_956,U_955,U_954,U_953] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_954),U_955))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_956),U_957)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_956),U_957))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_954),U_955)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_954),U_955) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_956),U_957)
      | ~ class_Groups_Oordered__ab__group__add(U_953) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

cnf(f_216_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_956),U_957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_954),U_955))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_954),U_955) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_956),U_957)
    | ~ class_Groups_Oordered__ab__group__add(U_953) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_954),U_955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_953),U_956),U_957))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_954),U_955) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_953),U_956),U_957)
    | ~ class_Groups_Oordered__ab__group__add(U_953) ),
    inference(clausify,[status(thm)],[f_216_2]) ).

fof(f_217_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_217_2,plain,
    ! [U_961,U_960,U_959,U_958] : c_Nitpick_Ofold__graph_H(U_958,U_959,U_960,U_961,c_Orderings_Obot__class_Obot(tc_fun(U_958,tc_HOL_Obool)),U_961),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

cnf(f_217_3,plain,
    c_Nitpick_Ofold__graph_H(U_958,U_959,U_960,U_961,c_Orderings_Obot__class_Obot(tc_fun(U_958,tc_HOL_Obool)),U_961),
    inference(clausify,[status(thm)],[f_217_2]) ).

fof(f_218_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_218_2,plain,
    ! [U_965,U_964,U_963,U_962] : c_Nitpick_Ofold__graph_H(U_962,U_963,U_964,U_965,c_Orderings_Obot__class_Obot(tc_fun(U_962,tc_HOL_Obool)),U_965),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    c_Nitpick_Ofold__graph_H(U_962,U_963,U_964,U_965,c_Orderings_Obot__class_Obot(tc_fun(U_962,tc_HOL_Obool)),U_965),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_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_219_2,plain,
    ! [U_969,U_968,U_967,U_966] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_967,U_966)),U_968),U_969))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_969),U_968))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_968),U_969)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_969),U_968))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_968),U_969)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_967,U_966)),U_968),U_969)) ) )
      | ~ class_Orderings_Oord(U_966) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

cnf(f_219_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_968),U_969))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_967,U_966)),U_968),U_969))
    | ~ class_Orderings_Oord(U_966) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

cnf(f_219_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_969),U_968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_967,U_966)),U_968),U_969))
    | ~ class_Orderings_Oord(U_966) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

cnf(f_219_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_967,U_966)),U_968),U_969))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_969),U_968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_967,U_966)),U_968),U_969))
    | ~ class_Orderings_Oord(U_966) ),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_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_220_2,plain,
    ! [U_972,U_971,U_970] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_970),U_971),U_972))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_970),U_972),U_971)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_970),U_972),U_971))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_970),U_971),U_972)) ) )
      | ~ class_Orderings_Olinorder(U_970) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

cnf(f_220_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_970),U_972),U_971))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_970),U_971),U_972))
    | ~ class_Orderings_Olinorder(U_970) ),
    inference(clausify,[status(thm)],[f_220_2]) ).

cnf(f_220_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_970),U_971),U_972))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_970),U_972),U_971))
    | ~ class_Orderings_Olinorder(U_970) ),
    inference(clausify,[status(thm)],[f_220_2]) ).

fof(f_221_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_221_2,plain,
    ! [U_975,U_974,U_973] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_973),U_974),U_975))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_973),U_975),U_974)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_973),U_975),U_974))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_973),U_974),U_975)) ) )
      | ~ class_Orderings_Olinorder(U_973) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

cnf(f_221_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_973),U_975),U_974))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_973),U_974),U_975))
    | ~ class_Orderings_Olinorder(U_973) ),
    inference(clausify,[status(thm)],[f_221_2]) ).

cnf(f_221_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_973),U_974),U_975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_973),U_975),U_974))
    | ~ class_Orderings_Olinorder(U_973) ),
    inference(clausify,[status(thm)],[f_221_2]) ).

fof(f_222_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_222_2,plain,
    ! [U_978,U_977,U_976] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_976),U_978),U_977))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_976),U_977),U_978))
      | ~ class_Orderings_Olinorder(U_976) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

cnf(f_222_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_976),U_978),U_977))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_976),U_977),U_978))
    | ~ class_Orderings_Olinorder(U_976) ),
    inference(clausify,[status(thm)],[f_222_2]) ).

fof(f_223_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_223_2,plain,
    ! [U_981,U_980,U_979] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_979),U_980),U_981))
          | U_980 = U_981
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_979),U_980),U_981)) )
        & ( ( U_980 != U_981
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_979),U_980),U_981)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_979),U_980),U_981)) ) )
      | ~ class_Orderings_Oorder(U_979) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

cnf(f_223_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_979),U_980),U_981))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_979),U_980),U_981))
    | ~ class_Orderings_Oorder(U_979) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( U_980 != U_981
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_979),U_980),U_981))
    | ~ class_Orderings_Oorder(U_979) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

cnf(f_223_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_979),U_980),U_981))
    | U_980 = U_981
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_979),U_980),U_981))
    | ~ class_Orderings_Oorder(U_979) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

fof(f_224_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_224_2,plain,
    ! [U_984,U_983,U_982] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_982),U_983),U_984))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_984),U_983))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_983),U_984)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_984),U_983))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_983),U_984)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_982),U_983),U_984)) ) )
      | ~ class_Orderings_Opreorder(U_982) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_983),U_984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_982),U_983),U_984))
    | ~ class_Orderings_Opreorder(U_982) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_984),U_983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_982),U_983),U_984))
    | ~ class_Orderings_Opreorder(U_982) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

cnf(f_224_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_982),U_983),U_984))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_984),U_983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_982),U_983),U_984))
    | ~ class_Orderings_Opreorder(U_982) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_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_225_2,plain,
    ! [U_987,U_986,U_985] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
          | ( U_986 != U_987
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_986),U_987)) ) )
        & ( U_986 = U_987
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_986),U_987))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987)) ) )
      | ~ class_Orderings_Oorder(U_985) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( U_986 = U_987
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_986),U_987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
    | ~ class_Orderings_Oorder(U_985) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_986),U_987))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
    | ~ class_Orderings_Oorder(U_985) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

cnf(f_225_5,plain,
    ( U_986 != U_987
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
    | ~ class_Orderings_Oorder(U_985) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_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_226_2,plain,
    ! [U_990,U_989,U_988] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_988),U_990),U_989))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_988),U_989),U_990))
      | ~ class_Orderings_Olinorder(U_988) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_988),U_990),U_989))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_988),U_989),U_990))
    | ~ class_Orderings_Olinorder(U_988) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_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_227_2,plain,
    ! [U_993,U_992,U_991] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_991),U_993),U_992))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_991),U_992),U_993))
      | ~ class_Orderings_Olinorder(U_991) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_991),U_993),U_992))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_991),U_992),U_993))
    | ~ class_Orderings_Olinorder(U_991) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_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_228_2,plain,
    ! [U_996,U_995,U_994] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_994),U_995),U_996))
          | U_995 != U_996 )
        & ( U_995 = U_996
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_994),U_995),U_996)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_994),U_995),U_996))
      | ~ class_Orderings_Olinorder(U_994) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( U_995 = U_996
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_994),U_995),U_996))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_994),U_995),U_996))
    | ~ class_Orderings_Olinorder(U_994) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

cnf(f_228_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_994),U_995),U_996))
    | U_995 != U_996
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_994),U_995),U_996))
    | ~ class_Orderings_Olinorder(U_994) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_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_229_2,plain,
    ! [U_999,U_998,U_997] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_998),U_999))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_997),U_998),U_999))
      | U_998 = U_999
      | ~ class_Orderings_Oorder(U_997) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_998),U_999))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_997),U_998),U_999))
    | U_998 = U_999
    | ~ class_Orderings_Oorder(U_997) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_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_230_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__eq(U_1000),U_1002),U_1001))
      | U_1001 = U_1002
      | ~ class_Orderings_Oorder(U_1000) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1000),U_1002),U_1001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1000),U_1002),U_1001))
    | U_1001 = U_1002
    | ~ class_Orderings_Oorder(U_1000) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_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_231_2,plain,
    ! [U_1005,U_1004,U_1003] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1005),U_1004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1003),U_1004),U_1005))
      | ~ class_Orderings_Olinorder(U_1003) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1005),U_1004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1003),U_1004),U_1005))
    | ~ class_Orderings_Olinorder(U_1003) ),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_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_232_2,plain,
    ! [U_1008,U_1007,U_1006] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1006),U_1007),U_1008))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1006),U_1007),U_1008))
      | ~ class_Orderings_Opreorder(U_1006) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1006),U_1007),U_1008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1006),U_1007),U_1008))
    | ~ class_Orderings_Opreorder(U_1006) ),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_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_233_2,plain,
    ! [U_1011,U_1010,U_1009] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1009),U_1010),U_1011))
          | U_1010 != U_1011 )
        & ( U_1010 = U_1011
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1009),U_1010),U_1011)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1009),U_1010),U_1011))
      | ~ class_Orderings_Olinorder(U_1009) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( U_1010 = U_1011
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1009),U_1010),U_1011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1009),U_1010),U_1011))
    | ~ class_Orderings_Olinorder(U_1009) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1009),U_1010),U_1011))
    | U_1010 != U_1011
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1009),U_1010),U_1011))
    | ~ class_Orderings_Olinorder(U_1009) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_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_234_2,plain,
    ! [U_1014,U_1013,U_1012] :
      ( U_1013 = U_1014
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1012),U_1013),U_1014))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1012),U_1013),U_1014))
      | ~ class_Orderings_Oorder(U_1012) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( U_1013 = U_1014
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1012),U_1013),U_1014))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1012),U_1013),U_1014))
    | ~ class_Orderings_Oorder(U_1012) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_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_235_2,plain,
    ! [U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1017))
      | U_1016 = U_1017
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1015),U_1016),U_1017))
      | ~ class_Orderings_Oorder(U_1015) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1017))
    | U_1016 = U_1017
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1015),U_1016),U_1017))
    | ~ class_Orderings_Oorder(U_1015) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_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_236_2,plain,
    ! [U_1020,U_1019,U_1018] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1018),U_1019),U_1020))
      | U_1020 = U_1019
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1018),U_1019),U_1020))
      | ~ class_Orderings_Oorder(U_1018) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1018),U_1019),U_1020))
    | U_1020 = U_1019
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1018),U_1019),U_1020))
    | ~ class_Orderings_Oorder(U_1018) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_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_237_2,plain,
    ! [U_1024,U_1023,U_1022,U_1021] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1021),U_1022),U_1024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1021),U_1023),U_1024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1021),U_1022),U_1023))
      | ~ class_Orderings_Opreorder(U_1021) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1021),U_1022),U_1024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1021),U_1023),U_1024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1021),U_1022),U_1023))
    | ~ class_Orderings_Opreorder(U_1021) ),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_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_238_2,plain,
    ! [U_1028,U_1027,U_1026,U_1025] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1025),U_1028),U_1027))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1025),U_1028),U_1026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1025),U_1026),U_1027))
      | ~ class_Orderings_Oorder(U_1025) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1025),U_1028),U_1027))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1025),U_1028),U_1026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1025),U_1026),U_1027))
    | ~ class_Orderings_Oorder(U_1025) ),
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_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_239_2,plain,
    ! [U_1032,U_1031,U_1030,U_1029] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1029),U_1030),U_1032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1029),U_1031),U_1032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1029),U_1030),U_1031))
      | ~ class_Orderings_Opreorder(U_1029) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

cnf(f_239_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1029),U_1030),U_1032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1029),U_1031),U_1032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1029),U_1030),U_1031))
    | ~ class_Orderings_Opreorder(U_1029) ),
    inference(clausify,[status(thm)],[f_239_2]) ).

fof(f_240_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_240_2,plain,
    ! [U_1036,U_1035,U_1034,U_1033] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1036),U_1035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1036),U_1034))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1033),U_1034),U_1035))
      | ~ class_Orderings_Oorder(U_1033) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

cnf(f_240_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1036),U_1035))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1036),U_1034))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1033),U_1034),U_1035))
    | ~ class_Orderings_Oorder(U_1033) ),
    inference(clausify,[status(thm)],[f_240_2]) ).

fof(f_241_1,plain,
    ! [V_ca_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_241_2,plain,
    ! [U_1040,U_1039,U_1038,U_1037] :
      ( hBOOL(hAPP(hAPP(c_member(U_1037),U_1040),U_1039))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1037),U_1040),U_1038))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1037,tc_HOL_Obool)),U_1038),U_1039)) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1037),U_1040),U_1039))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1037),U_1040),U_1038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1037,tc_HOL_Obool)),U_1038),U_1039)) ),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_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_242_2,plain,
    ! [U_1042,U_1041] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1041,tc_HOL_Obool)),U_1042),c_Orderings_Obot__class_Obot(tc_fun(U_1041,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1041,tc_HOL_Obool)),U_1042),c_Orderings_Obot__class_Obot(tc_fun(U_1041,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_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_243_2,plain,
    ! [U_1046,U_1045,U_1044,U_1043] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1043),U_1044),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1043),U_1046),U_1045)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1043),U_1044),U_1045))
      | ~ class_Lattices_Osemilattice__sup(U_1043) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1043),U_1044),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1043),U_1046),U_1045)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1043),U_1044),U_1045))
    | ~ class_Lattices_Osemilattice__sup(U_1043) ),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_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_244_2,plain,
    ! [U_1050,U_1049,U_1048,U_1047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1047),U_1048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1047),U_1049),U_1050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1047),U_1048),U_1049))
      | ~ class_Lattices_Osemilattice__sup(U_1047) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1047),U_1048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1047),U_1049),U_1050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1047),U_1048),U_1049))
    | ~ class_Lattices_Osemilattice__sup(U_1047) ),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_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_245_2,plain,
    ! [U_1053,U_1052,U_1051] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1051,tc_HOL_Obool)),U_1052),U_1053))
        | U_1052 = U_1053
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1051,tc_HOL_Obool)),U_1052),U_1053)) )
      & ( ( U_1052 != U_1053
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1051,tc_HOL_Obool)),U_1052),U_1053)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1051,tc_HOL_Obool)),U_1052),U_1053)) ) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ( ! [U_1059,U_1057,U_1055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1055,tc_HOL_Obool)),U_1057),U_1059))
        | U_1057 = U_1059
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1055,tc_HOL_Obool)),U_1057),U_1059)) )
    & ! [U_1058,U_1056,U_1054] :
        ( ( U_1056 != U_1058
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1054,tc_HOL_Obool)),U_1056),U_1058)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1054,tc_HOL_Obool)),U_1056),U_1058)) ) ),
    inference(miniscope,[status(thm)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1054,tc_HOL_Obool)),U_1056),U_1058))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1054,tc_HOL_Obool)),U_1056),U_1058)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_5,plain,
    ( U_1056 != U_1058
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1054,tc_HOL_Obool)),U_1056),U_1058)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1055,tc_HOL_Obool)),U_1057),U_1059))
    | U_1057 = U_1059
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1055,tc_HOL_Obool)),U_1057),U_1059)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_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_246_2,plain,
    ! [U_1062,U_1061,U_1060] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1060,tc_HOL_Obool)),U_1061),U_1062))
        | ( U_1061 != U_1062
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1060,tc_HOL_Obool)),U_1061),U_1062)) ) )
      & ( U_1061 = U_1062
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1060,tc_HOL_Obool)),U_1061),U_1062))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1060,tc_HOL_Obool)),U_1061),U_1062)) ) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ( ! [U_1068,U_1066,U_1064] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1066),U_1068))
        | ( U_1066 != U_1068
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1064,tc_HOL_Obool)),U_1066),U_1068)) ) )
    & ! [U_1067,U_1065,U_1063] :
        ( U_1065 = U_1067
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1063,tc_HOL_Obool)),U_1065),U_1067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1065),U_1067)) ) ),
    inference(miniscope,[status(thm)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( U_1065 = U_1067
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1063,tc_HOL_Obool)),U_1065),U_1067))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1065),U_1067)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1064,tc_HOL_Obool)),U_1066),U_1068))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1066),U_1068)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_6,plain,
    ( U_1066 != U_1068
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1066),U_1068)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_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_247_2,plain,
    ! [U_1071,U_1070,U_1069] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1070),U_1071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1069,tc_HOL_Obool)),U_1070),U_1071)) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

cnf(f_247_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1070),U_1071))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1069,tc_HOL_Obool)),U_1070),U_1071)) ),
    inference(clausify,[status(thm)],[f_247_2]) ).

fof(f_248_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_248_2,plain,
    ! [U_1075,U_1074,U_1073,U_1072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1072,tc_HOL_Obool)),U_1073),U_1075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1072,tc_HOL_Obool)),U_1074),U_1075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1072,tc_HOL_Obool)),U_1073),U_1074)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1072,tc_HOL_Obool)),U_1073),U_1075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1072,tc_HOL_Obool)),U_1074),U_1075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1072,tc_HOL_Obool)),U_1073),U_1074)) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_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_249_2,plain,
    ! [U_1079,U_1078,U_1077,U_1076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1076,tc_HOL_Obool)),U_1077),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1076,tc_HOL_Obool)),U_1078),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1076,tc_HOL_Obool)),U_1077),U_1078)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1076,tc_HOL_Obool)),U_1077),U_1079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1076,tc_HOL_Obool)),U_1078),U_1079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1076,tc_HOL_Obool)),U_1077),U_1078)) ),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_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_250_2,plain,
    ! [U_1080] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_1080),c_Orderings_Obot__class_Obot(tc_fun(U_1080,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_1080),c_Orderings_Obot__class_Obot(tc_fun(U_1080,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_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_251_2,plain,
    ! [U_1083,U_1082,U_1081] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1081),hAPP(hAPP(c_Set_Oinsert(U_1081),U_1082),U_1083)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1081),U_1083)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1081),U_1083))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1081),hAPP(hAPP(c_Set_Oinsert(U_1081),U_1082),U_1083))) ) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ( ! [U_1089,U_1087,U_1085] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),hAPP(hAPP(c_Set_Oinsert(U_1085),U_1087),U_1089)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1089)) )
    & ! [U_1088,U_1086,U_1084] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1084),U_1088))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1084),hAPP(hAPP(c_Set_Oinsert(U_1084),U_1086),U_1088))) ) ),
    inference(miniscope,[status(thm)],[f_251_2]) ).

cnf(f_251_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1084),U_1088))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1084),hAPP(hAPP(c_Set_Oinsert(U_1084),U_1086),U_1088))) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

cnf(f_251_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),hAPP(hAPP(c_Set_Oinsert(U_1085),U_1087),U_1089)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1089)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_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_252_2,plain,
    ! [U_1092,U_1091,U_1090] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1090),U_1091))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1090),U_1092))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1090,tc_HOL_Obool)),U_1091),U_1092)) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1090),U_1091))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1090),U_1092))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1090,tc_HOL_Obool)),U_1091),U_1092)) ),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_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_253_2,plain,
    ! [U_1095,U_1094,U_1093] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1093),U_1095))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,tc_HOL_Obool)),U_1095),U_1094))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1093),U_1094)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

cnf(f_253_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1093),U_1095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,tc_HOL_Obool)),U_1095),U_1094))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1093),U_1094)) ),
    inference(clausify,[status(thm)],[f_253_2]) ).

fof(f_254_1,plain,
    ! [V_Ga_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_Ga_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).

fof(f_254_2,plain,
    ! [U_1098,U_1097,U_1096] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1096,tc_HOL_Obool)),U_1097),U_1098)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1098))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1097)) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

cnf(f_254_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1096,tc_HOL_Obool)),U_1097),U_1098)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1098))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1096),U_1097)) ),
    inference(clausify,[status(thm)],[f_254_2]) ).

fof(f_255_1,plain,
    ! [V_Ga_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_Ga_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_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_Ga_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).

fof(f_255_2,plain,
    ! [U_1101,U_1100,U_1099] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1099,tc_HOL_Obool)),U_1100),U_1101)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),U_1101))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),U_1100)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),U_1101))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),U_1100)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1099),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1099,tc_HOL_Obool)),U_1100),U_1101))) ) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ( ! [U_1107,U_1105,U_1103] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1103,tc_HOL_Obool)),U_1105),U_1107)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1107))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1105)) )
    & ! [U_1106,U_1104,U_1102] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),U_1106))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),U_1104)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1102,tc_HOL_Obool)),U_1104),U_1106))) ) ),
    inference(miniscope,[status(thm)],[f_255_2]) ).

cnf(f_255_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),U_1104))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1102,tc_HOL_Obool)),U_1104),U_1106))) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

cnf(f_255_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),U_1106))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1102,tc_HOL_Obool)),U_1104),U_1106))) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

cnf(f_255_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1103,tc_HOL_Obool)),U_1105),U_1107)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1107))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1103),U_1105)) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_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_256_2,plain,
    ! [U_1110,U_1109,U_1108] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1108,tc_HOL_Obool)),U_1110),U_1109)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1110)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1110))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1108,tc_HOL_Obool)),U_1110),U_1109))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1109)) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1110))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1108,tc_HOL_Obool)),U_1110),U_1109)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1109)) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1108,tc_HOL_Obool)),U_1110),U_1109)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1110))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1108),U_1109)) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_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_257_2,plain,
    ! [U_1114,U_1113,U_1112,U_1111] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1111,U_1112,U_1113,U_1114,c_Orderings_Obot__class_Obot(tc_fun(U_1111,tc_HOL_Obool))),U_1114)),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

cnf(f_257_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1111,U_1112,U_1113,U_1114,c_Orderings_Obot__class_Obot(tc_fun(U_1111,tc_HOL_Obool))),U_1114)),
    inference(clausify,[status(thm)],[f_257_2]) ).

fof(f_258_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_258_2,plain,
    ! [U_1118,U_1117,U_1116,U_1115] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1115,U_1116,U_1117,U_1118,c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool))),U_1118)),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

cnf(f_258_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1115,U_1116,U_1117,U_1118,c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool))),U_1118)),
    inference(clausify,[status(thm)],[f_258_2]) ).

fof(f_259_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_259_2,plain,
    ! [U_1123,U_1122,U_1121,U_1120,U_1119] :
      ( U_1123 = U_1122
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1119,U_1120,U_1121,U_1122,c_Orderings_Obot__class_Obot(tc_fun(U_1119,tc_HOL_Obool))),U_1123)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_1123,U_1122] :
      ( ! [U_1121,U_1120,U_1119] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1119,U_1120,U_1121,U_1122,c_Orderings_Obot__class_Obot(tc_fun(U_1119,tc_HOL_Obool))),U_1123))
      | U_1123 = U_1122 ),
    inference(miniscope,[status(thm)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1119,U_1120,U_1121,U_1122,c_Orderings_Obot__class_Obot(tc_fun(U_1119,tc_HOL_Obool))),U_1123))
    | U_1123 = U_1122 ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_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_260_2,plain,
    ! [U_1127,U_1126,U_1125,U_1124] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1125),hAPP(hAPP(c_Set_Oinsert(U_1124),U_1126),U_1127))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1125),U_1127))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1125),U_1127)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1125),hAPP(hAPP(c_Set_Oinsert(U_1124),U_1126),U_1127)))) ) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ( ! [U_1135,U_1133,U_1131,U_1129] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),hAPP(hAPP(c_Set_Oinsert(U_1129),U_1133),U_1135))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),U_1135))) )
    & ! [U_1134,U_1132,U_1130,U_1128] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),U_1134)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),hAPP(hAPP(c_Set_Oinsert(U_1128),U_1132),U_1134)))) ) ),
    inference(miniscope,[status(thm)],[f_260_2]) ).

cnf(f_260_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),U_1134)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),hAPP(hAPP(c_Set_Oinsert(U_1128),U_1132),U_1134)))) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

cnf(f_260_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),hAPP(hAPP(c_Set_Oinsert(U_1129),U_1133),U_1135))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1129,tc_HOL_Obool)),U_1131),U_1135))) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_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_261_2,plain,
    ! [U_1142,U_1141,U_1140,U_1139,U_1138,U_1137,U_1136] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1136,U_1139,U_1140,U_1141,hAPP(hAPP(c_Set_Oinsert(U_1136),U_1137),U_1138)),hAPP(hAPP(U_1140,U_1137),U_1142)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1136,U_1139,U_1140,U_1141,U_1138),U_1142))
      | hBOOL(hAPP(hAPP(c_member(U_1136),U_1137),U_1138)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1136,U_1139,U_1140,U_1141,hAPP(hAPP(c_Set_Oinsert(U_1136),U_1137),U_1138)),hAPP(hAPP(U_1140,U_1137),U_1142)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1136,U_1139,U_1140,U_1141,U_1138),U_1142))
    | hBOOL(hAPP(hAPP(c_member(U_1136),U_1137),U_1138)) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_1,plain,
    ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = V_b_2
          | V_ca_2 != V_d_2 )
        & ( V_ca_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_ca_2),V_d_2)
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_262_2,plain,
    ! [U_1147,U_1146,U_1145,U_1144,U_1143] :
      ( ( ( U_1144 = U_1145
          | U_1146 != U_1147 )
        & ( U_1146 = U_1147
          | U_1144 != U_1145 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1144),U_1145) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1146),U_1147)
      | ~ class_Groups_Oab__group__add(U_1143) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( U_1146 = U_1147
    | U_1144 != U_1145
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1144),U_1145) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1146),U_1147)
    | ~ class_Groups_Oab__group__add(U_1143) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

cnf(f_262_4,plain,
    ( U_1144 = U_1145
    | U_1146 != U_1147
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1144),U_1145) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1143),U_1146),U_1147)
    | ~ class_Groups_Oab__group__add(U_1143) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_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_263_2,plain,
    ! [U_1155,U_1154,U_1153,U_1152,U_1151,U_1150,U_1149,U_1148] :
      ( hAPP(U_1153,U_1154) = hAPP(hAPP(U_1150,hAPP(U_1152,U_1155)),hAPP(U_1153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1149,tc_HOL_Obool)),U_1154),hAPP(hAPP(c_Set_Oinsert(U_1149),U_1155),c_Orderings_Obot__class_Obot(tc_fun(U_1149,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1149),U_1155),U_1154))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1149),U_1154))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1148,U_1149,U_1150,U_1151,U_1152,U_1153) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_1155,U_1154,U_1153,U_1152,U_1151,U_1150,U_1149] :
      ( ! [U_1148] : ~ c_Finite__Set_Ofolding__image__simple(U_1148,U_1149,U_1150,U_1151,U_1152,U_1153)
      | hAPP(U_1153,U_1154) = hAPP(hAPP(U_1150,hAPP(U_1152,U_1155)),hAPP(U_1153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1149,tc_HOL_Obool)),U_1154),hAPP(hAPP(c_Set_Oinsert(U_1149),U_1155),c_Orderings_Obot__class_Obot(tc_fun(U_1149,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1149),U_1155),U_1154))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1149),U_1154)) ),
    inference(miniscope,[status(thm)],[f_263_2]) ).

cnf(f_263_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1148,U_1149,U_1150,U_1151,U_1152,U_1153)
    | hAPP(U_1153,U_1154) = hAPP(hAPP(U_1150,hAPP(U_1152,U_1155)),hAPP(U_1153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1149,tc_HOL_Obool)),U_1154),hAPP(hAPP(c_Set_Oinsert(U_1149),U_1155),c_Orderings_Obot__class_Obot(tc_fun(U_1149,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1149),U_1155),U_1154))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1149),U_1154)) ),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_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_264_2,plain,
    ! [U_1163,U_1162,U_1161,U_1160,U_1159,U_1158,U_1157,U_1156] :
      ( hAPP(U_1161,hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),U_1162)) = hAPP(hAPP(U_1158,hAPP(U_1160,U_1163)),hAPP(U_1161,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1157,tc_HOL_Obool)),U_1162),hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),c_Orderings_Obot__class_Obot(tc_fun(U_1157,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1157),U_1162))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1156,U_1157,U_1158,U_1159,U_1160,U_1161) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_1163,U_1162,U_1161,U_1160,U_1159,U_1158,U_1157] :
      ( ! [U_1156] : ~ c_Finite__Set_Ofolding__image__simple(U_1156,U_1157,U_1158,U_1159,U_1160,U_1161)
      | hAPP(U_1161,hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),U_1162)) = hAPP(hAPP(U_1158,hAPP(U_1160,U_1163)),hAPP(U_1161,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1157,tc_HOL_Obool)),U_1162),hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),c_Orderings_Obot__class_Obot(tc_fun(U_1157,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1157),U_1162)) ),
    inference(miniscope,[status(thm)],[f_264_2]) ).

cnf(f_264_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1156,U_1157,U_1158,U_1159,U_1160,U_1161)
    | hAPP(U_1161,hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),U_1162)) = hAPP(hAPP(U_1158,hAPP(U_1160,U_1163)),hAPP(U_1161,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1157,tc_HOL_Obool)),U_1162),hAPP(hAPP(c_Set_Oinsert(U_1157),U_1163),c_Orderings_Obot__class_Obot(tc_fun(U_1157,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1157),U_1162)) ),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_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_265_2,plain,
    ! [U_1166,U_1165,U_1164] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_1164,U_1165) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1164),U_1166),c_Big__Operators_Olattice__class_OSup__fin(U_1164,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_1164,U_1165) = U_1166
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1164),U_1166),U_1165))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1164),U_1165))
      | ~ class_Lattices_Olattice(U_1164) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1164,U_1165) = U_1166
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1164),U_1166),U_1165))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1164),U_1165))
    | ~ class_Lattices_Olattice(U_1164) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1164,U_1165) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1164),U_1166),c_Big__Operators_Olattice__class_OSup__fin(U_1164,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1164,tc_HOL_Obool)),U_1165),hAPP(hAPP(c_Set_Oinsert(U_1164),U_1166),c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1164,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1164),U_1166),U_1165))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1164),U_1165))
    | ~ class_Lattices_Olattice(U_1164) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_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_266_2,plain,
    ! [U_1177,U_1176,U_1175,U_1174,U_1173,U_1172,U_1171] :
      ( ( c_Nitpick_Ofold__graph_H(U_1171,U_1172,U_1173,U_1174,U_1175,hAPP(hAPP(U_1173,U_1176),U_1177))
        | ( ! [U_1170,U_1169] :
              ( ~ c_Nitpick_Ofold__graph_H(U_1171,U_1172,U_1173,U_1174,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1171,tc_HOL_Obool)),U_1175),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))),U_1169)
              | ~ hBOOL(hAPP(hAPP(c_member(U_1171),U_1170),U_1175))
              | hAPP(hAPP(U_1173,U_1176),U_1177) != hAPP(hAPP(U_1173,U_1170),U_1169) )
          & ( hAPP(hAPP(U_1173,U_1176),U_1177) != U_1174
            | U_1175 != c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)) ) ) )
      & ( ? [U_1168,U_1167] :
            ( c_Nitpick_Ofold__graph_H(U_1171,U_1172,U_1173,U_1174,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1171,tc_HOL_Obool)),U_1175),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))),U_1167)
            & hBOOL(hAPP(hAPP(c_member(U_1171),U_1168),U_1175))
            & hAPP(hAPP(U_1173,U_1176),U_1177) = hAPP(hAPP(U_1173,U_1168),U_1167) )
        | ( hAPP(hAPP(U_1173,U_1176),U_1177) = U_1174
          & U_1175 = c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_1171,U_1172,U_1173,U_1174,U_1175,hAPP(hAPP(U_1173,U_1176),U_1177)) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_1191,U_1189,U_1187,U_1185,U_1183,U_1181,U_1179] :
        ( c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,U_1187,hAPP(hAPP(U_1183,U_1189),U_1191))
        | ( ! [U_1170] :
              ( ! [U_1169] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1179,tc_HOL_Obool)),U_1187),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)))),U_1169)
                  | hAPP(hAPP(U_1183,U_1189),U_1191) != hAPP(hAPP(U_1183,U_1170),U_1169) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_1179),U_1170),U_1187)) )
          & ( hAPP(hAPP(U_1183,U_1189),U_1191) != U_1185
            | U_1187 != c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)) ) ) )
    & ! [U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178] :
        ( ? [U_1168] :
            ( ? [U_1167] :
                ( c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1178,tc_HOL_Obool)),U_1186),hAPP(hAPP(c_Set_Oinsert(U_1178),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)))),U_1167)
                & hAPP(hAPP(U_1182,U_1188),U_1190) = hAPP(hAPP(U_1182,U_1168),U_1167) )
            & hBOOL(hAPP(hAPP(c_member(U_1178),U_1168),U_1186)) )
        | ( hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
          & U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ) ),
    inference(miniscope,[status(thm)],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_1191,U_1189,U_1187,U_1185,U_1183,U_1181,U_1179] :
        ( c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,U_1187,hAPP(hAPP(U_1183,U_1189),U_1191))
        | ( ! [U_1170] :
              ( ! [U_1169] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1179,tc_HOL_Obool)),U_1187),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)))),U_1169)
                  | hAPP(hAPP(U_1183,U_1189),U_1191) != hAPP(hAPP(U_1183,U_1170),U_1169) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_1179),U_1170),U_1187)) )
          & ( hAPP(hAPP(U_1183,U_1189),U_1191) != U_1185
            | U_1187 != c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)) ) ) )
    & ! [U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178] :
        ( ( ? [U_1167] :
              ( c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1178,tc_HOL_Obool)),U_1186),hAPP(hAPP(c_Set_Oinsert(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)))),U_1167)
              & hAPP(hAPP(U_1182,U_1188),U_1190) = hAPP(hAPP(U_1182,sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),U_1167) )
          & hBOOL(hAPP(hAPP(c_member(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),U_1186)) )
        | ( hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
          & U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_1168,sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))],[f_266_3]) ).

fof(f_266_5,plain,
    ( ! [U_1191,U_1189,U_1187,U_1185,U_1183,U_1181,U_1179] :
        ( c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,U_1187,hAPP(hAPP(U_1183,U_1189),U_1191))
        | ( ! [U_1170] :
              ( ! [U_1169] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1179,tc_HOL_Obool)),U_1187),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)))),U_1169)
                  | hAPP(hAPP(U_1183,U_1189),U_1191) != hAPP(hAPP(U_1183,U_1170),U_1169) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_1179),U_1170),U_1187)) )
          & ( hAPP(hAPP(U_1183,U_1189),U_1191) != U_1185
            | U_1187 != c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)) ) ) )
    & ! [U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178] :
        ( ( c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1178,tc_HOL_Obool)),U_1186),hAPP(hAPP(c_Set_Oinsert(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)))),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
          & hAPP(hAPP(U_1182,U_1188),U_1190) = hAPP(hAPP(U_1182,sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
          & hBOOL(hAPP(hAPP(c_member(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),U_1186)) )
        | ( hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
          & U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_1167,sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))],[f_266_4]) ).

cnf(f_266_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),U_1186))
    | U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_7,plain,
    ( hAPP(hAPP(U_1182,U_1188),U_1190) = hAPP(hAPP(U_1182,sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
    | U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1178,tc_HOL_Obool)),U_1186),hAPP(hAPP(c_Set_Oinsert(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)))),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
    | U_1186 = c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),U_1186))
    | hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_10,plain,
    ( hAPP(hAPP(U_1182,U_1188),U_1190) = hAPP(hAPP(U_1182,sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
    | hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_11,plain,
    ( c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1178,tc_HOL_Obool)),U_1186),hAPP(hAPP(c_Set_Oinsert(U_1178),sK13(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178)),c_Orderings_Obot__class_Obot(tc_fun(U_1178,tc_HOL_Obool)))),sK14(U_1190,U_1188,U_1186,U_1184,U_1182,U_1180,U_1178))
    | hAPP(hAPP(U_1182,U_1188),U_1190) = U_1184
    | ~ c_Nitpick_Ofold__graph_H(U_1178,U_1180,U_1182,U_1184,U_1186,hAPP(hAPP(U_1182,U_1188),U_1190)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_12,plain,
    ( hAPP(hAPP(U_1183,U_1189),U_1191) != U_1185
    | U_1187 != c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool))
    | c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,U_1187,hAPP(hAPP(U_1183,U_1189),U_1191)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_13,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1179,tc_HOL_Obool)),U_1187),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1179,tc_HOL_Obool)))),U_1169)
    | hAPP(hAPP(U_1183,U_1189),U_1191) != hAPP(hAPP(U_1183,U_1170),U_1169)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1179),U_1170),U_1187))
    | c_Nitpick_Ofold__graph_H(U_1179,U_1181,U_1183,U_1185,U_1187,hAPP(hAPP(U_1183,U_1189),U_1191)) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

fof(f_267_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_267_2,plain,
    ! [U_1197,U_1196,U_1195,U_1194] :
      ( hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(U_1196,U_1197)),U_1197))
      | ? [U_1193,U_1192] : ~ hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(hAPP(U_1195,U_1193),U_1192)),hAPP(hAPP(c_Set_Oinsert(U_1194),U_1193),hAPP(hAPP(c_Set_Oinsert(U_1194),U_1192),c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))))))
      | U_1197 = c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1194),U_1197))
      | ~ c_Finite__Set_Ofolding__one(U_1194,U_1195,U_1196) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_1197,U_1196,U_1195,U_1194] :
      ( hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(U_1196,U_1197)),U_1197))
      | ? [U_1192] : ~ hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(hAPP(U_1195,sK15(U_1197,U_1196,U_1195,U_1194)),U_1192)),hAPP(hAPP(c_Set_Oinsert(U_1194),sK15(U_1197,U_1196,U_1195,U_1194)),hAPP(hAPP(c_Set_Oinsert(U_1194),U_1192),c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))))))
      | U_1197 = c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1194),U_1197))
      | ~ c_Finite__Set_Ofolding__one(U_1194,U_1195,U_1196) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1193,sK15(U_1197,U_1196,U_1195,U_1194))],[f_267_2]) ).

fof(f_267_4,plain,
    ! [U_1197,U_1196,U_1195,U_1194] :
      ( hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(U_1196,U_1197)),U_1197))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(hAPP(U_1195,sK15(U_1197,U_1196,U_1195,U_1194)),sK16(U_1197,U_1196,U_1195,U_1194))),hAPP(hAPP(c_Set_Oinsert(U_1194),sK15(U_1197,U_1196,U_1195,U_1194)),hAPP(hAPP(c_Set_Oinsert(U_1194),sK16(U_1197,U_1196,U_1195,U_1194)),c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))))))
      | U_1197 = c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1194),U_1197))
      | ~ c_Finite__Set_Ofolding__one(U_1194,U_1195,U_1196) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1192,sK16(U_1197,U_1196,U_1195,U_1194))],[f_267_3]) ).

cnf(f_267_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(U_1196,U_1197)),U_1197))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1194),hAPP(hAPP(U_1195,sK15(U_1197,U_1196,U_1195,U_1194)),sK16(U_1197,U_1196,U_1195,U_1194))),hAPP(hAPP(c_Set_Oinsert(U_1194),sK15(U_1197,U_1196,U_1195,U_1194)),hAPP(hAPP(c_Set_Oinsert(U_1194),sK16(U_1197,U_1196,U_1195,U_1194)),c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))))))
    | U_1197 = c_Orderings_Obot__class_Obot(tc_fun(U_1194,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1194),U_1197))
    | ~ c_Finite__Set_Ofolding__one(U_1194,U_1195,U_1196) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

fof(f_268_1,plain,
    ! [V_Pa_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_268_2,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
      | ? [U_1199,U_1198] :
          ( ~ hBOOL(hAPP(U_1202,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1200,tc_HOL_Obool)),U_1198),hAPP(hAPP(c_Set_Oinsert(U_1200),U_1199),c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_1202,U_1198))
          & hBOOL(hAPP(hAPP(c_member(U_1200),U_1199),U_1198))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1198)) )
      | ~ hBOOL(hAPP(U_1202,U_1201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
      | ? [U_1198] :
          ( ~ hBOOL(hAPP(U_1202,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1200,tc_HOL_Obool)),U_1198),hAPP(hAPP(c_Set_Oinsert(U_1200),sK17(U_1202,U_1201,U_1200)),c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_1202,U_1198))
          & hBOOL(hAPP(hAPP(c_member(U_1200),sK17(U_1202,U_1201,U_1200)),U_1198))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1198)) )
      | ~ hBOOL(hAPP(U_1202,U_1201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1199,sK17(U_1202,U_1201,U_1200))],[f_268_2]) ).

fof(f_268_4,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_1202,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1200,tc_HOL_Obool)),sK18(U_1202,U_1201,U_1200)),hAPP(hAPP(c_Set_Oinsert(U_1200),sK17(U_1202,U_1201,U_1200)),c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_1202,sK18(U_1202,U_1201,U_1200)))
        & hBOOL(hAPP(hAPP(c_member(U_1200),sK17(U_1202,U_1201,U_1200)),sK18(U_1202,U_1201,U_1200)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),sK18(U_1202,U_1201,U_1200))) )
      | ~ hBOOL(hAPP(U_1202,U_1201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1198,sK18(U_1202,U_1201,U_1200))],[f_268_3]) ).

cnf(f_268_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),sK18(U_1202,U_1201,U_1200)))
    | hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1202,U_1201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1200),sK17(U_1202,U_1201,U_1200)),sK18(U_1202,U_1201,U_1200)))
    | hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1202,U_1201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_7,plain,
    ( hBOOL(hAPP(U_1202,sK18(U_1202,U_1201,U_1200)))
    | hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1202,U_1201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_8,plain,
    ( ~ hBOOL(hAPP(U_1202,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1200,tc_HOL_Obool)),sK18(U_1202,U_1201,U_1200)),hAPP(hAPP(c_Set_Oinsert(U_1200),sK17(U_1202,U_1201,U_1200)),c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))))
    | hBOOL(hAPP(U_1202,c_Orderings_Obot__class_Obot(tc_fun(U_1200,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_1202,U_1201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201)) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

fof(f_269_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_269_2,plain,
    ! [U_1207,U_1206,U_1205,U_1204,U_1203] :
      ( hAPP(U_1205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1203,tc_HOL_Obool)),U_1206),U_1207)) = hAPP(hAPP(U_1204,hAPP(U_1205,U_1206)),hAPP(U_1205,U_1207))
      | U_1207 = c_Orderings_Obot__class_Obot(tc_fun(U_1203,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1203),U_1207))
      | U_1206 = c_Orderings_Obot__class_Obot(tc_fun(U_1203,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1203),U_1206))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1203,U_1204,U_1205) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( hAPP(U_1205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1203,tc_HOL_Obool)),U_1206),U_1207)) = hAPP(hAPP(U_1204,hAPP(U_1205,U_1206)),hAPP(U_1205,U_1207))
    | U_1207 = c_Orderings_Obot__class_Obot(tc_fun(U_1203,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1203),U_1207))
    | U_1206 = c_Orderings_Obot__class_Obot(tc_fun(U_1203,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1203),U_1206))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1203,U_1204,U_1205) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_1,plain,
    ! [V_Pa_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_F_2))
      | ? [B_a,B_F] :
          ( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
          & hBOOL(hAPP(V_Pa_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_Pa_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_270_2,plain,
    ! [U_1213,U_1212,U_1211,U_1210] :
      ( hBOOL(hAPP(U_1213,U_1211))
      | ? [U_1209,U_1208] :
          ( ~ hBOOL(hAPP(U_1213,hAPP(hAPP(c_Set_Oinsert(U_1210),U_1209),U_1208)))
          & hBOOL(hAPP(U_1213,U_1208))
          & ~ hBOOL(hAPP(hAPP(c_member(U_1210),U_1209),U_1208))
          & hBOOL(hAPP(hAPP(c_member(U_1210),U_1209),U_1212))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1208)) )
      | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_1213,U_1212,U_1211,U_1210] :
      ( hBOOL(hAPP(U_1213,U_1211))
      | ? [U_1208] :
          ( ~ hBOOL(hAPP(U_1213,hAPP(hAPP(c_Set_Oinsert(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),U_1208)))
          & hBOOL(hAPP(U_1213,U_1208))
          & ~ hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),U_1208))
          & hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),U_1212))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1208)) )
      | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1209,sK19(U_1213,U_1212,U_1211,U_1210))],[f_270_2]) ).

fof(f_270_4,plain,
    ! [U_1213,U_1212,U_1211,U_1210] :
      ( hBOOL(hAPP(U_1213,U_1211))
      | ( ~ hBOOL(hAPP(U_1213,hAPP(hAPP(c_Set_Oinsert(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),sK20(U_1213,U_1212,U_1211,U_1210))))
        & hBOOL(hAPP(U_1213,sK20(U_1213,U_1212,U_1211,U_1210)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),sK20(U_1213,U_1212,U_1211,U_1210)))
        & hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),U_1212))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),sK20(U_1213,U_1212,U_1211,U_1210))) )
      | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1208,sK20(U_1213,U_1212,U_1211,U_1210))],[f_270_3]) ).

cnf(f_270_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),sK20(U_1213,U_1212,U_1211,U_1210)))
    | hBOOL(hAPP(U_1213,U_1211))
    | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),U_1212))
    | hBOOL(hAPP(U_1213,U_1211))
    | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),sK20(U_1213,U_1212,U_1211,U_1210)))
    | hBOOL(hAPP(U_1213,U_1211))
    | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_8,plain,
    ( hBOOL(hAPP(U_1213,sK20(U_1213,U_1212,U_1211,U_1210)))
    | hBOOL(hAPP(U_1213,U_1211))
    | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_9,plain,
    ( ~ hBOOL(hAPP(U_1213,hAPP(hAPP(c_Set_Oinsert(U_1210),sK19(U_1213,U_1212,U_1211,U_1210)),sK20(U_1213,U_1212,U_1211,U_1210))))
    | hBOOL(hAPP(U_1213,U_1211))
    | ~ hBOOL(hAPP(U_1213,c_Orderings_Obot__class_Obot(tc_fun(U_1210,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1210,tc_HOL_Obool)),U_1211),U_1212))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1210),U_1211)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

fof(f_271_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_271_2,plain,
    ! [U_1218,U_1217,U_1216,U_1215,U_1214] :
      ( hAPP(hAPP(U_1215,hAPP(U_1216,U_1218)),hAPP(U_1216,U_1217)) = hAPP(U_1216,U_1217)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1214,tc_HOL_Obool)),U_1218),U_1217))
      | U_1218 = c_Orderings_Obot__class_Obot(tc_fun(U_1214,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1214),U_1217))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1214,U_1215,U_1216) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    ( hAPP(hAPP(U_1215,hAPP(U_1216,U_1218)),hAPP(U_1216,U_1217)) = hAPP(U_1216,U_1217)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1214,tc_HOL_Obool)),U_1218),U_1217))
    | U_1218 = c_Orderings_Obot__class_Obot(tc_fun(U_1214,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1214),U_1217))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1214,U_1215,U_1216) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_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_272_2,plain,
    ! [U_1223,U_1222,U_1221,U_1220,U_1219] :
      ( hAPP(U_1221,hAPP(hAPP(c_Set_Oinsert(U_1219),U_1223),U_1222)) = hAPP(hAPP(U_1220,U_1223),hAPP(U_1221,U_1222))
      | U_1222 = c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1219),U_1222))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1219,U_1220,U_1221) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    ( hAPP(U_1221,hAPP(hAPP(c_Set_Oinsert(U_1219),U_1223),U_1222)) = hAPP(hAPP(U_1220,U_1223),hAPP(U_1221,U_1222))
    | U_1222 = c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1219),U_1222))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1219,U_1220,U_1221) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_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_273_2,plain,
    ! [U_1226,U_1225,U_1224] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),U_1225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1224),U_1226),c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),U_1225)) = U_1226
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1224),U_1225))
      | ~ class_Lattices_Olattice(U_1224) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),U_1225)) = U_1226
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1224),U_1225))
    | ~ class_Lattices_Olattice(U_1224) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),U_1225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1224),U_1226),c_Big__Operators_Olattice__class_OSup__fin(U_1224,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1224,tc_HOL_Obool)),U_1225),hAPP(hAPP(c_Set_Oinsert(U_1224),U_1226),c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1224,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1224),U_1225))
    | ~ class_Lattices_Olattice(U_1224) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_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_274_2,plain,
    ! [U_1230,U_1229,U_1228,U_1227] :
      ( hAPP(hAPP(U_1228,U_1230),U_1230) = U_1230
      | ~ c_Finite__Set_Ofolding__one__idem(U_1227,U_1228,U_1229) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_1230,U_1229,U_1228] :
      ( ! [U_1227] : ~ c_Finite__Set_Ofolding__one__idem(U_1227,U_1228,U_1229)
      | hAPP(hAPP(U_1228,U_1230),U_1230) = U_1230 ),
    inference(miniscope,[status(thm)],[f_274_2]) ).

cnf(f_274_4,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_1227,U_1228,U_1229)
    | hAPP(hAPP(U_1228,U_1230),U_1230) = U_1230 ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_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_275_2,plain,
    ! [U_1236,U_1235,U_1234,U_1233,U_1232,U_1231] :
      ( hAPP(U_1236,c_Orderings_Obot__class_Obot(tc_fun(U_1232,tc_HOL_Obool))) = U_1234
      | ~ c_Finite__Set_Ofolding__image__simple(U_1231,U_1232,U_1233,U_1234,U_1235,U_1236) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_1236,U_1235,U_1234,U_1233,U_1232] :
      ( ! [U_1231] : ~ c_Finite__Set_Ofolding__image__simple(U_1231,U_1232,U_1233,U_1234,U_1235,U_1236)
      | hAPP(U_1236,c_Orderings_Obot__class_Obot(tc_fun(U_1232,tc_HOL_Obool))) = U_1234 ),
    inference(miniscope,[status(thm)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1231,U_1232,U_1233,U_1234,U_1235,U_1236)
    | hAPP(U_1236,c_Orderings_Obot__class_Obot(tc_fun(U_1232,tc_HOL_Obool))) = U_1234 ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_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_276_2,plain,
    ! [U_1238,U_1237] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1237,hAPP(hAPP(c_Set_Oinsert(U_1237),U_1238),c_Orderings_Obot__class_Obot(tc_fun(U_1237,tc_HOL_Obool)))) = U_1238
      | ~ class_Lattices_Olattice(U_1237) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1237,hAPP(hAPP(c_Set_Oinsert(U_1237),U_1238),c_Orderings_Obot__class_Obot(tc_fun(U_1237,tc_HOL_Obool)))) = U_1238
    | ~ class_Lattices_Olattice(U_1237) ),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_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_277_2,plain,
    ! [U_1241,U_1240,U_1239] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1239),U_1241),c_Big__Operators_Olattice__class_OSup__fin(U_1239,U_1240)) = c_Big__Operators_Olattice__class_OSup__fin(U_1239,U_1240)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1239),U_1241),U_1240))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1239),U_1240))
      | ~ class_Lattices_Olattice(U_1239) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

cnf(f_277_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1239),U_1241),c_Big__Operators_Olattice__class_OSup__fin(U_1239,U_1240)) = c_Big__Operators_Olattice__class_OSup__fin(U_1239,U_1240)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1239),U_1241),U_1240))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1239),U_1240))
    | ~ class_Lattices_Olattice(U_1239) ),
    inference(clausify,[status(thm)],[f_277_2]) ).

fof(f_278_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_278_2,plain,
    ! [U_1246,U_1245,U_1244,U_1243,U_1242] :
      ( hAPP(hAPP(U_1243,U_1246),hAPP(U_1244,U_1245)) = hAPP(U_1244,U_1245)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1242),U_1246),U_1245))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1242),U_1245))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1242,U_1243,U_1244) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    ( hAPP(hAPP(U_1243,U_1246),hAPP(U_1244,U_1245)) = hAPP(U_1244,U_1245)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1242),U_1246),U_1245))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1242),U_1245))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1242,U_1243,U_1244) ),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_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_279_2,plain,
    ! [U_1249,U_1248,U_1247] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1247,hAPP(hAPP(c_Set_Oinsert(U_1247),U_1249),U_1248)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1247),U_1249),c_Big__Operators_Olattice__class_OSup__fin(U_1247,U_1248))
      | U_1248 = c_Orderings_Obot__class_Obot(tc_fun(U_1247,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1247),U_1248))
      | ~ class_Lattices_Olattice(U_1247) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1247,hAPP(hAPP(c_Set_Oinsert(U_1247),U_1249),U_1248)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1247),U_1249),c_Big__Operators_Olattice__class_OSup__fin(U_1247,U_1248))
    | U_1248 = c_Orderings_Obot__class_Obot(tc_fun(U_1247,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1247),U_1248))
    | ~ class_Lattices_Olattice(U_1247) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_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_280_2,plain,
    ! [U_1252,U_1251,U_1250] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1250),c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1252)),c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1251)) = c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1251)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1250,tc_HOL_Obool)),U_1252),U_1251))
      | U_1252 = c_Orderings_Obot__class_Obot(tc_fun(U_1250,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1250),U_1251))
      | ~ class_Lattices_Olattice(U_1250) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1250),c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1252)),c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1251)) = c_Big__Operators_Olattice__class_OSup__fin(U_1250,U_1251)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1250,tc_HOL_Obool)),U_1252),U_1251))
    | U_1252 = c_Orderings_Obot__class_Obot(tc_fun(U_1250,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1250),U_1251))
    | ~ class_Lattices_Olattice(U_1250) ),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_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_281_2,plain,
    ! [U_1255,U_1254,U_1253] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1253,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1253,tc_HOL_Obool)),U_1254),U_1255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1253),c_Big__Operators_Olattice__class_OSup__fin(U_1253,U_1254)),c_Big__Operators_Olattice__class_OSup__fin(U_1253,U_1255))
      | U_1255 = c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1253),U_1255))
      | U_1254 = c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1253),U_1254))
      | ~ class_Lattices_Olattice(U_1253) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

cnf(f_281_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1253,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1253,tc_HOL_Obool)),U_1254),U_1255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1253),c_Big__Operators_Olattice__class_OSup__fin(U_1253,U_1254)),c_Big__Operators_Olattice__class_OSup__fin(U_1253,U_1255))
    | U_1255 = c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1253),U_1255))
    | U_1254 = c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1253),U_1254))
    | ~ class_Lattices_Olattice(U_1253) ),
    inference(clausify,[status(thm)],[f_281_2]) ).

fof(f_282_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_282_2,plain,
    ! [U_1263,U_1262,U_1261,U_1260,U_1259,U_1258,U_1257,U_1256] :
      ( hAPP(U_1261,hAPP(hAPP(c_Set_Oinsert(U_1257),U_1263),U_1262)) = hAPP(hAPP(U_1258,hAPP(U_1260,U_1263)),hAPP(U_1261,U_1262))
      | hBOOL(hAPP(hAPP(c_member(U_1257),U_1263),U_1262))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1262))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1256,U_1257,U_1258,U_1259,U_1260,U_1261) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_1263,U_1262,U_1261,U_1260,U_1259,U_1258,U_1257] :
      ( ! [U_1256] : ~ c_Finite__Set_Ofolding__image__simple(U_1256,U_1257,U_1258,U_1259,U_1260,U_1261)
      | hAPP(U_1261,hAPP(hAPP(c_Set_Oinsert(U_1257),U_1263),U_1262)) = hAPP(hAPP(U_1258,hAPP(U_1260,U_1263)),hAPP(U_1261,U_1262))
      | hBOOL(hAPP(hAPP(c_member(U_1257),U_1263),U_1262))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1262)) ),
    inference(miniscope,[status(thm)],[f_282_2]) ).

cnf(f_282_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1256,U_1257,U_1258,U_1259,U_1260,U_1261)
    | hAPP(U_1261,hAPP(hAPP(c_Set_Oinsert(U_1257),U_1263),U_1262)) = hAPP(hAPP(U_1258,hAPP(U_1260,U_1263)),hAPP(U_1261,U_1262))
    | hBOOL(hAPP(hAPP(c_member(U_1257),U_1263),U_1262))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1262)) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_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_283_2,plain,
    ! [U_1266,U_1265,U_1264] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1264,hAPP(hAPP(c_Set_Oinsert(U_1264),U_1266),U_1265)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1264),U_1266),c_Big__Operators_Olattice__class_OSup__fin(U_1264,U_1265))
      | U_1265 = c_Orderings_Obot__class_Obot(tc_fun(U_1264,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_1264),U_1266),U_1265))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1264),U_1265))
      | ~ class_Lattices_Olattice(U_1264) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1264,hAPP(hAPP(c_Set_Oinsert(U_1264),U_1266),U_1265)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1264),U_1266),c_Big__Operators_Olattice__class_OSup__fin(U_1264,U_1265))
    | U_1265 = c_Orderings_Obot__class_Obot(tc_fun(U_1264,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_1264),U_1266),U_1265))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1264),U_1265))
    | ~ class_Lattices_Olattice(U_1264) ),
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_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_284_2,plain,
    ! [U_1270,U_1269] :
      ( hBOOL(hAPP(hAPP(c_member(U_1269),c_Big__Operators_Olattice__class_OSup__fin(U_1269,U_1270)),U_1270))
      | ? [U_1268,U_1267] : ~ hBOOL(hAPP(hAPP(c_member(U_1269),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1269),U_1268),U_1267)),hAPP(hAPP(c_Set_Oinsert(U_1269),U_1268),hAPP(hAPP(c_Set_Oinsert(U_1269),U_1267),c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))))))
      | U_1270 = c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1270))
      | ~ class_Lattices_Olattice(U_1269) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_1270,U_1269] :
      ( hBOOL(hAPP(hAPP(c_member(U_1269),c_Big__Operators_Olattice__class_OSup__fin(U_1269,U_1270)),U_1270))
      | ? [U_1267] : ~ hBOOL(hAPP(hAPP(c_member(U_1269),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1269),sK21(U_1270,U_1269)),U_1267)),hAPP(hAPP(c_Set_Oinsert(U_1269),sK21(U_1270,U_1269)),hAPP(hAPP(c_Set_Oinsert(U_1269),U_1267),c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))))))
      | U_1270 = c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1270))
      | ~ class_Lattices_Olattice(U_1269) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1268,sK21(U_1270,U_1269))],[f_284_2]) ).

fof(f_284_4,plain,
    ! [U_1270,U_1269] :
      ( hBOOL(hAPP(hAPP(c_member(U_1269),c_Big__Operators_Olattice__class_OSup__fin(U_1269,U_1270)),U_1270))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1269),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1269),sK21(U_1270,U_1269)),sK22(U_1270,U_1269))),hAPP(hAPP(c_Set_Oinsert(U_1269),sK21(U_1270,U_1269)),hAPP(hAPP(c_Set_Oinsert(U_1269),sK22(U_1270,U_1269)),c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))))))
      | U_1270 = c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1270))
      | ~ class_Lattices_Olattice(U_1269) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1267,sK22(U_1270,U_1269))],[f_284_3]) ).

cnf(f_284_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1269),c_Big__Operators_Olattice__class_OSup__fin(U_1269,U_1270)),U_1270))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1269),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1269),sK21(U_1270,U_1269)),sK22(U_1270,U_1269))),hAPP(hAPP(c_Set_Oinsert(U_1269),sK21(U_1270,U_1269)),hAPP(hAPP(c_Set_Oinsert(U_1269),sK22(U_1270,U_1269)),c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))))))
    | U_1270 = c_Orderings_Obot__class_Obot(tc_fun(U_1269,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1270))
    | ~ class_Lattices_Olattice(U_1269) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

fof(f_285_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_285_2,plain,
    ! [U_1277,U_1276,U_1275,U_1274,U_1273] :
      ( ? [U_1272,U_1271] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_1273),U_1272),U_1271))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1273,U_1273,U_1274,U_1272,U_1271),U_1277))
          & hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276) = hAPP(hAPP(c_Set_Oinsert(U_1273),U_1272),U_1271) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_1277,U_1276,U_1275,U_1274,U_1273] :
      ( ? [U_1271] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),U_1271))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1273,U_1273,U_1274,sK23(U_1277,U_1276,U_1275,U_1274,U_1273),U_1271),U_1277))
          & hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276) = hAPP(hAPP(c_Set_Oinsert(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),U_1271) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1272,sK23(U_1277,U_1276,U_1275,U_1274,U_1273))],[f_285_2]) ).

fof(f_285_4,plain,
    ! [U_1277,U_1276,U_1275,U_1274,U_1273] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),sK24(U_1277,U_1276,U_1275,U_1274,U_1273)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1273,U_1273,U_1274,sK23(U_1277,U_1276,U_1275,U_1274,U_1273),sK24(U_1277,U_1276,U_1275,U_1274,U_1273)),U_1277))
        & hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276) = hAPP(hAPP(c_Set_Oinsert(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),sK24(U_1277,U_1276,U_1275,U_1274,U_1273)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1271,sK24(U_1277,U_1276,U_1275,U_1274,U_1273))],[f_285_3]) ).

cnf(f_285_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276) = hAPP(hAPP(c_Set_Oinsert(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),sK24(U_1277,U_1276,U_1275,U_1274,U_1273))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1273,U_1273,U_1274,sK23(U_1277,U_1276,U_1275,U_1274,U_1273),sK24(U_1277,U_1276,U_1275,U_1274,U_1273)),U_1277))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1273),sK23(U_1277,U_1276,U_1275,U_1274,U_1273)),sK24(U_1277,U_1276,U_1275,U_1274,U_1273)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1273,U_1274,hAPP(hAPP(c_Set_Oinsert(U_1273),U_1275),U_1276)),U_1277)) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

fof(f_286_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_286_2,plain,
    ! [U_1286,U_1285,U_1284,U_1283,U_1282] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1282,U_1283,hAPP(hAPP(c_Set_Oinsert(U_1282),U_1284),U_1285)),U_1286))
        | ! [U_1281,U_1280] :
            ( hBOOL(hAPP(hAPP(c_member(U_1282),U_1281),U_1280))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1282,U_1282,U_1283,U_1281,U_1280),U_1286))
            | hAPP(hAPP(c_Set_Oinsert(U_1282),U_1284),U_1285) != hAPP(hAPP(c_Set_Oinsert(U_1282),U_1281),U_1280) ) )
      & ( ? [U_1279,U_1278] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_1282),U_1279),U_1278))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1282,U_1282,U_1283,U_1279,U_1278),U_1286))
            & hAPP(hAPP(c_Set_Oinsert(U_1282),U_1284),U_1285) = hAPP(hAPP(c_Set_Oinsert(U_1282),U_1279),U_1278) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1282,U_1283,hAPP(hAPP(c_Set_Oinsert(U_1282),U_1284),U_1285)),U_1286)) ) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ( ! [U_1296,U_1294,U_1292,U_1290,U_1288] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1288,U_1290,hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294)),U_1296))
        | ! [U_1281,U_1280] :
            ( hBOOL(hAPP(hAPP(c_member(U_1288),U_1281),U_1280))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1288,U_1288,U_1290,U_1281,U_1280),U_1296))
            | hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294) != hAPP(hAPP(c_Set_Oinsert(U_1288),U_1281),U_1280) ) )
    & ! [U_1295,U_1293,U_1291,U_1289,U_1287] :
        ( ? [U_1279,U_1278] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_1287),U_1279),U_1278))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1287,U_1287,U_1289,U_1279,U_1278),U_1295))
            & hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293) = hAPP(hAPP(c_Set_Oinsert(U_1287),U_1279),U_1278) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ) ),
    inference(miniscope,[status(thm)],[f_286_2]) ).

fof(f_286_4,plain,
    ( ! [U_1296,U_1294,U_1292,U_1290,U_1288] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1288,U_1290,hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294)),U_1296))
        | ! [U_1281,U_1280] :
            ( hBOOL(hAPP(hAPP(c_member(U_1288),U_1281),U_1280))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1288,U_1288,U_1290,U_1281,U_1280),U_1296))
            | hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294) != hAPP(hAPP(c_Set_Oinsert(U_1288),U_1281),U_1280) ) )
    & ! [U_1295,U_1293,U_1291,U_1289,U_1287] :
        ( ? [U_1278] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),U_1278))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1287,U_1287,U_1289,sK25(U_1295,U_1293,U_1291,U_1289,U_1287),U_1278),U_1295))
            & hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293) = hAPP(hAPP(c_Set_Oinsert(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),U_1278) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1279,sK25(U_1295,U_1293,U_1291,U_1289,U_1287))],[f_286_3]) ).

fof(f_286_5,plain,
    ( ! [U_1296,U_1294,U_1292,U_1290,U_1288] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1288,U_1290,hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294)),U_1296))
        | ! [U_1281,U_1280] :
            ( hBOOL(hAPP(hAPP(c_member(U_1288),U_1281),U_1280))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1288,U_1288,U_1290,U_1281,U_1280),U_1296))
            | hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294) != hAPP(hAPP(c_Set_Oinsert(U_1288),U_1281),U_1280) ) )
    & ! [U_1295,U_1293,U_1291,U_1289,U_1287] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),sK26(U_1295,U_1293,U_1291,U_1289,U_1287)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1287,U_1287,U_1289,sK25(U_1295,U_1293,U_1291,U_1289,U_1287),sK26(U_1295,U_1293,U_1291,U_1289,U_1287)),U_1295))
          & hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293) = hAPP(hAPP(c_Set_Oinsert(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),sK26(U_1295,U_1293,U_1291,U_1289,U_1287)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1278,sK26(U_1295,U_1293,U_1291,U_1289,U_1287))],[f_286_4]) ).

cnf(f_286_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293) = hAPP(hAPP(c_Set_Oinsert(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),sK26(U_1295,U_1293,U_1291,U_1289,U_1287))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ),
    inference(clausify,[status(thm)],[f_286_5]) ).

cnf(f_286_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1287,U_1287,U_1289,sK25(U_1295,U_1293,U_1291,U_1289,U_1287),sK26(U_1295,U_1293,U_1291,U_1289,U_1287)),U_1295))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ),
    inference(clausify,[status(thm)],[f_286_5]) ).

cnf(f_286_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1287),sK25(U_1295,U_1293,U_1291,U_1289,U_1287)),sK26(U_1295,U_1293,U_1291,U_1289,U_1287)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1287,U_1289,hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),U_1293)),U_1295)) ),
    inference(clausify,[status(thm)],[f_286_5]) ).

cnf(f_286_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1288,U_1290,hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294)),U_1296))
    | hBOOL(hAPP(hAPP(c_member(U_1288),U_1281),U_1280))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1288,U_1288,U_1290,U_1281,U_1280),U_1296))
    | hAPP(hAPP(c_Set_Oinsert(U_1288),U_1292),U_1294) != hAPP(hAPP(c_Set_Oinsert(U_1288),U_1281),U_1280) ),
    inference(clausify,[status(thm)],[f_286_5]) ).

fof(f_287_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_287_2,plain,
    ! [U_1301,U_1300,U_1299,U_1298,U_1297] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1298,U_1297),U_1301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1297),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1298,U_1297),U_1301),U_1299)),hAPP(U_1301,U_1300))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1298),U_1300),U_1299))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),U_1299))
      | ~ class_Rings_Oring(U_1297) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1298,U_1297),U_1301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1297),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1298,U_1297),U_1301),U_1299)),hAPP(U_1301,U_1300))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1298),U_1300),U_1299))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1298),U_1299))
    | ~ class_Rings_Oring(U_1297) ),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_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_288_2,plain,
    ! [U_1306,U_1305,U_1304,U_1303,U_1302] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1303,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),U_1304)
          | hBOOL(hAPP(hAPP(c_member(U_1303),U_1305),U_1304)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1303,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1302),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),U_1304)),hAPP(U_1306,U_1305))
          | ~ hBOOL(hAPP(hAPP(c_member(U_1303),U_1305),U_1304)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),U_1304))
      | ~ class_Groups_Oab__group__add(U_1302) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1303,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1302),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),U_1304)),hAPP(U_1306,U_1305))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1303),U_1305),U_1304))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),U_1304))
    | ~ class_Groups_Oab__group__add(U_1302) ),
    inference(clausify,[status(thm)],[f_288_2]) ).

cnf(f_288_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1303,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1303),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1303,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1303,U_1302),U_1306),U_1304)
    | hBOOL(hAPP(hAPP(c_member(U_1303),U_1305),U_1304))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1303),U_1304))
    | ~ class_Groups_Oab__group__add(U_1302) ),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_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_289_2,plain,
    ! [U_1311,U_1310,U_1309,U_1308,U_1307] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1307,U_1307,c_Groups_Otimes__class_Otimes(U_1307),U_1311,hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1307,tc_HOL_Obool)),U_1309),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1311),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool)))))),U_1310))
      | hBOOL(hAPP(hAPP(c_member(U_1307),U_1308),U_1309))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1307),U_1311),U_1309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1307,U_1307,c_Groups_Otimes__class_Otimes(U_1307),U_1308,U_1309),U_1310))
      | ~ class_Groups_Oab__semigroup__mult(U_1307) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1307,U_1307,c_Groups_Otimes__class_Otimes(U_1307),U_1311,hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1307,tc_HOL_Obool)),U_1309),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1311),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool)))))),U_1310))
    | hBOOL(hAPP(hAPP(c_member(U_1307),U_1308),U_1309))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1307),U_1311),U_1309))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1307,U_1307,c_Groups_Otimes__class_Otimes(U_1307),U_1308,U_1309),U_1310))
    | ~ class_Groups_Oab__semigroup__mult(U_1307) ),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_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_290_2,plain,
    ! [U_1314,U_1313,U_1312] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1312,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1312,tc_HOL_Obool)),U_1313),U_1314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1312),c_Big__Operators_Olattice__class_OSup__fin(U_1312,U_1313)),c_Big__Operators_Olattice__class_OSup__fin(U_1312,U_1314))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1312,tc_HOL_Obool)),U_1313),U_1314) != c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
      | U_1314 = c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1312),U_1314))
      | U_1313 = c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1312),U_1313))
      | ~ class_Lattices_Olattice(U_1312) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

cnf(f_290_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1312,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1312,tc_HOL_Obool)),U_1313),U_1314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1312),c_Big__Operators_Olattice__class_OSup__fin(U_1312,U_1313)),c_Big__Operators_Olattice__class_OSup__fin(U_1312,U_1314))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1312,tc_HOL_Obool)),U_1313),U_1314) != c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
    | U_1314 = c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1312),U_1314))
    | U_1313 = c_Orderings_Obot__class_Obot(tc_fun(U_1312,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1312),U_1313))
    | ~ class_Lattices_Olattice(U_1312) ),
    inference(clausify,[status(thm)],[f_290_2]) ).

fof(f_291_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_291_2,plain,
    ! [U_1317,U_1316,U_1315] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1315),c_Big__Operators_Olattice__class_OSup__fin(U_1315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317))),c_Big__Operators_Olattice__class_OSup__fin(U_1315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1315),c_Big__Operators_Olattice__class_OSup__fin(U_1315,U_1316)),c_Big__Operators_Olattice__class_OSup__fin(U_1315,U_1317))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317) = c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1315),U_1317))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1315),U_1316))
      | ~ class_Lattices_Olattice(U_1315) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1315),c_Big__Operators_Olattice__class_OSup__fin(U_1315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317))),c_Big__Operators_Olattice__class_OSup__fin(U_1315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1315),c_Big__Operators_Olattice__class_OSup__fin(U_1315,U_1316)),c_Big__Operators_Olattice__class_OSup__fin(U_1315,U_1317))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1315,tc_HOL_Obool)),U_1316),U_1317) = c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1315),U_1317))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1315),U_1316))
    | ~ class_Lattices_Olattice(U_1315) ),
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_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_292_2,plain,
    ! [U_1325,U_1324,U_1323,U_1322,U_1321,U_1320,U_1319,U_1318] :
      ( hAPP(U_1323,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1319,tc_HOL_Obool)),U_1324),U_1325)) = hAPP(hAPP(U_1320,hAPP(U_1323,U_1324)),hAPP(U_1323,U_1325))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1325))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1324))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1318,U_1319,U_1320,U_1321,U_1322,U_1323) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_1325,U_1324,U_1323,U_1322,U_1321,U_1320,U_1319] :
      ( ! [U_1318] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1318,U_1319,U_1320,U_1321,U_1322,U_1323)
      | hAPP(U_1323,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1319,tc_HOL_Obool)),U_1324),U_1325)) = hAPP(hAPP(U_1320,hAPP(U_1323,U_1324)),hAPP(U_1323,U_1325))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1325))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1324)) ),
    inference(miniscope,[status(thm)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1318,U_1319,U_1320,U_1321,U_1322,U_1323)
    | hAPP(U_1323,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1319,tc_HOL_Obool)),U_1324),U_1325)) = hAPP(hAPP(U_1320,hAPP(U_1323,U_1324)),hAPP(U_1323,U_1325))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1325))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1319),U_1324)) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_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_293_2,plain,
    ! [U_1333,U_1332,U_1331,U_1330,U_1329,U_1328,U_1327,U_1326] :
      ( hAPP(hAPP(U_1328,hAPP(U_1331,U_1333)),hAPP(U_1331,U_1332)) = hAPP(U_1331,U_1332)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1327,tc_HOL_Obool)),U_1333),U_1332))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1327),U_1332))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1326,U_1327,U_1328,U_1329,U_1330,U_1331) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_1333,U_1332,U_1331,U_1330,U_1329,U_1328,U_1327] :
      ( ! [U_1326] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1326,U_1327,U_1328,U_1329,U_1330,U_1331)
      | hAPP(hAPP(U_1328,hAPP(U_1331,U_1333)),hAPP(U_1331,U_1332)) = hAPP(U_1331,U_1332)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1327,tc_HOL_Obool)),U_1333),U_1332))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1327),U_1332)) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1326,U_1327,U_1328,U_1329,U_1330,U_1331)
    | hAPP(hAPP(U_1328,hAPP(U_1331,U_1333)),hAPP(U_1331,U_1332)) = hAPP(U_1331,U_1332)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1327,tc_HOL_Obool)),U_1333),U_1332))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1327),U_1332)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_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_294_2,plain,
    ! [U_1336,U_1335,U_1334] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1334,hAPP(hAPP(c_Set_Oinsert(U_1334),U_1336),U_1335)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1334,U_1334,c_Lattices_Osemilattice__sup__class_Osup(U_1334)),U_1336),U_1335)
      | hBOOL(hAPP(hAPP(c_member(U_1334),U_1336),U_1335))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1334),U_1335))
      | ~ class_Lattices_Olattice(U_1334) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

cnf(f_294_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1334,hAPP(hAPP(c_Set_Oinsert(U_1334),U_1336),U_1335)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1334,U_1334,c_Lattices_Osemilattice__sup__class_Osup(U_1334)),U_1336),U_1335)
    | hBOOL(hAPP(hAPP(c_member(U_1334),U_1336),U_1335))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1334),U_1335))
    | ~ class_Lattices_Olattice(U_1334) ),
    inference(clausify,[status(thm)],[f_294_2]) ).

fof(f_295_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_295_2,plain,
    ! [U_1340,U_1339,U_1338,U_1337] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1340,tc_HOL_Obool)),U_1337),U_1339),U_1338))
      | ~ hBOOL(hAPP(U_1339,U_1338))
      | ~ hBOOL(hAPP(U_1337,U_1338)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

cnf(f_295_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1340,tc_HOL_Obool)),U_1337),U_1339),U_1338))
    | ~ hBOOL(hAPP(U_1339,U_1338))
    | ~ hBOOL(hAPP(U_1337,U_1338)) ),
    inference(clausify,[status(thm)],[f_295_2]) ).

fof(f_296_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_296_2,plain,
    ! [U_1344,U_1343,U_1342,U_1341] :
      ( ( hBOOL(hAPP(U_1343,U_1344))
        & hBOOL(hAPP(U_1342,U_1344)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343),U_1344)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1344,U_1343,U_1342] :
      ( ! [U_1341] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343),U_1344))
      | ( hBOOL(hAPP(U_1343,U_1344))
        & hBOOL(hAPP(U_1342,U_1344)) ) ),
    inference(miniscope,[status(thm)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( hBOOL(hAPP(U_1342,U_1344))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343),U_1344)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

cnf(f_296_5,plain,
    ( hBOOL(hAPP(U_1343,U_1344))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343),U_1344)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_IntI]) ).

fof(f_297_2,plain,
    ! [U_1348,U_1347,U_1346,U_1345] :
      ( hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1345,tc_HOL_Obool)),U_1347),U_1348)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),U_1348))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),U_1347)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1345,tc_HOL_Obool)),U_1347),U_1348)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),U_1348))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1345),U_1346),U_1347)) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_298_2,plain,
    ! [U_1352,U_1351,U_1350,U_1349] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1352))
        & hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1351)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1349,tc_HOL_Obool)),U_1351),U_1352))) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1351))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1349,tc_HOL_Obool)),U_1351),U_1352))) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),U_1352))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1349),U_1350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1349,tc_HOL_Obool)),U_1351),U_1352))) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_1,plain,
    ! [V_Ga_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_Ga_2)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).

fof(f_299_2,plain,
    ! [U_1355,U_1354,U_1353] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1353,tc_HOL_Obool)),U_1354),U_1355)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1355))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1354)) ) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

cnf(f_299_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1354))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1353,tc_HOL_Obool)),U_1354),U_1355))) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),U_1355))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_1353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1353,tc_HOL_Obool)),U_1354),U_1355))) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

fof(f_300_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_300_2,plain,
    ! [U_1357,U_1356] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1356),U_1357),U_1357) = U_1357
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_1356) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

cnf(f_300_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1356),U_1357),U_1357) = U_1357
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_1356) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

fof(f_301_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_301_2,plain,
    ! [U_1359,U_1358] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1358),U_1359),U_1359) = U_1359
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_1358) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

cnf(f_301_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1358),U_1359),U_1359) = U_1359
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_1358) ),
    inference(clausify,[status(thm)],[f_301_2]) ).

fof(f_302_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_302_2,plain,
    ! [U_1361,U_1360] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1360),U_1361),U_1361) = U_1361
      | ~ class_Lattices_Osemilattice__inf(U_1360) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

cnf(f_302_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1360),U_1361),U_1361) = U_1361
    | ~ class_Lattices_Osemilattice__inf(U_1360) ),
    inference(clausify,[status(thm)],[f_302_2]) ).

fof(f_303_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_303_2,plain,
    ! [U_1363,U_1362] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1362),U_1363),U_1363) = U_1363
      | ~ class_Lattices_Osemilattice__inf(U_1362) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

cnf(f_303_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1362),U_1363),U_1363) = U_1363
    | ~ class_Lattices_Osemilattice__inf(U_1362) ),
    inference(clausify,[status(thm)],[f_303_2]) ).

fof(f_304_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_304_2,plain,
    ! [U_1366,U_1365,U_1364] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),U_1365),U_1366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),U_1366),U_1365)
      | ~ class_Lattices_Osemilattice__inf(U_1364) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

cnf(f_304_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),U_1365),U_1366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1364),U_1366),U_1365)
    | ~ class_Lattices_Osemilattice__inf(U_1364) ),
    inference(clausify,[status(thm)],[f_304_2]) ).

fof(f_305_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_305_2,plain,
    ! [U_1369,U_1368,U_1367] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1367),U_1368),U_1369) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1367),U_1369),U_1368)
      | ~ class_Lattices_Olattice(U_1367) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1367),U_1368),U_1369) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1367),U_1369),U_1368)
    | ~ class_Lattices_Olattice(U_1367) ),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_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_306_2,plain,
    ! [U_1372,U_1371,U_1370] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1370),U_1371),U_1372) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1370),U_1372),U_1371)
      | ~ class_Lattices_Osemilattice__inf(U_1370) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

cnf(f_306_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1370),U_1371),U_1372) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1370),U_1372),U_1371)
    | ~ class_Lattices_Osemilattice__inf(U_1370) ),
    inference(clausify,[status(thm)],[f_306_2]) ).

fof(f_307_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_307_2,plain,
    ! [U_1375,U_1374,U_1373] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1375)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_1373) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1375)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_1373) ),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_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_308_2,plain,
    ! [U_1378,U_1377,U_1376] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),U_1378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),U_1378)
      | ~ class_Lattices_Osemilattice__inf(U_1376) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),U_1378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1376),U_1377),U_1378)
    | ~ class_Lattices_Osemilattice__inf(U_1376) ),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_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_309_2,plain,
    ! [U_1381,U_1380,U_1379] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),U_1381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),U_1381)
      | ~ class_Lattices_Olattice(U_1379) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),U_1381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1379),U_1380),U_1381)
    | ~ class_Lattices_Olattice(U_1379) ),
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_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_310_2,plain,
    ! [U_1384,U_1383,U_1382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),U_1384)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),U_1384)
      | ~ class_Lattices_Osemilattice__inf(U_1382) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

cnf(f_310_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),U_1384)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1382),U_1383),U_1384)
    | ~ class_Lattices_Osemilattice__inf(U_1382) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

fof(f_311_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_311_2,plain,
    ! [U_1388,U_1387,U_1386,U_1385] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1387),U_1388)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1387),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1386),U_1388))
      | ~ class_Lattices_Osemilattice__inf(U_1385) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

cnf(f_311_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1387),U_1388)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1387),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1385),U_1386),U_1388))
    | ~ class_Lattices_Osemilattice__inf(U_1385) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

fof(f_312_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_312_2,plain,
    ! [U_1392,U_1391,U_1390,U_1389] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1390),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1391),U_1392)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1391),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1390),U_1392))
      | ~ class_Lattices_Olattice(U_1389) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

cnf(f_312_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1390),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1391),U_1392)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1391),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1389),U_1390),U_1392))
    | ~ class_Lattices_Olattice(U_1389) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

fof(f_313_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_313_2,plain,
    ! [U_1396,U_1395,U_1394,U_1393] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1394),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1395),U_1396)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1395),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1394),U_1396))
      | ~ class_Lattices_Osemilattice__inf(U_1393) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1394),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1395),U_1396)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1395),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1393),U_1394),U_1396))
    | ~ class_Lattices_Osemilattice__inf(U_1393) ),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_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_314_2,plain,
    ! [U_1400,U_1399,U_1398,U_1397] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1398),U_1399)),U_1400) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1398),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1399),U_1400))
      | ~ class_Lattices_Osemilattice__inf(U_1397) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

cnf(f_314_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1398),U_1399)),U_1400) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1398),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1397),U_1399),U_1400))
    | ~ class_Lattices_Osemilattice__inf(U_1397) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_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_315_2,plain,
    ! [U_1404,U_1403,U_1402,U_1401] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1402),U_1403)),U_1404) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1402),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1403),U_1404))
      | ~ class_Lattices_Olattice(U_1401) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

cnf(f_315_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1402),U_1403)),U_1404) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1402),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1401),U_1403),U_1404))
    | ~ class_Lattices_Olattice(U_1401) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_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_316_2,plain,
    ! [U_1408,U_1407,U_1406,U_1405] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1406),U_1407)),U_1408) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1407),U_1408))
      | ~ class_Lattices_Osemilattice__inf(U_1405) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

cnf(f_316_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1406),U_1407)),U_1408) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1405),U_1407),U_1408))
    | ~ class_Lattices_Osemilattice__inf(U_1405) ),
    inference(clausify,[status(thm)],[f_316_2]) ).

fof(f_317_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_317_2,plain,
    ! [U_1413,U_1412,U_1411,U_1410,U_1409] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1410,U_1409)),U_1411),U_1412),U_1413) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1409),hAPP(U_1411,U_1413)),hAPP(U_1412,U_1413))
      | ~ class_Lattices_Olattice(U_1409) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1410,U_1409)),U_1411),U_1412),U_1413) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1409),hAPP(U_1411,U_1413)),hAPP(U_1412,U_1413))
    | ~ class_Lattices_Olattice(U_1409) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_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_318_2,plain,
    ! [U_1417,U_1416,U_1415,U_1414] :
      ( hBOOL(hAPP(U_1415,U_1417))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1414,tc_HOL_Obool)),U_1415),U_1416),U_1417)) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_1417,U_1416,U_1415] :
      ( ! [U_1414] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1414,tc_HOL_Obool)),U_1415),U_1416),U_1417))
      | hBOOL(hAPP(U_1415,U_1417)) ),
    inference(miniscope,[status(thm)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1414,tc_HOL_Obool)),U_1415),U_1416),U_1417))
    | hBOOL(hAPP(U_1415,U_1417)) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_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_319_2,plain,
    ! [U_1421,U_1420,U_1419,U_1418] :
      ( hBOOL(hAPP(U_1420,U_1421))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1418,tc_HOL_Obool)),U_1419),U_1420),U_1421)) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_1421,U_1420] :
      ( ! [U_1419,U_1418] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1418,tc_HOL_Obool)),U_1419),U_1420),U_1421))
      | hBOOL(hAPP(U_1420,U_1421)) ),
    inference(miniscope,[status(thm)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1418,tc_HOL_Obool)),U_1419),U_1420),U_1421))
    | hBOOL(hAPP(U_1420,U_1421)) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_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_320_2,plain,
    ! [U_1423,U_1422] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1422,tc_HOL_Obool)),U_1423),U_1423) = U_1423,
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1422,tc_HOL_Obool)),U_1423),U_1423) = U_1423,
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_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_321_2,plain,
    ! [U_1426,U_1425,U_1424] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1424,tc_HOL_Obool)),U_1425),U_1426) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1424,tc_HOL_Obool)),U_1426),U_1425),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1424,tc_HOL_Obool)),U_1425),U_1426) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1424,tc_HOL_Obool)),U_1426),U_1425),
    inference(clausify,[status(thm)],[f_321_2]) ).

fof(f_322_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_322_2,plain,
    ! [U_1429,U_1428,U_1427] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),U_1429)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),U_1429),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),U_1429)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1427,tc_HOL_Obool)),U_1428),U_1429),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_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_323_2,plain,
    ! [U_1433,U_1432,U_1431,U_1430] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1431),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1432),U_1433)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1431),U_1433)),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1431),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1432),U_1433)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1430,tc_HOL_Obool)),U_1431),U_1433)),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_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_324_2,plain,
    ! [U_1437,U_1436,U_1435,U_1434] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1435),U_1436)),U_1437) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1436),U_1437)),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1435),U_1436)),U_1437) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1434,tc_HOL_Obool)),U_1436),U_1437)),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_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_325_2,plain,
    ! [U_1439,U_1438] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1438),U_1439),U_1439) = U_1439
      | ~ class_Lattices_Olattice(U_1438) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

cnf(f_325_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1438),U_1439),U_1439) = U_1439
    | ~ class_Lattices_Olattice(U_1438) ),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_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_326_2,plain,
    ! [U_1443,U_1442,U_1441,U_1440] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),U_1442)),U_1443) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1442),U_1443))
      | ~ class_Groups_Oab__semigroup__mult(U_1440) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),U_1442)),U_1443) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1442),U_1443))
    | ~ class_Groups_Oab__semigroup__mult(U_1440) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_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_327_2,plain,
    ! [U_1450,U_1449,U_1448,U_1447,U_1446,U_1445,U_1444] :
      ( hAPP(hAPP(U_1446,U_1450),U_1450) = U_1450
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1444,U_1445,U_1446,U_1447,U_1448,U_1449) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ! [U_1450,U_1449,U_1448,U_1447,U_1446] :
      ( ! [U_1445,U_1444] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1444,U_1445,U_1446,U_1447,U_1448,U_1449)
      | hAPP(hAPP(U_1446,U_1450),U_1450) = U_1450 ),
    inference(miniscope,[status(thm)],[f_327_2]) ).

cnf(f_327_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1444,U_1445,U_1446,U_1447,U_1448,U_1449)
    | hAPP(hAPP(U_1446,U_1450),U_1450) = U_1450 ),
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_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_328_2,plain,
    ! [U_1454,U_1453,U_1452,U_1451] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1451,U_1451,c_Lattices_Osemilattice__inf__class_Oinf(U_1451)),U_1453),hAPP(hAPP(c_Set_Oinsert(U_1451),U_1454),U_1452)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1454),hAPP(hAPP(c_Finite__Set_Ofold(U_1451,U_1451,c_Lattices_Osemilattice__inf__class_Oinf(U_1451)),U_1453),U_1452))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1451),U_1452))
      | ~ class_Lattices_Osemilattice__inf(U_1451) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1451,U_1451,c_Lattices_Osemilattice__inf__class_Oinf(U_1451)),U_1453),hAPP(hAPP(c_Set_Oinsert(U_1451),U_1454),U_1452)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1451),U_1454),hAPP(hAPP(c_Finite__Set_Ofold(U_1451,U_1451,c_Lattices_Osemilattice__inf__class_Oinf(U_1451)),U_1453),U_1452))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1451),U_1452))
    | ~ class_Lattices_Osemilattice__inf(U_1451) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_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_329_2,plain,
    ! [U_1458,U_1457,U_1456,U_1455] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),U_1458))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),U_1457)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1455),U_1457),U_1458)))
      | ~ class_Lattices_Osemilattice__inf(U_1455) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),U_1457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1455),U_1457),U_1458)))
    | ~ class_Lattices_Osemilattice__inf(U_1455) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),U_1458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1455),U_1456),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1455),U_1457),U_1458)))
    | ~ class_Lattices_Osemilattice__inf(U_1455) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_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_330_2,plain,
    ! [U_1463,U_1462,U_1461,U_1460,U_1459] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1459),U_1460),U_1462)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1459),U_1461),U_1463)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),U_1462),U_1463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),U_1460),U_1461))
      | ~ class_Lattices_Osemilattice__inf(U_1459) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1459),U_1460),U_1462)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1459),U_1461),U_1463)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),U_1462),U_1463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1459),U_1460),U_1461))
    | ~ class_Lattices_Osemilattice__inf(U_1459) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_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_331_2,plain,
    ! [U_1467,U_1466,U_1465,U_1464] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1464),U_1466),U_1467)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),U_1467))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),U_1466))
      | ~ class_Lattices_Osemilattice__inf(U_1464) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1464),U_1466),U_1467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),U_1467))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1464),U_1465),U_1466))
    | ~ class_Lattices_Osemilattice__inf(U_1464) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_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_332_2,plain,
    ! [U_1471,U_1470,U_1469,U_1468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1468),U_1470),U_1471)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),U_1471))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),U_1470))
      | ~ class_Lattices_Osemilattice__inf(U_1468) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1468),U_1470),U_1471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),U_1471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1468),U_1469),U_1470))
    | ~ class_Lattices_Osemilattice__inf(U_1468) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_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_333_2,plain,
    ! [U_1474,U_1473,U_1472] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1472),U_1474),U_1473) = U_1473
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1472),U_1473),U_1474))
      | ~ class_Lattices_Osemilattice__inf(U_1472) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1472),U_1474),U_1473) = U_1473
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1472),U_1473),U_1474))
    | ~ class_Lattices_Osemilattice__inf(U_1472) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_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_334_2,plain,
    ! [U_1477,U_1476,U_1475] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1475),U_1476),U_1477) = U_1476
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
      | ~ class_Lattices_Osemilattice__inf(U_1475) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

cnf(f_334_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1475),U_1476),U_1477) = U_1476
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
    | ~ class_Lattices_Osemilattice__inf(U_1475) ),
    inference(clausify,[status(thm)],[f_334_2]) ).

fof(f_335_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_335_2,plain,
    ! [U_1481,U_1480,U_1479,U_1478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1478),U_1481),U_1479)),U_1480))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1480))
      | ~ class_Lattices_Osemilattice__inf(U_1478) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1478),U_1481),U_1479)),U_1480))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1480))
    | ~ class_Lattices_Osemilattice__inf(U_1478) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_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_336_2,plain,
    ! [U_1485,U_1484,U_1483,U_1482] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1482),U_1483),U_1485)),U_1484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),U_1484))
      | ~ class_Lattices_Osemilattice__inf(U_1482) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1482),U_1483),U_1485)),U_1484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),U_1484))
    | ~ class_Lattices_Osemilattice__inf(U_1482) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_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_337_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_Lattices_Osemilattice__inf__class_Oinf(U_1486),U_1488),U_1489)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1489))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1489))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1486),U_1488),U_1489))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_1486) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1486),U_1488),U_1489)))
    | ~ class_Lattices_Osemilattice__inf(U_1486) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1489))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1486),U_1488),U_1489)))
    | ~ class_Lattices_Osemilattice__inf(U_1486) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

cnf(f_337_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1486),U_1488),U_1489)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1489))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488))
    | ~ class_Lattices_Osemilattice__inf(U_1486) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_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_338_2,plain,
    ! [U_1492,U_1491,U_1490] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1490),U_1491),U_1492) != U_1491 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1490),U_1491),U_1492) = U_1491
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_1490) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1490),U_1491),U_1492) = U_1491
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
    | ~ class_Lattices_Osemilattice__inf(U_1490) ),
    inference(clausify,[status(thm)],[f_338_2]) ).

cnf(f_338_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1490),U_1491),U_1492) != U_1491
    | ~ class_Lattices_Osemilattice__inf(U_1490) ),
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_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_339_2,plain,
    ! [U_1495,U_1494,U_1493] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1493),U_1494),U_1495)),U_1495))
      | ~ class_Lattices_Osemilattice__inf(U_1493) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1493),U_1494),U_1495)),U_1495))
    | ~ class_Lattices_Osemilattice__inf(U_1493) ),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_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_340_2,plain,
    ! [U_1498,U_1497,U_1496] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1496),U_1497),U_1498)),U_1498))
      | ~ class_Lattices_Olattice(U_1496) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1496),U_1497),U_1498)),U_1498))
    | ~ class_Lattices_Olattice(U_1496) ),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_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_341_2,plain,
    ! [U_1501,U_1500,U_1499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1499),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1499),U_1500),U_1501)),U_1500))
      | ~ class_Lattices_Osemilattice__inf(U_1499) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1499),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1499),U_1500),U_1501)),U_1500))
    | ~ class_Lattices_Osemilattice__inf(U_1499) ),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_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_342_2,plain,
    ! [U_1504,U_1503,U_1502] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1502),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1502),U_1503),U_1504)),U_1503))
      | ~ class_Lattices_Olattice(U_1502) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1502),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1502),U_1503),U_1504)),U_1503))
    | ~ class_Lattices_Olattice(U_1502) ),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_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_343_2,plain,
    ! [U_1508,U_1507,U_1506,U_1505] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1505),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1505),U_1506),U_1508)),U_1507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1505),U_1506),U_1507))
      | ~ class_Lattices_Osemilattice__inf(U_1505) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1505),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1505),U_1506),U_1508)),U_1507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1505),U_1506),U_1507))
    | ~ class_Lattices_Osemilattice__inf(U_1505) ),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_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_344_2,plain,
    ! [U_1512,U_1511,U_1510,U_1509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1509),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1509),U_1512),U_1510)),U_1511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1509),U_1510),U_1511))
      | ~ class_Lattices_Osemilattice__inf(U_1509) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1509),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1509),U_1512),U_1510)),U_1511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1509),U_1510),U_1511))
    | ~ class_Lattices_Osemilattice__inf(U_1509) ),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_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_345_2,plain,
    ! [U_1514,U_1513] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1513),c_Orderings_Obot__class_Obot(U_1513)),U_1514) = c_Orderings_Obot__class_Obot(U_1513)
      | ~ class_Lattices_Obounded__lattice__bot(U_1513) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1513),c_Orderings_Obot__class_Obot(U_1513)),U_1514) = c_Orderings_Obot__class_Obot(U_1513)
    | ~ class_Lattices_Obounded__lattice__bot(U_1513) ),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_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_346_2,plain,
    ! [U_1516,U_1515] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1515),U_1516),c_Orderings_Obot__class_Obot(U_1515)) = c_Orderings_Obot__class_Obot(U_1515)
      | ~ class_Lattices_Obounded__lattice__bot(U_1515) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1515),U_1516),c_Orderings_Obot__class_Obot(U_1515)) = c_Orderings_Obot__class_Obot(U_1515)
    | ~ class_Lattices_Obounded__lattice__bot(U_1515) ),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_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_347_2,plain,
    ! [U_1520,U_1519,U_1518,U_1517] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1517),U_1518),U_1519)),U_1520) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1518),U_1520)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1519),U_1520))
      | ~ class_Lattices_Odistrib__lattice(U_1517) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1517),U_1518),U_1519)),U_1520) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1518),U_1520)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1517),U_1519),U_1520))
    | ~ class_Lattices_Odistrib__lattice(U_1517) ),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_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_348_2,plain,
    ! [U_1524,U_1523,U_1522,U_1521] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1521),U_1522),U_1523)),U_1524) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),U_1522),U_1524)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),U_1523),U_1524))
      | ~ class_Lattices_Odistrib__lattice(U_1521) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

cnf(f_348_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1521),U_1522),U_1523)),U_1524) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),U_1522),U_1524)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1521),U_1523),U_1524))
    | ~ class_Lattices_Odistrib__lattice(U_1521) ),
    inference(clausify,[status(thm)],[f_348_2]) ).

fof(f_349_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_349_2,plain,
    ! [U_1528,U_1527,U_1526,U_1525] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1525),U_1527),U_1528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1525),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),U_1527)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),U_1528))
      | ~ class_Lattices_Odistrib__lattice(U_1525) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1525),U_1527),U_1528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1525),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),U_1527)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1525),U_1526),U_1528))
    | ~ class_Lattices_Odistrib__lattice(U_1525) ),
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_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_350_2,plain,
    ! [U_1532,U_1531,U_1530,U_1529] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1529),U_1531),U_1532)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),U_1531)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),U_1532))
      | ~ class_Lattices_Odistrib__lattice(U_1529) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

cnf(f_350_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1529),U_1531),U_1532)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),U_1531)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1529),U_1530),U_1532))
    | ~ class_Lattices_Odistrib__lattice(U_1529) ),
    inference(clausify,[status(thm)],[f_350_2]) ).

fof(f_351_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_351_2,plain,
    ! [U_1535,U_1534,U_1533] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1533),U_1534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1533),U_1534),U_1535)) = U_1534
      | ~ class_Lattices_Olattice(U_1533) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1533),U_1534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1533),U_1534),U_1535)) = U_1534
    | ~ class_Lattices_Olattice(U_1533) ),
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_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_352_2,plain,
    ! [U_1538,U_1537,U_1536] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1536),U_1537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1536),U_1537),U_1538)) = U_1537
      | ~ class_Lattices_Olattice(U_1536) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1536),U_1537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1536),U_1537),U_1538)) = U_1537
    | ~ class_Lattices_Olattice(U_1536) ),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_353_2,plain,
    ! [U_1542,U_1541,U_1540,U_1539] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1539,tc_HOL_Obool)),U_1541),U_1542)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),U_1542))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),U_1541)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),U_1542))
          & hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),U_1541)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1539),U_1540),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1539,tc_HOL_Obool)),U_1541),U_1542))) ) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ( ! [U_1550,U_1548,U_1546,U_1544] :
        ( hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1544,tc_HOL_Obool)),U_1548),U_1550)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),U_1550))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),U_1548)) )
    & ! [U_1549,U_1547,U_1545,U_1543] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),U_1549))
          & hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),U_1547)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1543,tc_HOL_Obool)),U_1547),U_1549))) ) ),
    inference(miniscope,[status(thm)],[f_353_2]) ).

cnf(f_353_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),U_1547))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1543,tc_HOL_Obool)),U_1547),U_1549))) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),U_1549))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1543),U_1545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1543,tc_HOL_Obool)),U_1547),U_1549))) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1544,tc_HOL_Obool)),U_1548),U_1550)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),U_1550))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1544),U_1546),U_1548)) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_354_2,plain,
    ! [U_1554,U_1553,U_1552,U_1551] :
      ( hBOOL(hAPP(hAPP(c_member(U_1551),U_1552),U_1553))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1551,tc_HOL_Obool)),U_1553),U_1554))) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1551),U_1552),U_1553))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1551),U_1552),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1551,tc_HOL_Obool)),U_1553),U_1554))) ),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_355_2,plain,
    ! [U_1558,U_1557,U_1556,U_1555] :
      ( hBOOL(hAPP(hAPP(c_member(U_1555),U_1556),U_1558))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1555),U_1556),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1555,tc_HOL_Obool)),U_1557),U_1558))) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

cnf(f_355_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1555),U_1556),U_1558))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1555),U_1556),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1555,tc_HOL_Obool)),U_1557),U_1558))) ),
    inference(clausify,[status(thm)],[f_355_2]) ).

fof(f_356_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_356_2,plain,
    ! [U_1562,U_1561,U_1560,U_1559] : hAPP(hAPP(c_Finite__Set_Ofold(U_1559,U_1560,U_1561),U_1562),c_Orderings_Obot__class_Obot(tc_fun(U_1559,tc_HOL_Obool))) = U_1562,
    inference(variable_rename,[status(thm)],[f_356_1]) ).

cnf(f_356_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_1559,U_1560,U_1561),U_1562),c_Orderings_Obot__class_Obot(tc_fun(U_1559,tc_HOL_Obool))) = U_1562,
    inference(clausify,[status(thm)],[f_356_2]) ).

fof(f_357_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_357_2,plain,
    ! [U_1564,U_1563] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1563,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1563,tc_HOL_Obool))),U_1564) = c_Orderings_Obot__class_Obot(tc_fun(U_1563,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1563,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1563,tc_HOL_Obool))),U_1564) = c_Orderings_Obot__class_Obot(tc_fun(U_1563,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_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_358_2,plain,
    ! [U_1566,U_1565] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1565,tc_HOL_Obool)),U_1566),c_Orderings_Obot__class_Obot(tc_fun(U_1565,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1565,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

cnf(f_358_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1565,tc_HOL_Obool)),U_1566),c_Orderings_Obot__class_Obot(tc_fun(U_1565,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1565,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_358_2]) ).

fof(f_359_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_359_2,plain,
    ! [U_1573,U_1572,U_1571] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1571,tc_HOL_Obool)),U_1572),U_1573) = c_Orderings_Obot__class_Obot(tc_fun(U_1571,tc_HOL_Obool))
        | ? [U_1570] :
            ( ? [U_1569] :
                ( U_1570 = U_1569
                & hBOOL(hAPP(hAPP(c_member(U_1571),U_1569),U_1573)) )
            & hBOOL(hAPP(hAPP(c_member(U_1571),U_1570),U_1572)) ) )
      & ( ! [U_1568] :
            ( ! [U_1567] :
                ( U_1568 != U_1567
                | ~ hBOOL(hAPP(hAPP(c_member(U_1571),U_1567),U_1573)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1571),U_1568),U_1572)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1571,tc_HOL_Obool)),U_1572),U_1573) != c_Orderings_Obot__class_Obot(tc_fun(U_1571,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1579,U_1577,U_1575] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))
        | ? [U_1570] :
            ( ? [U_1569] :
                ( U_1570 = U_1569
                & hBOOL(hAPP(hAPP(c_member(U_1575),U_1569),U_1579)) )
            & hBOOL(hAPP(hAPP(c_member(U_1575),U_1570),U_1577)) ) )
    & ! [U_1578,U_1576,U_1574] :
        ( ! [U_1568] :
            ( ! [U_1567] :
                ( U_1568 != U_1567
                | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1567),U_1578)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1568),U_1576)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1578) != c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_1579,U_1577,U_1575] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))
        | ( ? [U_1569] :
              ( sK27(U_1579,U_1577,U_1575) = U_1569
              & hBOOL(hAPP(hAPP(c_member(U_1575),U_1569),U_1579)) )
          & hBOOL(hAPP(hAPP(c_member(U_1575),sK27(U_1579,U_1577,U_1575)),U_1577)) ) )
    & ! [U_1578,U_1576,U_1574] :
        ( ! [U_1568] :
            ( ! [U_1567] :
                ( U_1568 != U_1567
                | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1567),U_1578)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1568),U_1576)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1578) != c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1570,sK27(U_1579,U_1577,U_1575))],[f_359_3]) ).

fof(f_359_5,plain,
    ( ! [U_1579,U_1577,U_1575] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))
        | ( sK27(U_1579,U_1577,U_1575) = sK28(U_1579,U_1577,U_1575)
          & hBOOL(hAPP(hAPP(c_member(U_1575),sK28(U_1579,U_1577,U_1575)),U_1579))
          & hBOOL(hAPP(hAPP(c_member(U_1575),sK27(U_1579,U_1577,U_1575)),U_1577)) ) )
    & ! [U_1578,U_1576,U_1574] :
        ( ! [U_1568] :
            ( ! [U_1567] :
                ( U_1568 != U_1567
                | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1567),U_1578)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1568),U_1576)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1578) != c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1569,sK28(U_1579,U_1577,U_1575))],[f_359_4]) ).

cnf(f_359_6,plain,
    ( U_1568 != U_1567
    | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1567),U_1578))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1568),U_1576))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1578) != c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_359_5]) ).

cnf(f_359_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1575),sK27(U_1579,U_1577,U_1575)),U_1577))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_359_5]) ).

cnf(f_359_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1575),sK28(U_1579,U_1577,U_1575)),U_1579))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_359_5]) ).

cnf(f_359_9,plain,
    ( sK27(U_1579,U_1577,U_1575) = sK28(U_1579,U_1577,U_1575)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1579) = c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_359_5]) ).

fof(f_360_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_360_2,plain,
    ! [U_1583,U_1582,U_1581,U_1580] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1580,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),U_1582)),hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),U_1583)) = hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1580,tc_HOL_Obool)),U_1582),U_1583)),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1580,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),U_1582)),hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),U_1583)) = hAPP(hAPP(c_Set_Oinsert(U_1580),U_1581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1580,tc_HOL_Obool)),U_1582),U_1583)),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_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_361_2,plain,
    ! [U_1586,U_1585,U_1584] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1584,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1584,tc_HOL_Obool)),U_1585),U_1586)),U_1585)),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1584,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1584,tc_HOL_Obool)),U_1585),U_1586)),U_1585)),
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_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_362_2,plain,
    ! [U_1589,U_1588,U_1587] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1587,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1587,tc_HOL_Obool)),U_1588),U_1589)),U_1589)),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1587,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1587,tc_HOL_Obool)),U_1588),U_1589)),U_1589)),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_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_363_2,plain,
    ! [U_1592,U_1591,U_1590] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1590,tc_HOL_Obool)),U_1591),U_1592) = U_1591
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1590,tc_HOL_Obool)),U_1591),U_1592)) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

cnf(f_363_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1590,tc_HOL_Obool)),U_1591),U_1592) = U_1591
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1590,tc_HOL_Obool)),U_1591),U_1592)) ),
    inference(clausify,[status(thm)],[f_363_2]) ).

fof(f_364_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_364_2,plain,
    ! [U_1595,U_1594,U_1593] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1593,tc_HOL_Obool)),U_1595),U_1594) = U_1594
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1593,tc_HOL_Obool)),U_1594),U_1595)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1593,tc_HOL_Obool)),U_1595),U_1594) = U_1594
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1593,tc_HOL_Obool)),U_1594),U_1595)) ),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_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_365_2,plain,
    ! [U_1599,U_1598,U_1597,U_1596] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1596,tc_HOL_Obool)),U_1598),U_1599)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),U_1599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),U_1598)) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

cnf(f_365_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1596,tc_HOL_Obool)),U_1598),U_1599)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),U_1599))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1596,tc_HOL_Obool)),U_1597),U_1598)) ),
    inference(clausify,[status(thm)],[f_365_2]) ).

fof(f_366_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_366_2,plain,
    ! [U_1604,U_1603,U_1602,U_1601,U_1600] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),U_1601),U_1603)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),U_1602),U_1604)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),U_1603),U_1604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),U_1601),U_1602)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),U_1601),U_1603)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),U_1602),U_1604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),U_1603),U_1604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1600,tc_HOL_Obool)),U_1601),U_1602)) ),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_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_367_2,plain,
    ! [U_1608,U_1607,U_1606,U_1605] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),U_1607),U_1608)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),U_1607)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),U_1608)),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),U_1607),U_1608)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1605,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),U_1607)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1605,tc_HOL_Obool)),U_1606),U_1608)),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_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_368_2,plain,
    ! [U_1612,U_1611,U_1610,U_1609] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1609,tc_HOL_Obool)),U_1611),U_1612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1609,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),U_1611)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),U_1612)),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1609,tc_HOL_Obool)),U_1611),U_1612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1609,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),U_1611)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1609,tc_HOL_Obool)),U_1610),U_1612)),
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_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_369_2,plain,
    ! [U_1616,U_1615,U_1614,U_1613] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1613,tc_HOL_Obool)),U_1614),U_1615)),U_1616) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1613,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),U_1614),U_1616)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),U_1615),U_1616)),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1613,tc_HOL_Obool)),U_1614),U_1615)),U_1616) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1613,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),U_1614),U_1616)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1613,tc_HOL_Obool)),U_1615),U_1616)),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_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_370_2,plain,
    ! [U_1620,U_1619,U_1618,U_1617] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1617,tc_HOL_Obool)),U_1618),U_1619)),U_1620) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1617,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),U_1618),U_1620)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),U_1619),U_1620)),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1617,tc_HOL_Obool)),U_1618),U_1619)),U_1620) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1617,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),U_1618),U_1620)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1617,tc_HOL_Obool)),U_1619),U_1620)),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_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_371_2,plain,
    ! [U_1624,U_1623,U_1622,U_1621] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1622),U_1623)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1623),U_1624))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1624),U_1622)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1622),U_1623)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1623),U_1624))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1624),U_1622)),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1622),U_1623)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1623),U_1624))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),U_1624),U_1622)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1621,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1622),U_1623)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1623),U_1624))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1621,tc_HOL_Obool)),U_1624),U_1622)),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_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_372_2,plain,
    ! [U_1628,U_1627,U_1626,U_1625] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1625,tc_HOL_Obool)),U_1627),U_1628)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1625,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),U_1627)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),U_1628)),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1625,tc_HOL_Obool)),U_1627),U_1628)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1625,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),U_1627)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1625,tc_HOL_Obool)),U_1626),U_1628)),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_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_373_2,plain,
    ! [U_1632,U_1631,U_1630,U_1629] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1629,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1629,tc_HOL_Obool)),U_1630),U_1631)),U_1632) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1629,tc_HOL_Obool)),U_1630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1629,tc_HOL_Obool)),U_1631),U_1632)),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

cnf(f_373_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1629,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1629,tc_HOL_Obool)),U_1630),U_1631)),U_1632) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1629,tc_HOL_Obool)),U_1630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1629,tc_HOL_Obool)),U_1631),U_1632)),
    inference(clausify,[status(thm)],[f_373_2]) ).

fof(f_374_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_374_2,plain,
    ! [U_1636,U_1635,U_1634,U_1633] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1633,tc_HOL_Obool)),U_1634),U_1635)),U_1636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1633,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),U_1634),U_1636)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),U_1635),U_1636)),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

cnf(f_374_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1633,tc_HOL_Obool)),U_1634),U_1635)),U_1636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1633,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),U_1634),U_1636)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1633,tc_HOL_Obool)),U_1635),U_1636)),
    inference(clausify,[status(thm)],[f_374_2]) ).

fof(f_375_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_375_2,plain,
    ! [U_1640,U_1639,U_1638,U_1637] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1637,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1638),U_1639)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1640),U_1639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1637,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1638),U_1639)),U_1640),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

cnf(f_375_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1637,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1638),U_1639)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1640),U_1639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1637,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1637,tc_HOL_Obool)),U_1638),U_1639)),U_1640),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_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_376_2,plain,
    ! [U_1644,U_1643,U_1642,U_1641] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1641),hAPP(hAPP(c_Finite__Set_Ofold(U_1641,U_1641,c_Lattices_Osemilattice__inf__class_Oinf(U_1641)),U_1644),U_1642)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1641),U_1643),U_1644)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1641),U_1643),U_1642))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1641),U_1642))
      | ~ class_Lattices_Osemilattice__inf(U_1641) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

cnf(f_376_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1641),hAPP(hAPP(c_Finite__Set_Ofold(U_1641,U_1641,c_Lattices_Osemilattice__inf__class_Oinf(U_1641)),U_1644),U_1642)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1641),U_1643),U_1644)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1641),U_1643),U_1642))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1641),U_1642))
    | ~ class_Lattices_Osemilattice__inf(U_1641) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

fof(f_377_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_377_2,plain,
    ! [U_1648,U_1647,U_1646,U_1645] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1645),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1645),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),U_1647)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),U_1648))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1645),U_1647),U_1648))))
      | ~ class_Lattices_Olattice(U_1645) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1645),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1645),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),U_1647)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),U_1648))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1645),U_1646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1645),U_1647),U_1648))))
    | ~ class_Lattices_Olattice(U_1645) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_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_378_2,plain,
    ! [U_1652,U_1651,U_1650,U_1649] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1649),U_1651),U_1652))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),U_1651)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),U_1652))))
      | ~ class_Lattices_Olattice(U_1649) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1649),U_1651),U_1652))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),U_1651)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1649),U_1650),U_1652))))
    | ~ class_Lattices_Olattice(U_1649) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_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_379_2,plain,
    ! [U_1656,U_1655,U_1654,U_1653] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1653,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1653),U_1654),U_1656)),U_1655) = hAPP(hAPP(c_Set_Oinsert(U_1653),U_1654),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1653,tc_HOL_Obool)),U_1656),U_1655))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1653),U_1654),U_1655)) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1653,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1653),U_1654),U_1656)),U_1655) = hAPP(hAPP(c_Set_Oinsert(U_1653),U_1654),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1653,tc_HOL_Obool)),U_1656),U_1655))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1653),U_1654),U_1655)) ),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_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_380_2,plain,
    ! [U_1660,U_1659,U_1658,U_1657] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1657,tc_HOL_Obool)),U_1659),hAPP(hAPP(c_Set_Oinsert(U_1657),U_1658),U_1660)) = hAPP(hAPP(c_Set_Oinsert(U_1657),U_1658),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1657,tc_HOL_Obool)),U_1659),U_1660))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1657),U_1658),U_1659)) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1657,tc_HOL_Obool)),U_1659),hAPP(hAPP(c_Set_Oinsert(U_1657),U_1658),U_1660)) = hAPP(hAPP(c_Set_Oinsert(U_1657),U_1658),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1657,tc_HOL_Obool)),U_1659),U_1660))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1657),U_1658),U_1659)) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_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_381_2,plain,
    ! [U_1664,U_1663,U_1662,U_1661] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1661,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1661),U_1662),U_1664)),U_1663) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1661,tc_HOL_Obool)),U_1664),U_1663)
      | hBOOL(hAPP(hAPP(c_member(U_1661),U_1662),U_1663)) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1661,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1661),U_1662),U_1664)),U_1663) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1661,tc_HOL_Obool)),U_1664),U_1663)
    | hBOOL(hAPP(hAPP(c_member(U_1661),U_1662),U_1663)) ),
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_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_382_2,plain,
    ! [U_1668,U_1667,U_1666,U_1665] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1665,tc_HOL_Obool)),U_1667),hAPP(hAPP(c_Set_Oinsert(U_1665),U_1666),U_1668)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1665,tc_HOL_Obool)),U_1667),U_1668)
      | hBOOL(hAPP(hAPP(c_member(U_1665),U_1666),U_1667)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1665,tc_HOL_Obool)),U_1667),hAPP(hAPP(c_Set_Oinsert(U_1665),U_1666),U_1668)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1665,tc_HOL_Obool)),U_1667),U_1668)
    | hBOOL(hAPP(hAPP(c_member(U_1665),U_1666),U_1667)) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_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_383_2,plain,
    ! [U_1672,U_1671,U_1670,U_1669] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1669,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1669),U_1670),U_1672)),U_1671) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1669,tc_HOL_Obool)),U_1672),U_1671)
        | hBOOL(hAPP(hAPP(c_member(U_1669),U_1670),U_1671)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1669,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1669),U_1670),U_1672)),U_1671) = hAPP(hAPP(c_Set_Oinsert(U_1669),U_1670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1669,tc_HOL_Obool)),U_1672),U_1671))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1669),U_1670),U_1671)) ) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ( ! [U_1680,U_1678,U_1676,U_1674] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1674,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1674),U_1676),U_1680)),U_1678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1674,tc_HOL_Obool)),U_1680),U_1678)
        | hBOOL(hAPP(hAPP(c_member(U_1674),U_1676),U_1678)) )
    & ! [U_1679,U_1677,U_1675,U_1673] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1673,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1673),U_1675),U_1679)),U_1677) = hAPP(hAPP(c_Set_Oinsert(U_1673),U_1675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1673,tc_HOL_Obool)),U_1679),U_1677))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1673),U_1675),U_1677)) ) ),
    inference(miniscope,[status(thm)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1673,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1673),U_1675),U_1679)),U_1677) = hAPP(hAPP(c_Set_Oinsert(U_1673),U_1675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1673,tc_HOL_Obool)),U_1679),U_1677))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1673),U_1675),U_1677)) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

cnf(f_383_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1674,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1674),U_1676),U_1680)),U_1678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1674,tc_HOL_Obool)),U_1680),U_1678)
    | hBOOL(hAPP(hAPP(c_member(U_1674),U_1676),U_1678)) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_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_384_2,plain,
    ! [U_1684,U_1683,U_1682,U_1681] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1681,tc_HOL_Obool)),U_1683),hAPP(hAPP(c_Set_Oinsert(U_1681),U_1682),U_1684)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1681,tc_HOL_Obool)),U_1683),U_1684)
        | hBOOL(hAPP(hAPP(c_member(U_1681),U_1682),U_1683)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1681,tc_HOL_Obool)),U_1683),hAPP(hAPP(c_Set_Oinsert(U_1681),U_1682),U_1684)) = hAPP(hAPP(c_Set_Oinsert(U_1681),U_1682),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1681,tc_HOL_Obool)),U_1683),U_1684))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1681),U_1682),U_1683)) ) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ( ! [U_1692,U_1690,U_1688,U_1686] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1686,tc_HOL_Obool)),U_1690),hAPP(hAPP(c_Set_Oinsert(U_1686),U_1688),U_1692)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1686,tc_HOL_Obool)),U_1690),U_1692)
        | hBOOL(hAPP(hAPP(c_member(U_1686),U_1688),U_1690)) )
    & ! [U_1691,U_1689,U_1687,U_1685] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1685,tc_HOL_Obool)),U_1689),hAPP(hAPP(c_Set_Oinsert(U_1685),U_1687),U_1691)) = hAPP(hAPP(c_Set_Oinsert(U_1685),U_1687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1685,tc_HOL_Obool)),U_1689),U_1691))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1685),U_1687),U_1689)) ) ),
    inference(miniscope,[status(thm)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1685,tc_HOL_Obool)),U_1689),hAPP(hAPP(c_Set_Oinsert(U_1685),U_1687),U_1691)) = hAPP(hAPP(c_Set_Oinsert(U_1685),U_1687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1685,tc_HOL_Obool)),U_1689),U_1691))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1685),U_1687),U_1689)) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

cnf(f_384_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1686,tc_HOL_Obool)),U_1690),hAPP(hAPP(c_Set_Oinsert(U_1686),U_1688),U_1692)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1686,tc_HOL_Obool)),U_1690),U_1692)
    | hBOOL(hAPP(hAPP(c_member(U_1686),U_1688),U_1690)) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_385_2,plain,
    ! [U_1695,U_1694,U_1693] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1693,tc_HOL_Obool)),U_1694),U_1695) = U_1694
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1693,tc_HOL_Obool)),U_1694),U_1695) != c_Orderings_Obot__class_Obot(tc_fun(U_1693,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

cnf(f_385_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1693,tc_HOL_Obool)),U_1694),U_1695) = U_1694
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1693,tc_HOL_Obool)),U_1694),U_1695) != c_Orderings_Obot__class_Obot(tc_fun(U_1693,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

fof(f_386_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_386_2,plain,
    ! [U_1698,U_1697,U_1696] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1696,tc_HOL_Obool)),U_1697),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1696,tc_HOL_Obool)),U_1698),U_1697)) = c_Orderings_Obot__class_Obot(tc_fun(U_1696,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1696,tc_HOL_Obool)),U_1697),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1696,tc_HOL_Obool)),U_1698),U_1697)) = c_Orderings_Obot__class_Obot(tc_fun(U_1696,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_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_387_2,plain,
    ! [U_1702,U_1701,U_1700,U_1699] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1699,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1699,tc_HOL_Obool)),U_1700),U_1701)),U_1702) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1699,tc_HOL_Obool)),U_1700),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1699,tc_HOL_Obool)),U_1701),U_1702))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1699,tc_HOL_Obool)),U_1702),U_1700)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1699,tc_HOL_Obool)),U_1702),U_1700))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1699,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1699,tc_HOL_Obool)),U_1700),U_1701)),U_1702) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1699,tc_HOL_Obool)),U_1700),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1699,tc_HOL_Obool)),U_1701),U_1702)) ) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ( ! [U_1710,U_1708,U_1706,U_1704] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1704,tc_HOL_Obool)),U_1706),U_1708)),U_1710) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1704,tc_HOL_Obool)),U_1706),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1704,tc_HOL_Obool)),U_1708),U_1710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1704,tc_HOL_Obool)),U_1710),U_1706)) )
    & ! [U_1709,U_1707,U_1705,U_1703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1703,tc_HOL_Obool)),U_1709),U_1705))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1703,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1703,tc_HOL_Obool)),U_1705),U_1707)),U_1709) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1703,tc_HOL_Obool)),U_1705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1703,tc_HOL_Obool)),U_1707),U_1709)) ) ),
    inference(miniscope,[status(thm)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1703,tc_HOL_Obool)),U_1709),U_1705))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1703,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1703,tc_HOL_Obool)),U_1705),U_1707)),U_1709) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1703,tc_HOL_Obool)),U_1705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1703,tc_HOL_Obool)),U_1707),U_1709)) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1704,tc_HOL_Obool)),U_1706),U_1708)),U_1710) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1704,tc_HOL_Obool)),U_1706),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1704,tc_HOL_Obool)),U_1708),U_1710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1704,tc_HOL_Obool)),U_1710),U_1706)) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_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_388_2,plain,
    ! [U_1714,U_1713,U_1712,U_1711] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1711,tc_HOL_Obool)),U_1713),U_1714)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1711,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),U_1713)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),U_1714)),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1711,tc_HOL_Obool)),U_1713),U_1714)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1711,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),U_1713)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1711,tc_HOL_Obool)),U_1712),U_1714)),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_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_389_2,plain,
    ! [U_1718,U_1717,U_1716,U_1715] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1715,tc_HOL_Obool)),U_1717),U_1718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1715,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),U_1717)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),U_1718)),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

cnf(f_389_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1715,tc_HOL_Obool)),U_1717),U_1718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1715,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),U_1717)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1715,tc_HOL_Obool)),U_1716),U_1718)),
    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__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_390_2,plain,
    ! [U_1721,U_1720,U_1719] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1719,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1719,tc_HOL_Obool)),U_1720),U_1721)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1719,tc_HOL_Obool)),U_1720),U_1721)) = U_1720,
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1719,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1719,tc_HOL_Obool)),U_1720),U_1721)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1719,tc_HOL_Obool)),U_1720),U_1721)) = U_1720,
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_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_391_2,plain,
    ! [U_1725,U_1724,U_1723,U_1722] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1722,tc_HOL_Obool)),U_1724),U_1723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),U_1724)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),U_1723))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1722,tc_HOL_Obool)),U_1723),U_1724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1722),U_1723)) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1722,tc_HOL_Obool)),U_1724),U_1723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),U_1724)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1722,tc_Nat_Onat),U_1725),U_1723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1722,tc_HOL_Obool)),U_1723),U_1724))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1722),U_1723)) ),
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_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_392_2,plain,
    ! [U_1728,U_1727,U_1726] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1726,tc_HOL_Obool)),U_1727),U_1728) = hAPP(hAPP(c_Finite__Set_Ofold(U_1726,tc_fun(U_1726,tc_HOL_Obool),c_Set_Oinsert(U_1726)),U_1728),U_1727)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1726),U_1727)) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

cnf(f_392_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1726,tc_HOL_Obool)),U_1727),U_1728) = hAPP(hAPP(c_Finite__Set_Ofold(U_1726,tc_fun(U_1726,tc_HOL_Obool),c_Set_Oinsert(U_1726)),U_1728),U_1727)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1726),U_1727)) ),
    inference(clausify,[status(thm)],[f_392_2]) ).

fof(f_393_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_393_2,plain,
    ! [U_1732,U_1731,U_1730,U_1729] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1729,U_1729,c_Lattices_Osemilattice__sup__class_Osup(U_1729)),U_1731),hAPP(hAPP(c_Set_Oinsert(U_1729),U_1732),U_1730)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1729),U_1732),hAPP(hAPP(c_Finite__Set_Ofold(U_1729,U_1729,c_Lattices_Osemilattice__sup__class_Osup(U_1729)),U_1731),U_1730))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1729),U_1730))
      | ~ class_Lattices_Osemilattice__sup(U_1729) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1729,U_1729,c_Lattices_Osemilattice__sup__class_Osup(U_1729)),U_1731),hAPP(hAPP(c_Set_Oinsert(U_1729),U_1732),U_1730)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1729),U_1732),hAPP(hAPP(c_Finite__Set_Ofold(U_1729,U_1729,c_Lattices_Osemilattice__sup__class_Osup(U_1729)),U_1731),U_1730))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1729),U_1730))
    | ~ class_Lattices_Osemilattice__sup(U_1729) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_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_394_2,plain,
    ! [U_1735,U_1734,U_1733] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1733),U_1735),c_Big__Operators_Olattice__class_OSup__fin(U_1733,U_1734)) = U_1735
      | ~ hBOOL(hAPP(hAPP(c_member(U_1733),U_1735),U_1734))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1733),U_1734))
      | ~ class_Lattices_Olattice(U_1733) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

cnf(f_394_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1733),U_1735),c_Big__Operators_Olattice__class_OSup__fin(U_1733,U_1734)) = U_1735
    | ~ hBOOL(hAPP(hAPP(c_member(U_1733),U_1735),U_1734))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1733),U_1734))
    | ~ class_Lattices_Olattice(U_1733) ),
    inference(clausify,[status(thm)],[f_394_2]) ).

fof(f_395_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_395_2,plain,
    ! [U_1740,U_1739,U_1738,U_1737,U_1736] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1736,U_1736,c_Groups_Otimes__class_Otimes(U_1736),U_1740,hAPP(hAPP(c_Set_Oinsert(U_1736),U_1737),U_1738)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1736),U_1740),U_1739)))
      | hBOOL(hAPP(hAPP(c_member(U_1736),U_1737),U_1738))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1736,U_1736,c_Groups_Otimes__class_Otimes(U_1736),U_1737,U_1738),U_1739))
      | ~ class_Groups_Oab__semigroup__mult(U_1736) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1736,U_1736,c_Groups_Otimes__class_Otimes(U_1736),U_1740,hAPP(hAPP(c_Set_Oinsert(U_1736),U_1737),U_1738)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1736),U_1740),U_1739)))
    | hBOOL(hAPP(hAPP(c_member(U_1736),U_1737),U_1738))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1736,U_1736,c_Groups_Otimes__class_Otimes(U_1736),U_1737,U_1738),U_1739))
    | ~ class_Groups_Oab__semigroup__mult(U_1736) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_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_396_2,plain,
    ! [U_1745,U_1744,U_1743,U_1742,U_1741] :
      ( hAPP(U_1743,hAPP(hAPP(c_Set_Oinsert(U_1741),U_1745),U_1744)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1741,U_1741,U_1742),U_1745),U_1744)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1741),U_1744))
      | ~ c_Finite__Set_Ofolding__one__idem(U_1741,U_1742,U_1743) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( hAPP(U_1743,hAPP(hAPP(c_Set_Oinsert(U_1741),U_1745),U_1744)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1741,U_1741,U_1742),U_1745),U_1744)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1741),U_1744))
    | ~ c_Finite__Set_Ofolding__one__idem(U_1741,U_1742,U_1743) ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_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_397_2,plain,
    ! [U_1753,U_1752,U_1751,U_1750,U_1749,U_1748,U_1747,U_1746] :
      ( hAPP(hAPP(U_1748,hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))),hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))) = hAPP(hAPP(U_1748,hAPP(U_1751,U_1752)),hAPP(U_1751,U_1753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1752))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1746,U_1747,U_1748,U_1749,U_1750,U_1751) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1753,U_1752,U_1751,U_1750,U_1749,U_1748,U_1747] :
      ( ! [U_1746] : ~ c_Finite__Set_Ofolding__image__simple(U_1746,U_1747,U_1748,U_1749,U_1750,U_1751)
      | hAPP(hAPP(U_1748,hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))),hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))) = hAPP(hAPP(U_1748,hAPP(U_1751,U_1752)),hAPP(U_1751,U_1753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1752)) ),
    inference(miniscope,[status(thm)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1746,U_1747,U_1748,U_1749,U_1750,U_1751)
    | hAPP(hAPP(U_1748,hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))),hAPP(U_1751,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1747,tc_HOL_Obool)),U_1752),U_1753))) = hAPP(hAPP(U_1748,hAPP(U_1751,U_1752)),hAPP(U_1751,U_1753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1747),U_1752)) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_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_398_2,plain,
    ! [U_1757,U_1756,U_1755,U_1754] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1754,tc_Nat_Onat),U_1757),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1754,tc_HOL_Obool)),U_1756),hAPP(hAPP(c_Set_Oinsert(U_1754),U_1755),c_Orderings_Obot__class_Obot(tc_fun(U_1754,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1754,tc_Nat_Onat),U_1757),U_1756)
        | hBOOL(hAPP(hAPP(c_member(U_1754),U_1755),U_1756)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1754,tc_Nat_Onat),U_1757),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1754,tc_HOL_Obool)),U_1756),hAPP(hAPP(c_Set_Oinsert(U_1754),U_1755),c_Orderings_Obot__class_Obot(tc_fun(U_1754,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1754,tc_Nat_Onat),U_1757),U_1756)),hAPP(U_1757,U_1755))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1754),U_1755),U_1756)) ) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ( ! [U_1765,U_1763,U_1761,U_1759] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1759,tc_Nat_Onat),U_1765),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1759,tc_HOL_Obool)),U_1763),hAPP(hAPP(c_Set_Oinsert(U_1759),U_1761),c_Orderings_Obot__class_Obot(tc_fun(U_1759,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1759,tc_Nat_Onat),U_1765),U_1763)
        | hBOOL(hAPP(hAPP(c_member(U_1759),U_1761),U_1763)) )
    & ! [U_1764,U_1762,U_1760,U_1758] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1758,tc_Nat_Onat),U_1764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),U_1762),hAPP(hAPP(c_Set_Oinsert(U_1758),U_1760),c_Orderings_Obot__class_Obot(tc_fun(U_1758,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1758,tc_Nat_Onat),U_1764),U_1762)),hAPP(U_1764,U_1760))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1758),U_1760),U_1762)) ) ),
    inference(miniscope,[status(thm)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1758,tc_Nat_Onat),U_1764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1758,tc_HOL_Obool)),U_1762),hAPP(hAPP(c_Set_Oinsert(U_1758),U_1760),c_Orderings_Obot__class_Obot(tc_fun(U_1758,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1758,tc_Nat_Onat),U_1764),U_1762)),hAPP(U_1764,U_1760))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1758),U_1760),U_1762)) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

cnf(f_398_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1759,tc_Nat_Onat),U_1765),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1759,tc_HOL_Obool)),U_1763),hAPP(hAPP(c_Set_Oinsert(U_1759),U_1761),c_Orderings_Obot__class_Obot(tc_fun(U_1759,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1759,tc_Nat_Onat),U_1765),U_1763)
    | hBOOL(hAPP(hAPP(c_member(U_1759),U_1761),U_1763)) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_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_399_2,plain,
    ! [U_1770,U_1769,U_1768,U_1767,U_1766] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1767,tc_HOL_Obool)),U_1768),U_1769)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1766),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),U_1768)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),U_1769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1767,tc_HOL_Obool)),U_1769),U_1768))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1767),U_1768))
      | ~ class_Groups_Oab__group__add(U_1766) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1767,tc_HOL_Obool)),U_1768),U_1769)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1766),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),U_1768)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1767,U_1766),U_1770),U_1769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1767,tc_HOL_Obool)),U_1769),U_1768))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1767),U_1768))
    | ~ class_Groups_Oab__group__add(U_1766) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_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_400_2,plain,
    ! [U_1774,U_1773,U_1772,U_1771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1771),U_1773),U_1774)),hAPP(hAPP(c_Finite__Set_Ofold(U_1771,U_1771,c_Lattices_Osemilattice__sup__class_Osup(U_1771)),U_1774),U_1772)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1771),U_1773),U_1772))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1771),U_1772))
      | ~ class_Lattices_Osemilattice__sup(U_1771) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1771),U_1773),U_1774)),hAPP(hAPP(c_Finite__Set_Ofold(U_1771,U_1771,c_Lattices_Osemilattice__sup__class_Osup(U_1771)),U_1774),U_1772)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1771),U_1773),U_1772))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1771),U_1772))
    | ~ class_Lattices_Osemilattice__sup(U_1771) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_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_401_2,plain,
    ! [U_1777,U_1776,U_1775] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_1775,hAPP(hAPP(c_Set_Oinsert(U_1775),U_1777),U_1776)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1775,U_1775,c_Lattices_Osemilattice__sup__class_Osup(U_1775)),U_1777),U_1776)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1775),U_1776))
      | ~ class_Lattices_Olattice(U_1775) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

cnf(f_401_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_1775,hAPP(hAPP(c_Set_Oinsert(U_1775),U_1777),U_1776)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1775,U_1775,c_Lattices_Osemilattice__sup__class_Osup(U_1775)),U_1777),U_1776)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1775),U_1776))
    | ~ class_Lattices_Olattice(U_1775) ),
    inference(clausify,[status(thm)],[f_401_2]) ).

fof(f_402_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_402_2,plain,
    ! [U_1782,U_1781,U_1780,U_1779,U_1778] :
      ( hAPP(U_1780,hAPP(hAPP(c_Set_Oinsert(U_1778),U_1782),U_1781)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1778,U_1778,U_1779),U_1782),U_1781)
      | hBOOL(hAPP(hAPP(c_member(U_1778),U_1782),U_1781))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1778),U_1781))
      | ~ c_Finite__Set_Ofolding__one(U_1778,U_1779,U_1780) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

cnf(f_402_3,plain,
    ( hAPP(U_1780,hAPP(hAPP(c_Set_Oinsert(U_1778),U_1782),U_1781)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1778,U_1778,U_1779),U_1782),U_1781)
    | hBOOL(hAPP(hAPP(c_member(U_1778),U_1782),U_1781))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1778),U_1781))
    | ~ c_Finite__Set_Ofolding__one(U_1778,U_1779,U_1780) ),
    inference(clausify,[status(thm)],[f_402_2]) ).

fof(f_403_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_403_2,plain,
    ! [U_1790,U_1789,U_1788,U_1787,U_1786,U_1785,U_1784,U_1783] :
      ( hAPP(U_1788,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790)) = hAPP(hAPP(U_1785,hAPP(U_1788,U_1789)),hAPP(U_1788,U_1790))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790) != c_Orderings_Obot__class_Obot(tc_fun(U_1784,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1790))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1789))
      | ~ c_Finite__Set_Ofolding__image__simple(U_1783,U_1784,U_1785,U_1786,U_1787,U_1788) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1790,U_1789,U_1788,U_1787,U_1786,U_1785,U_1784] :
      ( ! [U_1783] : ~ c_Finite__Set_Ofolding__image__simple(U_1783,U_1784,U_1785,U_1786,U_1787,U_1788)
      | hAPP(U_1788,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790)) = hAPP(hAPP(U_1785,hAPP(U_1788,U_1789)),hAPP(U_1788,U_1790))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790) != c_Orderings_Obot__class_Obot(tc_fun(U_1784,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1790))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1789)) ),
    inference(miniscope,[status(thm)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_1783,U_1784,U_1785,U_1786,U_1787,U_1788)
    | hAPP(U_1788,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790)) = hAPP(hAPP(U_1785,hAPP(U_1788,U_1789)),hAPP(U_1788,U_1790))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1784,tc_HOL_Obool)),U_1789),U_1790) != c_Orderings_Obot__class_Obot(tc_fun(U_1784,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1790))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1784),U_1789)) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_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_404_2,plain,
    ! [U_1795,U_1794,U_1793,U_1792,U_1791] :
      ( hAPP(hAPP(U_1792,hAPP(U_1793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795))),hAPP(U_1793,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795))) = hAPP(hAPP(U_1792,hAPP(U_1793,U_1794)),hAPP(U_1793,U_1795))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795) = c_Orderings_Obot__class_Obot(tc_fun(U_1791,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1791),U_1795))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1791),U_1794))
      | ~ c_Finite__Set_Ofolding__one(U_1791,U_1792,U_1793) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

cnf(f_404_3,plain,
    ( hAPP(hAPP(U_1792,hAPP(U_1793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795))),hAPP(U_1793,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795))) = hAPP(hAPP(U_1792,hAPP(U_1793,U_1794)),hAPP(U_1793,U_1795))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1791,tc_HOL_Obool)),U_1794),U_1795) = c_Orderings_Obot__class_Obot(tc_fun(U_1791,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1791),U_1795))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1791),U_1794))
    | ~ c_Finite__Set_Ofolding__one(U_1791,U_1792,U_1793) ),
    inference(clausify,[status(thm)],[f_404_2]) ).

fof(f_405_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_405_2,plain,
    ! [U_1800,U_1799,U_1798,U_1797,U_1796] :
      ( hAPP(U_1798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1796,tc_HOL_Obool)),U_1799),U_1800)) = hAPP(hAPP(U_1797,hAPP(U_1798,U_1799)),hAPP(U_1798,U_1800))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),U_1799),U_1800) != c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
      | U_1800 = c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1796),U_1800))
      | U_1799 = c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1796),U_1799))
      | ~ c_Finite__Set_Ofolding__one(U_1796,U_1797,U_1798) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

cnf(f_405_3,plain,
    ( hAPP(U_1798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1796,tc_HOL_Obool)),U_1799),U_1800)) = hAPP(hAPP(U_1797,hAPP(U_1798,U_1799)),hAPP(U_1798,U_1800))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1796,tc_HOL_Obool)),U_1799),U_1800) != c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
    | U_1800 = c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1796),U_1800))
    | U_1799 = c_Orderings_Obot__class_Obot(tc_fun(U_1796,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1796),U_1799))
    | ~ c_Finite__Set_Ofolding__one(U_1796,U_1797,U_1798) ),
    inference(clausify,[status(thm)],[f_405_2]) ).

fof(f_406_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_406_2,plain,
    ! [U_1808,U_1807,U_1806,U_1805,U_1804,U_1803,U_1802,U_1801] :
      ( hAPP(hAPP(U_1803,hAPP(U_1805,U_1808)),hAPP(U_1806,U_1807)) = hAPP(U_1806,U_1807)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1802),U_1808),U_1807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1802),U_1807))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1801,U_1802,U_1803,U_1804,U_1805,U_1806) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1808,U_1807,U_1806,U_1805,U_1804,U_1803,U_1802] :
      ( ! [U_1801] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1801,U_1802,U_1803,U_1804,U_1805,U_1806)
      | hAPP(hAPP(U_1803,hAPP(U_1805,U_1808)),hAPP(U_1806,U_1807)) = hAPP(U_1806,U_1807)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1802),U_1808),U_1807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1802),U_1807)) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

cnf(f_406_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1801,U_1802,U_1803,U_1804,U_1805,U_1806)
    | hAPP(hAPP(U_1803,hAPP(U_1805,U_1808)),hAPP(U_1806,U_1807)) = hAPP(U_1806,U_1807)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1802),U_1808),U_1807))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1802),U_1807)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_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_407_2,plain,
    ! [U_1816,U_1815,U_1814,U_1813,U_1812,U_1811,U_1810,U_1809] :
      ( hAPP(U_1814,hAPP(hAPP(c_Set_Oinsert(U_1810),U_1816),U_1815)) = hAPP(hAPP(U_1811,hAPP(U_1813,U_1816)),hAPP(U_1814,U_1815))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1815))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_1809,U_1810,U_1811,U_1812,U_1813,U_1814) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1816,U_1815,U_1814,U_1813,U_1812,U_1811,U_1810] :
      ( ! [U_1809] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1809,U_1810,U_1811,U_1812,U_1813,U_1814)
      | hAPP(U_1814,hAPP(hAPP(c_Set_Oinsert(U_1810),U_1816),U_1815)) = hAPP(hAPP(U_1811,hAPP(U_1813,U_1816)),hAPP(U_1814,U_1815))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1815)) ),
    inference(miniscope,[status(thm)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1809,U_1810,U_1811,U_1812,U_1813,U_1814)
    | hAPP(U_1814,hAPP(hAPP(c_Set_Oinsert(U_1810),U_1816),U_1815)) = hAPP(hAPP(U_1811,hAPP(U_1813,U_1816)),hAPP(U_1814,U_1815))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1815)) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_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_408_2,plain,
    ! [U_1822,U_1821,U_1820,U_1819,U_1818,U_1817] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1817,U_1818,U_1819),U_1822),U_1820) = hAPP(hAPP(U_1819,U_1821),hAPP(hAPP(c_Finite__Set_Ofold(U_1817,U_1818,U_1819),U_1822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1817,tc_HOL_Obool)),U_1820),hAPP(hAPP(c_Set_Oinsert(U_1817),U_1821),c_Orderings_Obot__class_Obot(tc_fun(U_1817,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1817),U_1821),U_1820))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1817),U_1820))
      | ~ c_Finite__Set_Ofun__left__comm(U_1817,U_1818,U_1819) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1817,U_1818,U_1819),U_1822),U_1820) = hAPP(hAPP(U_1819,U_1821),hAPP(hAPP(c_Finite__Set_Ofold(U_1817,U_1818,U_1819),U_1822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1817,tc_HOL_Obool)),U_1820),hAPP(hAPP(c_Set_Oinsert(U_1817),U_1821),c_Orderings_Obot__class_Obot(tc_fun(U_1817,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1817),U_1821),U_1820))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1817),U_1820))
    | ~ c_Finite__Set_Ofun__left__comm(U_1817,U_1818,U_1819) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_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_409_2,plain,
    ! [U_1828,U_1827,U_1826,U_1825,U_1824,U_1823] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1823,U_1824,U_1825),U_1827),hAPP(hAPP(c_Set_Oinsert(U_1823),U_1828),U_1826)) = hAPP(hAPP(U_1825,U_1828),hAPP(hAPP(c_Finite__Set_Ofold(U_1823,U_1824,U_1825),U_1827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1823,tc_HOL_Obool)),U_1826),hAPP(hAPP(c_Set_Oinsert(U_1823),U_1828),c_Orderings_Obot__class_Obot(tc_fun(U_1823,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1823),U_1826))
      | ~ c_Finite__Set_Ofun__left__comm(U_1823,U_1824,U_1825) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1823,U_1824,U_1825),U_1827),hAPP(hAPP(c_Set_Oinsert(U_1823),U_1828),U_1826)) = hAPP(hAPP(U_1825,U_1828),hAPP(hAPP(c_Finite__Set_Ofold(U_1823,U_1824,U_1825),U_1827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1823,tc_HOL_Obool)),U_1826),hAPP(hAPP(c_Set_Oinsert(U_1823),U_1828),c_Orderings_Obot__class_Obot(tc_fun(U_1823,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1823),U_1826))
    | ~ c_Finite__Set_Ofun__left__comm(U_1823,U_1824,U_1825) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_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_410_2,plain,
    ! [U_1831,U_1830,U_1829] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_1829,U_1830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1829),U_1831),c_Big__Operators_Olattice__class_OInf__fin(U_1829,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_1829,U_1830) = U_1831
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_1829),U_1831),U_1830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1829),U_1830))
      | ~ class_Lattices_Olattice(U_1829) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1829,U_1830) = U_1831
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1829),U_1831),U_1830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1829),U_1830))
    | ~ class_Lattices_Olattice(U_1829) ),
    inference(clausify,[status(thm)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1829,U_1830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1829),U_1831),c_Big__Operators_Olattice__class_OInf__fin(U_1829,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1829,tc_HOL_Obool)),U_1830),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1831),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1829),U_1831),U_1830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1829),U_1830))
    | ~ class_Lattices_Olattice(U_1829) ),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_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_411_2,plain,
    ! [U_1837,U_1836,U_1835,U_1834,U_1833,U_1832] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1832,U_1833,U_1834),U_1837),hAPP(hAPP(c_Set_Oinsert(U_1832),U_1836),U_1835)) = hAPP(hAPP(U_1834,U_1836),hAPP(hAPP(c_Finite__Set_Ofold(U_1832,U_1833,U_1834),U_1837),U_1835))
      | hBOOL(hAPP(hAPP(c_member(U_1832),U_1836),U_1835))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1832),U_1835))
      | ~ c_Finite__Set_Ofun__left__comm(U_1832,U_1833,U_1834) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

cnf(f_411_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1832,U_1833,U_1834),U_1837),hAPP(hAPP(c_Set_Oinsert(U_1832),U_1836),U_1835)) = hAPP(hAPP(U_1834,U_1836),hAPP(hAPP(c_Finite__Set_Ofold(U_1832,U_1833,U_1834),U_1837),U_1835))
    | hBOOL(hAPP(hAPP(c_member(U_1832),U_1836),U_1835))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1832),U_1835))
    | ~ c_Finite__Set_Ofun__left__comm(U_1832,U_1833,U_1834) ),
    inference(clausify,[status(thm)],[f_411_2]) ).

fof(f_412_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_412_2,plain,
    ! [U_1843,U_1842,U_1841,U_1840,U_1839,U_1838] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1838,U_1839,U_1840),U_1843),hAPP(hAPP(c_Set_Oinsert(U_1838),U_1842),U_1841)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1838,U_1839,U_1840),hAPP(hAPP(U_1840,U_1842),U_1843)),U_1841)
      | hBOOL(hAPP(hAPP(c_member(U_1838),U_1842),U_1841))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1838),U_1841))
      | ~ c_Finite__Set_Ofun__left__comm(U_1838,U_1839,U_1840) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1838,U_1839,U_1840),U_1843),hAPP(hAPP(c_Set_Oinsert(U_1838),U_1842),U_1841)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1838,U_1839,U_1840),hAPP(hAPP(U_1840,U_1842),U_1843)),U_1841)
    | hBOOL(hAPP(hAPP(c_member(U_1838),U_1842),U_1841))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1838),U_1841))
    | ~ c_Finite__Set_Ofun__left__comm(U_1838,U_1839,U_1840) ),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_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_413_2,plain,
    ! [U_1849,U_1848,U_1847,U_1846,U_1845] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1848),U_1847)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1849),U_1847)))
      | ? [U_1844] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(U_1848,U_1844)),hAPP(U_1849,U_1844)))
          & hBOOL(hAPP(hAPP(c_member(U_1846),U_1844),U_1847)) )
      | U_1847 = c_Orderings_Obot__class_Obot(tc_fun(U_1846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1846),U_1847))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1845)
      | ~ class_Groups_Ocomm__monoid__add(U_1845) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1849,U_1848,U_1847,U_1846,U_1845] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1848),U_1847)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1849),U_1847)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(U_1848,sK29(U_1849,U_1848,U_1847,U_1846,U_1845))),hAPP(U_1849,sK29(U_1849,U_1848,U_1847,U_1846,U_1845))))
        & hBOOL(hAPP(hAPP(c_member(U_1846),sK29(U_1849,U_1848,U_1847,U_1846,U_1845)),U_1847)) )
      | U_1847 = c_Orderings_Obot__class_Obot(tc_fun(U_1846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1846),U_1847))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1845)
      | ~ class_Groups_Ocomm__monoid__add(U_1845) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1844,sK29(U_1849,U_1848,U_1847,U_1846,U_1845))],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1846),sK29(U_1849,U_1848,U_1847,U_1846,U_1845)),U_1847))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1848),U_1847)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1849),U_1847)))
    | U_1847 = c_Orderings_Obot__class_Obot(tc_fun(U_1846,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1846),U_1847))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1845)
    | ~ class_Groups_Ocomm__monoid__add(U_1845) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

cnf(f_413_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(U_1848,sK29(U_1849,U_1848,U_1847,U_1846,U_1845))),hAPP(U_1849,sK29(U_1849,U_1848,U_1847,U_1846,U_1845))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1845),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1848),U_1847)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1846,U_1845),U_1849),U_1847)))
    | U_1847 = c_Orderings_Obot__class_Obot(tc_fun(U_1846,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1846),U_1847))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1845)
    | ~ class_Groups_Ocomm__monoid__add(U_1845) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_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_414_2,plain,
    ! [U_1854,U_1853,U_1852,U_1851,U_1850] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1851,U_1850),U_1854),U_1852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1850),hAPP(U_1854,U_1853)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1851,U_1850),U_1854),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1851,tc_HOL_Obool)),U_1852),hAPP(hAPP(c_Set_Oinsert(U_1851),U_1853),c_Orderings_Obot__class_Obot(tc_fun(U_1851,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1851),U_1853),U_1852))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1851),U_1852))
      | ~ class_Groups_Ocomm__monoid__add(U_1850) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

cnf(f_414_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1851,U_1850),U_1854),U_1852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1850),hAPP(U_1854,U_1853)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1851,U_1850),U_1854),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1851,tc_HOL_Obool)),U_1852),hAPP(hAPP(c_Set_Oinsert(U_1851),U_1853),c_Orderings_Obot__class_Obot(tc_fun(U_1851,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1851),U_1853),U_1852))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1851),U_1852))
    | ~ class_Groups_Ocomm__monoid__add(U_1850) ),
    inference(clausify,[status(thm)],[f_414_2]) ).

fof(f_415_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_415_2,plain,
    ! [U_1859,U_1858,U_1857,U_1856,U_1855] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1856,U_1855),U_1859),U_1857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1855),hAPP(U_1859,U_1858)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1856,U_1855),U_1859),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1856,tc_HOL_Obool)),U_1857),hAPP(hAPP(c_Set_Oinsert(U_1856),U_1858),c_Orderings_Obot__class_Obot(tc_fun(U_1856,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1856),U_1858),U_1857))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1856),U_1857))
      | ~ class_Groups_Ocomm__monoid__add(U_1855) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1856,U_1855),U_1859),U_1857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1855),hAPP(U_1859,U_1858)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1856,U_1855),U_1859),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1856,tc_HOL_Obool)),U_1857),hAPP(hAPP(c_Set_Oinsert(U_1856),U_1858),c_Orderings_Obot__class_Obot(tc_fun(U_1856,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1856),U_1858),U_1857))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1856),U_1857))
    | ~ class_Groups_Ocomm__monoid__add(U_1855) ),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_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_416_2,plain,
    ! [U_1862,U_1861,U_1860] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_1860,hAPP(hAPP(c_Set_Oinsert(U_1860),U_1862),U_1861)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1860,U_1860,c_Lattices_Osemilattice__inf__class_Oinf(U_1860)),U_1862),U_1861)
      | hBOOL(hAPP(hAPP(c_member(U_1860),U_1862),U_1861))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1860),U_1861))
      | ~ class_Lattices_Olattice(U_1860) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1860,hAPP(hAPP(c_Set_Oinsert(U_1860),U_1862),U_1861)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1860,U_1860,c_Lattices_Osemilattice__inf__class_Oinf(U_1860)),U_1862),U_1861)
    | hBOOL(hAPP(hAPP(c_member(U_1860),U_1862),U_1861))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1860),U_1861))
    | ~ class_Lattices_Olattice(U_1860) ),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_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_417_2,plain,
    ! [U_1865,U_1864,U_1863] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1863),c_Big__Operators_Olattice__class_OInf__fin(U_1863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865))),c_Big__Operators_Olattice__class_OInf__fin(U_1863,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1863),c_Big__Operators_Olattice__class_OInf__fin(U_1863,U_1864)),c_Big__Operators_Olattice__class_OInf__fin(U_1863,U_1865))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865) = c_Orderings_Obot__class_Obot(tc_fun(U_1863,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1863),U_1865))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1863),U_1864))
      | ~ class_Lattices_Olattice(U_1863) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1863),c_Big__Operators_Olattice__class_OInf__fin(U_1863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865))),c_Big__Operators_Olattice__class_OInf__fin(U_1863,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1863),c_Big__Operators_Olattice__class_OInf__fin(U_1863,U_1864)),c_Big__Operators_Olattice__class_OInf__fin(U_1863,U_1865))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865) = c_Orderings_Obot__class_Obot(tc_fun(U_1863,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1863),U_1865))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1863),U_1864))
    | ~ class_Lattices_Olattice(U_1863) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_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_418_2,plain,
    ! [U_1869,U_1868,U_1867,U_1866] :
      ( U_1867 = U_1869
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1866),U_1867),U_1868) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1866),U_1869),U_1868)
      | ~ class_Groups_Ocancel__semigroup__add(U_1866) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( U_1867 = U_1869
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1866),U_1867),U_1868) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1866),U_1869),U_1868)
    | ~ class_Groups_Ocancel__semigroup__add(U_1866) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_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_419_2,plain,
    ! [U_1873,U_1872,U_1871,U_1870] :
      ( U_1872 = U_1873
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1870),U_1871),U_1872) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1870),U_1871),U_1873)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_1870) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    ( U_1872 = U_1873
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1870),U_1871),U_1872) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1870),U_1871),U_1873)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_1870) ),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_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_420_2,plain,
    ! [U_1877,U_1876,U_1875,U_1874] :
      ( U_1876 = U_1877
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1874),U_1875),U_1876) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1874),U_1875),U_1877)
      | ~ class_Groups_Ocancel__semigroup__add(U_1874) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    ( U_1876 = U_1877
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1874),U_1875),U_1876) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1874),U_1875),U_1877)
    | ~ class_Groups_Ocancel__semigroup__add(U_1874) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_1,plain,
    ! [V_ca_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_ca_2),V_a_2)
          | V_b_2 != V_ca_2 )
        & ( V_b_2 = V_ca_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_ca_2),V_a_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_421_2,plain,
    ! [U_1881,U_1880,U_1879,U_1878] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1879),U_1880) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1881),U_1880)
          | U_1879 != U_1881 )
        & ( U_1879 = U_1881
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1879),U_1880) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1881),U_1880) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_1878) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ( U_1879 = U_1881
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1879),U_1880) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1881),U_1880)
    | ~ class_Groups_Ocancel__semigroup__add(U_1878) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

cnf(f_421_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1879),U_1880) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1878),U_1881),U_1880)
    | U_1879 != U_1881
    | ~ class_Groups_Ocancel__semigroup__add(U_1878) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [V_ca_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_ca_2)
          | V_b_2 != V_ca_2 )
        & ( V_b_2 = V_ca_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_ca_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_422_2,plain,
    ! [U_1885,U_1884,U_1883,U_1882] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1885)
          | U_1884 != U_1885 )
        & ( U_1884 = U_1885
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1884) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1885) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_1882) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    ( U_1884 = U_1885
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1884) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1885)
    | ~ class_Groups_Ocancel__semigroup__add(U_1882) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

cnf(f_422_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1882),U_1883),U_1885)
    | U_1884 != U_1885
    | ~ class_Groups_Ocancel__semigroup__add(U_1882) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_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_423_2,plain,
    ! [U_1889,U_1888,U_1887,U_1886] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1887),U_1888)),U_1889) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1888),U_1889))
      | ~ class_Groups_Oab__semigroup__add(U_1886) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1887),U_1888)),U_1889) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1886),U_1888),U_1889))
    | ~ class_Groups_Oab__semigroup__add(U_1886) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_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_424_2,plain,
    ! [U_1895,U_1894,U_1893,U_1892,U_1891,U_1890] :
      ( hAPP(hAPP(U_1892,U_1893),hAPP(hAPP(U_1892,U_1894),U_1895)) = hAPP(hAPP(U_1892,U_1894),hAPP(hAPP(U_1892,U_1893),U_1895))
      | ~ c_Finite__Set_Ofun__left__comm(U_1890,U_1891,U_1892) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1895,U_1894,U_1893,U_1892] :
      ( ! [U_1891,U_1890] : ~ c_Finite__Set_Ofun__left__comm(U_1890,U_1891,U_1892)
      | hAPP(hAPP(U_1892,U_1893),hAPP(hAPP(U_1892,U_1894),U_1895)) = hAPP(hAPP(U_1892,U_1894),hAPP(hAPP(U_1892,U_1893),U_1895)) ),
    inference(miniscope,[status(thm)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_1890,U_1891,U_1892)
    | hAPP(hAPP(U_1892,U_1893),hAPP(hAPP(U_1892,U_1894),U_1895)) = hAPP(hAPP(U_1892,U_1894),hAPP(hAPP(U_1892,U_1893),U_1895)) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [V_b_2,V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_425_2,plain,
    ! [U_1899,U_1898,U_1897,U_1896] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1897),U_1898)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1899),U_1898)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),U_1897),U_1899)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),U_1897),U_1899))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1897),U_1898)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1899),U_1898))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1896) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),U_1897),U_1899))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1897),U_1898)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1899),U_1898)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1896) ),
    inference(clausify,[status(thm)],[f_425_2]) ).

cnf(f_425_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1897),U_1898)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1896),U_1899),U_1898)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1896),U_1897),U_1899))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1896) ),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_426_2,plain,
    ! [U_1903,U_1902,U_1901,U_1900] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1902)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1903)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1903)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1903))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1902)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1903))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1900) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1903))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1902)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1903)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1900) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

cnf(f_426_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1902)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1900),U_1901),U_1903)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1900),U_1902),U_1903))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1900) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_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_427_2,plain,
    ! [U_1907,U_1906,U_1905,U_1904] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1904),U_1905),U_1907)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1904),U_1906),U_1907)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1904),U_1905),U_1906))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1904) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1904),U_1905),U_1907)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1904),U_1906),U_1907)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1904),U_1905),U_1906))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1904) ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_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_428_2,plain,
    ! [U_1911,U_1910,U_1909,U_1908] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1908),U_1911),U_1909)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1908),U_1911),U_1910)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1908),U_1909),U_1910))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1908) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1908),U_1911),U_1909)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1908),U_1911),U_1910)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1908),U_1909),U_1910))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1908) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_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_429_2,plain,
    ! [U_1916,U_1915,U_1914,U_1913,U_1912] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1912),U_1913),U_1915)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1912),U_1914),U_1916)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),U_1915),U_1916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),U_1913),U_1914))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1912) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1912),U_1913),U_1915)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1912),U_1914),U_1916)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),U_1915),U_1916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1912),U_1913),U_1914))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1912) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_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_430_2,plain,
    ! [U_1920,U_1919,U_1918,U_1917] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917),U_1918),U_1920))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1917),U_1918),U_1919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1917),U_1920),U_1919)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1917) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917),U_1918),U_1920))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1917),U_1918),U_1919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1917),U_1920),U_1919)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1917) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_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_431_2,plain,
    ! [U_1924,U_1923,U_1922,U_1921] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1921),U_1923),U_1924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1921),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1921),U_1922),U_1923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1921),U_1922),U_1924)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1921) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1921),U_1923),U_1924))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1921),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1921),U_1922),U_1923)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1921),U_1922),U_1924)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1921) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [V_b_2,V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_432_2,plain,
    ! [U_1928,U_1927,U_1926,U_1925] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1926),U_1927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1928),U_1927)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),U_1926),U_1928)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),U_1926),U_1928))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1926),U_1927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1928),U_1927))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1925) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),U_1926),U_1928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1926),U_1927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1928),U_1927)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1925) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1926),U_1927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1925),U_1928),U_1927)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1925),U_1926),U_1928))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1925) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_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_433_2,plain,
    ! [U_1932,U_1931,U_1930,U_1929] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1931)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1932)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),U_1931),U_1932)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),U_1931),U_1932))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1931)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1932))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1929) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),U_1931),U_1932))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1931)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1932)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1929) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1931)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1929),U_1930),U_1932)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1929),U_1931),U_1932))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1929) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_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_434_2,plain,
    ! [U_1936,U_1935,U_1934,U_1933] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1933),U_1934),U_1936)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1933),U_1935),U_1936)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1933),U_1934),U_1935))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1933) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

cnf(f_434_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1933),U_1934),U_1936)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1933),U_1935),U_1936)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1933),U_1934),U_1935))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1933) ),
    inference(clausify,[status(thm)],[f_434_2]) ).

fof(f_435_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_435_2,plain,
    ! [U_1940,U_1939,U_1938,U_1937] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1937),U_1940),U_1938)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1937),U_1940),U_1939)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1937),U_1938),U_1939))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1937) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1937),U_1940),U_1938)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1937),U_1940),U_1939)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1937),U_1938),U_1939))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1937) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_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_436_2,plain,
    ! [U_1945,U_1944,U_1943,U_1942,U_1941] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1944)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1943),U_1945)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1944),U_1945))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1943))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1941) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1944)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1943),U_1945)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1944),U_1945))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1943))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1941) ),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_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_437_2,plain,
    ! [U_1949,U_1948,U_1947,U_1946] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1946),U_1947),U_1949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1946),U_1947),U_1948)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1946),U_1949),U_1948)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1946) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1946),U_1947),U_1949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1946),U_1947),U_1948)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1946),U_1949),U_1948)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1946) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_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_438_2,plain,
    ! [U_1953,U_1952,U_1951,U_1950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),U_1952),U_1953))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1953)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1950) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),U_1952),U_1953))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1953)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1950) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_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_439_2,plain,
    ! [U_1956,U_1955,U_1954] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1954),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1954),U_1955),U_1956)),U_1956) = U_1955
      | ~ class_Groups_Ogroup__add(U_1954) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1954),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1954),U_1955),U_1956)),U_1956) = U_1955
    | ~ class_Groups_Ogroup__add(U_1954) ),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_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_440_2,plain,
    ! [U_1959,U_1958,U_1957] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1959)),U_1959) = U_1958
      | ~ class_Groups_Ogroup__add(U_1957) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1959)),U_1959) = U_1958
    | ~ class_Groups_Ogroup__add(U_1957) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_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_441_2,plain,
    ! [U_1960] :
      ( c_Finite__Set_Ofun__left__comm(U_1960,U_1960,c_Groups_Otimes__class_Otimes(U_1960))
      | ~ class_Groups_Oab__semigroup__mult(U_1960) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_1960,U_1960,c_Groups_Otimes__class_Otimes(U_1960))
    | ~ class_Groups_Oab__semigroup__mult(U_1960) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_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_442_2,plain,
    ! [U_1965,U_1964,U_1963,U_1962,U_1961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1961),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1963),U_1965)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),U_1964),U_1965))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1961),U_1962),U_1963))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1961) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1961),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1963),U_1965)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),U_1964),U_1965))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1961),U_1962),U_1963))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1961) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_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_443_2,plain,
    ! [U_1970,U_1969,U_1968,U_1967,U_1966] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1968),U_1970)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),U_1969),U_1970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1966),U_1967),U_1968))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1966) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1968),U_1970)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),U_1969),U_1970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1966),U_1967),U_1968))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1966) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_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_444_2,plain,
    ! [U_1977,U_1976,U_1975,U_1974,U_1973,U_1972,U_1971] :
      ( U_1977 = U_1976
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1971,U_1972,U_1973,U_1974,U_1975),U_1977))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1971,U_1972,U_1973,U_1974,U_1975),U_1976))
      | ~ c_Finite__Set_Ofun__left__comm(U_1971,U_1972,U_1973) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( U_1977 = U_1976
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1971,U_1972,U_1973,U_1974,U_1975),U_1977))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1971,U_1972,U_1973,U_1974,U_1975),U_1976))
    | ~ c_Finite__Set_Ofun__left__comm(U_1971,U_1972,U_1973) ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_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_445_2,plain,
    ! [U_1979,U_1978] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_1978,hAPP(hAPP(c_Set_Oinsert(U_1978),U_1979),c_Orderings_Obot__class_Obot(tc_fun(U_1978,tc_HOL_Obool)))) = U_1979
      | ~ class_Lattices_Olattice(U_1978) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_1978,hAPP(hAPP(c_Set_Oinsert(U_1978),U_1979),c_Orderings_Obot__class_Obot(tc_fun(U_1978,tc_HOL_Obool)))) = U_1979
    | ~ class_Lattices_Olattice(U_1978) ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_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_446_2,plain,
    ! [U_1983,U_1982,U_1981,U_1980] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1980,tc_HOL_Obool)),U_1981),U_1982)) = 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_1980,tc_Nat_Onat),U_1983),U_1981)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),U_1982))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1980,tc_HOL_Obool)),U_1981),U_1982)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1980),U_1982))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1980),U_1981)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

cnf(f_446_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1980,tc_HOL_Obool)),U_1981),U_1982)) = 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_1980,tc_Nat_Onat),U_1983),U_1981)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),U_1982))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1980,tc_Nat_Onat),U_1983),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1980,tc_HOL_Obool)),U_1981),U_1982)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1980),U_1982))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1980),U_1981)) ),
    inference(clausify,[status(thm)],[f_446_2]) ).

fof(f_447_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_447_2,plain,
    ! [U_1989,U_1988,U_1987,U_1986,U_1985,U_1984] :
      ( hAPP(hAPP(U_1986,U_1988),hAPP(hAPP(c_Finite__Set_Ofold(U_1984,U_1985,U_1986),U_1989),U_1987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1984,U_1985,U_1986),hAPP(hAPP(U_1986,U_1988),U_1989)),U_1987)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1984),U_1987))
      | ~ c_Finite__Set_Ofun__left__comm(U_1984,U_1985,U_1986) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    ( hAPP(hAPP(U_1986,U_1988),hAPP(hAPP(c_Finite__Set_Ofold(U_1984,U_1985,U_1986),U_1989),U_1987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1984,U_1985,U_1986),hAPP(hAPP(U_1986,U_1988),U_1989)),U_1987)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1984),U_1987))
    | ~ c_Finite__Set_Ofun__left__comm(U_1984,U_1985,U_1986) ),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_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_448_2,plain,
    ! [U_1992,U_1991,U_1990] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1990),U_1992),c_Big__Operators_Olattice__class_OInf__fin(U_1990,U_1991)) = U_1992
      | ~ hBOOL(hAPP(hAPP(c_member(U_1990),U_1992),U_1991))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1990),U_1991))
      | ~ class_Lattices_Olattice(U_1990) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1990),U_1992),c_Big__Operators_Olattice__class_OInf__fin(U_1990,U_1991)) = U_1992
    | ~ hBOOL(hAPP(hAPP(c_member(U_1990),U_1992),U_1991))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1990),U_1991))
    | ~ class_Lattices_Olattice(U_1990) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_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_449_2,plain,
    ! [U_1995,U_1994,U_1993] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1993),U_1995),c_Big__Operators_Olattice__class_OInf__fin(U_1993,U_1994)) = c_Big__Operators_Olattice__class_OInf__fin(U_1993,U_1994)
      | ~ hBOOL(hAPP(hAPP(c_member(U_1993),U_1995),U_1994))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1993),U_1994))
      | ~ class_Lattices_Olattice(U_1993) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1993),U_1995),c_Big__Operators_Olattice__class_OInf__fin(U_1993,U_1994)) = c_Big__Operators_Olattice__class_OInf__fin(U_1993,U_1994)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1993),U_1995),U_1994))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1993),U_1994))
    | ~ class_Lattices_Olattice(U_1993) ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_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_450_2,plain,
    ! [U_2001,U_2000,U_1999,U_1998,U_1997,U_1996] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_1996,U_1997,U_1998),U_1999),U_2000) = U_2001
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1996,U_1997,U_1998,U_1999,U_2000),U_2001))
      | ~ c_Finite__Set_Ofun__left__comm(U_1996,U_1997,U_1998) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_1996,U_1997,U_1998),U_1999),U_2000) = U_2001
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1996,U_1997,U_1998,U_1999,U_2000),U_2001))
    | ~ c_Finite__Set_Ofun__left__comm(U_1996,U_1997,U_1998) ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_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_451_2,plain,
    ! [U_2006,U_2005,U_2004,U_2003,U_2002] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2003,U_2002),U_2006),hAPP(hAPP(c_Set_Oinsert(U_2003),U_2005),U_2004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2002),hAPP(U_2006,U_2005)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2003,U_2002),U_2006),U_2004))
      | hBOOL(hAPP(hAPP(c_member(U_2003),U_2005),U_2004))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2003),U_2004))
      | ~ class_Groups_Ocomm__monoid__add(U_2002) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2003,U_2002),U_2006),hAPP(hAPP(c_Set_Oinsert(U_2003),U_2005),U_2004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2002),hAPP(U_2006,U_2005)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2003,U_2002),U_2006),U_2004))
    | hBOOL(hAPP(hAPP(c_member(U_2003),U_2005),U_2004))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2003),U_2004))
    | ~ class_Groups_Ocomm__monoid__add(U_2002) ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_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_452_2,plain,
    ! [U_2011,U_2010,U_2009,U_2008,U_2007] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2008,U_2007),U_2011),hAPP(hAPP(c_Set_Oinsert(U_2008),U_2010),U_2009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),hAPP(U_2011,U_2010)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2008,U_2007),U_2011),U_2009))
      | hBOOL(hAPP(hAPP(c_member(U_2008),U_2010),U_2009))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2008),U_2009))
      | ~ class_Groups_Ocomm__monoid__add(U_2007) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2008,U_2007),U_2011),hAPP(hAPP(c_Set_Oinsert(U_2008),U_2010),U_2009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),hAPP(U_2011,U_2010)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2008,U_2007),U_2011),U_2009))
    | hBOOL(hAPP(hAPP(c_member(U_2008),U_2010),U_2009))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2008),U_2009))
    | ~ class_Groups_Ocomm__monoid__add(U_2007) ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_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_453_2,plain,
    ! [U_2016,U_2015,U_2014,U_2013,U_2012] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2012),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2013,tc_HOL_Obool)),U_2014),U_2015))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2013,tc_HOL_Obool)),U_2014),U_2015))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2012),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),U_2014)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),U_2015))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2013),U_2015))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2013),U_2014))
      | ~ class_Groups_Ocomm__monoid__add(U_2012) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

cnf(f_453_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2012),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2013,tc_HOL_Obool)),U_2014),U_2015))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2013,tc_HOL_Obool)),U_2014),U_2015))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2012),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),U_2014)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2013,U_2012),U_2016),U_2015))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2013),U_2015))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2013),U_2014))
    | ~ class_Groups_Ocomm__monoid__add(U_2012) ),
    inference(clausify,[status(thm)],[f_453_2]) ).

fof(f_454_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_454_2,plain,
    ! [U_2019,U_2018,U_2017] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2017,hAPP(hAPP(c_Set_Oinsert(U_2017),U_2019),U_2018)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2017),U_2019),c_Big__Operators_Olattice__class_OInf__fin(U_2017,U_2018))
      | U_2018 = c_Orderings_Obot__class_Obot(tc_fun(U_2017,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2017),U_2018))
      | ~ class_Lattices_Olattice(U_2017) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2017,hAPP(hAPP(c_Set_Oinsert(U_2017),U_2019),U_2018)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2017),U_2019),c_Big__Operators_Olattice__class_OInf__fin(U_2017,U_2018))
    | U_2018 = c_Orderings_Obot__class_Obot(tc_fun(U_2017,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2017),U_2018))
    | ~ class_Lattices_Olattice(U_2017) ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_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_455_2,plain,
    ! [U_2022,U_2021,U_2020] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2020),c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2022)),c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2021)) = c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2021)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2020,tc_HOL_Obool)),U_2022),U_2021))
      | U_2022 = c_Orderings_Obot__class_Obot(tc_fun(U_2020,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2020),U_2021))
      | ~ class_Lattices_Olattice(U_2020) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2020),c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2022)),c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2021)) = c_Big__Operators_Olattice__class_OInf__fin(U_2020,U_2021)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2020,tc_HOL_Obool)),U_2022),U_2021))
    | U_2022 = c_Orderings_Obot__class_Obot(tc_fun(U_2020,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2020),U_2021))
    | ~ class_Lattices_Olattice(U_2020) ),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_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_456_2,plain,
    ! [U_2025,U_2024,U_2023] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2023,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2023,tc_HOL_Obool)),U_2024),U_2025)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2023),c_Big__Operators_Olattice__class_OInf__fin(U_2023,U_2024)),c_Big__Operators_Olattice__class_OInf__fin(U_2023,U_2025))
      | U_2025 = c_Orderings_Obot__class_Obot(tc_fun(U_2023,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2023),U_2025))
      | U_2024 = c_Orderings_Obot__class_Obot(tc_fun(U_2023,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2023),U_2024))
      | ~ class_Lattices_Olattice(U_2023) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

cnf(f_456_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2023,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2023,tc_HOL_Obool)),U_2024),U_2025)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2023),c_Big__Operators_Olattice__class_OInf__fin(U_2023,U_2024)),c_Big__Operators_Olattice__class_OInf__fin(U_2023,U_2025))
    | U_2025 = c_Orderings_Obot__class_Obot(tc_fun(U_2023,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2023),U_2025))
    | U_2024 = c_Orderings_Obot__class_Obot(tc_fun(U_2023,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2023),U_2024))
    | ~ class_Lattices_Olattice(U_2023) ),
    inference(clausify,[status(thm)],[f_456_2]) ).

fof(f_457_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_457_2,plain,
    ! [U_2027,U_2026] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2026),c_Big__Operators_Olattice__class_OInf__fin(U_2026,U_2027)),c_Big__Operators_Olattice__class_OSup__fin(U_2026,U_2027)))
      | U_2027 = c_Orderings_Obot__class_Obot(tc_fun(U_2026,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2026),U_2027))
      | ~ class_Lattices_Olattice(U_2026) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

cnf(f_457_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2026),c_Big__Operators_Olattice__class_OInf__fin(U_2026,U_2027)),c_Big__Operators_Olattice__class_OSup__fin(U_2026,U_2027)))
    | U_2027 = c_Orderings_Obot__class_Obot(tc_fun(U_2026,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2026),U_2027))
    | ~ class_Lattices_Olattice(U_2026) ),
    inference(clausify,[status(thm)],[f_457_2]) ).

fof(f_458_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_458_2,plain,
    ! [U_2030,U_2029,U_2028] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2028,hAPP(hAPP(c_Set_Oinsert(U_2028),U_2030),U_2029)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),U_2029)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2028),U_2029))
      | ~ class_Lattices_Olattice(U_2028) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

cnf(f_458_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2028,hAPP(hAPP(c_Set_Oinsert(U_2028),U_2030),U_2029)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2028,U_2028,c_Lattices_Osemilattice__inf__class_Oinf(U_2028)),U_2030),U_2029)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2028),U_2029))
    | ~ class_Lattices_Olattice(U_2028) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

fof(f_459_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_459_2,plain,
    ! [U_2035,U_2034,U_2033,U_2032,U_2031] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,U_2031),U_2034),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2035),U_2033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(U_2034,U_2035)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,U_2031),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_2035),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033))
      | ~ class_Groups_Ocomm__monoid__add(U_2031) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

cnf(f_459_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,U_2031),U_2034),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2035),U_2033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(U_2034,U_2035)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2032,U_2031),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_2035),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033))
    | ~ class_Groups_Ocomm__monoid__add(U_2031) ),
    inference(clausify,[status(thm)],[f_459_2]) ).

fof(f_460_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_460_2,plain,
    ! [U_2040,U_2039,U_2038,U_2037,U_2036] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2037,tc_HOL_Obool)),U_2038),U_2039)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),U_2038)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),U_2039))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2037,tc_HOL_Obool)),U_2038),U_2039) != c_Orderings_Obot__class_Obot(tc_fun(U_2037,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2037),U_2039))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2037),U_2038))
      | ~ class_Groups_Ocomm__monoid__add(U_2036) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

cnf(f_460_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2037,tc_HOL_Obool)),U_2038),U_2039)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),U_2038)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2037,U_2036),U_2040),U_2039))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2037,tc_HOL_Obool)),U_2038),U_2039) != c_Orderings_Obot__class_Obot(tc_fun(U_2037,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2037),U_2039))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2037),U_2038))
    | ~ class_Groups_Ocomm__monoid__add(U_2036) ),
    inference(clausify,[status(thm)],[f_460_2]) ).

fof(f_461_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_461_2,plain,
    ! [U_2045,U_2044,U_2043,U_2042,U_2041] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2042,tc_HOL_Obool)),U_2043),U_2044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2041),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),U_2043)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),U_2044))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2042,tc_HOL_Obool)),U_2043),U_2044)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2044))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2043))
      | ~ class_Groups_Oab__group__add(U_2041) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

cnf(f_461_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2042,tc_HOL_Obool)),U_2043),U_2044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2041),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),U_2043)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),U_2044))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2042,U_2041),U_2045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2042,tc_HOL_Obool)),U_2043),U_2044)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2044))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2042),U_2043))
    | ~ class_Groups_Oab__group__add(U_2041) ),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_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_462_2,plain,
    ! [U_2050,U_2049,U_2048,U_2047,U_2046] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2046,U_2047,U_2048,U_2050,U_2049),hAPP(hAPP(c_Finite__Set_Ofold(U_2046,U_2047,U_2048),U_2050),U_2049)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2046),U_2049))
      | ~ c_Finite__Set_Ofun__left__comm(U_2046,U_2047,U_2048) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2046,U_2047,U_2048,U_2050,U_2049),hAPP(hAPP(c_Finite__Set_Ofold(U_2046,U_2047,U_2048),U_2050),U_2049)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2046),U_2049))
    | ~ c_Finite__Set_Ofun__left__comm(U_2046,U_2047,U_2048) ),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_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_463_2,plain,
    ! [U_2053,U_2052,U_2051] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2051,hAPP(hAPP(c_Set_Oinsert(U_2051),U_2053),U_2052)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2051),U_2053),c_Big__Operators_Olattice__class_OInf__fin(U_2051,U_2052))
      | U_2052 = c_Orderings_Obot__class_Obot(tc_fun(U_2051,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_2051),U_2053),U_2052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2051),U_2052))
      | ~ class_Lattices_Olattice(U_2051) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

cnf(f_463_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2051,hAPP(hAPP(c_Set_Oinsert(U_2051),U_2053),U_2052)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2051),U_2053),c_Big__Operators_Olattice__class_OInf__fin(U_2051,U_2052))
    | U_2052 = c_Orderings_Obot__class_Obot(tc_fun(U_2051,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_2051),U_2053),U_2052))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2051),U_2052))
    | ~ class_Lattices_Olattice(U_2051) ),
    inference(clausify,[status(thm)],[f_463_2]) ).

fof(f_464_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_464_2,plain,
    ! [U_2056,U_2055,U_2054] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),U_2055)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2054),U_2056),c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),U_2055)) = U_2056
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2054),U_2055))
      | ~ class_Lattices_Olattice(U_2054) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),U_2055)) = U_2056
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2054),U_2055))
    | ~ class_Lattices_Olattice(U_2054) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),U_2055)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2054),U_2056),c_Big__Operators_Olattice__class_OInf__fin(U_2054,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2054,tc_HOL_Obool)),U_2055),hAPP(hAPP(c_Set_Oinsert(U_2054),U_2056),c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2054,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2054),U_2055))
    | ~ class_Lattices_Olattice(U_2054) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_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_465_2,plain,
    ! [U_2059,U_2058,U_2057] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2057,tc_HOL_Obool)),U_2058),U_2059)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2057),c_Big__Operators_Olattice__class_OInf__fin(U_2057,U_2058)),c_Big__Operators_Olattice__class_OInf__fin(U_2057,U_2059))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2057,tc_HOL_Obool)),U_2058),U_2059) != c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
      | U_2059 = c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2057),U_2059))
      | U_2058 = c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2057),U_2058))
      | ~ class_Lattices_Olattice(U_2057) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2057,tc_HOL_Obool)),U_2058),U_2059)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2057),c_Big__Operators_Olattice__class_OInf__fin(U_2057,U_2058)),c_Big__Operators_Olattice__class_OInf__fin(U_2057,U_2059))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2057,tc_HOL_Obool)),U_2058),U_2059) != c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
    | U_2059 = c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2057),U_2059))
    | U_2058 = c_Orderings_Obot__class_Obot(tc_fun(U_2057,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2057),U_2058))
    | ~ class_Lattices_Olattice(U_2057) ),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_466_2,plain,
    ! [U_2065,U_2064,U_2063,U_2062,U_2061,U_2060] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2061),U_2062)),U_2063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2064),U_2062)),U_2065)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2060),U_2064),U_2061)),U_2062)),U_2065))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2060),U_2064),U_2061)),U_2062)),U_2065)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2061),U_2062)),U_2063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2064),U_2062)),U_2065))) ) )
      | ~ class_Rings_Oordered__ring(U_2060) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

cnf(f_466_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2060),U_2064),U_2061)),U_2062)),U_2065)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2061),U_2062)),U_2063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2064),U_2062)),U_2065)))
    | ~ class_Rings_Oordered__ring(U_2060) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2061),U_2062)),U_2063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),U_2064),U_2062)),U_2065)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2060),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2060),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2060),U_2064),U_2061)),U_2062)),U_2065)))
    | ~ class_Rings_Oordered__ring(U_2060) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

fof(f_467_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_467_2,plain,
    ! [U_2071,U_2070,U_2069,U_2068,U_2067,U_2066] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2067),U_2068)),U_2069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2070),U_2068)),U_2071)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2066),U_2067),U_2070)),U_2068)),U_2069)),U_2071)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2066),U_2067),U_2070)),U_2068)),U_2069)),U_2071))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2067),U_2068)),U_2069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2070),U_2068)),U_2071))) ) )
      | ~ class_Rings_Oordered__ring(U_2066) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

cnf(f_467_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2066),U_2067),U_2070)),U_2068)),U_2069)),U_2071))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2067),U_2068)),U_2069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2070),U_2068)),U_2071)))
    | ~ class_Rings_Oordered__ring(U_2066) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2067),U_2068)),U_2069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2070),U_2068)),U_2071)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2066),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2066),U_2067),U_2070)),U_2068)),U_2069)),U_2071))
    | ~ class_Rings_Oordered__ring(U_2066) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

fof(f_468_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_468_2,plain,
    ! [U_2077,U_2076,U_2075,U_2074,U_2073,U_2072] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2073),U_2074)),U_2075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2076),U_2074)),U_2077)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),U_2075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2076),U_2073)),U_2074)),U_2077))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),U_2075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2076),U_2073)),U_2074)),U_2077)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2073),U_2074)),U_2075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2076),U_2074)),U_2077))) ) )
      | ~ class_Rings_Oordered__ring(U_2072) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),U_2075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2076),U_2073)),U_2074)),U_2077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2073),U_2074)),U_2075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2076),U_2074)),U_2077)))
    | ~ class_Rings_Oordered__ring(U_2072) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2073),U_2074)),U_2075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),U_2076),U_2074)),U_2077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2072),U_2075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2072),U_2076),U_2073)),U_2074)),U_2077)))
    | ~ class_Rings_Oordered__ring(U_2072) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_469_2,plain,
    ! [U_2083,U_2082,U_2081,U_2080,U_2079,U_2078] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2079),U_2080)),U_2081)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2082),U_2080)),U_2083)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2078),U_2079),U_2082)),U_2080)),U_2081)),U_2083)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2078),U_2079),U_2082)),U_2080)),U_2081)),U_2083))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2079),U_2080)),U_2081)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2082),U_2080)),U_2083))) ) )
      | ~ class_Rings_Oordered__ring(U_2078) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2078),U_2079),U_2082)),U_2080)),U_2081)),U_2083))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2079),U_2080)),U_2081)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2082),U_2080)),U_2083)))
    | ~ class_Rings_Oordered__ring(U_2078) ),
    inference(clausify,[status(thm)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2079),U_2080)),U_2081)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),U_2082),U_2080)),U_2083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2078),U_2079),U_2082)),U_2080)),U_2081)),U_2083))
    | ~ class_Rings_Oordered__ring(U_2078) ),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_470_2,plain,
    ! [U_2089,U_2088,U_2087,U_2086,U_2085,U_2084] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2085),U_2086)),U_2087) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2088),U_2086)),U_2089)
          | U_2087 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2084),U_2088),U_2085)),U_2086)),U_2089) )
        & ( U_2087 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2084),U_2088),U_2085)),U_2086)),U_2089)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2085),U_2086)),U_2087) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2088),U_2086)),U_2089) ) )
      | ~ class_Rings_Oring(U_2084) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    ( U_2087 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2084),U_2088),U_2085)),U_2086)),U_2089)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2085),U_2086)),U_2087) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2088),U_2086)),U_2089)
    | ~ class_Rings_Oring(U_2084) ),
    inference(clausify,[status(thm)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2085),U_2086)),U_2087) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),U_2088),U_2086)),U_2089)
    | U_2087 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2084),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2084),U_2088),U_2085)),U_2086)),U_2089)
    | ~ class_Rings_Oring(U_2084) ),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_471_2,plain,
    ! [U_2095,U_2094,U_2093,U_2092,U_2091,U_2090] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)),U_2093) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2094),U_2092)),U_2095)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2090),U_2091),U_2094)),U_2092)),U_2093) != U_2095 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2090),U_2091),U_2094)),U_2092)),U_2093) = U_2095
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)),U_2093) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2094),U_2092)),U_2095) ) )
      | ~ class_Rings_Oring(U_2090) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

cnf(f_471_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2090),U_2091),U_2094)),U_2092)),U_2093) = U_2095
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)),U_2093) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2094),U_2092)),U_2095)
    | ~ class_Rings_Oring(U_2090) ),
    inference(clausify,[status(thm)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)),U_2093) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2094),U_2092)),U_2095)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2090),U_2091),U_2094)),U_2092)),U_2093) != U_2095
    | ~ class_Rings_Oring(U_2090) ),
    inference(clausify,[status(thm)],[f_471_2]) ).

fof(f_472_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_472_2,plain,
    ! [U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097] :
      ( ? [U_2096] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2097,tc_HOL_Obool)),U_2101),hAPP(hAPP(c_Set_Oinsert(U_2097),U_2103),c_Orderings_Obot__class_Obot(tc_fun(U_2097,tc_HOL_Obool))))),U_2096))
          & U_2102 = hAPP(hAPP(U_2099,U_2103),U_2096) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2097),U_2103),U_2101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,U_2101),U_2102))
      | ~ c_Finite__Set_Ofun__left__comm(U_2097,U_2098,U_2099) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2097,tc_HOL_Obool)),U_2101),hAPP(hAPP(c_Set_Oinsert(U_2097),U_2103),c_Orderings_Obot__class_Obot(tc_fun(U_2097,tc_HOL_Obool))))),sK30(U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097)))
        & U_2102 = hAPP(hAPP(U_2099,U_2103),sK30(U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2097),U_2103),U_2101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,U_2101),U_2102))
      | ~ c_Finite__Set_Ofun__left__comm(U_2097,U_2098,U_2099) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2096,sK30(U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097))],[f_472_2]) ).

cnf(f_472_4,plain,
    ( U_2102 = hAPP(hAPP(U_2099,U_2103),sK30(U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2097),U_2103),U_2101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,U_2101),U_2102))
    | ~ c_Finite__Set_Ofun__left__comm(U_2097,U_2098,U_2099) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

cnf(f_472_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2097,tc_HOL_Obool)),U_2101),hAPP(hAPP(c_Set_Oinsert(U_2097),U_2103),c_Orderings_Obot__class_Obot(tc_fun(U_2097,tc_HOL_Obool))))),sK30(U_2103,U_2102,U_2101,U_2100,U_2099,U_2098,U_2097)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2097),U_2103),U_2101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2097,U_2098,U_2099,U_2100,U_2101),U_2102))
    | ~ c_Finite__Set_Ofun__left__comm(U_2097,U_2098,U_2099) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_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_473_2,plain,
    ! [U_2107,U_2106] :
      ( hBOOL(hAPP(hAPP(c_member(U_2106),c_Big__Operators_Olattice__class_OInf__fin(U_2106,U_2107)),U_2107))
      | ? [U_2105,U_2104] : ~ hBOOL(hAPP(hAPP(c_member(U_2106),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2106),U_2105),U_2104)),hAPP(hAPP(c_Set_Oinsert(U_2106),U_2105),hAPP(hAPP(c_Set_Oinsert(U_2106),U_2104),c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))))))
      | U_2107 = c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2106),U_2107))
      | ~ class_Lattices_Olattice(U_2106) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_2107,U_2106] :
      ( hBOOL(hAPP(hAPP(c_member(U_2106),c_Big__Operators_Olattice__class_OInf__fin(U_2106,U_2107)),U_2107))
      | ? [U_2104] : ~ hBOOL(hAPP(hAPP(c_member(U_2106),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2106),sK31(U_2107,U_2106)),U_2104)),hAPP(hAPP(c_Set_Oinsert(U_2106),sK31(U_2107,U_2106)),hAPP(hAPP(c_Set_Oinsert(U_2106),U_2104),c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))))))
      | U_2107 = c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2106),U_2107))
      | ~ class_Lattices_Olattice(U_2106) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2105,sK31(U_2107,U_2106))],[f_473_2]) ).

fof(f_473_4,plain,
    ! [U_2107,U_2106] :
      ( hBOOL(hAPP(hAPP(c_member(U_2106),c_Big__Operators_Olattice__class_OInf__fin(U_2106,U_2107)),U_2107))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2106),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2106),sK31(U_2107,U_2106)),sK32(U_2107,U_2106))),hAPP(hAPP(c_Set_Oinsert(U_2106),sK31(U_2107,U_2106)),hAPP(hAPP(c_Set_Oinsert(U_2106),sK32(U_2107,U_2106)),c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))))))
      | U_2107 = c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2106),U_2107))
      | ~ class_Lattices_Olattice(U_2106) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2104,sK32(U_2107,U_2106))],[f_473_3]) ).

cnf(f_473_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2106),c_Big__Operators_Olattice__class_OInf__fin(U_2106,U_2107)),U_2107))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2106),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2106),sK31(U_2107,U_2106)),sK32(U_2107,U_2106))),hAPP(hAPP(c_Set_Oinsert(U_2106),sK31(U_2107,U_2106)),hAPP(hAPP(c_Set_Oinsert(U_2106),sK32(U_2107,U_2106)),c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))))))
    | U_2107 = c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2106),U_2107))
    | ~ class_Lattices_Olattice(U_2106) ),
    inference(clausify,[status(thm)],[f_473_4]) ).

fof(f_474_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_474_2,plain,
    ! [U_2111,U_2110,U_2109,U_2108] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2108),U_2110),U_2111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),U_2110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),U_2111))
      | ~ class_Rings_Ocomm__semiring__1(U_2108) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

cnf(f_474_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2108),U_2110),U_2111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),U_2110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2108),U_2109),U_2111))
    | ~ class_Rings_Ocomm__semiring__1(U_2108) ),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
      ( ( ( ( V_ca_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_ca_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_ca_2)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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_ca_2))
          | V_ca_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_475_2,plain,
    ! [U_2116,U_2115,U_2114,U_2113,U_2112] :
      ( ( ( ( U_2115 != U_2116
            & U_2113 != U_2114 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2116)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2115)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2116)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2115))
          | U_2115 = U_2116
          | U_2113 = U_2114 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2112) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

cnf(f_475_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2116)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2115))
    | U_2115 = U_2116
    | U_2113 = U_2114
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2112) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( U_2113 != U_2114
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2116)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2115))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2112) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

cnf(f_475_5,plain,
    ( U_2115 != U_2116
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2116)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2115))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2112) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

fof(f_476_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_476_2,plain,
    ! [U_2119,U_2118,U_2117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2119),U_2118))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2118),U_2119))
      | U_2118 = U_2119
      | ~ class_Rings_Olinordered__idom(U_2117) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

cnf(f_476_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2119),U_2118))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2118),U_2119))
    | U_2118 = U_2119
    | ~ class_Rings_Olinordered__idom(U_2117) ),
    inference(clausify,[status(thm)],[f_476_2]) ).

fof(f_477_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_477_2,plain,
    ! [U_2124,U_2123,U_2122,U_2121,U_2120] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2123),U_2124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2122),U_2124))
      | ~ class_Rings_Ocomm__semiring__1(U_2120) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2123),U_2124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2122),U_2124))
    | ~ class_Rings_Ocomm__semiring__1(U_2120) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_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_478_2,plain,
    ! [U_2128,U_2127,U_2126,U_2125] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),U_2126),U_2127)),U_2128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),U_2126),U_2128)),U_2127)
      | ~ class_Rings_Ocomm__semiring__1(U_2125) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),U_2126),U_2127)),U_2128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2125),U_2126),U_2128)),U_2127)
    | ~ class_Rings_Ocomm__semiring__1(U_2125) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_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_479_2,plain,
    ! [U_2132,U_2131,U_2130,U_2129] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2130),U_2131)),U_2132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2131),U_2132))
      | ~ class_Rings_Ocomm__semiring__1(U_2129) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2130),U_2131)),U_2132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2129),U_2131),U_2132))
    | ~ class_Rings_Ocomm__semiring__1(U_2129) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_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_480_2,plain,
    ! [U_2136,U_2135,U_2134,U_2133] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2135),U_2136)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),U_2135)),U_2136)
      | ~ class_Rings_Ocomm__semiring__1(U_2133) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2135),U_2136)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2133),U_2134),U_2135)),U_2136)
    | ~ class_Rings_Ocomm__semiring__1(U_2133) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_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_481_2,plain,
    ! [U_2140,U_2139,U_2138,U_2137] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2138),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2139),U_2140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2138),U_2140))
      | ~ class_Rings_Ocomm__semiring__1(U_2137) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

cnf(f_481_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2138),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2139),U_2140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),U_2138),U_2140))
    | ~ class_Rings_Ocomm__semiring__1(U_2137) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

fof(f_482_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_482_2,plain,
    ! [U_2143,U_2142,U_2141] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2141),U_2142),U_2143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2141),U_2143),U_2142)
      | ~ class_Rings_Ocomm__semiring__1(U_2141) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2141),U_2142),U_2143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2141),U_2143),U_2142)
    | ~ class_Rings_Ocomm__semiring__1(U_2141) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_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_483_2,plain,
    ! [U_2148,U_2147,U_2146,U_2145,U_2144] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2148)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2146),U_2148))
      | ~ class_Rings_Ocomm__semiring__1(U_2144) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2148)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2146),U_2148))
    | ~ class_Rings_Ocomm__semiring__1(U_2144) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_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_484_2,plain,
    ! [U_2153,U_2152,U_2151,U_2150,U_2149] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2152),U_2153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),U_2153))
      | ~ class_Rings_Ocomm__semiring__1(U_2149) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

cnf(f_484_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2152),U_2153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),U_2153))
    | ~ class_Rings_Ocomm__semiring__1(U_2149) ),
    inference(clausify,[status(thm)],[f_484_2]) ).

fof(f_485_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_485_2,plain,
    ! [U_2158,U_2157,U_2156,U_2155,U_2154] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2156)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2157),U_2158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2157),U_2158)))
      | ~ class_Rings_Ocomm__semiring__1(U_2154) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

cnf(f_485_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2156)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2157),U_2158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2157),U_2158)))
    | ~ class_Rings_Ocomm__semiring__1(U_2154) ),
    inference(clausify,[status(thm)],[f_485_2]) ).

fof(f_486_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_486_2,plain,
    ! [U_2162,U_2161,U_2160,U_2159] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),U_2160),U_2161)),U_2162) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),U_2160),U_2162)),U_2161)
      | ~ class_Rings_Ocomm__semiring__1(U_2159) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

cnf(f_486_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),U_2160),U_2161)),U_2162) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2159),U_2160),U_2162)),U_2161)
    | ~ class_Rings_Ocomm__semiring__1(U_2159) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

fof(f_487_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_487_2,plain,
    ! [U_2166,U_2165,U_2164,U_2163] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2165)),U_2166) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2166))
      | ~ class_Rings_Ocomm__semiring__1(U_2163) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2165)),U_2166) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2166))
    | ~ class_Rings_Ocomm__semiring__1(U_2163) ),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_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_488_2,plain,
    ! [U_2170,U_2169,U_2168,U_2167] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2169),U_2170)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2168),U_2169)),U_2170)
      | ~ class_Rings_Ocomm__semiring__1(U_2167) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2169),U_2170)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2167),U_2168),U_2169)),U_2170)
    | ~ class_Rings_Ocomm__semiring__1(U_2167) ),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_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_489_2,plain,
    ! [U_2174,U_2173,U_2172,U_2171] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2173),U_2174)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2172),U_2174))
      | ~ class_Rings_Ocomm__semiring__1(U_2171) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2173),U_2174)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2171),U_2172),U_2174))
    | ~ class_Rings_Ocomm__semiring__1(U_2171) ),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_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_490_2,plain,
    ! [U_2177,U_2176,U_2175] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2176),U_2177) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2177),U_2176)
      | ~ class_Rings_Ocomm__semiring__1(U_2175) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2176),U_2177) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2177),U_2176)
    | ~ class_Rings_Ocomm__semiring__1(U_2175) ),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_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_491_2,plain,
    ! [U_2182,U_2181,U_2180,U_2179,U_2178] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2180))
          | ( U_2180 != U_2182
            & U_2179 != U_2181 ) )
        & ( U_2180 = U_2182
          | U_2179 = U_2181
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2182)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2180)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2178) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( U_2180 = U_2182
    | U_2179 = U_2181
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2182)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2180))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2178) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

cnf(f_491_4,plain,
    ( U_2179 != U_2181
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2180))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2178) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

cnf(f_491_5,plain,
    ( U_2180 != U_2182
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2182)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2182)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2181),U_2180))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2178) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_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_492_2,plain,
    ! [U_2187,U_2186,U_2185,U_2184,U_2183] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),U_2184),U_2185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),U_2186),U_2185)),U_2187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),U_2184),U_2186)),U_2185)),U_2187)
      | ~ class_Rings_Osemiring(U_2183) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

cnf(f_492_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),U_2184),U_2185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),U_2186),U_2185)),U_2187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2183),U_2184),U_2186)),U_2185)),U_2187)
    | ~ class_Rings_Osemiring(U_2183) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_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_493_2,plain,
    ! [U_2191,U_2190,U_2189,U_2188] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2191),U_2190)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2188),U_2189),U_2191)),U_2190)
      | ~ class_Rings_Ocomm__semiring__1(U_2188) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

cnf(f_493_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2190)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2191),U_2190)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2188),U_2189),U_2191)),U_2190)
    | ~ class_Rings_Ocomm__semiring__1(U_2188) ),
    inference(clausify,[status(thm)],[f_493_2]) ).

fof(f_494_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_494_2,plain,
    ! [U_2195,U_2194,U_2193,U_2192] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2192),U_2193),U_2194)),U_2195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),U_2193),U_2195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),U_2194),U_2195))
      | ~ class_Rings_Ocomm__semiring__1(U_2192) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

cnf(f_494_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2192),U_2193),U_2194)),U_2195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),U_2193),U_2195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2192),U_2194),U_2195))
    | ~ class_Rings_Ocomm__semiring__1(U_2192) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_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_495_2,plain,
    ! [U_2199,U_2198,U_2197,U_2196] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2196),U_2197),U_2198)),U_2199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),U_2197),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),U_2198),U_2199))
      | ~ class_Rings_Ocomm__semiring(U_2196) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

cnf(f_495_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2196),U_2197),U_2198)),U_2199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),U_2197),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2196),U_2198),U_2199))
    | ~ class_Rings_Ocomm__semiring(U_2196) ),
    inference(clausify,[status(thm)],[f_495_2]) ).

fof(f_496_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_496_2,plain,
    ! [U_2201,U_2200] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2200),U_2201)) = U_2200
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2200),U_2201)) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

cnf(f_496_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2200),U_2201)) = U_2200
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2200),U_2201)) ),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_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_497_2,plain,
    ! [U_2204,U_2203,U_2202] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2203),U_2204)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2202),U_2204)),U_2203)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2202),U_2204)),U_2203))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2203),U_2204))) ) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_2210,U_2208,U_2206] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2208),U_2210)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2206),U_2210)),U_2208)) )
    & ! [U_2209,U_2207,U_2205] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2205),U_2209)),U_2207))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2207),U_2209))) ) ),
    inference(miniscope,[status(thm)],[f_497_2]) ).

cnf(f_497_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2205),U_2209)),U_2207))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2207),U_2209))) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2208),U_2210)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2206),U_2210)),U_2208)) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_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_498_2,plain,
    ! [U_2213,U_2212,U_2211] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2211),U_2212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2213),U_2212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2211),U_2213),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

cnf(f_498_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2211),U_2212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2213),U_2212)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2211),U_2213),
    inference(clausify,[status(thm)],[f_498_2]) ).

fof(f_499_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_499_2,plain,
    ! [U_2216,U_2215,U_2214] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2214),U_2215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2214),U_2216)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2215),U_2216),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

cnf(f_499_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2214),U_2215)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2214),U_2216)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2215),U_2216),
    inference(clausify,[status(thm)],[f_499_2]) ).

fof(f_500_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_500_2,plain,
    ! [U_2219,U_2218,U_2217] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2217),U_2218)),U_2219) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2218),U_2219)),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

cnf(f_500_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2217),U_2218)),U_2219) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2218),U_2219)),
    inference(clausify,[status(thm)],[f_500_2]) ).

fof(f_501_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_501_2,plain,
    ! [U_2221,U_2220] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2220),U_2221)),U_2220) = U_2221,
    inference(variable_rename,[status(thm)],[f_501_1]) ).

cnf(f_501_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2220),U_2221)),U_2220) = U_2221,
    inference(clausify,[status(thm)],[f_501_2]) ).

fof(f_502_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_502_2,plain,
    ! [U_2223,U_2222] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2222),U_2223)),U_2223) = U_2222,
    inference(variable_rename,[status(thm)],[f_502_1]) ).

cnf(f_502_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2222),U_2223)),U_2223) = U_2222,
    inference(clausify,[status(thm)],[f_502_2]) ).

fof(f_503_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_503_2,plain,
    ! [U_2226,U_2225,U_2224] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2226),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2225),U_2224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2226),U_2224)),U_2225)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2224),U_2225)) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

cnf(f_503_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2226),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2225),U_2224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2226),U_2224)),U_2225)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2224),U_2225)) ),
    inference(clausify,[status(thm)],[f_503_2]) ).

fof(f_504_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_504_2,plain,
    ! [U_2229,U_2228,U_2227] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2227),U_2228)),U_2229))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2229),U_2228))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2229),U_2228)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2227),U_2228)),U_2229)) ) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_2235,U_2233,U_2231] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2231),U_2233)),U_2235))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2235),U_2233))) )
    & ! [U_2234,U_2232,U_2230] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2234),U_2232)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2230),U_2232)),U_2234)) ) ),
    inference(miniscope,[status(thm)],[f_504_2]) ).

cnf(f_504_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2234),U_2232)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2230),U_2232)),U_2234)) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_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_2231),U_2233)),U_2235))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2235),U_2233))) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_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_505_2,plain,
    ! [U_2238,U_2237,U_2236] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2237),U_2238)),U_2236)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2236),U_2237)) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

cnf(f_505_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2237),U_2238)),U_2236)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2236),U_2237)) ),
    inference(clausify,[status(thm)],[f_505_2]) ).

fof(f_506_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_506_2,plain,
    ! [U_2239] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2239),U_2239))),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

cnf(f_506_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2239),U_2239))),
    inference(clausify,[status(thm)],[f_506_2]) ).

fof(f_507_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_507_2,plain,
    ! [U_2240] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2240)))),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

cnf(f_507_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2240)))),
    inference(clausify,[status(thm)],[f_507_2]) ).

fof(f_508_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_508_2,plain,
    ! [U_2243,U_2242,U_2241] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2243)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2243)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2241),U_2242)) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

cnf(f_508_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_2241),U_2243)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2243)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2241),U_2242)) ),
    inference(clausify,[status(thm)],[f_508_2]) ).

fof(f_509_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_509_2,plain,
    ! [U_2246,U_2245,U_2244] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2244)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2245)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2244),U_2245)) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

cnf(f_509_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_2246),U_2244)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2245)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2244),U_2245)) ),
    inference(clausify,[status(thm)],[f_509_2]) ).

fof(f_510_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_510_2,plain,
    ! [U_2250,U_2249,U_2248,U_2247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2247),U_2249)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2248),U_2250)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2249),U_2250))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2247),U_2248)) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

cnf(f_510_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_2247),U_2249)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2248),U_2250)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2249),U_2250))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2247),U_2248)) ),
    inference(clausify,[status(thm)],[f_510_2]) ).

fof(f_511_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_511_2,plain,
    ! [U_2252,U_2251] :
      ( U_2251 = U_2252
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2252),U_2251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2251),U_2252)) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

cnf(f_511_3,plain,
    ( U_2251 = U_2252
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2252),U_2251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2251),U_2252)) ),
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_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_512_2,plain,
    ! [U_2255,U_2254,U_2253] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2253),U_2255))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2254),U_2255))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2253),U_2254)) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

cnf(f_512_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2253),U_2255))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2254),U_2255))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2253),U_2254)) ),
    inference(clausify,[status(thm)],[f_512_2]) ).

fof(f_513_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_513_2,plain,
    ! [U_2257,U_2256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2256),U_2257))
      | U_2256 != U_2257 ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

cnf(f_513_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2256),U_2257))
    | U_2256 != U_2257 ),
    inference(clausify,[status(thm)],[f_513_2]) ).

fof(f_514_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_514_2,plain,
    ! [U_2259,U_2258] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2258))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2258),U_2259)) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

cnf(f_514_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2258))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2258),U_2259)) ),
    inference(clausify,[status(thm)],[f_514_2]) ).

fof(f_515_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_515_2,plain,
    ! [U_2260] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2260),U_2260)),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2260),U_2260)),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_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_516_2,plain,
    ! [U_2261] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2261),U_2261)),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

cnf(f_516_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2261),U_2261)),
    inference(clausify,[status(thm)],[f_516_2]) ).

fof(f_517_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_517_2,plain,
    ! [U_2263,U_2262] :
      ( ( U_2262 != U_2263
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2263),U_2262))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2262),U_2263)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2263),U_2262))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2262),U_2263))
        | U_2262 = U_2263 ) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ( ! [U_2267,U_2265] :
        ( U_2265 != U_2267
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2267),U_2265))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2265),U_2267)) ) )
    & ! [U_2266,U_2264] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2266),U_2264))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2264),U_2266))
        | U_2264 = U_2266 ) ),
    inference(miniscope,[status(thm)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2266),U_2264))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2264),U_2266))
    | U_2264 = U_2266 ),
    inference(clausify,[status(thm)],[f_517_3]) ).

cnf(f_517_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2265),U_2267))
    | U_2265 != U_2267 ),
    inference(clausify,[status(thm)],[f_517_3]) ).

cnf(f_517_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2267),U_2265))
    | U_2265 != U_2267 ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_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_518_2,plain,
    ! [U_2269,U_2268] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2269),U_2268))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2268),U_2269))
      | U_2268 = U_2269 ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

cnf(f_518_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2269),U_2268))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2268),U_2269))
    | U_2268 = U_2269 ),
    inference(clausify,[status(thm)],[f_518_2]) ).

fof(f_519_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_519_2,plain,
    ! [U_2270] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2270),U_2270)),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

cnf(f_519_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2270),U_2270)),
    inference(clausify,[status(thm)],[f_519_2]) ).

fof(f_520_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_520_2,plain,
    ! [U_2272,U_2271] :
      ( U_2272 != U_2271
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2271),U_2272)) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

cnf(f_520_3,plain,
    ( U_2272 != U_2271
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2271),U_2272)) ),
    inference(clausify,[status(thm)],[f_520_2]) ).

fof(f_521_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_521_2,plain,
    ! [U_2274,U_2273] :
      ( U_2273 != U_2274
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2273),U_2274)) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

cnf(f_521_3,plain,
    ( U_2273 != U_2274
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2273),U_2274)) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

fof(f_522_1,plain,
    ! [V_Pa_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_Pa_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_522_2,plain,
    ! [U_2277,U_2276,U_2275] :
      ( hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
      | ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2276),U_2275)) )
      | ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
        & U_2275 = U_2276 )
      | ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2275),U_2276)) ) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

cnf(f_522_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | U_2275 = U_2276
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2275),U_2276)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | U_2275 = U_2276
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2275),U_2276)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2275),U_2276)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2275),U_2276)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | U_2275 = U_2276
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | U_2275 = U_2276
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

cnf(f_522_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275))
    | ~ hBOOL(hAPP(hAPP(U_2277,U_2276),U_2275)) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

fof(f_523_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_523_2,plain,
    ! [U_2279,U_2278] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2278),U_2279))
        | U_2278 = U_2279
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2278),U_2279)) )
      & ( ( U_2278 != U_2279
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2278),U_2279)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2278),U_2279)) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ( ! [U_2283,U_2281] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2281),U_2283))
        | U_2281 = U_2283
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2281),U_2283)) )
    & ! [U_2282,U_2280] :
        ( ( U_2280 != U_2282
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2280),U_2282)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2280),U_2282)) ) ),
    inference(miniscope,[status(thm)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2280),U_2282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2280),U_2282)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

cnf(f_523_5,plain,
    ( U_2280 != U_2282
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2280),U_2282)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

cnf(f_523_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2281),U_2283))
    | U_2281 = U_2283
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2281),U_2283)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_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_524_2,plain,
    ! [U_2285,U_2284] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2284),U_2285))
        | ( U_2284 != U_2285
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2284),U_2285)) ) )
      & ( U_2284 = U_2285
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2284),U_2285))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2284),U_2285)) ) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ( ! [U_2289,U_2287] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2287),U_2289))
        | ( U_2287 != U_2289
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2287),U_2289)) ) )
    & ! [U_2288,U_2286] :
        ( U_2286 = U_2288
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2286),U_2288))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2286),U_2288)) ) ),
    inference(miniscope,[status(thm)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( U_2286 = U_2288
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2286),U_2288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2286),U_2288)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

cnf(f_524_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2287),U_2289))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2287),U_2289)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

cnf(f_524_6,plain,
    ( U_2287 != U_2289
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2287),U_2289)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_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_525_2,plain,
    ! [U_2291,U_2290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2290),U_2291))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2290),U_2291)) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

cnf(f_525_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2290),U_2291))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2290),U_2291)) ),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_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_526_2,plain,
    ! [U_2293,U_2292] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2292),U_2293))
      | U_2292 = U_2293
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2292),U_2293)) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

cnf(f_526_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2292),U_2293))
    | U_2292 = U_2293
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2292),U_2293)) ),
    inference(clausify,[status(thm)],[f_526_2]) ).

fof(f_527_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_527_2,plain,
    ! [U_2295,U_2294] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2294),U_2295))
      | ( U_2294 != U_2295
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2294),U_2295)) ) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

cnf(f_527_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2294),U_2295))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2294),U_2295)) ),
    inference(clausify,[status(thm)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( U_2294 != U_2295
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2294),U_2295)) ),
    inference(clausify,[status(thm)],[f_527_2]) ).

fof(f_528_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_528_2,plain,
    ! [U_2298,U_2297,U_2296] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2296),U_2298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2296),U_2297)),U_2298)) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

cnf(f_528_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2296),U_2298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2296),U_2297)),U_2298)) ),
    inference(clausify,[status(thm)],[f_528_2]) ).

fof(f_529_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_529_2,plain,
    ! [U_2302,U_2301,U_2300,U_2299] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2301),U_2302))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2301),U_2300) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2299),U_2302)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2299),U_2300)) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

cnf(f_529_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2301),U_2302))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2301),U_2300) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2299),U_2302)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2299),U_2300)) ),
    inference(clausify,[status(thm)],[f_529_2]) ).

fof(f_530_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_530_2,plain,
    ! [U_2306,U_2305,U_2304,U_2303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2303),U_2305)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2304),U_2306)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2305),U_2306))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2303),U_2304)) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

cnf(f_530_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2303),U_2305)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2304),U_2306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2305),U_2306))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2303),U_2304)) ),
    inference(clausify,[status(thm)],[f_530_2]) ).

fof(f_531_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_531_2,plain,
    ! [U_2309,U_2308,U_2307] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2307),U_2309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2308),U_2309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2307),U_2308)) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

cnf(f_531_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2307),U_2309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2308),U_2309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2307),U_2308)) ),
    inference(clausify,[status(thm)],[f_531_2]) ).

fof(f_532_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_532_2,plain,
    ! [U_2312,U_2311,U_2310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2312),U_2311)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2310),U_2311)) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

cnf(f_532_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2312),U_2311)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2310),U_2311)) ),
    inference(clausify,[status(thm)],[f_532_2]) ).

fof(f_533_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_533_2,plain,
    ! [U_2315,U_2314,U_2313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2313),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2314),U_2315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2313),U_2314)) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

cnf(f_533_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2313),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2314),U_2315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2313),U_2314)) ),
    inference(clausify,[status(thm)],[f_533_2]) ).

fof(f_534_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_534_2,plain,
    ! [U_2318,U_2317,U_2316] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2316),U_2317)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2316),U_2318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2317),U_2318)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2317),U_2318))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2316),U_2317)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2316),U_2318))) ) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ( ! [U_2324,U_2322] :
        ( ! [U_2320] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2320),U_2322)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2320),U_2324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2322),U_2324)) )
    & ! [U_2323,U_2321] :
        ( ! [U_2319] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2319),U_2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2319),U_2323)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2321),U_2323)) ) ),
    inference(miniscope,[status(thm)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2319),U_2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2319),U_2323)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2321),U_2323)) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

cnf(f_534_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2320),U_2322)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2320),U_2324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2322),U_2324)) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_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_535_2,plain,
    ! [U_2326,U_2325] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2325),U_2326)),U_2326)),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2325),U_2326)),U_2326)),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_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_536_2,plain,
    ! [U_2328,U_2327] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2327),U_2328)),U_2327)),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2327),U_2328)),U_2327)),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_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_537_2,plain,
    ! [U_2331,U_2330,U_2329] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2329),U_2330) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2331),U_2330)
        | U_2329 != U_2331 )
      & ( U_2329 = U_2331
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2329),U_2330) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2331),U_2330) ) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ( ! [U_2337,U_2335,U_2333] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2333),U_2335) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2337),U_2335)
        | U_2333 != U_2337 )
    & ! [U_2336,U_2334,U_2332] :
        ( U_2332 = U_2336
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2332),U_2334) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2336),U_2334) ) ),
    inference(miniscope,[status(thm)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( U_2332 = U_2336
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2332),U_2334) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2336),U_2334) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

cnf(f_537_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2333),U_2335) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2337),U_2335)
    | U_2333 != U_2337 ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_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_538_2,plain,
    ! [U_2340,U_2339,U_2338] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2338),U_2339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2338),U_2340)
        | U_2339 != U_2340 )
      & ( U_2339 = U_2340
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2338),U_2339) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2338),U_2340) ) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ( ! [U_2346,U_2344] :
        ( ! [U_2342] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2344) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2346)
        | U_2344 != U_2346 )
    & ! [U_2345,U_2343] :
        ( ! [U_2341] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2341),U_2343) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2341),U_2345)
        | U_2343 = U_2345 ) ),
    inference(miniscope,[status(thm)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2341),U_2343) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2341),U_2345)
    | U_2343 = U_2345 ),
    inference(clausify,[status(thm)],[f_538_3]) ).

cnf(f_538_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2344) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2342),U_2346)
    | U_2344 != U_2346 ),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_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_539_2,plain,
    ! [U_2349,U_2348,U_2347] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),U_2348)),U_2349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2348),U_2349)),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),U_2348)),U_2349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2347),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2348),U_2349)),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_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_540_2,plain,
    ! [U_2352,U_2351,U_2350] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2351),U_2352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2351),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2350),U_2352)),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

cnf(f_540_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2351),U_2352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2351),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2350),U_2352)),
    inference(clausify,[status(thm)],[f_540_2]) ).

fof(f_541_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_541_2,plain,
    ! [U_2354,U_2353] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2353),U_2354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),U_2353),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2353),U_2354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2354),U_2353),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_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_542_2,plain,
    ! [U_2356,U_2355] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2356),U_2355))),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

cnf(f_542_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2356),U_2355))),
    inference(clausify,[status(thm)],[f_542_2]) ).

fof(f_543_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_543_2,plain,
    ! [U_2358,U_2357] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2357),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2357),U_2358))),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

cnf(f_543_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2357),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2357),U_2358))),
    inference(clausify,[status(thm)],[f_543_2]) ).

fof(f_544_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_544_2,plain,
    ! [U_2362,U_2361] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2361),U_2362))
        | ! [U_2360] : U_2362 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2360) )
      & ( ? [U_2359] : U_2362 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2361),U_2359)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2361),U_2362)) ) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ( ! [U_2366,U_2364] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366))
        | ! [U_2360] : U_2366 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2364),U_2360) )
    & ! [U_2365,U_2363] :
        ( ? [U_2359] : U_2365 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2363),U_2359)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ) ),
    inference(miniscope,[status(thm)],[f_544_2]) ).

fof(f_544_4,plain,
    ( ! [U_2366,U_2364] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366))
        | ! [U_2360] : U_2366 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2364),U_2360) )
    & ! [U_2365,U_2363] :
        ( U_2365 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2363),sK33(U_2365,U_2363))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2359,sK33(U_2365,U_2363))],[f_544_3]) ).

cnf(f_544_5,plain,
    ( U_2365 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2363),sK33(U_2365,U_2363))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365)) ),
    inference(clausify,[status(thm)],[f_544_4]) ).

cnf(f_544_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2364),U_2366))
    | U_2366 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2364),U_2360) ),
    inference(clausify,[status(thm)],[f_544_4]) ).

fof(f_545_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_545_2,plain,
    ! [U_2369,U_2368,U_2367] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2367),U_2368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2367),U_2369)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2368),U_2369)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2368),U_2369))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2367),U_2368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2367),U_2369))) ) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ( ! [U_2375,U_2373] :
        ( ! [U_2371] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2371),U_2373)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2371),U_2375)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2373),U_2375)) )
    & ! [U_2374,U_2372] :
        ( ! [U_2370] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2370),U_2372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2370),U_2374)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2372),U_2374)) ) ),
    inference(miniscope,[status(thm)],[f_545_2]) ).

cnf(f_545_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_2370),U_2372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2370),U_2374)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2372),U_2374)) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

cnf(f_545_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_2371),U_2373)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2371),U_2375)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2373),U_2375)) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_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_546_2,plain,
    ! [U_2378,U_2377,U_2376] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2378)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),U_2377)) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

cnf(f_546_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2378)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2376),U_2377)) ),
    inference(clausify,[status(thm)],[f_546_2]) ).

fof(f_547_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_547_2,plain,
    ! [U_2381,U_2380,U_2379] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2381),U_2380)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2379),U_2380)) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

cnf(f_547_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2381),U_2380)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2379),U_2380)) ),
    inference(clausify,[status(thm)],[f_547_2]) ).

fof(f_548_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_548_2,plain,
    ! [U_2384,U_2383,U_2382] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2382),U_2384)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2382),U_2383)) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_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_2382),U_2384)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2382),U_2383)) ),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_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_549_2,plain,
    ! [U_2388,U_2387,U_2386,U_2385] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2388)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2387),U_2388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2385),U_2386)) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

cnf(f_549_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_2385),U_2387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2388)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2387),U_2388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2385),U_2386)) ),
    inference(clausify,[status(thm)],[f_549_2]) ).

fof(f_550_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_550_2,plain,
    ! [U_2391,U_2390,U_2389] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2390),U_2391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2389),U_2390)),U_2391)) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_2391,U_2390] :
      ( ! [U_2389] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2389),U_2390)),U_2391))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2390),U_2391)) ),
    inference(miniscope,[status(thm)],[f_550_2]) ).

cnf(f_550_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_2389),U_2390)),U_2391))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2390),U_2391)) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_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_551_2,plain,
    ! [U_2394,U_2393,U_2392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2392),U_2394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2392),U_2393)),U_2394)) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

cnf(f_551_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2392),U_2394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2392),U_2393)),U_2394)) ),
    inference(clausify,[status(thm)],[f_551_2]) ).

fof(f_552_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_552_2,plain,
    ! [U_2397,U_2396,U_2395] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2396),U_2397))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2395),U_2397)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2395),U_2396)),U_2397)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

cnf(f_552_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2395),U_2397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2395),U_2396)),U_2397)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2396),U_2397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2395),U_2396)),U_2397)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

fof(f_553_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_553_2,plain,
    ! [U_2400,U_2399,U_2398] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2399),U_2400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2399)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2400)),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

cnf(f_553_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2399),U_2400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2399)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2400)),
    inference(clausify,[status(thm)],[f_553_2]) ).

fof(f_554_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_554_2,plain,
    ! [U_2403,U_2402,U_2401] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2401),U_2402)),U_2403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2401),U_2403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2402),U_2403)),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

cnf(f_554_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2401),U_2402)),U_2403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2401),U_2403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2402),U_2403)),
    inference(clausify,[status(thm)],[f_554_2]) ).

fof(f_555_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_555_2,plain,
    ! [U_2406,U_2405,U_2404] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2404),U_2405)),U_2406) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2406)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2405),U_2406)),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

cnf(f_555_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2404),U_2405)),U_2406) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2406)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2405),U_2406)),
    inference(clausify,[status(thm)],[f_555_2]) ).

fof(f_556_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_556_2,plain,
    ! [U_2409,U_2408,U_2407] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2408),U_2409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),U_2408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),U_2409)),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

cnf(f_556_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2408),U_2409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),U_2408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2407),U_2409)),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_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_557_2,plain,
    ! [U_2412,U_2411,U_2410] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2411),U_2410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2412),U_2410)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2411),U_2412)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2411),U_2412))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2411),U_2410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2412),U_2410))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2411)) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2411),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2411),U_2410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2412),U_2410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2411)) ),
    inference(clausify,[status(thm)],[f_557_2]) ).

cnf(f_557_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_2411),U_2410)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2412),U_2410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2411),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2410),U_2411)) ),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_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_558_2,plain,
    ! [U_2415,U_2414,U_2413] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2414),U_2413)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2415),U_2413)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2414),U_2415)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2413),U_2415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2413),U_2414)) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

cnf(f_558_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2414),U_2413)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2415),U_2413)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2414),U_2415)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2413),U_2415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2413),U_2414)) ),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_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_559_2,plain,
    ! [U_2418,U_2417,U_2416] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2417),U_2416) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2418),U_2416)
          | U_2417 != U_2418 )
        & ( U_2417 = U_2418
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2417),U_2416) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2418),U_2416) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2417)) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    ( U_2417 = U_2418
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2417),U_2416) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2418),U_2416)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2418))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2417)) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

cnf(f_559_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2417),U_2416) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2418),U_2416)
    | U_2417 != U_2418
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2418))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2416),U_2417)) ),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_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_560_2,plain,
    ! [U_2420,U_2419] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2420),U_2419)) = U_2419
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2419),U_2420)) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

cnf(f_560_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2420),U_2419)) = U_2419
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2419),U_2420)) ),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_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_561_2,plain,
    ! [U_2423,U_2422,U_2421] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2421),U_2423)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2422),U_2423)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2421),U_2422)) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_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_2421),U_2423)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2422),U_2423)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2421),U_2422)) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_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_562_2,plain,
    ! [U_2426,U_2425,U_2424] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2426),U_2425)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2426),U_2424)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2424),U_2425)) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

cnf(f_562_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_2426),U_2425)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2426),U_2424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2424),U_2425)) ),
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_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_563_2,plain,
    ! [U_2428,U_2427] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2427),U_2428)),U_2427)),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

cnf(f_563_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_2427),U_2428)),U_2427)),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_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_564_2,plain,
    ! [U_2431,U_2430,U_2429] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2429),U_2430)),U_2431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2429),U_2431)),U_2430),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

cnf(f_564_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2429),U_2430)),U_2431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2429),U_2431)),U_2430),
    inference(clausify,[status(thm)],[f_564_2]) ).

fof(f_565_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_565_2,plain,
    ! [U_2434,U_2433,U_2432] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2432),U_2434)),U_2433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2432),U_2433)) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2432),U_2434)),U_2433))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2432),U_2433)) ),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_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_566_2,plain,
    ! [U_2437,U_2436,U_2435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2435),U_2437)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2436),U_2437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2437),U_2435))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2435),U_2436)) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2435),U_2437)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2436),U_2437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2437),U_2435))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2435),U_2436)) ),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_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_567_2,plain,
    ! [U_2440,U_2439,U_2438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2440),U_2439)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2440),U_2438)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2438),U_2440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2438),U_2439)) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2440),U_2439)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2440),U_2438)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2438),U_2440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2438),U_2439)) ),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_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_568_2,plain,
    ! [U_2443,U_2442,U_2441] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2442),U_2441)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2443),U_2441)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2442),U_2443)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2442),U_2443))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2442),U_2441)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2443),U_2441))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2443))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2442)) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2442),U_2443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2442),U_2441)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2443),U_2441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2442)) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

cnf(f_568_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2442),U_2441)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2443),U_2441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2442),U_2443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2441),U_2442)) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_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_569_2,plain,
    ! [U_2446,U_2445,U_2444] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2445),U_2446)),U_2444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2445),U_2444)),U_2446)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2444),U_2445)) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2445),U_2446)),U_2444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2445),U_2444)),U_2446)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2444),U_2445)) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_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_570_2,plain,
    ! [U_2449,U_2448,U_2447] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2448),U_2447)),U_2449) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2448),U_2449)),U_2447)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2447),U_2448)) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

cnf(f_570_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2448),U_2447)),U_2449) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2448),U_2449)),U_2447)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2447),U_2448)) ),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_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_571_2,plain,
    ! [U_2452,U_2451,U_2450] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),U_2451)),U_2450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2451),U_2450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2450),U_2451)) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),U_2451)),U_2450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2451),U_2450))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2450),U_2451)) ),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_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_572_2,plain,
    ! [U_2455,U_2454,U_2453] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2454),U_2453) = U_2455
          | U_2454 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2455),U_2453) )
        & ( U_2454 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2455),U_2453)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2454),U_2453) != U_2455 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2453),U_2454)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    ( U_2454 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2455),U_2453)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2454),U_2453) != U_2455
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2453),U_2454)) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2454),U_2453) = U_2455
    | U_2454 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2455),U_2453)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2453),U_2454)) ),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_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_573_2,plain,
    ! [U_2457,U_2456] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2457),U_2456)),U_2456) = U_2457
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2456),U_2457)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

cnf(f_573_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2457),U_2456)),U_2456) = U_2457
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2456),U_2457)) ),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_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_574_2,plain,
    ! [U_2460,U_2459,U_2458] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2459),U_2458)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2460),U_2458)),U_2459)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2460),U_2458)),U_2459))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2459),U_2458))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2458),U_2459)) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

cnf(f_574_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_2460),U_2458)),U_2459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2459),U_2458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2458),U_2459)) ),
    inference(clausify,[status(thm)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2459),U_2458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2460),U_2458)),U_2459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2458),U_2459)) ),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_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_575_2,plain,
    ! [U_2463,U_2462,U_2461] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2462),U_2461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2463),U_2462)),U_2461)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2461),U_2462)) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

cnf(f_575_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2462),U_2461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2463),U_2462)),U_2461)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2461),U_2462)) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_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_576_2,plain,
    ! [U_2465,U_2464] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2465),U_2464)) = U_2465
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2464),U_2465)) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2465),U_2464)) = U_2465
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2464),U_2465)) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_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_577_2,plain,
    ! [U_2470,U_2469,U_2468,U_2467,U_2466] :
      ( ( ( 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_2467),U_2468)),U_2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2466),U_2468)),U_2470)))
          | ~ 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_2467),U_2466)),U_2468)),U_2469)),U_2470)) )
        & ( 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_2467),U_2466)),U_2468)),U_2469)),U_2470))
          | ~ 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_2467),U_2468)),U_2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2466),U_2468)),U_2470))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2466),U_2467)) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

cnf(f_577_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_2467),U_2466)),U_2468)),U_2469)),U_2470))
    | ~ 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_2467),U_2468)),U_2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2466),U_2468)),U_2470)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2466),U_2467)) ),
    inference(clausify,[status(thm)],[f_577_2]) ).

cnf(f_577_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_2467),U_2468)),U_2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2466),U_2468)),U_2470)))
    | ~ 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_2467),U_2466)),U_2468)),U_2469)),U_2470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2466),U_2467)) ),
    inference(clausify,[status(thm)],[f_577_2]) ).

fof(f_578_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_578_2,plain,
    ! [U_2475,U_2474,U_2473,U_2472,U_2471] :
      ( ( ( 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_2471),U_2473)),U_2474)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2473)),U_2475)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2474),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_2472),U_2471)),U_2473)),U_2475))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2474),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_2472),U_2471)),U_2473)),U_2475)))
          | ~ 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_2471),U_2473)),U_2474)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2473)),U_2475))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2471),U_2472)) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2474),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_2472),U_2471)),U_2473)),U_2475)))
    | ~ 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_2471),U_2473)),U_2474)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2473)),U_2475)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2471),U_2472)) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

cnf(f_578_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_2471),U_2473)),U_2474)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2473)),U_2475)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2474),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_2472),U_2471)),U_2473)),U_2475)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2471),U_2472)) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_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_579_2,plain,
    ! [U_2480,U_2479,U_2478,U_2477,U_2476] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2478)),U_2479) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2478)),U_2480)
          | U_2479 != 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_2477),U_2476)),U_2478)),U_2480) )
        & ( U_2479 = 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_2477),U_2476)),U_2478)),U_2480)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2478)),U_2479) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2478)),U_2480) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2476),U_2477)) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( U_2479 = 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_2477),U_2476)),U_2478)),U_2480)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2478)),U_2479) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2478)),U_2480)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2476),U_2477)) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2478)),U_2479) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2478)),U_2480)
    | U_2479 != 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_2477),U_2476)),U_2478)),U_2480)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2476),U_2477)) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_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_580_2,plain,
    ! [U_2485,U_2484,U_2483,U_2482,U_2481] :
      ( 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_2481),U_2483)),U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2483)),U_2485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2484),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_2482),U_2481)),U_2483)),U_2485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2481),U_2482)) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

cnf(f_580_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_2481),U_2483)),U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2483)),U_2485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2484),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_2482),U_2481)),U_2483)),U_2485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2481),U_2482)) ),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_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_581_2,plain,
    ! [U_2490,U_2489,U_2488,U_2487,U_2486] :
      ( ( ( 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_2486),U_2488)),U_2489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2487),U_2488)),U_2490)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2489),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_2487),U_2486)),U_2488)),U_2490))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2489),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_2487),U_2486)),U_2488)),U_2490)))
          | ~ 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_2486),U_2488)),U_2489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2487),U_2488)),U_2490))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2486),U_2487)) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

cnf(f_581_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2489),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_2487),U_2486)),U_2488)),U_2490)))
    | ~ 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_2486),U_2488)),U_2489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2487),U_2488)),U_2490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2486),U_2487)) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

cnf(f_581_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_2486),U_2488)),U_2489)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2487),U_2488)),U_2490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2489),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_2487),U_2486)),U_2488)),U_2490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2486),U_2487)) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

fof(f_582_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_582_2,plain,
    ! [U_2495,U_2494,U_2493,U_2492,U_2491] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2492),U_2493)),U_2494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2491),U_2493)),U_2495)
          | 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_2492),U_2491)),U_2493)),U_2494) != U_2495 )
        & ( 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_2492),U_2491)),U_2493)),U_2494) = U_2495
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2492),U_2493)),U_2494) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2491),U_2493)),U_2495) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2491),U_2492)) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_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_2492),U_2491)),U_2493)),U_2494) = U_2495
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2492),U_2493)),U_2494) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2491),U_2493)),U_2495)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2491),U_2492)) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

cnf(f_582_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2492),U_2493)),U_2494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2491),U_2493)),U_2495)
    | 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_2492),U_2491)),U_2493)),U_2494) != U_2495
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2491),U_2492)) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_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_583_2,plain,
    ! [U_2500,U_2499,U_2498,U_2497,U_2496] :
      ( 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_2497),U_2498)),U_2499)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2496),U_2498)),U_2500)) = 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_2497),U_2496)),U_2498)),U_2499)),U_2500)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2496),U_2497)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_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_2497),U_2498)),U_2499)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2496),U_2498)),U_2500)) = 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_2497),U_2496)),U_2498)),U_2499)),U_2500)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2496),U_2497)) ),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_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_584_2,plain,
    ! [U_2505,U_2504,U_2503,U_2502,U_2501] :
      ( ( ( 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_2502),U_2503)),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2505)))
          | ~ 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_2502),U_2501)),U_2503)),U_2504)),U_2505)) )
        & ( 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_2502),U_2501)),U_2503)),U_2504)),U_2505))
          | ~ 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_2502),U_2503)),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2505))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2501),U_2502)) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_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_2502),U_2501)),U_2503)),U_2504)),U_2505))
    | ~ 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_2502),U_2503)),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2505)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2501),U_2502)) ),
    inference(clausify,[status(thm)],[f_584_2]) ).

cnf(f_584_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_2502),U_2503)),U_2504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2505)))
    | ~ 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_2502),U_2501)),U_2503)),U_2504)),U_2505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2501),U_2502)) ),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_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_585_2,plain,
    ! [U_2508,U_2507,U_2506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2507),U_2508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2506),U_2507)) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

cnf(f_585_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2507),U_2508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2506),U_2507)) ),
    inference(clausify,[status(thm)],[f_585_2]) ).

fof(f_586_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_586_2,plain,
    ! [U_2511,U_2510,U_2509] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2509),U_2510)),U_2511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2510),U_2511)),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

cnf(f_586_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2509),U_2510)),U_2511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2510),U_2511)),
    inference(clausify,[status(thm)],[f_586_2]) ).

fof(f_587_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_587_2,plain,
    ! [U_2513,U_2512] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2513),U_2512),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2513),U_2512),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_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_588_2,plain,
    ! [U_2517,U_2516,U_2515,U_2514] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2514),U_2515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2515)),U_2517)) = 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_2514),U_2516)),U_2515)),U_2517),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

cnf(f_588_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2514),U_2515)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2515)),U_2517)) = 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_2514),U_2516)),U_2515)),U_2517),
    inference(clausify,[status(thm)],[f_588_2]) ).

fof(f_589_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_589_2,plain,
    ! [U_2520,U_2519,U_2518] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2518),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2519),U_2520)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2518),U_2519)) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2518),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2519),U_2520)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2518),U_2519)) ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_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_590_2,plain,
    ! [U_2523,U_2522,U_2521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2523),U_2522)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2521),U_2522)) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2523),U_2522)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2521),U_2522)) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_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_591_2,plain,
    ! [U_2525,U_2524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2524),U_2525))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2524),U_2525)) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2524),U_2525))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2524),U_2525)) ),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_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_592_2,plain,
    ! [U_2528,U_2527,U_2526] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2528),U_2527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2526),U_2527)) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

cnf(f_592_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2528),U_2527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2526),U_2527)) ),
    inference(clausify,[status(thm)],[f_592_2]) ).

fof(f_593_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_593_2,plain,
    ! [U_2530,U_2529] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2529,U_2530) = hAPP(hAPP(c_Finite__Set_Ofold(U_2529,U_2529,c_Lattices_Osemilattice__sup__class_Osup(U_2529)),c_Orderings_Obot__class_Obot(U_2529)),U_2530)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2529),U_2530))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2529) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2529,U_2530) = hAPP(hAPP(c_Finite__Set_Ofold(U_2529,U_2529,c_Lattices_Osemilattice__sup__class_Osup(U_2529)),c_Orderings_Obot__class_Obot(U_2529)),U_2530)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2529),U_2530))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2529) ),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_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_594_2,plain,
    ! [U_2533,U_2532,U_2531] :
      ( hAPP(c_Finite__Set_Ofold1(U_2531,c_Groups_Otimes__class_Otimes(U_2531)),hAPP(hAPP(c_Set_Oinsert(U_2531),U_2533),U_2532)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2531,U_2531,c_Groups_Otimes__class_Otimes(U_2531)),U_2533),U_2532)
      | hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),U_2532))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2531),U_2532))
      | ~ class_Groups_Oab__semigroup__mult(U_2531) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2531,c_Groups_Otimes__class_Otimes(U_2531)),hAPP(hAPP(c_Set_Oinsert(U_2531),U_2533),U_2532)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2531,U_2531,c_Groups_Otimes__class_Otimes(U_2531)),U_2533),U_2532)
    | hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),U_2532))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2531),U_2532))
    | ~ class_Groups_Oab__semigroup__mult(U_2531) ),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_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_595_2,plain,
    ! [U_2536,U_2535,U_2534] :
      ( hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2534,tc_HOL_Obool)),U_2535),U_2536)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2534),hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),U_2535)),hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),U_2536))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2534,tc_HOL_Obool)),U_2535),U_2536) != c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
      | U_2536 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2536))
      | U_2535 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2535))
      | ~ class_Groups_Oab__semigroup__mult(U_2534) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

cnf(f_595_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2534,tc_HOL_Obool)),U_2535),U_2536)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2534),hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),U_2535)),hAPP(c_Finite__Set_Ofold1(U_2534,c_Groups_Otimes__class_Otimes(U_2534)),U_2536))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2534,tc_HOL_Obool)),U_2535),U_2536) != c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
    | U_2536 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2536))
    | U_2535 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2535))
    | ~ class_Groups_Oab__semigroup__mult(U_2534) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_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_596_2,plain,
    ! [U_2539,U_2538,U_2537] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2537,tc_HOL_Obool)),U_2538),hAPP(hAPP(c_Set_Oinsert(U_2537),U_2539),c_Orderings_Obot__class_Obot(tc_fun(U_2537,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2537),U_2538)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2537),U_2539),U_2538))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2537),U_2538)) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2537,tc_HOL_Obool)),U_2538),hAPP(hAPP(c_Set_Oinsert(U_2537),U_2539),c_Orderings_Obot__class_Obot(tc_fun(U_2537,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2537),U_2538)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2537),U_2539),U_2538))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2537),U_2538)) ),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_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_597_2,plain,
    ! [U_2543,U_2542,U_2541,U_2540] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2543),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2540),U_2541)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2543),U_2541))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2542),U_2541))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2540),U_2541)) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

cnf(f_597_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2543),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2540),U_2541)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2543),U_2541))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2542),U_2541))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2540),U_2541)) ),
    inference(clausify,[status(thm)],[f_597_2]) ).

fof(f_598_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_598_2,plain,
    ! [U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546,U_2545] :
      ( hAPP(U_2550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)) = hAPP(hAPP(U_2547,hAPP(U_2550,U_2551)),hAPP(U_2550,U_2552))
      | ? [U_2544] :
          ( hAPP(U_2549,U_2544) != U_2548
          & hBOOL(hAPP(hAPP(c_member(U_2546),U_2544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2552))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2551))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2545,U_2546,U_2547,U_2548,U_2549,U_2550) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546] :
      ( ! [U_2545] : ~ c_Finite__Set_Ofolding__image__simple(U_2545,U_2546,U_2547,U_2548,U_2549,U_2550)
      | hAPP(U_2550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)) = hAPP(hAPP(U_2547,hAPP(U_2550,U_2551)),hAPP(U_2550,U_2552))
      | ? [U_2544] :
          ( hAPP(U_2549,U_2544) != U_2548
          & hBOOL(hAPP(hAPP(c_member(U_2546),U_2544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2552))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2551)) ),
    inference(miniscope,[status(thm)],[f_598_2]) ).

fof(f_598_4,plain,
    ! [U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546] :
      ( ! [U_2545] : ~ c_Finite__Set_Ofolding__image__simple(U_2545,U_2546,U_2547,U_2548,U_2549,U_2550)
      | hAPP(U_2550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)) = hAPP(hAPP(U_2547,hAPP(U_2550,U_2551)),hAPP(U_2550,U_2552))
      | ( hAPP(U_2549,sK34(U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546)) != U_2548
        & hBOOL(hAPP(hAPP(c_member(U_2546),sK34(U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2552))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2551)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2544,sK34(U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546))],[f_598_3]) ).

cnf(f_598_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2546),sK34(U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)))
    | hAPP(U_2550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)) = hAPP(hAPP(U_2547,hAPP(U_2550,U_2551)),hAPP(U_2550,U_2552))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2552))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2551))
    | ~ c_Finite__Set_Ofolding__image__simple(U_2545,U_2546,U_2547,U_2548,U_2549,U_2550) ),
    inference(clausify,[status(thm)],[f_598_4]) ).

cnf(f_598_6,plain,
    ( hAPP(U_2549,sK34(U_2552,U_2551,U_2550,U_2549,U_2548,U_2547,U_2546)) != U_2548
    | hAPP(U_2550,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2546,tc_HOL_Obool)),U_2551),U_2552)) = hAPP(hAPP(U_2547,hAPP(U_2550,U_2551)),hAPP(U_2550,U_2552))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2552))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2551))
    | ~ c_Finite__Set_Ofolding__image__simple(U_2545,U_2546,U_2547,U_2548,U_2549,U_2550) ),
    inference(clausify,[status(thm)],[f_598_4]) ).

fof(f_599_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_599_2,plain,
    ! [U_2555,U_2554,U_2553] :
      ( hAPP(c_Finite__Set_Ofold1(U_2553,c_Groups_Otimes__class_Otimes(U_2553)),hAPP(hAPP(c_Set_Oinsert(U_2553),U_2555),U_2554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2553),U_2555),hAPP(c_Finite__Set_Ofold1(U_2553,c_Groups_Otimes__class_Otimes(U_2553)),U_2554))
      | hBOOL(hAPP(hAPP(c_member(U_2553),U_2555),U_2554))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2553),U_2554))
      | U_2554 = c_Orderings_Obot__class_Obot(tc_fun(U_2553,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_2553) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

cnf(f_599_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2553,c_Groups_Otimes__class_Otimes(U_2553)),hAPP(hAPP(c_Set_Oinsert(U_2553),U_2555),U_2554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2553),U_2555),hAPP(c_Finite__Set_Ofold1(U_2553,c_Groups_Otimes__class_Otimes(U_2553)),U_2554))
    | hBOOL(hAPP(hAPP(c_member(U_2553),U_2555),U_2554))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2553),U_2554))
    | U_2554 = c_Orderings_Obot__class_Obot(tc_fun(U_2553,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_2553) ),
    inference(clausify,[status(thm)],[f_599_2]) ).

fof(f_600_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_600_2,plain,
    ! [U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557] :
      ( ? [U_2556] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,U_2562),U_2556))
          & U_2563 = hAPP(hAPP(U_2559,U_2561),U_2556) )
      | hBOOL(hAPP(hAPP(c_member(U_2557),U_2561),U_2562))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,hAPP(hAPP(c_Set_Oinsert(U_2557),U_2561),U_2562)),U_2563))
      | ~ c_Finite__Set_Ofun__left__comm(U_2557,U_2558,U_2559) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,U_2562),sK35(U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557)))
        & U_2563 = hAPP(hAPP(U_2559,U_2561),sK35(U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557)) )
      | hBOOL(hAPP(hAPP(c_member(U_2557),U_2561),U_2562))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,hAPP(hAPP(c_Set_Oinsert(U_2557),U_2561),U_2562)),U_2563))
      | ~ c_Finite__Set_Ofun__left__comm(U_2557,U_2558,U_2559) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2556,sK35(U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557))],[f_600_2]) ).

cnf(f_600_4,plain,
    ( U_2563 = hAPP(hAPP(U_2559,U_2561),sK35(U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557))
    | hBOOL(hAPP(hAPP(c_member(U_2557),U_2561),U_2562))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,hAPP(hAPP(c_Set_Oinsert(U_2557),U_2561),U_2562)),U_2563))
    | ~ c_Finite__Set_Ofun__left__comm(U_2557,U_2558,U_2559) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,U_2562),sK35(U_2563,U_2562,U_2561,U_2560,U_2559,U_2558,U_2557)))
    | hBOOL(hAPP(hAPP(c_member(U_2557),U_2561),U_2562))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_2557,U_2558,U_2559,U_2560,hAPP(hAPP(c_Set_Oinsert(U_2557),U_2561),U_2562)),U_2563))
    | ~ c_Finite__Set_Ofun__left__comm(U_2557,U_2558,U_2559) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_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_601_2,plain,
    ! [U_2569,U_2568,U_2567,U_2566,U_2565,U_2564] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2564,U_2565,U_2566),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2564),U_2569),U_2567)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2564,U_2565,U_2566),hAPP(hAPP(U_2566,U_2569),U_2568)),U_2567)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2564),U_2567))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_2564,U_2565,U_2566) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

cnf(f_601_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2564,U_2565,U_2566),U_2568),hAPP(hAPP(c_Set_Oinsert(U_2564),U_2569),U_2567)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2564,U_2565,U_2566),hAPP(hAPP(U_2566,U_2569),U_2568)),U_2567)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2564),U_2567))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_2564,U_2565,U_2566) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

fof(f_602_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_602_2,plain,
    ! [U_2574,U_2573,U_2572,U_2571,U_2570] :
      ( hAPP(hAPP(U_2572,U_2573),hAPP(hAPP(U_2572,U_2573),U_2574)) = hAPP(hAPP(U_2572,U_2573),U_2574)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_2570,U_2571,U_2572) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_2574,U_2573,U_2572] :
      ( ! [U_2571,U_2570] : ~ c_Finite__Set_Ofun__left__comm__idem(U_2570,U_2571,U_2572)
      | hAPP(hAPP(U_2572,U_2573),hAPP(hAPP(U_2572,U_2573),U_2574)) = hAPP(hAPP(U_2572,U_2573),U_2574) ),
    inference(miniscope,[status(thm)],[f_602_2]) ).

cnf(f_602_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_2570,U_2571,U_2572)
    | hAPP(hAPP(U_2572,U_2573),hAPP(hAPP(U_2572,U_2573),U_2574)) = hAPP(hAPP(U_2572,U_2573),U_2574) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_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_603_2,plain,
    ! [U_2576,U_2575] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2575,tc_HOL_Obool)),U_2576))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2575),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2575,tc_HOL_Obool),U_2576))) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

cnf(f_603_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2575,tc_HOL_Obool)),U_2576))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2575),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2575,tc_HOL_Obool),U_2576))) ),
    inference(clausify,[status(thm)],[f_603_2]) ).

fof(f_604_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_604_2,plain,
    ! [U_2577] : c_Finite__Set_Ofun__left__comm__idem(U_2577,tc_fun(U_2577,tc_HOL_Obool),c_Set_Oinsert(U_2577)),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

cnf(f_604_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_2577,tc_fun(U_2577,tc_HOL_Obool),c_Set_Oinsert(U_2577)),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_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_605_2,plain,
    ! [U_2578] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_2578,U_2578,c_Groups_Otimes__class_Otimes(U_2578))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2578) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

cnf(f_605_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_2578,U_2578,c_Groups_Otimes__class_Otimes(U_2578))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2578) ),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_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_606_2,plain,
    ! [U_2579] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_2579,U_2579,c_Lattices_Osemilattice__sup__class_Osup(U_2579))
      | ~ class_Lattices_Osemilattice__sup(U_2579) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

cnf(f_606_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_2579,U_2579,c_Lattices_Osemilattice__sup__class_Osup(U_2579))
    | ~ class_Lattices_Osemilattice__sup(U_2579) ),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_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_607_2,plain,
    ! [U_2580] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_2580,U_2580,c_Lattices_Osemilattice__inf__class_Oinf(U_2580))
      | ~ class_Lattices_Osemilattice__inf(U_2580) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_2580,U_2580,c_Lattices_Osemilattice__inf__class_Oinf(U_2580))
    | ~ class_Lattices_Osemilattice__inf(U_2580) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_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_608_2,plain,
    ! [U_2584,U_2583,U_2582,U_2581] :
      ( hAPP(U_2581,hAPP(hAPP(c_Set_Oinsert(U_2582),U_2584),c_Orderings_Obot__class_Obot(tc_fun(U_2582,tc_HOL_Obool)))) = U_2584
      | U_2581 != c_Finite__Set_Ofold1(U_2582,U_2583) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

cnf(f_608_3,plain,
    ( hAPP(U_2581,hAPP(hAPP(c_Set_Oinsert(U_2582),U_2584),c_Orderings_Obot__class_Obot(tc_fun(U_2582,tc_HOL_Obool)))) = U_2584
    | U_2581 != c_Finite__Set_Ofold1(U_2582,U_2583) ),
    inference(clausify,[status(thm)],[f_608_2]) ).

fof(f_609_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_609_2,plain,
    ! [U_2587,U_2586,U_2585] : hAPP(c_Finite__Set_Ofold1(U_2585,U_2586),hAPP(hAPP(c_Set_Oinsert(U_2585),U_2587),c_Orderings_Obot__class_Obot(tc_fun(U_2585,tc_HOL_Obool)))) = U_2587,
    inference(variable_rename,[status(thm)],[f_609_1]) ).

cnf(f_609_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_2585,U_2586),hAPP(hAPP(c_Set_Oinsert(U_2585),U_2587),c_Orderings_Obot__class_Obot(tc_fun(U_2585,tc_HOL_Obool)))) = U_2587,
    inference(clausify,[status(thm)],[f_609_2]) ).

fof(f_610_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_610_2,plain,
    ! [U_2591,U_2590,U_2589,U_2588] :
      ( hAPP(U_2590,U_2591) = hAPP(c_Finite__Set_Ofold1(U_2588,U_2589),U_2591)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2588),U_2591))
      | ~ c_Finite__Set_Ofolding__one(U_2588,U_2589,U_2590) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

cnf(f_610_3,plain,
    ( hAPP(U_2590,U_2591) = hAPP(c_Finite__Set_Ofold1(U_2588,U_2589),U_2591)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2588),U_2591))
    | ~ c_Finite__Set_Ofolding__one(U_2588,U_2589,U_2590) ),
    inference(clausify,[status(thm)],[f_610_2]) ).

fof(f_611_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_611_2,plain,
    ! [U_2594,U_2593,U_2592] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2592),U_2593)),hAPP(c_Finite__Set_Ocard(U_2592),hAPP(hAPP(c_Set_Oinsert(U_2592),U_2594),U_2593))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2592),U_2593)) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

cnf(f_611_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2592),U_2593)),hAPP(c_Finite__Set_Ocard(U_2592),hAPP(hAPP(c_Set_Oinsert(U_2592),U_2594),U_2593))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2592),U_2593)) ),
    inference(clausify,[status(thm)],[f_611_2]) ).

fof(f_612_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_612_2,plain,
    ! [U_2597,U_2596,U_2595] :
      ( U_2597 = U_2596
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2595),U_2596)),hAPP(c_Finite__Set_Ocard(U_2595),U_2597)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2595,tc_HOL_Obool)),U_2597),U_2596))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2595),U_2596)) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

cnf(f_612_3,plain,
    ( U_2597 = U_2596
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2595),U_2596)),hAPP(c_Finite__Set_Ocard(U_2595),U_2597)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2595,tc_HOL_Obool)),U_2597),U_2596))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2595),U_2596)) ),
    inference(clausify,[status(thm)],[f_612_2]) ).

fof(f_613_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_613_2,plain,
    ! [U_2600,U_2599,U_2598] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2598),U_2600)),hAPP(c_Finite__Set_Ocard(U_2598),U_2599)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2598,tc_HOL_Obool)),U_2600),U_2599))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2598),U_2599)) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

cnf(f_613_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2598),U_2600)),hAPP(c_Finite__Set_Ocard(U_2598),U_2599)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2598,tc_HOL_Obool)),U_2600),U_2599))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2598),U_2599)) ),
    inference(clausify,[status(thm)],[f_613_2]) ).

fof(f_614_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_614_2,plain,
    ! [U_2603,U_2602,U_2601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2601),U_2603)),hAPP(c_Finite__Set_Ocard(U_2601),U_2602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2601,tc_HOL_Obool)),U_2603),U_2602))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),U_2602)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

cnf(f_614_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2601),U_2603)),hAPP(c_Finite__Set_Ocard(U_2601),U_2602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2601,tc_HOL_Obool)),U_2603),U_2602))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),U_2602)) ),
    inference(clausify,[status(thm)],[f_614_2]) ).

fof(f_615_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_615_2,plain,
    ! [U_2605,U_2604] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_2604,U_2605) = hAPP(c_Finite__Set_Ofold1(U_2604,c_Lattices_Osemilattice__sup__class_Osup(U_2604)),U_2605)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2604),U_2605))
      | ~ class_Lattices_Olattice(U_2604) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

cnf(f_615_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2604,U_2605) = hAPP(c_Finite__Set_Ofold1(U_2604,c_Lattices_Osemilattice__sup__class_Osup(U_2604)),U_2605)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2604),U_2605))
    | ~ class_Lattices_Olattice(U_2604) ),
    inference(clausify,[status(thm)],[f_615_2]) ).

fof(f_616_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_616_2,plain,
    ! [U_2607,U_2606] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_2606,U_2607) = hAPP(c_Finite__Set_Ofold1(U_2606,c_Lattices_Osemilattice__inf__class_Oinf(U_2606)),U_2607)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2606),U_2607))
      | ~ class_Lattices_Olattice(U_2606) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

cnf(f_616_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2606,U_2607) = hAPP(c_Finite__Set_Ofold1(U_2606,c_Lattices_Osemilattice__inf__class_Oinf(U_2606)),U_2607)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2606),U_2607))
    | ~ class_Lattices_Olattice(U_2606) ),
    inference(clausify,[status(thm)],[f_616_2]) ).

fof(f_617_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_617_2,plain,
    ! [U_2610,U_2609,U_2608] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2608),U_2609)),hAPP(c_Finite__Set_Ocard(U_2608),U_2610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2608),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2608,tc_HOL_Obool)),U_2609),U_2610))),hAPP(c_Finite__Set_Ocard(U_2608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2608,tc_HOL_Obool)),U_2609),U_2610)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2610))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2609)) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

cnf(f_617_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2608),U_2609)),hAPP(c_Finite__Set_Ocard(U_2608),U_2610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2608),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2608,tc_HOL_Obool)),U_2609),U_2610))),hAPP(c_Finite__Set_Ocard(U_2608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2608,tc_HOL_Obool)),U_2609),U_2610)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2610))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2609)) ),
    inference(clausify,[status(thm)],[f_617_2]) ).

fof(f_618_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_618_2,plain,
    ! [U_2613,U_2612,U_2611] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2611),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2611,tc_HOL_Obool)),U_2612),U_2613))),hAPP(c_Finite__Set_Ocard(U_2611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2611,tc_HOL_Obool)),U_2612),U_2613))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2611),U_2612)),hAPP(c_Finite__Set_Ocard(U_2611),U_2613))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2613))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2612)) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

cnf(f_618_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2611),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2611,tc_HOL_Obool)),U_2612),U_2613))),hAPP(c_Finite__Set_Ocard(U_2611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2611,tc_HOL_Obool)),U_2612),U_2613))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2611),U_2612)),hAPP(c_Finite__Set_Ocard(U_2611),U_2613))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2613))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2612)) ),
    inference(clausify,[status(thm)],[f_618_2]) ).

fof(f_619_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_619_2,plain,
    ! [U_2616,U_2615,U_2614] :
      ( hAPP(c_Finite__Set_Ocard(U_2614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2614,tc_HOL_Obool)),U_2616),U_2615)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2614),U_2616)),hAPP(c_Finite__Set_Ocard(U_2614),U_2615))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2614,tc_HOL_Obool)),U_2615),U_2616))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2614),U_2615)) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

cnf(f_619_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2614,tc_HOL_Obool)),U_2616),U_2615)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2614),U_2616)),hAPP(c_Finite__Set_Ocard(U_2614),U_2615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2614,tc_HOL_Obool)),U_2615),U_2616))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2614),U_2615)) ),
    inference(clausify,[status(thm)],[f_619_2]) ).

fof(f_620_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_620_2,plain,
    ! [U_2619,U_2618,U_2617] :
      ( hAPP(c_Finite__Set_Ocard(U_2617),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2617),U_2618)),hAPP(c_Finite__Set_Ocard(U_2617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619))) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

cnf(f_620_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2617),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2617),U_2618)),hAPP(c_Finite__Set_Ocard(U_2617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2617,tc_HOL_Obool)),U_2618),U_2619))) ),
    inference(clausify,[status(thm)],[f_620_2]) ).

fof(f_621_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_621_2,plain,
    ! [U_2622,U_2621,U_2620] :
      ( 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_2620),U_2622)),hAPP(c_Finite__Set_Ocard(U_2620),U_2621))),hAPP(c_Finite__Set_Ocard(U_2620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2622),U_2621))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2621)) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

cnf(f_621_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_2620),U_2622)),hAPP(c_Finite__Set_Ocard(U_2620),U_2621))),hAPP(c_Finite__Set_Ocard(U_2620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2622),U_2621))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2621)) ),
    inference(clausify,[status(thm)],[f_621_2]) ).

fof(f_622_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_622_2,plain,
    ! [U_2625,U_2624,U_2623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2623,tc_HOL_Obool)),U_2625),U_2624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2623),U_2625)),hAPP(c_Finite__Set_Ocard(U_2623),U_2624)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2623,tc_HOL_Obool)),U_2625),U_2624))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2623),U_2624)) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

cnf(f_622_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2623,tc_HOL_Obool)),U_2625),U_2624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2623),U_2625)),hAPP(c_Finite__Set_Ocard(U_2623),U_2624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2623,tc_HOL_Obool)),U_2625),U_2624))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2623),U_2624)) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

fof(f_623_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_623_2,plain,
    ! [U_2628,U_2627,U_2626] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2626),U_2628),c_Complete__Lattice_OSup__class_OSup(U_2626,U_2627)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2626,U_2626,c_Lattices_Osemilattice__sup__class_Osup(U_2626)),U_2628),U_2627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2626),U_2627))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2626) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

cnf(f_623_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2626),U_2628),c_Complete__Lattice_OSup__class_OSup(U_2626,U_2627)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2626,U_2626,c_Lattices_Osemilattice__sup__class_Osup(U_2626)),U_2628),U_2627)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2626),U_2627))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2626) ),
    inference(clausify,[status(thm)],[f_623_2]) ).

fof(f_624_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_624_2,plain,
    ! [U_2631,U_2630,U_2629] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2629),hAPP(c_Finite__Set_Ofold1(U_2629,c_Lattices_Osemilattice__inf__class_Oinf(U_2629)),U_2630)),U_2631))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2629),U_2631),U_2630))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2629),U_2630))
      | ~ class_Lattices_Osemilattice__inf(U_2629) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

cnf(f_624_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2629),hAPP(c_Finite__Set_Ofold1(U_2629,c_Lattices_Osemilattice__inf__class_Oinf(U_2629)),U_2630)),U_2631))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2629),U_2631),U_2630))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2629),U_2630))
    | ~ class_Lattices_Osemilattice__inf(U_2629) ),
    inference(clausify,[status(thm)],[f_624_2]) ).

fof(f_625_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_625_2,plain,
    ! [U_2636,U_2635,U_2634] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635)))
          | ? [U_2633] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),U_2633))
              & hBOOL(hAPP(hAPP(c_member(U_2634),U_2633),U_2635)) ) )
        & ( ! [U_2632] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),U_2632))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2634),U_2632),U_2635)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635))) ) )
      | U_2635 = c_Orderings_Obot__class_Obot(tc_fun(U_2634,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),U_2635))
      | ~ class_Lattices_Osemilattice__inf(U_2634) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_2636,U_2635,U_2634] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),sK36(U_2636,U_2635,U_2634)))
            & hBOOL(hAPP(hAPP(c_member(U_2634),sK36(U_2636,U_2635,U_2634)),U_2635)) ) )
        & ( ! [U_2632] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),U_2632))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2634),U_2632),U_2635)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635))) ) )
      | U_2635 = c_Orderings_Obot__class_Obot(tc_fun(U_2634,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),U_2635))
      | ~ class_Lattices_Osemilattice__inf(U_2634) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2633,sK36(U_2636,U_2635,U_2634))],[f_625_2]) ).

cnf(f_625_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),U_2632))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2634),U_2632),U_2635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635)))
    | U_2635 = c_Orderings_Obot__class_Obot(tc_fun(U_2634,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),U_2635))
    | ~ class_Lattices_Osemilattice__inf(U_2634) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2634),sK36(U_2636,U_2635,U_2634)),U_2635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635)))
    | U_2635 = c_Orderings_Obot__class_Obot(tc_fun(U_2634,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),U_2635))
    | ~ class_Lattices_Osemilattice__inf(U_2634) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),sK36(U_2636,U_2635,U_2634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2634),U_2636),hAPP(c_Finite__Set_Ofold1(U_2634,c_Lattices_Osemilattice__inf__class_Oinf(U_2634)),U_2635)))
    | U_2635 = c_Orderings_Obot__class_Obot(tc_fun(U_2634,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2634),U_2635))
    | ~ class_Lattices_Osemilattice__inf(U_2634) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_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_626_2,plain,
    ! [U_2638,U_2637] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_2637,U_2638) = c_Complete__Lattice_OSup__class_OSup(U_2637,U_2638)
      | U_2638 = c_Orderings_Obot__class_Obot(tc_fun(U_2637,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2637),U_2638))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2637) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

cnf(f_626_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2637,U_2638) = c_Complete__Lattice_OSup__class_OSup(U_2637,U_2638)
    | U_2638 = c_Orderings_Obot__class_Obot(tc_fun(U_2637,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2637),U_2638))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2637) ),
    inference(clausify,[status(thm)],[f_626_2]) ).

fof(f_627_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_627_2,plain,
    ! [U_2641,U_2640,U_2639] :
      ( hAPP(c_Finite__Set_Ofold1(U_2639,c_Groups_Otimes__class_Otimes(U_2639)),hAPP(hAPP(c_Set_Oinsert(U_2639),U_2641),U_2640)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2639),U_2641),hAPP(c_Finite__Set_Ofold1(U_2639,c_Groups_Otimes__class_Otimes(U_2639)),U_2640))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2639),U_2640))
      | U_2640 = c_Orderings_Obot__class_Obot(tc_fun(U_2639,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2639) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

cnf(f_627_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2639,c_Groups_Otimes__class_Otimes(U_2639)),hAPP(hAPP(c_Set_Oinsert(U_2639),U_2641),U_2640)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2639),U_2641),hAPP(c_Finite__Set_Ofold1(U_2639,c_Groups_Otimes__class_Otimes(U_2639)),U_2640))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2639),U_2640))
    | U_2640 = c_Orderings_Obot__class_Obot(tc_fun(U_2639,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2639) ),
    inference(clausify,[status(thm)],[f_627_2]) ).

fof(f_628_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_628_2,plain,
    ! [U_2644,U_2643,U_2642] :
      ( hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2642,tc_HOL_Obool)),U_2643),U_2644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2642),hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),U_2643)),hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),U_2644))
      | U_2644 = c_Orderings_Obot__class_Obot(tc_fun(U_2642,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2644))
      | U_2643 = c_Orderings_Obot__class_Obot(tc_fun(U_2642,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2643))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2642) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

cnf(f_628_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2642,tc_HOL_Obool)),U_2643),U_2644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2642),hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),U_2643)),hAPP(c_Finite__Set_Ofold1(U_2642,c_Groups_Otimes__class_Otimes(U_2642)),U_2644))
    | U_2644 = c_Orderings_Obot__class_Obot(tc_fun(U_2642,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2644))
    | U_2643 = c_Orderings_Obot__class_Obot(tc_fun(U_2642,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2642),U_2643))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2642) ),
    inference(clausify,[status(thm)],[f_628_2]) ).

fof(f_629_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_629_2,plain,
    ! [U_2647,U_2646,U_2645] :
      ( hAPP(c_Finite__Set_Ofold1(U_2645,c_Groups_Otimes__class_Otimes(U_2645)),hAPP(hAPP(c_Set_Oinsert(U_2645),U_2647),U_2646)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2645,U_2645,c_Groups_Otimes__class_Otimes(U_2645)),U_2647),U_2646)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2645),U_2646))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2645) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

cnf(f_629_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_2645,c_Groups_Otimes__class_Otimes(U_2645)),hAPP(hAPP(c_Set_Oinsert(U_2645),U_2647),U_2646)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2645,U_2645,c_Groups_Otimes__class_Otimes(U_2645)),U_2647),U_2646)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2645),U_2646))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2645) ),
    inference(clausify,[status(thm)],[f_629_2]) ).

fof(f_630_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_630_2,plain,
    ! [U_2650,U_2649,U_2648] :
      ( hAPP(c_Finite__Set_Ocard(U_2648),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2648,tc_HOL_Obool)),U_2649),U_2650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2648),U_2649)),hAPP(c_Finite__Set_Ocard(U_2648),U_2650))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2648,tc_HOL_Obool)),U_2649),U_2650) != c_Orderings_Obot__class_Obot(tc_fun(U_2648,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2648),U_2650))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2648),U_2649)) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

cnf(f_630_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2648),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2648,tc_HOL_Obool)),U_2649),U_2650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2648),U_2649)),hAPP(c_Finite__Set_Ocard(U_2648),U_2650))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2648,tc_HOL_Obool)),U_2649),U_2650) != c_Orderings_Obot__class_Obot(tc_fun(U_2648,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2648),U_2650))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2648),U_2649)) ),
    inference(clausify,[status(thm)],[f_630_2]) ).

fof(f_631_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_631_2,plain,
    ! [U_2653,U_2652,U_2651] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2651),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2651,tc_HOL_Obool)),U_2652),hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),c_Orderings_Obot__class_Obot(tc_fun(U_2651,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2651),U_2652)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2651),U_2652)) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

cnf(f_631_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2651),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2651,tc_HOL_Obool)),U_2652),hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),c_Orderings_Obot__class_Obot(tc_fun(U_2651,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2651),U_2652)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2651),U_2652)) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

fof(f_632_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_632_2,plain,
    ! [U_2659,U_2658,U_2657,U_2656,U_2655,U_2654] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_2654,U_2655,U_2656),U_2658),hAPP(hAPP(c_Set_Oinsert(U_2654),U_2659),U_2657)) = hAPP(hAPP(U_2656,U_2659),hAPP(hAPP(c_Finite__Set_Ofold(U_2654,U_2655,U_2656),U_2658),U_2657))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2654),U_2657))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_2654,U_2655,U_2656) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

cnf(f_632_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_2654,U_2655,U_2656),U_2658),hAPP(hAPP(c_Set_Oinsert(U_2654),U_2659),U_2657)) = hAPP(hAPP(U_2656,U_2659),hAPP(hAPP(c_Finite__Set_Ofold(U_2654,U_2655,U_2656),U_2658),U_2657))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2654),U_2657))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_2654,U_2655,U_2656) ),
    inference(clausify,[status(thm)],[f_632_2]) ).

fof(f_633_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_633_2,plain,
    ! [U_2662,U_2661,U_2660] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2660,hAPP(hAPP(c_Set_Oinsert(U_2660),U_2661),hAPP(hAPP(c_Set_Oinsert(U_2660),U_2662),c_Orderings_Obot__class_Obot(tc_fun(U_2660,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2660),U_2661),U_2662)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2660) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

cnf(f_633_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2660,hAPP(hAPP(c_Set_Oinsert(U_2660),U_2661),hAPP(hAPP(c_Set_Oinsert(U_2660),U_2662),c_Orderings_Obot__class_Obot(tc_fun(U_2660,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2660),U_2661),U_2662)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2660) ),
    inference(clausify,[status(thm)],[f_633_2]) ).

fof(f_634_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_634_2,plain,
    ! [U_2666,U_2665,U_2664,U_2663] :
      ( hAPP(U_2665,U_2666) = hAPP(c_Finite__Set_Ofold1(U_2663,U_2664),U_2666)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2663),U_2666))
      | ~ c_Big__Operators_Osemilattice__big(U_2663,U_2664,U_2665) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

cnf(f_634_3,plain,
    ( hAPP(U_2665,U_2666) = hAPP(c_Finite__Set_Ofold1(U_2663,U_2664),U_2666)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2663),U_2666))
    | ~ c_Big__Operators_Osemilattice__big(U_2663,U_2664,U_2665) ),
    inference(clausify,[status(thm)],[f_634_2]) ).

fof(f_635_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_635_2,plain,
    ! [U_2669,U_2668,U_2667] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2667,hAPP(hAPP(c_Set_Oinsert(U_2667),U_2668),U_2669)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2667),U_2668),c_Complete__Lattice_OSup__class_OSup(U_2667,U_2669))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2667) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

cnf(f_635_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2667,hAPP(hAPP(c_Set_Oinsert(U_2667),U_2668),U_2669)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2667),U_2668),c_Complete__Lattice_OSup__class_OSup(U_2667,U_2669))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2667) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

fof(f_636_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_636_2,plain,
    ! [U_2671,U_2670] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2670,hAPP(hAPP(c_Set_Oinsert(U_2670),U_2671),c_Orderings_Obot__class_Obot(tc_fun(U_2670,tc_HOL_Obool)))) = U_2671
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2670) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

cnf(f_636_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2670,hAPP(hAPP(c_Set_Oinsert(U_2670),U_2671),c_Orderings_Obot__class_Obot(tc_fun(U_2670,tc_HOL_Obool)))) = U_2671
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2670) ),
    inference(clausify,[status(thm)],[f_636_2]) ).

fof(f_637_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_637_2,plain,
    ! [U_2672] :
      ( c_Complete__Lattice_OSup__class_OSup(U_2672,c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_2672)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2672) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

cnf(f_637_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_2672,c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_2672)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2672) ),
    inference(clausify,[status(thm)],[f_637_2]) ).

fof(f_638_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_638_2,plain,
    ! [U_2675,U_2674,U_2673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2674),c_Complete__Lattice_OSup__class_OSup(U_2673,U_2675)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2673),U_2674),U_2675))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2673) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

cnf(f_638_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2674),c_Complete__Lattice_OSup__class_OSup(U_2673,U_2675)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2673),U_2674),U_2675))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2673) ),
    inference(clausify,[status(thm)],[f_638_2]) ).

fof(f_639_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_639_2,plain,
    ! [U_2679,U_2678,U_2677,U_2676] :
      ( hBOOL(hAPP(hAPP(c_member(U_2676),U_2679),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2678)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2676),U_2679),U_2677))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2676,tc_HOL_Obool)),U_2677),U_2678)) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

cnf(f_639_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2676),U_2679),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2676,tc_HOL_Obool),U_2678)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2676),U_2679),U_2677))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2676,tc_HOL_Obool)),U_2677),U_2678)) ),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_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_640_2,plain,
    ! [U_2682,U_2681,U_2680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2680,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2680,tc_HOL_Obool),U_2681)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2680,tc_HOL_Obool),U_2682)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2680,tc_HOL_Obool),tc_HOL_Obool)),U_2681),U_2682)) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2680,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2680,tc_HOL_Obool),U_2681)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2680,tc_HOL_Obool),U_2682)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_2680,tc_HOL_Obool),tc_HOL_Obool)),U_2681),U_2682)) ),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_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_641_2,plain,
    ! [U_2686,U_2685] :
      ( hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(c_Finite__Set_Ofold1(U_2685,c_Groups_Otimes__class_Otimes(U_2685)),U_2686)),U_2686))
      | ? [U_2684,U_2683] : ~ hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2685),U_2684),U_2683)),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2684),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2683),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))))))
      | U_2686 = c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2685),U_2686))
      | ~ class_Groups_Oab__semigroup__mult(U_2685) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_2686,U_2685] :
      ( hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(c_Finite__Set_Ofold1(U_2685,c_Groups_Otimes__class_Otimes(U_2685)),U_2686)),U_2686))
      | ? [U_2683] : ~ hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2685),sK37(U_2686,U_2685)),U_2683)),hAPP(hAPP(c_Set_Oinsert(U_2685),sK37(U_2686,U_2685)),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2683),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))))))
      | U_2686 = c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2685),U_2686))
      | ~ class_Groups_Oab__semigroup__mult(U_2685) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2684,sK37(U_2686,U_2685))],[f_641_2]) ).

fof(f_641_4,plain,
    ! [U_2686,U_2685] :
      ( hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(c_Finite__Set_Ofold1(U_2685,c_Groups_Otimes__class_Otimes(U_2685)),U_2686)),U_2686))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2685),sK37(U_2686,U_2685)),sK38(U_2686,U_2685))),hAPP(hAPP(c_Set_Oinsert(U_2685),sK37(U_2686,U_2685)),hAPP(hAPP(c_Set_Oinsert(U_2685),sK38(U_2686,U_2685)),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))))))
      | U_2686 = c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2685),U_2686))
      | ~ class_Groups_Oab__semigroup__mult(U_2685) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2683,sK38(U_2686,U_2685))],[f_641_3]) ).

cnf(f_641_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(c_Finite__Set_Ofold1(U_2685,c_Groups_Otimes__class_Otimes(U_2685)),U_2686)),U_2686))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2685),sK37(U_2686,U_2685)),sK38(U_2686,U_2685))),hAPP(hAPP(c_Set_Oinsert(U_2685),sK37(U_2686,U_2685)),hAPP(hAPP(c_Set_Oinsert(U_2685),sK38(U_2686,U_2685)),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))))))
    | U_2686 = c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2685),U_2686))
    | ~ class_Groups_Oab__semigroup__mult(U_2685) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

fof(f_642_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_642_2,plain,
    ! [U_2687] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2687,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2687,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2687,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

cnf(f_642_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2687,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2687,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2687,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_642_2]) ).

fof(f_643_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_643_2,plain,
    ! [U_2690,U_2689,U_2688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2689),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2688,tc_HOL_Obool),U_2690)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2688,tc_HOL_Obool)),U_2689),U_2690)) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

cnf(f_643_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2689),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2688,tc_HOL_Obool),U_2690)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2688,tc_HOL_Obool)),U_2689),U_2690)) ),
    inference(clausify,[status(thm)],[f_643_2]) ).

fof(f_644_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_644_2,plain,
    ! [U_2693,U_2692,U_2691] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2691,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2691,tc_HOL_Obool)),U_2692),U_2693)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2691,tc_HOL_Obool)),U_2692),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2691,tc_HOL_Obool),U_2693)),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

cnf(f_644_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2691,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2691,tc_HOL_Obool)),U_2692),U_2693)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2691,tc_HOL_Obool)),U_2692),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2691,tc_HOL_Obool),U_2693)),
    inference(clausify,[status(thm)],[f_644_2]) ).

fof(f_645_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_645_2,plain,
    ! [U_2696,U_2695,U_2694] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2694,tc_HOL_Obool)),U_2695),U_2696) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2694,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2694,tc_HOL_Obool)),U_2695),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2694,tc_HOL_Obool)),U_2696),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2694,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2694,tc_HOL_Obool)),U_2695),U_2696) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2694,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2694,tc_HOL_Obool)),U_2695),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2694,tc_HOL_Obool)),U_2696),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_2694,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_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_646_2,plain,
    ! [U_2699,U_2698,U_2697] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2697,tc_HOL_Obool),tc_HOL_Obool)),U_2698),U_2699)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2697,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),U_2698)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),U_2699)),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_2697,tc_HOL_Obool),tc_HOL_Obool)),U_2698),U_2699)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2697,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),U_2698)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2697,tc_HOL_Obool),U_2699)),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_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_647_2,plain,
    ! [U_2704,U_2703,U_2702] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2702,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2702,tc_HOL_Obool),U_2703)),U_2704) = c_Orderings_Obot__class_Obot(tc_fun(U_2702,tc_HOL_Obool))
        | ? [U_2701] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2702,tc_HOL_Obool)),U_2701),U_2704) != c_Orderings_Obot__class_Obot(tc_fun(U_2702,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2702,tc_HOL_Obool)),U_2701),U_2703)) ) )
      & ( ! [U_2700] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2702,tc_HOL_Obool)),U_2700),U_2704) = c_Orderings_Obot__class_Obot(tc_fun(U_2702,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2702,tc_HOL_Obool)),U_2700),U_2703)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2702,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2702,tc_HOL_Obool),U_2703)),U_2704) != c_Orderings_Obot__class_Obot(tc_fun(U_2702,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ( ! [U_2710,U_2708,U_2706] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2706,tc_HOL_Obool),U_2708)),U_2710) = c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool))
        | ? [U_2701] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),U_2701),U_2710) != c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2706,tc_HOL_Obool)),U_2701),U_2708)) ) )
    & ! [U_2709,U_2707,U_2705] :
        ( ! [U_2700] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2709) = c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2707)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2705,tc_HOL_Obool),U_2707)),U_2709) != c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_647_2]) ).

fof(f_647_4,plain,
    ( ! [U_2710,U_2708,U_2706] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2706,tc_HOL_Obool),U_2708)),U_2710) = c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),sK39(U_2710,U_2708,U_2706)),U_2710) != c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2706,tc_HOL_Obool)),sK39(U_2710,U_2708,U_2706)),U_2708)) ) )
    & ! [U_2709,U_2707,U_2705] :
        ( ! [U_2700] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2709) = c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2707)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2705,tc_HOL_Obool),U_2707)),U_2709) != c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2701,sK39(U_2710,U_2708,U_2706))],[f_647_3]) ).

cnf(f_647_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2709) = c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2705,tc_HOL_Obool)),U_2700),U_2707))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2705,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2705,tc_HOL_Obool),U_2707)),U_2709) != c_Orderings_Obot__class_Obot(tc_fun(U_2705,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_647_4]) ).

cnf(f_647_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2706,tc_HOL_Obool)),sK39(U_2710,U_2708,U_2706)),U_2708))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2706,tc_HOL_Obool),U_2708)),U_2710) = c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_647_4]) ).

cnf(f_647_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),sK39(U_2710,U_2708,U_2706)),U_2710) != c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2706,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2706,tc_HOL_Obool),U_2708)),U_2710) = c_Orderings_Obot__class_Obot(tc_fun(U_2706,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_647_4]) ).

fof(f_648_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_648_2,plain,
    ! [U_2713,U_2712,U_2711] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2711,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_2711,tc_HOL_Obool),tc_HOL_Obool)),U_2712),U_2713))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2711,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),U_2712)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),U_2713)))),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

cnf(f_648_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2711,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_2711,tc_HOL_Obool),tc_HOL_Obool)),U_2712),U_2713))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2711,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),U_2712)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2711,tc_HOL_Obool),U_2713)))),
    inference(clausify,[status(thm)],[f_648_2]) ).

fof(f_649_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_649_2,plain,
    ! [U_2718,U_2717,U_2716] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718))
          | ? [U_2715] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),U_2715),U_2718))
              & hBOOL(hAPP(hAPP(c_member(U_2716),U_2715),U_2717)) ) )
        & ( ! [U_2714] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),U_2714),U_2718))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2714),U_2717)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2716) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ! [U_2718,U_2717,U_2716] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),sK40(U_2718,U_2717,U_2716)),U_2718))
            & hBOOL(hAPP(hAPP(c_member(U_2716),sK40(U_2718,U_2717,U_2716)),U_2717)) ) )
        & ( ! [U_2714] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),U_2714),U_2718))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2714),U_2717)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2716) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2715,sK40(U_2718,U_2717,U_2716))],[f_649_2]) ).

cnf(f_649_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),U_2714),U_2718))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2716),U_2714),U_2717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2716) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2716),sK40(U_2718,U_2717,U_2716)),U_2717))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2716) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),sK40(U_2718,U_2717,U_2716)),U_2718))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2716),c_Complete__Lattice_OSup__class_OSup(U_2716,U_2717)),U_2718))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2716) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_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_650_2,plain,
    ! [U_2723,U_2722,U_2721] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723)))
          | ! [U_2720] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),U_2720))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2720),U_2723)) ) )
        & ( ? [U_2719] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),U_2719))
              & hBOOL(hAPP(hAPP(c_member(U_2721),U_2719),U_2723)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723))) ) )
      | ~ class_Orderings_Olinorder(U_2721)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2721) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_2723,U_2722,U_2721] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723)))
          | ! [U_2720] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),U_2720))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2720),U_2723)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),sK41(U_2723,U_2722,U_2721)))
            & hBOOL(hAPP(hAPP(c_member(U_2721),sK41(U_2723,U_2722,U_2721)),U_2723)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723))) ) )
      | ~ class_Orderings_Olinorder(U_2721)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2721) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2719,sK41(U_2723,U_2722,U_2721))],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2721),sK41(U_2723,U_2722,U_2721)),U_2723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723)))
    | ~ class_Orderings_Olinorder(U_2721)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2721) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),sK41(U_2723,U_2722,U_2721)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723)))
    | ~ class_Orderings_Olinorder(U_2721)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2721) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),c_Complete__Lattice_OSup__class_OSup(U_2721,U_2723)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),U_2722),U_2720))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2720),U_2723))
    | ~ class_Orderings_Olinorder(U_2721)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2721) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_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_651_2,plain,
    ! [U_2726,U_2725,U_2724] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_2724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2724,tc_HOL_Obool)),U_2725),hAPP(hAPP(c_Set_Oinsert(U_2724),U_2726),c_Orderings_Obot__class_Obot(tc_fun(U_2724,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_2724),U_2725)
          | hBOOL(hAPP(hAPP(c_member(U_2724),U_2726),U_2725)) )
        & ( hAPP(c_Finite__Set_Ocard(U_2724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2724,tc_HOL_Obool)),U_2725),hAPP(hAPP(c_Set_Oinsert(U_2724),U_2726),c_Orderings_Obot__class_Obot(tc_fun(U_2724,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2724),U_2725)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2724),U_2726),U_2725)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2724),U_2725)) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

cnf(f_651_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2724,tc_HOL_Obool)),U_2725),hAPP(hAPP(c_Set_Oinsert(U_2724),U_2726),c_Orderings_Obot__class_Obot(tc_fun(U_2724,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2724),U_2725)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2724),U_2726),U_2725))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2724),U_2725)) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2724,tc_HOL_Obool)),U_2725),hAPP(hAPP(c_Set_Oinsert(U_2724),U_2726),c_Orderings_Obot__class_Obot(tc_fun(U_2724,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_2724),U_2725)
    | hBOOL(hAPP(hAPP(c_member(U_2724),U_2726),U_2725))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2724),U_2725)) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

fof(f_652_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_652_2,plain,
    ! [U_2729,U_2728,U_2727] :
      ( hAPP(c_Finite__Set_Ocard(U_2727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2727,tc_HOL_Obool)),U_2728),hAPP(hAPP(c_Set_Oinsert(U_2727),U_2729),c_Orderings_Obot__class_Obot(tc_fun(U_2727,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2727),U_2728)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2727),U_2729),U_2728))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2727),U_2728)) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2727,tc_HOL_Obool)),U_2728),hAPP(hAPP(c_Set_Oinsert(U_2727),U_2729),c_Orderings_Obot__class_Obot(tc_fun(U_2727,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2727),U_2728)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2727),U_2729),U_2728))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2727),U_2728)) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_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_653_2,plain,
    ! [U_2732,U_2731,U_2730] :
      ( hAPP(c_Finite__Set_Ocard(U_2730),U_2731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_2730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2730,tc_HOL_Obool)),U_2731),hAPP(hAPP(c_Set_Oinsert(U_2730),U_2732),c_Orderings_Obot__class_Obot(tc_fun(U_2730,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2730),U_2732),U_2731))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2730),U_2731)) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

cnf(f_653_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2730),U_2731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_2730),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2730,tc_HOL_Obool)),U_2731),hAPP(hAPP(c_Set_Oinsert(U_2730),U_2732),c_Orderings_Obot__class_Obot(tc_fun(U_2730,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2730),U_2732),U_2731))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2730),U_2731)) ),
    inference(clausify,[status(thm)],[f_653_2]) ).

fof(f_654_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_654_2,plain,
    ! [U_2735,U_2734] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2734,tc_HOL_Obool),U_2735)))
      | ? [U_2733] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),U_2733))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2734,tc_HOL_Obool)),U_2733),U_2735)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2734,tc_HOL_Obool)),U_2735)) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_2735,U_2734] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2734,tc_HOL_Obool),U_2735)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),sK42(U_2735,U_2734)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2734,tc_HOL_Obool)),sK42(U_2735,U_2734)),U_2735)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2734,tc_HOL_Obool)),U_2735)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2733,sK42(U_2735,U_2734))],[f_654_2]) ).

cnf(f_654_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2734,tc_HOL_Obool)),sK42(U_2735,U_2734)),U_2735))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2734,tc_HOL_Obool),U_2735)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2734,tc_HOL_Obool)),U_2735)) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

cnf(f_654_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),sK42(U_2735,U_2734)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2734),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2734,tc_HOL_Obool),U_2735)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2734,tc_HOL_Obool)),U_2735)) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_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_655_2,plain,
    ! [U_2738,U_2737,U_2736] :
      ( hAPP(c_Finite__Set_Ocard(U_2736),hAPP(hAPP(c_Set_Oinsert(U_2736),U_2738),U_2737)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_2736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),U_2737),hAPP(hAPP(c_Set_Oinsert(U_2736),U_2738),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

cnf(f_655_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2736),hAPP(hAPP(c_Set_Oinsert(U_2736),U_2738),U_2737)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_2736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2736,tc_HOL_Obool)),U_2737),hAPP(hAPP(c_Set_Oinsert(U_2736),U_2738),c_Orderings_Obot__class_Obot(tc_fun(U_2736,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2736),U_2737)) ),
    inference(clausify,[status(thm)],[f_655_2]) ).

fof(f_656_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_656_2,plain,
    ! [U_2742,U_2741,U_2740,U_2739] :
      ( hAPP(c_Finite__Set_Ocard(U_2739),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2739,tc_HOL_Obool)),U_2740),hAPP(hAPP(c_Set_Oinsert(U_2739),U_2741),U_2742))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2739),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2739,tc_HOL_Obool)),U_2740),U_2742))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_2739),U_2741),U_2742))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2739),U_2741),U_2740))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2740)) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

cnf(f_656_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_2739),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2739,tc_HOL_Obool)),U_2740),hAPP(hAPP(c_Set_Oinsert(U_2739),U_2741),U_2742))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2739),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2739,tc_HOL_Obool)),U_2740),U_2742))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_2739),U_2741),U_2742))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2739),U_2741),U_2740))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2739),U_2740)) ),
    inference(clausify,[status(thm)],[f_656_2]) ).

fof(f_657_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_657_2,plain,
    ! [U_2745,U_2744,U_2743] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_2743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2743,tc_HOL_Obool)),U_2744),hAPP(hAPP(c_Set_Oinsert(U_2743),U_2745),c_Orderings_Obot__class_Obot(tc_fun(U_2743,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_2743),U_2744)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2743),U_2745),U_2744))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2743),U_2744)) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_2743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2743,tc_HOL_Obool)),U_2744),hAPP(hAPP(c_Set_Oinsert(U_2743),U_2745),c_Orderings_Obot__class_Obot(tc_fun(U_2743,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_2743),U_2744)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2743),U_2745),U_2744))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2743),U_2744)) ),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_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_658_2,plain,
    ! [U_2750,U_2749,U_2748,U_2747,U_2746] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2747,U_2746),U_2750),U_2748) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2746),hAPP(U_2750,U_2749)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2747,U_2746),U_2750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2747,tc_HOL_Obool)),U_2748),hAPP(hAPP(c_Set_Oinsert(U_2747),U_2749),c_Orderings_Obot__class_Obot(tc_fun(U_2747,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2747),U_2749),U_2748))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2747),U_2748))
      | ~ class_Groups_Ocomm__monoid__mult(U_2746) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

cnf(f_658_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2747,U_2746),U_2750),U_2748) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2746),hAPP(U_2750,U_2749)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2747,U_2746),U_2750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2747,tc_HOL_Obool)),U_2748),hAPP(hAPP(c_Set_Oinsert(U_2747),U_2749),c_Orderings_Obot__class_Obot(tc_fun(U_2747,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2747),U_2749),U_2748))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2747),U_2748))
    | ~ class_Groups_Ocomm__monoid__mult(U_2746) ),
    inference(clausify,[status(thm)],[f_658_2]) ).

fof(f_659_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_659_2,plain,
    ! [U_2755,U_2754,U_2753] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
      | ? [U_2752] :
          ( ? [U_2751] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2752),U_2751) != c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
              & U_2752 != U_2751
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2751),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2752),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_2755,U_2754,U_2753] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
      | ( ? [U_2751] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),U_2751) != c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
            & sK43(U_2755,U_2754,U_2753) != U_2751
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2751),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2752,sK43(U_2755,U_2754,U_2753))],[f_659_2]) ).

fof(f_659_4,plain,
    ! [U_2755,U_2754,U_2753] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),sK44(U_2755,U_2754,U_2753)) != c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
        & sK43(U_2755,U_2754,U_2753) != sK44(U_2755,U_2754,U_2753)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),sK44(U_2755,U_2754,U_2753)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2751,sK44(U_2755,U_2754,U_2753))],[f_659_3]) ).

cnf(f_659_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),sK44(U_2755,U_2754,U_2753)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_7,plain,
    ( sK43(U_2755,U_2754,U_2753) != sK44(U_2755,U_2754,U_2753)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

cnf(f_659_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),sK43(U_2755,U_2754,U_2753)),sK44(U_2755,U_2754,U_2753)) != c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2753,tc_HOL_Obool)),U_2754),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2753,tc_HOL_Obool),U_2755)) = c_Orderings_Obot__class_Obot(tc_fun(U_2753,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2753,tc_HOL_Obool)),U_2754),U_2755)) ),
    inference(clausify,[status(thm)],[f_659_4]) ).

fof(f_660_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_660_2,plain,
    ! [U_2756] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2756),hAPP(c_Nat_OSuc,U_2756))),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2756),hAPP(c_Nat_OSuc,U_2756))),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_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_661_2,plain,
    ! [U_2758,U_2757] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2757)),hAPP(c_Nat_OSuc,U_2758)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2757),U_2758)) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

cnf(f_661_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2757)),hAPP(c_Nat_OSuc,U_2758)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2757),U_2758)) ),
    inference(clausify,[status(thm)],[f_661_2]) ).

fof(f_662_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_662_2,plain,
    ! [U_2762,U_2761,U_2760,U_2759] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2760,U_2759),U_2762),U_2761) = c_Groups_Oone__class_Oone(U_2759)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2760),U_2761))
      | ~ class_Groups_Ocomm__monoid__mult(U_2759) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2760,U_2759),U_2762),U_2761) = c_Groups_Oone__class_Oone(U_2759)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2760),U_2761))
    | ~ class_Groups_Ocomm__monoid__mult(U_2759) ),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_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_663_2,plain,
    ! [U_2766,U_2765,U_2764,U_2763] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2764,U_2763),U_2766),U_2765) = c_Groups_Oone__class_Oone(U_2763)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2764),U_2765))
      | ~ class_Groups_Ocomm__monoid__mult(U_2763) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2764,U_2763),U_2766),U_2765) = c_Groups_Oone__class_Oone(U_2763)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2764),U_2765))
    | ~ class_Groups_Ocomm__monoid__mult(U_2763) ),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_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_664_2,plain,
    ! [U_2771,U_2770,U_2769] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_2768] :
              ( hAPP(U_2771,U_2768) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_2769),U_2768),U_2770)) ) )
        & ( ! [U_2767] :
              ( hAPP(U_2771,U_2767) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_2769),U_2767),U_2770)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2769),U_2770)) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2771,U_2770,U_2769] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_2771,sK45(U_2771,U_2770,U_2769)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_2769),sK45(U_2771,U_2770,U_2769)),U_2770)) ) )
        & ( ! [U_2767] :
              ( hAPP(U_2771,U_2767) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_2769),U_2767),U_2770)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2769),U_2770)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2768,sK45(U_2771,U_2770,U_2769))],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hAPP(U_2771,U_2767) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2769),U_2767),U_2770))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2769),U_2770)) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

cnf(f_664_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2769),sK45(U_2771,U_2770,U_2769)),U_2770))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2769),U_2770)) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

cnf(f_664_6,plain,
    ( hAPP(U_2771,sK45(U_2771,U_2770,U_2769)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2769,tc_Nat_Onat),U_2771),U_2770) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2769),U_2770)) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_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_665_2,plain,
    ! [U_2773,U_2772] :
      ( ( ( c_Groups_Oone__class_Oone(U_2772) = U_2773
          | U_2773 != c_Groups_Oone__class_Oone(U_2772) )
        & ( U_2773 = c_Groups_Oone__class_Oone(U_2772)
          | c_Groups_Oone__class_Oone(U_2772) != U_2773 ) )
      | ~ class_Groups_Oone(U_2772) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

cnf(f_665_3,plain,
    ( U_2773 = c_Groups_Oone__class_Oone(U_2772)
    | c_Groups_Oone__class_Oone(U_2772) != U_2773
    | ~ class_Groups_Oone(U_2772) ),
    inference(clausify,[status(thm)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( c_Groups_Oone__class_Oone(U_2772) = U_2773
    | U_2773 != c_Groups_Oone__class_Oone(U_2772)
    | ~ class_Groups_Oone(U_2772) ),
    inference(clausify,[status(thm)],[f_665_2]) ).

fof(f_666_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_666_2,plain,
    ! [U_2776,U_2775,U_2774] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2775,U_2774),U_2776),c_Orderings_Obot__class_Obot(tc_fun(U_2775,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_2774)
      | ~ class_Groups_Ocomm__monoid__mult(U_2774) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

cnf(f_666_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2775,U_2774),U_2776),c_Orderings_Obot__class_Obot(tc_fun(U_2775,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_2774)
    | ~ class_Groups_Ocomm__monoid__mult(U_2774) ),
    inference(clausify,[status(thm)],[f_666_2]) ).

fof(f_667_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_667_2,plain,
    ! [U_2779,U_2778,U_2777] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2778,U_2777),U_2779),c_Orderings_Obot__class_Obot(tc_fun(U_2778,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_2777)
      | ~ class_Groups_Ocomm__monoid__mult(U_2777) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

cnf(f_667_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2778,U_2777),U_2779),c_Orderings_Obot__class_Obot(tc_fun(U_2778,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_2777)
    | ~ class_Groups_Ocomm__monoid__mult(U_2777) ),
    inference(clausify,[status(thm)],[f_667_2]) ).

fof(f_668_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_668_2,plain,
    ! [U_2780] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2780)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2780,
    inference(variable_rename,[status(thm)],[f_668_1]) ).

cnf(f_668_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2780)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2780,
    inference(clausify,[status(thm)],[f_668_2]) ).

fof(f_669_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_669_2,plain,
    ! [U_2782,U_2781] :
      ( U_2781 = U_2782
      | hAPP(c_Nat_OSuc,U_2781) != hAPP(c_Nat_OSuc,U_2782) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( U_2781 = U_2782
    | hAPP(c_Nat_OSuc,U_2781) != hAPP(c_Nat_OSuc,U_2782) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_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_670_2,plain,
    ! [U_2784,U_2783] :
      ( ( hAPP(c_Nat_OSuc,U_2783) = hAPP(c_Nat_OSuc,U_2784)
        | U_2783 != U_2784 )
      & ( U_2783 = U_2784
        | hAPP(c_Nat_OSuc,U_2783) != hAPP(c_Nat_OSuc,U_2784) ) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ( ! [U_2788,U_2786] :
        ( hAPP(c_Nat_OSuc,U_2786) = hAPP(c_Nat_OSuc,U_2788)
        | U_2786 != U_2788 )
    & ! [U_2787,U_2785] :
        ( U_2785 = U_2787
        | hAPP(c_Nat_OSuc,U_2785) != hAPP(c_Nat_OSuc,U_2787) ) ),
    inference(miniscope,[status(thm)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( U_2785 = U_2787
    | hAPP(c_Nat_OSuc,U_2785) != hAPP(c_Nat_OSuc,U_2787) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

cnf(f_670_5,plain,
    ( hAPP(c_Nat_OSuc,U_2786) = hAPP(c_Nat_OSuc,U_2788)
    | U_2786 != U_2788 ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_671_2,plain,
    ! [U_2789] : hAPP(c_Nat_OSuc,U_2789) != U_2789,
    inference(variable_rename,[status(thm)],[f_671_1]) ).

cnf(f_671_3,plain,
    hAPP(c_Nat_OSuc,U_2789) != U_2789,
    inference(clausify,[status(thm)],[f_671_2]) ).

fof(f_672_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_672_2,plain,
    ! [U_2790] : U_2790 != hAPP(c_Nat_OSuc,U_2790),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    U_2790 != hAPP(c_Nat_OSuc,U_2790),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_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_673_2,plain,
    ! [U_2792,U_2791] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2791),U_2792),c_Groups_Oone__class_Oone(U_2791)) = U_2792
      | ~ class_Groups_Ocomm__monoid__mult(U_2791) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2791),U_2792),c_Groups_Oone__class_Oone(U_2791)) = U_2792
    | ~ class_Groups_Ocomm__monoid__mult(U_2791) ),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_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_674_2,plain,
    ! [U_2794,U_2793] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2794),c_Groups_Oone__class_Oone(U_2793)) = U_2794
      | ~ class_Groups_Omonoid__mult(U_2793) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2793),U_2794),c_Groups_Oone__class_Oone(U_2793)) = U_2794
    | ~ class_Groups_Omonoid__mult(U_2793) ),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_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_675_2,plain,
    ! [U_2796,U_2795] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2795),c_Groups_Oone__class_Oone(U_2795)),U_2796) = U_2796
      | ~ class_Groups_Ocomm__monoid__mult(U_2795) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2795),c_Groups_Oone__class_Oone(U_2795)),U_2796) = U_2796
    | ~ class_Groups_Ocomm__monoid__mult(U_2795) ),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_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_676_2,plain,
    ! [U_2798,U_2797] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2797),c_Groups_Oone__class_Oone(U_2797)),U_2798) = U_2798
      | ~ class_Groups_Omonoid__mult(U_2797) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

cnf(f_676_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2797),c_Groups_Oone__class_Oone(U_2797)),U_2798) = U_2798
    | ~ class_Groups_Omonoid__mult(U_2797) ),
    inference(clausify,[status(thm)],[f_676_2]) ).

fof(f_677_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_677_2,plain,
    ! [U_2800,U_2799] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2799),c_Groups_Oone__class_Oone(U_2799)),U_2800) = U_2800
      | ~ class_Rings_Ocomm__semiring__1(U_2799) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

cnf(f_677_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2799),c_Groups_Oone__class_Oone(U_2799)),U_2800) = U_2800
    | ~ class_Rings_Ocomm__semiring__1(U_2799) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

fof(f_678_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_678_2,plain,
    ! [U_2802,U_2801] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2801),U_2802),c_Groups_Oone__class_Oone(U_2801)) = U_2802
      | ~ class_Rings_Ocomm__semiring__1(U_2801) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

cnf(f_678_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2801),U_2802),c_Groups_Oone__class_Oone(U_2801)) = U_2802
    | ~ class_Rings_Ocomm__semiring__1(U_2801) ),
    inference(clausify,[status(thm)],[f_678_2]) ).

fof(f_679_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_679_2,plain,
    ! [U_2804,U_2803] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2803),U_2804))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2804),hAPP(c_Nat_OSuc,U_2803))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2804),hAPP(c_Nat_OSuc,U_2803)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2803),U_2804)) ) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ( ! [U_2808,U_2806] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2806),U_2808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2808),hAPP(c_Nat_OSuc,U_2806))) )
    & ! [U_2807,U_2805] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2807),hAPP(c_Nat_OSuc,U_2805)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2805),U_2807)) ) ),
    inference(miniscope,[status(thm)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2807),hAPP(c_Nat_OSuc,U_2805)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2805),U_2807)) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

cnf(f_679_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2806),U_2808))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2808),hAPP(c_Nat_OSuc,U_2806))) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_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_680_2,plain,
    ! [U_2810,U_2809] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2809),hAPP(c_Nat_OSuc,U_2810)))
        | ( U_2809 != U_2810
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2809),U_2810)) ) )
      & ( U_2809 = U_2810
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2809),U_2810))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2809),hAPP(c_Nat_OSuc,U_2810))) ) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ( ! [U_2814,U_2812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2812),hAPP(c_Nat_OSuc,U_2814)))
        | ( U_2812 != U_2814
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2812),U_2814)) ) )
    & ! [U_2813,U_2811] :
        ( U_2811 = U_2813
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2811),U_2813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2811),hAPP(c_Nat_OSuc,U_2813))) ) ),
    inference(miniscope,[status(thm)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( U_2811 = U_2813
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2811),U_2813))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2811),hAPP(c_Nat_OSuc,U_2813))) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

cnf(f_680_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2812),U_2814))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2812),hAPP(c_Nat_OSuc,U_2814))) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

cnf(f_680_6,plain,
    ( U_2812 != U_2814
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2812),hAPP(c_Nat_OSuc,U_2814))) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_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_681_2,plain,
    ! [U_2816,U_2815] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2815)),hAPP(c_Nat_OSuc,U_2816)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2815),U_2816)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2815),U_2816))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2815)),hAPP(c_Nat_OSuc,U_2816))) ) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ( ! [U_2820,U_2818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2818)),hAPP(c_Nat_OSuc,U_2820)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2818),U_2820)) )
    & ! [U_2819,U_2817] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2817),U_2819))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2817)),hAPP(c_Nat_OSuc,U_2819))) ) ),
    inference(miniscope,[status(thm)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2817),U_2819))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2817)),hAPP(c_Nat_OSuc,U_2819))) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2818)),hAPP(c_Nat_OSuc,U_2820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2818),U_2820)) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_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_682_2,plain,
    ! [U_2822,U_2821] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),hAPP(c_Nat_OSuc,U_2822)))
          | U_2821 != U_2822 )
        & ( U_2821 = U_2822
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),hAPP(c_Nat_OSuc,U_2822))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),U_2822)) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

cnf(f_682_3,plain,
    ( U_2821 = U_2822
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),hAPP(c_Nat_OSuc,U_2822)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),U_2822)) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),hAPP(c_Nat_OSuc,U_2822)))
    | U_2821 != U_2822
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2821),U_2822)) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

fof(f_683_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_683_2,plain,
    ! [U_2824,U_2823] :
      ( U_2824 = U_2823
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2823),hAPP(c_Nat_OSuc,U_2824)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2823),U_2824)) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

cnf(f_683_3,plain,
    ( U_2824 = U_2823
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2823),hAPP(c_Nat_OSuc,U_2824)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2823),U_2824)) ),
    inference(clausify,[status(thm)],[f_683_2]) ).

fof(f_684_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_684_2,plain,
    ! [U_2826,U_2825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2825),hAPP(c_Nat_OSuc,U_2826)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2825),U_2826)) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

cnf(f_684_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2825),hAPP(c_Nat_OSuc,U_2826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2825),U_2826)) ),
    inference(clausify,[status(thm)],[f_684_2]) ).

fof(f_685_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_685_2,plain,
    ! [U_2828,U_2827] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2827)),U_2828))
      | hAPP(c_Nat_OSuc,U_2827) = U_2828
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2827),U_2828)) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

cnf(f_685_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2827)),U_2828))
    | hAPP(c_Nat_OSuc,U_2827) = U_2828
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2827),U_2828)) ),
    inference(clausify,[status(thm)],[f_685_2]) ).

fof(f_686_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_686_2,plain,
    ! [U_2831,U_2830,U_2829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2829)),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2830),U_2831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2829),U_2830)) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

cnf(f_686_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2829)),U_2831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2830),U_2831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2829),U_2830)) ),
    inference(clausify,[status(thm)],[f_686_2]) ).

fof(f_687_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_687_2,plain,
    ! [U_2833,U_2832] :
      ( U_2832 = U_2833
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2832),U_2833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2832),hAPP(c_Nat_OSuc,U_2833))) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( U_2832 = U_2833
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2832),U_2833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2832),hAPP(c_Nat_OSuc,U_2833))) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_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_688_2,plain,
    ! [U_2835,U_2834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2834),U_2835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2834)),U_2835)) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2834),U_2835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2834)),U_2835)) ),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_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_689_2,plain,
    ! [U_2837,U_2836] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2836),U_2837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2836)),hAPP(c_Nat_OSuc,U_2837))) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2836),U_2837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2836)),hAPP(c_Nat_OSuc,U_2837))) ),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_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_690_2,plain,
    ! [U_2839,U_2838] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2838)),U_2839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2838),hAPP(c_Nat_OSuc,U_2839)),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

cnf(f_690_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2838)),U_2839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2838),hAPP(c_Nat_OSuc,U_2839)),
    inference(clausify,[status(thm)],[f_690_2]) ).

fof(f_691_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_691_2,plain,
    ! [U_2841,U_2840] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2840)),U_2841) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2840),U_2841)),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

cnf(f_691_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2840)),U_2841) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2840),U_2841)),
    inference(clausify,[status(thm)],[f_691_2]) ).

fof(f_692_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_692_2,plain,
    ! [U_2843,U_2842] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2842),hAPP(c_Nat_OSuc,U_2843)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2842),U_2843)),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

cnf(f_692_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2842),hAPP(c_Nat_OSuc,U_2843)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2842),U_2843)),
    inference(clausify,[status(thm)],[f_692_2]) ).

fof(f_693_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_693_2,plain,
    ! [U_2845,U_2844] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2844),U_2845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2844)),U_2845)) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2844),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2844)),U_2845)) ),
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_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_694_2,plain,
    ! [U_2847,U_2846] :
      ( U_2846 = hAPP(c_Nat_OSuc,U_2847)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),U_2847))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),hAPP(c_Nat_OSuc,U_2847))) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

cnf(f_694_3,plain,
    ( U_2846 = hAPP(c_Nat_OSuc,U_2847)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),U_2847))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),hAPP(c_Nat_OSuc,U_2847))) ),
    inference(clausify,[status(thm)],[f_694_2]) ).

fof(f_695_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_695_2,plain,
    ! [U_2849,U_2848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2848),hAPP(c_Nat_OSuc,U_2849)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2848),U_2849)) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

cnf(f_695_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2848),hAPP(c_Nat_OSuc,U_2849)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2848),U_2849)) ),
    inference(clausify,[status(thm)],[f_695_2]) ).

fof(f_696_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_696_2,plain,
    ! [U_2851,U_2850] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2850)),hAPP(c_Nat_OSuc,U_2851)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2850),U_2851)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2850),U_2851))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2850)),hAPP(c_Nat_OSuc,U_2851))) ) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ( ! [U_2855,U_2853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2853)),hAPP(c_Nat_OSuc,U_2855)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2853),U_2855)) )
    & ! [U_2854,U_2852] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2852),U_2854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2852)),hAPP(c_Nat_OSuc,U_2854))) ) ),
    inference(miniscope,[status(thm)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2852),U_2854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2852)),hAPP(c_Nat_OSuc,U_2854))) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

cnf(f_696_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2853)),hAPP(c_Nat_OSuc,U_2855)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2853),U_2855)) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_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_697_2,plain,
    ! [U_2857,U_2856] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2856),hAPP(c_Nat_OSuc,U_2857)))
        | ( U_2856 != hAPP(c_Nat_OSuc,U_2857)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2856),U_2857)) ) )
      & ( U_2856 = hAPP(c_Nat_OSuc,U_2857)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2856),U_2857))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2856),hAPP(c_Nat_OSuc,U_2857))) ) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ( ! [U_2861,U_2859] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2859),hAPP(c_Nat_OSuc,U_2861)))
        | ( U_2859 != hAPP(c_Nat_OSuc,U_2861)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2859),U_2861)) ) )
    & ! [U_2860,U_2858] :
        ( U_2858 = hAPP(c_Nat_OSuc,U_2860)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),U_2860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),hAPP(c_Nat_OSuc,U_2860))) ) ),
    inference(miniscope,[status(thm)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( U_2858 = hAPP(c_Nat_OSuc,U_2860)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),U_2860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),hAPP(c_Nat_OSuc,U_2860))) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2859),U_2861))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2859),hAPP(c_Nat_OSuc,U_2861))) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_6,plain,
    ( U_2859 != hAPP(c_Nat_OSuc,U_2861)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2859),hAPP(c_Nat_OSuc,U_2861))) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_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_698_2,plain,
    ! [U_2863,U_2862] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2862),U_2863))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2863)),U_2862)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2863)),U_2862))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2862),U_2863)) ) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ( ! [U_2867,U_2865] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2865),U_2867))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2867)),U_2865)) )
    & ! [U_2866,U_2864] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2866)),U_2864))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2866)) ) ),
    inference(miniscope,[status(thm)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2866)),U_2864))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2866)) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

cnf(f_698_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2865),U_2867))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2867)),U_2865)) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_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_699_2,plain,
    ! [U_2868] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2868)),U_2868)),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

cnf(f_699_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2868)),U_2868)),
    inference(clausify,[status(thm)],[f_699_2]) ).

fof(f_700_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_700_2,plain,
    ! [U_2870,U_2869] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2869)),hAPP(c_Nat_OSuc,U_2870)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2869),U_2870),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2869)),hAPP(c_Nat_OSuc,U_2870)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2869),U_2870),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_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_701_2,plain,
    ! [U_2873,U_2872,U_2871] : 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_2871)),U_2872)),hAPP(c_Nat_OSuc,U_2873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2871),U_2872)),U_2873),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_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_2871)),U_2872)),hAPP(c_Nat_OSuc,U_2873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2871),U_2872)),U_2873),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_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_702_2,plain,
    ! [U_2876,U_2875,U_2874] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2874)),U_2875) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2874)),U_2876)
        | U_2875 != U_2876 )
      & ( U_2875 = U_2876
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2874)),U_2875) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2874)),U_2876) ) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ( ! [U_2882,U_2880] :
        ( ! [U_2878] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2878)),U_2880) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2878)),U_2882)
        | U_2880 != U_2882 )
    & ! [U_2881,U_2879] :
        ( ! [U_2877] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2877)),U_2879) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2877)),U_2881)
        | U_2879 = U_2881 ) ),
    inference(miniscope,[status(thm)],[f_702_2]) ).

cnf(f_702_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2877)),U_2879) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2877)),U_2881)
    | U_2879 = U_2881 ),
    inference(clausify,[status(thm)],[f_702_3]) ).

cnf(f_702_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2878)),U_2880) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2878)),U_2882)
    | U_2880 != U_2882 ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_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_703_2,plain,
    ! [U_2883] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2883) = U_2883,
    inference(variable_rename,[status(thm)],[f_703_1]) ).

cnf(f_703_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2883) = U_2883,
    inference(clausify,[status(thm)],[f_703_2]) ).

fof(f_704_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_704_2,plain,
    ! [U_2885,U_2884] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2884),U_2885)
        | U_2885 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2884 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2885 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2884 = 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_2884),U_2885) ) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ( ! [U_2889,U_2887] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2889)
        | U_2889 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2887 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2888,U_2886] :
        ( ( U_2888 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2886 = 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_2886),U_2888) ) ),
    inference(miniscope,[status(thm)],[f_704_2]) ).

cnf(f_704_4,plain,
    ( U_2886 = 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_2886),U_2888) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_5,plain,
    ( U_2888 = 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_2886),U_2888) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2889)
    | U_2889 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2887 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_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_705_2,plain,
    ! [U_2890] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2890,
    inference(variable_rename,[status(thm)],[f_705_1]) ).

cnf(f_705_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2890,
    inference(clausify,[status(thm)],[f_705_2]) ).

fof(f_706_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_706_2,plain,
    ! [U_2892,U_2891] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2891),U_2892) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2892 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2891 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2892 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2891 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2891),U_2892) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ( ! [U_2896,U_2894] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2894),U_2896) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2896 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2894 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2895,U_2893] :
        ( ( U_2895 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2893 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2893),U_2895) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_706_2]) ).

cnf(f_706_4,plain,
    ( U_2893 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2893),U_2895) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_5,plain,
    ( U_2895 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2893),U_2895) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2894),U_2896) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2896 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2894 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_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_707_2,plain,
    ! [U_2898,U_2897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2897),U_2898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2897),U_2898),c_Groups_Oone__class_Oone(U_2897))))
      | ~ class_Rings_Olinordered__semidom(U_2897) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

cnf(f_707_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2897),U_2898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2897),U_2898),c_Groups_Oone__class_Oone(U_2897))))
    | ~ class_Rings_Olinordered__semidom(U_2897) ),
    inference(clausify,[status(thm)],[f_707_2]) ).

fof(f_708_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_708_2,plain,
    ! [U_2901,U_2900,U_2899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2899),U_2900),U_2901)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),U_2901))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),U_2900))
      | ~ class_Rings_Olinordered__semidom(U_2899) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

cnf(f_708_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2899),U_2900),U_2901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),U_2901))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2899),c_Groups_Oone__class_Oone(U_2899)),U_2900))
    | ~ class_Rings_Olinordered__semidom(U_2899) ),
    inference(clausify,[status(thm)],[f_708_2]) ).

fof(f_709_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_709_2,plain,
    ! [U_2904,U_2903,U_2902] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2902),U_2903),U_2904)),U_2904) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2902),U_2903),c_Groups_Oone__class_Oone(U_2902))),U_2904)
      | ~ class_Rings_Ocomm__semiring__1(U_2902) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

cnf(f_709_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2902),U_2903),U_2904)),U_2904) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2902),U_2903),c_Groups_Oone__class_Oone(U_2902))),U_2904)
    | ~ class_Rings_Ocomm__semiring__1(U_2902) ),
    inference(clausify,[status(thm)],[f_709_2]) ).

fof(f_710_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_710_2,plain,
    ! [U_2907,U_2906,U_2905] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2905),U_2906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2905),U_2907),U_2906)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2905),U_2907),c_Groups_Oone__class_Oone(U_2905))),U_2906)
      | ~ class_Rings_Ocomm__semiring__1(U_2905) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

cnf(f_710_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2905),U_2906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2905),U_2907),U_2906)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2905),U_2907),c_Groups_Oone__class_Oone(U_2905))),U_2906)
    | ~ class_Rings_Ocomm__semiring__1(U_2905) ),
    inference(clausify,[status(thm)],[f_710_2]) ).

fof(f_711_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_711_2,plain,
    ! [U_2909,U_2908] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2908),U_2909),U_2909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2908),c_Groups_Oone__class_Oone(U_2908)),c_Groups_Oone__class_Oone(U_2908))),U_2909)
      | ~ class_Rings_Ocomm__semiring__1(U_2908) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

cnf(f_711_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2908),U_2909),U_2909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2908),c_Groups_Oone__class_Oone(U_2908)),c_Groups_Oone__class_Oone(U_2908))),U_2909)
    | ~ class_Rings_Ocomm__semiring__1(U_2908) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

fof(f_712_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_712_2,plain,
    ! [U_2913,U_2912] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2912),U_2913))
        | ! [U_2911] : U_2913 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2912),U_2911)) )
      & ( ? [U_2910] : U_2913 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2912),U_2910))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2912),U_2913)) ) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ( ! [U_2917,U_2915] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2915),U_2917))
        | ! [U_2911] : U_2917 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2915),U_2911)) )
    & ! [U_2916,U_2914] :
        ( ? [U_2910] : U_2916 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2914),U_2910))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2914),U_2916)) ) ),
    inference(miniscope,[status(thm)],[f_712_2]) ).

fof(f_712_4,plain,
    ( ! [U_2917,U_2915] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2915),U_2917))
        | ! [U_2911] : U_2917 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2915),U_2911)) )
    & ! [U_2916,U_2914] :
        ( U_2916 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2914),sK46(U_2916,U_2914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2914),U_2916)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2910,sK46(U_2916,U_2914))],[f_712_3]) ).

cnf(f_712_5,plain,
    ( U_2916 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2914),sK46(U_2916,U_2914)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2914),U_2916)) ),
    inference(clausify,[status(thm)],[f_712_4]) ).

cnf(f_712_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2915),U_2917))
    | U_2917 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2915),U_2911)) ),
    inference(clausify,[status(thm)],[f_712_4]) ).

fof(f_713_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_713_2,plain,
    ! [U_2919,U_2918] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2918),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2919),U_2918)))),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

cnf(f_713_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2918),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2919),U_2918)))),
    inference(clausify,[status(thm)],[f_713_2]) ).

fof(f_714_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_714_2,plain,
    ! [U_2921,U_2920] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2920),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2920),U_2921)))),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2920),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2920),U_2921)))),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_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_715_2,plain,
    ! [U_2923,U_2922] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2922),U_2923))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2922)),U_2923)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2922)),U_2923))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2922),U_2923)) ) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ( ! [U_2927,U_2925] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2925),U_2927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2925)),U_2927)) )
    & ! [U_2926,U_2924] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2924)),U_2926))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2924),U_2926)) ) ),
    inference(miniscope,[status(thm)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2924)),U_2926))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2924),U_2926)) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2925),U_2927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2925)),U_2927)) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_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_716_2,plain,
    ! [U_2929,U_2928] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2928),hAPP(c_Nat_OSuc,U_2929)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2928),U_2929)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2928),U_2929))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2928),hAPP(c_Nat_OSuc,U_2929))) ) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ( ! [U_2933,U_2931] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2931),hAPP(c_Nat_OSuc,U_2933)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2931),U_2933)) )
    & ! [U_2932,U_2930] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2930),U_2932))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2930),hAPP(c_Nat_OSuc,U_2932))) ) ),
    inference(miniscope,[status(thm)],[f_716_2]) ).

cnf(f_716_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2930),U_2932))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2930),hAPP(c_Nat_OSuc,U_2932))) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

cnf(f_716_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2931),hAPP(c_Nat_OSuc,U_2933)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2931),U_2933)) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_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_717_2,plain,
    ! [U_2935,U_2934] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2934)),U_2935))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2934),U_2935)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2934),U_2935))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2934)),U_2935)) ) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ( ! [U_2939,U_2937] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2937)),U_2939))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2937),U_2939)) )
    & ! [U_2938,U_2936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2936),U_2938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2936)),U_2938)) ) ),
    inference(miniscope,[status(thm)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2936),U_2938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2936)),U_2938)) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

cnf(f_717_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2937)),U_2939))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2937),U_2939)) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_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_718_2,plain,
    ! [U_2941,U_2940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2940),hAPP(c_Nat_OSuc,U_2941)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2940),U_2941)) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

cnf(f_718_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2940),hAPP(c_Nat_OSuc,U_2941)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2940),U_2941)) ),
    inference(clausify,[status(thm)],[f_718_2]) ).

fof(f_719_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_719_2,plain,
    ! [U_2943,U_2942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2942)),U_2943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2942),U_2943)) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

cnf(f_719_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2942)),U_2943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2942),U_2943)) ),
    inference(clausify,[status(thm)],[f_719_2]) ).

fof(f_720_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_720_2,plain,
    ! [U_2945,U_2944] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2945),hAPP(c_Nat_OSuc,U_2944)))
          | U_2945 != U_2944 )
        & ( U_2945 = U_2944
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2945),hAPP(c_Nat_OSuc,U_2944))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2944),U_2945)) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

cnf(f_720_3,plain,
    ( U_2945 = U_2944
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2945),hAPP(c_Nat_OSuc,U_2944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2944),U_2945)) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

cnf(f_720_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2945),hAPP(c_Nat_OSuc,U_2944)))
    | U_2945 != U_2944
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2944),U_2945)) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

fof(f_721_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_721_2,plain,
    ! [U_2947,U_2946] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2946),U_2947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2946)),U_2947)) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

cnf(f_721_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2946),U_2947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2946)),U_2947)) ),
    inference(clausify,[status(thm)],[f_721_2]) ).

fof(f_722_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_722_2,plain,
    ! [U_2949,U_2948] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2948),U_2949)),hAPP(c_Nat_OSuc,U_2948))),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

cnf(f_722_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2948),U_2949)),hAPP(c_Nat_OSuc,U_2948))),
    inference(clausify,[status(thm)],[f_722_2]) ).

fof(f_723_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_723_2,plain,
    ! [U_2952,U_2951,U_2950] :
      ( ( 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_2950)),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2950)),U_2952)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2951),U_2952)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2951),U_2952))
        | ~ 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_2950)),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2950)),U_2952))) ) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ( ! [U_2958,U_2956] :
        ( ! [U_2954] : 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_2954)),U_2956)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2954)),U_2958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2956),U_2958)) )
    & ! [U_2957,U_2955] :
        ( ! [U_2953] : ~ 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_2953)),U_2955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2953)),U_2957)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2955),U_2957)) ) ),
    inference(miniscope,[status(thm)],[f_723_2]) ).

cnf(f_723_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_2953)),U_2955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2953)),U_2957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2955),U_2957)) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

cnf(f_723_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_2954)),U_2956)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2954)),U_2958)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2956),U_2958)) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_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_724_2,plain,
    ! [U_2960,U_2959] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2959),hAPP(c_Nat_OSuc,U_2960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2959),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2959),U_2960)),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

cnf(f_724_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2959),hAPP(c_Nat_OSuc,U_2960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2959),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2959),U_2960)),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_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_725_2,plain,
    ! [U_2962,U_2961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2961)),U_2962) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2961),U_2962)),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

cnf(f_725_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2961)),U_2962) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2961),U_2962)),
    inference(clausify,[status(thm)],[f_725_2]) ).

fof(f_726_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_726_2,plain,
    ! [U_2964,U_2963] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2964)),U_2963) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2964),U_2963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2963),U_2964)) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

cnf(f_726_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2964)),U_2963) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2964),U_2963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2963),U_2964)) ),
    inference(clausify,[status(thm)],[f_726_2]) ).

fof(f_727_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_727_2,plain,
    ! [U_2967,U_2966,U_2965] :
      ( ( 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_2965)),U_2966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2965)),U_2967)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2966),U_2967)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2966),U_2967))
        | ~ 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_2965)),U_2966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2965)),U_2967))) ) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ( ! [U_2973,U_2971] :
        ( ! [U_2969] : 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_2969)),U_2971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2969)),U_2973)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2971),U_2973)) )
    & ! [U_2972,U_2970] :
        ( ! [U_2968] : ~ 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_2968)),U_2970)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2968)),U_2972)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2970),U_2972)) ) ),
    inference(miniscope,[status(thm)],[f_727_2]) ).

cnf(f_727_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_2968)),U_2970)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2968)),U_2972)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2970),U_2972)) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_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_2969)),U_2971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2969)),U_2973)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2971),U_2973)) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_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_728_2,plain,
    ! [U_2976,U_2975,U_2974] :
      ( 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_2975),U_2974))),U_2976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2975)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2974),U_2976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2974),U_2975)) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

cnf(f_728_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_2975),U_2974))),U_2976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2975)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2974),U_2976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2974),U_2975)) ),
    inference(clausify,[status(thm)],[f_728_2]) ).

fof(f_729_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_729_2,plain,
    ! [U_2979,U_2978,U_2977] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2979),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2978),U_2977))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2979),U_2977)),hAPP(c_Nat_OSuc,U_2978))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2977),U_2978)) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

cnf(f_729_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2979),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2978),U_2977))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2979),U_2977)),hAPP(c_Nat_OSuc,U_2978))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2977),U_2978)) ),
    inference(clausify,[status(thm)],[f_729_2]) ).

fof(f_730_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_730_2,plain,
    ! [U_2984,U_2983,U_2982,U_2981,U_2980] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2981,U_2980),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2981),U_2983),U_2982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),hAPP(U_2984,U_2983)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2981,U_2980),U_2984),U_2982))
      | hBOOL(hAPP(hAPP(c_member(U_2981),U_2983),U_2982))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),U_2982))
      | ~ class_Groups_Ocomm__monoid__mult(U_2980) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

cnf(f_730_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2981,U_2980),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2981),U_2983),U_2982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),hAPP(U_2984,U_2983)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2981,U_2980),U_2984),U_2982))
    | hBOOL(hAPP(hAPP(c_member(U_2981),U_2983),U_2982))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),U_2982))
    | ~ class_Groups_Ocomm__monoid__mult(U_2980) ),
    inference(clausify,[status(thm)],[f_730_2]) ).

fof(f_731_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_731_2,plain,
    ! [U_2989,U_2988,U_2987,U_2986,U_2985] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2986,U_2985),U_2989),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),U_2987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2985),hAPP(U_2989,U_2988)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2986,U_2985),U_2989),U_2987))
      | hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
      | ~ class_Groups_Ocomm__monoid__mult(U_2985) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

cnf(f_731_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2986,U_2985),U_2989),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),U_2987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2985),hAPP(U_2989,U_2988)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2986,U_2985),U_2989),U_2987))
    | hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
    | ~ class_Groups_Ocomm__monoid__mult(U_2985) ),
    inference(clausify,[status(thm)],[f_731_2]) ).

fof(f_732_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_732_2,plain,
    ! [U_2994,U_2993,U_2992,U_2991,U_2990] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2990),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2991,tc_HOL_Obool)),U_2992),U_2993))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2991,tc_HOL_Obool)),U_2992),U_2993))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2990),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),U_2992)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),U_2993))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2991),U_2993))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2991),U_2992))
      | ~ class_Groups_Ocomm__monoid__mult(U_2990) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

cnf(f_732_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2990),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2991,tc_HOL_Obool)),U_2992),U_2993))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2991,tc_HOL_Obool)),U_2992),U_2993))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2990),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),U_2992)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2991,U_2990),U_2994),U_2993))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2991),U_2993))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2991),U_2992))
    | ~ class_Groups_Ocomm__monoid__mult(U_2990) ),
    inference(clausify,[status(thm)],[f_732_2]) ).

fof(f_733_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_733_2,plain,
    ! [U_2999,U_2998,U_2997,U_2996,U_2995] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2995),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2995),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),U_2997)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),U_2998))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2998))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2997))
      | ~ class_Groups_Ocomm__monoid__mult(U_2995) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

cnf(f_733_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2995),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2995),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),U_2997)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2996,U_2995),U_2999),U_2998))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2998))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2997))
    | ~ class_Groups_Ocomm__monoid__mult(U_2995) ),
    inference(clausify,[status(thm)],[f_733_2]) ).

fof(f_734_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_734_2,plain,
    ! [U_3002,U_3001,U_3000] :
      ( hAPP(c_Finite__Set_Ocard(U_3000),hAPP(hAPP(c_Set_Oinsert(U_3000),U_3002),U_3001)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3000),U_3001))
      | hBOOL(hAPP(hAPP(c_member(U_3000),U_3002),U_3001))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3001)) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

cnf(f_734_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3000),hAPP(hAPP(c_Set_Oinsert(U_3000),U_3002),U_3001)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3000),U_3001))
    | hBOOL(hAPP(hAPP(c_member(U_3000),U_3002),U_3001))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3001)) ),
    inference(clausify,[status(thm)],[f_734_2]) ).

fof(f_735_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_735_2,plain,
    ! [U_3005,U_3004,U_3003] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_3003),hAPP(hAPP(c_Set_Oinsert(U_3003),U_3005),U_3004)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3003),U_3004))
          | hBOOL(hAPP(hAPP(c_member(U_3003),U_3005),U_3004)) )
        & ( hAPP(c_Finite__Set_Ocard(U_3003),hAPP(hAPP(c_Set_Oinsert(U_3003),U_3005),U_3004)) = hAPP(c_Finite__Set_Ocard(U_3003),U_3004)
          | ~ hBOOL(hAPP(hAPP(c_member(U_3003),U_3005),U_3004)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3003),U_3004)) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

cnf(f_735_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3003),hAPP(hAPP(c_Set_Oinsert(U_3003),U_3005),U_3004)) = hAPP(c_Finite__Set_Ocard(U_3003),U_3004)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3003),U_3005),U_3004))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3003),U_3004)) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3003),hAPP(hAPP(c_Set_Oinsert(U_3003),U_3005),U_3004)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3003),U_3004))
    | hBOOL(hAPP(hAPP(c_member(U_3003),U_3005),U_3004))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3003),U_3004)) ),
    inference(clausify,[status(thm)],[f_735_2]) ).

fof(f_736_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_736_2,plain,
    ! [U_3010,U_3009,U_3008,U_3007,U_3006] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3007,U_3006),U_3009),hAPP(hAPP(c_Set_Oinsert(U_3007),U_3010),U_3008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),hAPP(U_3009,U_3010)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3007,U_3006),U_3009),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3007,tc_HOL_Obool)),U_3008),hAPP(hAPP(c_Set_Oinsert(U_3007),U_3010),c_Orderings_Obot__class_Obot(tc_fun(U_3007,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3007),U_3008))
      | ~ class_Groups_Ocomm__monoid__mult(U_3006) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

cnf(f_736_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3007,U_3006),U_3009),hAPP(hAPP(c_Set_Oinsert(U_3007),U_3010),U_3008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),hAPP(U_3009,U_3010)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3007,U_3006),U_3009),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3007,tc_HOL_Obool)),U_3008),hAPP(hAPP(c_Set_Oinsert(U_3007),U_3010),c_Orderings_Obot__class_Obot(tc_fun(U_3007,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3007),U_3008))
    | ~ class_Groups_Ocomm__monoid__mult(U_3006) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

fof(f_737_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_737_2,plain,
    ! [U_3015,U_3014,U_3013,U_3012,U_3011] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),U_3013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),U_3014))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014) != c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3014))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
      | ~ class_Groups_Ocomm__monoid__mult(U_3011) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

cnf(f_737_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),U_3013)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3012,U_3011),U_3015),U_3014))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3012,tc_HOL_Obool)),U_3013),U_3014) != c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3014))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
    | ~ class_Groups_Ocomm__monoid__mult(U_3011) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

fof(f_738_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_738_2,plain,
    ! [U_3020,U_3019,U_3018,U_3017,U_3016] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3017,tc_HOL_Obool)),U_3018),U_3019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),U_3018)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),U_3019))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3017,tc_HOL_Obool)),U_3018),U_3019) != c_Orderings_Obot__class_Obot(tc_fun(U_3017,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3019))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3018))
      | ~ class_Groups_Ocomm__monoid__mult(U_3016) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

cnf(f_738_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3017,tc_HOL_Obool)),U_3018),U_3019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),U_3018)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3017,U_3016),U_3020),U_3019))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3017,tc_HOL_Obool)),U_3018),U_3019) != c_Orderings_Obot__class_Obot(tc_fun(U_3017,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3019))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3018))
    | ~ class_Groups_Ocomm__monoid__mult(U_3016) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

fof(f_739_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_739_2,plain,
    ! [U_3023,U_3022,U_3021] :
      ( hAPP(c_Finite__Set_Ocard(U_3021),hAPP(hAPP(c_Set_Oinsert(U_3021),U_3023),U_3022)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3021),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3021,tc_HOL_Obool)),U_3022),hAPP(hAPP(c_Set_Oinsert(U_3021),U_3023),c_Orderings_Obot__class_Obot(tc_fun(U_3021,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3021),U_3022)) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3021),hAPP(hAPP(c_Set_Oinsert(U_3021),U_3023),U_3022)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_3021),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3021,tc_HOL_Obool)),U_3022),hAPP(hAPP(c_Set_Oinsert(U_3021),U_3023),c_Orderings_Obot__class_Obot(tc_fun(U_3021,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3021),U_3022)) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_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_740_2,plain,
    ! [U_3026,U_3025,U_3024] :
      ( hAPP(c_Finite__Set_Ocard(U_3024),hAPP(hAPP(c_Set_Oinsert(U_3024),U_3026),U_3025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3024),U_3025))
      | hBOOL(hAPP(hAPP(c_member(U_3024),U_3026),U_3025))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3024),U_3025)) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3024),hAPP(hAPP(c_Set_Oinsert(U_3024),U_3026),U_3025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3024),U_3025))
    | hBOOL(hAPP(hAPP(c_member(U_3024),U_3026),U_3025))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3024),U_3025)) ),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_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_741_2,plain,
    ! [U_3028,U_3027] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3027),hAPP(c_Nat_OSuc,U_3028)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3027),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3028),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

cnf(f_741_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3027),hAPP(c_Nat_OSuc,U_3028)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3027),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3028),
    inference(clausify,[status(thm)],[f_741_2]) ).

fof(f_742_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_742_2,plain,
    ! [U_3029] : hAPP(c_Nat_OSuc,U_3029) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3029),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

cnf(f_742_3,plain,
    hAPP(c_Nat_OSuc,U_3029) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3029),
    inference(clausify,[status(thm)],[f_742_2]) ).

fof(f_743_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_743_2,plain,
    ! [U_3030] : hAPP(c_Nat_OSuc,U_3030) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3030),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

cnf(f_743_3,plain,
    hAPP(c_Nat_OSuc,U_3030) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3030),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_743_2]) ).

fof(f_744_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_744_2,plain,
    ! [U_3036,U_3035,U_3034,U_3033,U_3032] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3032),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3034)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3035))
      | ? [U_3031] :
          ( hAPP(U_3036,U_3031) != c_Groups_Oone__class_Oone(U_3032)
          & hBOOL(hAPP(hAPP(c_member(U_3033),U_3031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3035))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3034))
      | ~ class_Groups_Ocomm__monoid__mult(U_3032) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ! [U_3036,U_3035,U_3034,U_3033,U_3032] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3032),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3034)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3035))
      | ( hAPP(U_3036,sK47(U_3036,U_3035,U_3034,U_3033,U_3032)) != c_Groups_Oone__class_Oone(U_3032)
        & hBOOL(hAPP(hAPP(c_member(U_3033),sK47(U_3036,U_3035,U_3034,U_3033,U_3032)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3035))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3034))
      | ~ class_Groups_Ocomm__monoid__mult(U_3032) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_3031,sK47(U_3036,U_3035,U_3034,U_3033,U_3032))],[f_744_2]) ).

cnf(f_744_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3033),sK47(U_3036,U_3035,U_3034,U_3033,U_3032)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3032),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3034)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3035))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3035))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3034))
    | ~ class_Groups_Ocomm__monoid__mult(U_3032) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

cnf(f_744_5,plain,
    ( hAPP(U_3036,sK47(U_3036,U_3035,U_3034,U_3033,U_3032)) != c_Groups_Oone__class_Oone(U_3032)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3033,tc_HOL_Obool)),U_3034),U_3035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3032),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3034)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3033,U_3032),U_3036),U_3035))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3035))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3033),U_3034))
    | ~ class_Groups_Ocomm__monoid__mult(U_3032) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_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_745_2,plain,
    ! [U_3042,U_3041,U_3040,U_3039,U_3038] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3038),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3040)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3041))
      | ? [U_3037] :
          ( hAPP(U_3042,U_3037) != c_Groups_Oone__class_Oone(U_3038)
          & hBOOL(hAPP(hAPP(c_member(U_3039),U_3037),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3041))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
      | ~ class_Groups_Ocomm__monoid__mult(U_3038) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_3042,U_3041,U_3040,U_3039,U_3038] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3038),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3040)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3041))
      | ( hAPP(U_3042,sK48(U_3042,U_3041,U_3040,U_3039,U_3038)) != c_Groups_Oone__class_Oone(U_3038)
        & hBOOL(hAPP(hAPP(c_member(U_3039),sK48(U_3042,U_3041,U_3040,U_3039,U_3038)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3041))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
      | ~ class_Groups_Ocomm__monoid__mult(U_3038) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_3037,sK48(U_3042,U_3041,U_3040,U_3039,U_3038))],[f_745_2]) ).

cnf(f_745_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3039),sK48(U_3042,U_3041,U_3040,U_3039,U_3038)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3038),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3040)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3041))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3041))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
    | ~ class_Groups_Ocomm__monoid__mult(U_3038) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

cnf(f_745_5,plain,
    ( hAPP(U_3042,sK48(U_3042,U_3041,U_3040,U_3039,U_3038)) != c_Groups_Oone__class_Oone(U_3038)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3039,tc_HOL_Obool)),U_3040),U_3041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3038),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3040)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3039,U_3038),U_3042),U_3041))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3041))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3039),U_3040))
    | ~ class_Groups_Ocomm__monoid__mult(U_3038) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_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_746_2,plain,
    ! [U_3047,U_3046,U_3045,U_3044,U_3043] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3044,tc_HOL_Obool)),U_3045),U_3046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3043),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),U_3045)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),U_3046))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3044,tc_HOL_Obool)),U_3045),U_3046) != c_Orderings_Obot__class_Obot(tc_fun(U_3044,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3046))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3045))
      | ~ class_Groups_Ocomm__monoid__mult(U_3043) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3044,tc_HOL_Obool)),U_3045),U_3046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3043),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),U_3045)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3043,U_3044,c_Groups_Otimes__class_Otimes(U_3043)),U_3047),c_Groups_Oone__class_Oone(U_3043)),U_3046))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3044,tc_HOL_Obool)),U_3045),U_3046) != c_Orderings_Obot__class_Obot(tc_fun(U_3044,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3046))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3045))
    | ~ class_Groups_Ocomm__monoid__mult(U_3043) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_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_747_2,plain,
    ! [U_3053,U_3052,U_3051,U_3050,U_3049] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3051)
      | ? [U_3048] :
          ( hAPP(U_3053,U_3048) != c_Groups_Oone__class_Oone(U_3049)
          & hBOOL(hAPP(hAPP(c_member(U_3050),U_3048),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3050,tc_HOL_Obool)),U_3051),U_3052))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3050,tc_HOL_Obool)),U_3052),U_3051))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
      | ~ class_Groups_Ocomm__monoid__mult(U_3049) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_3053,U_3052,U_3051,U_3050,U_3049] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3051)
      | ( hAPP(U_3053,sK49(U_3053,U_3052,U_3051,U_3050,U_3049)) != c_Groups_Oone__class_Oone(U_3049)
        & hBOOL(hAPP(hAPP(c_member(U_3050),sK49(U_3053,U_3052,U_3051,U_3050,U_3049)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3050,tc_HOL_Obool)),U_3051),U_3052))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3050,tc_HOL_Obool)),U_3052),U_3051))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
      | ~ class_Groups_Ocomm__monoid__mult(U_3049) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_3048,sK49(U_3053,U_3052,U_3051,U_3050,U_3049))],[f_747_2]) ).

cnf(f_747_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3050),sK49(U_3053,U_3052,U_3051,U_3050,U_3049)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3050,tc_HOL_Obool)),U_3051),U_3052)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3051)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3050,tc_HOL_Obool)),U_3052),U_3051))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
    | ~ class_Groups_Ocomm__monoid__mult(U_3049) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

cnf(f_747_5,plain,
    ( hAPP(U_3053,sK49(U_3053,U_3052,U_3051,U_3050,U_3049)) != c_Groups_Oone__class_Oone(U_3049)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3052) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3050,U_3049),U_3053),U_3051)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3050,tc_HOL_Obool)),U_3052),U_3051))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
    | ~ class_Groups_Ocomm__monoid__mult(U_3049) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_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_748_2,plain,
    ! [U_3059,U_3058,U_3057,U_3056,U_3055] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3057) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3058)
      | ? [U_3054] :
          ( hAPP(U_3059,U_3054) != c_Groups_Oone__class_Oone(U_3055)
          & hBOOL(hAPP(hAPP(c_member(U_3056),U_3054),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3056,tc_HOL_Obool)),U_3057),U_3058))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3056,tc_HOL_Obool)),U_3058),U_3057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3056),U_3057))
      | ~ class_Groups_Ocomm__monoid__mult(U_3055) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_3059,U_3058,U_3057,U_3056,U_3055] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3057) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3058)
      | ( hAPP(U_3059,sK50(U_3059,U_3058,U_3057,U_3056,U_3055)) != c_Groups_Oone__class_Oone(U_3055)
        & hBOOL(hAPP(hAPP(c_member(U_3056),sK50(U_3059,U_3058,U_3057,U_3056,U_3055)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3056,tc_HOL_Obool)),U_3057),U_3058))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3056,tc_HOL_Obool)),U_3058),U_3057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3056),U_3057))
      | ~ class_Groups_Ocomm__monoid__mult(U_3055) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3054,sK50(U_3059,U_3058,U_3057,U_3056,U_3055))],[f_748_2]) ).

cnf(f_748_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3056),sK50(U_3059,U_3058,U_3057,U_3056,U_3055)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3056,tc_HOL_Obool)),U_3057),U_3058)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3057) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3058)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3056,tc_HOL_Obool)),U_3058),U_3057))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3056),U_3057))
    | ~ class_Groups_Ocomm__monoid__mult(U_3055) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_5,plain,
    ( hAPP(U_3059,sK50(U_3059,U_3058,U_3057,U_3056,U_3055)) != c_Groups_Oone__class_Oone(U_3055)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3057) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3056,U_3055),U_3059),U_3058)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3056,tc_HOL_Obool)),U_3058),U_3057))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3056),U_3057))
    | ~ class_Groups_Ocomm__monoid__mult(U_3055) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_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_749_2,plain,
    ! [U_3064,U_3063,U_3062,U_3061,U_3060] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3060,U_3061,U_3062),U_3063),U_3064),c_Orderings_Obot__class_Obot(tc_fun(U_3061,tc_HOL_Obool))) = U_3064,
    inference(variable_rename,[status(thm)],[f_749_1]) ).

cnf(f_749_3,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3060,U_3061,U_3062),U_3063),U_3064),c_Orderings_Obot__class_Obot(tc_fun(U_3061,tc_HOL_Obool))) = U_3064,
    inference(clausify,[status(thm)],[f_749_2]) ).

fof(f_750_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_750_2,plain,
    ! [U_3071,U_3070,U_3069,U_3068,U_3067,U_3066,U_3065] :
      ( hAPP(U_3070,U_3071) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3065,U_3066,U_3067),U_3069),U_3068),U_3071)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3066),U_3071))
      | ~ c_Finite__Set_Ofolding__image__simple(U_3065,U_3066,U_3067,U_3068,U_3069,U_3070) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

cnf(f_750_3,plain,
    ( hAPP(U_3070,U_3071) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3065,U_3066,U_3067),U_3069),U_3068),U_3071)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3066),U_3071))
    | ~ c_Finite__Set_Ofolding__image__simple(U_3065,U_3066,U_3067,U_3068,U_3069,U_3070) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

fof(f_751_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_751_2,plain,
    ! [U_3077,U_3076,U_3075,U_3074,U_3073,U_3072] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3072,U_3073,c_Groups_Otimes__class_Otimes(U_3072)),U_3076),U_3077),hAPP(hAPP(c_Set_Oinsert(U_3073),U_3075),U_3074)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3072),hAPP(U_3076,U_3075)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3072,U_3073,c_Groups_Otimes__class_Otimes(U_3072)),U_3076),U_3077),U_3074))
      | hBOOL(hAPP(hAPP(c_member(U_3073),U_3075),U_3074))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3073),U_3074))
      | ~ class_Groups_Oab__semigroup__mult(U_3072) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

cnf(f_751_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3072,U_3073,c_Groups_Otimes__class_Otimes(U_3072)),U_3076),U_3077),hAPP(hAPP(c_Set_Oinsert(U_3073),U_3075),U_3074)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3072),hAPP(U_3076,U_3075)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3072,U_3073,c_Groups_Otimes__class_Otimes(U_3072)),U_3076),U_3077),U_3074))
    | hBOOL(hAPP(hAPP(c_member(U_3073),U_3075),U_3074))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3073),U_3074))
    | ~ class_Groups_Oab__semigroup__mult(U_3072) ),
    inference(clausify,[status(thm)],[f_751_2]) ).

fof(f_752_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_752_2,plain,
    ! [U_3081,U_3080,U_3079,U_3078] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3079,U_3078),U_3081),U_3080) = c_Groups_Oone__class_Oone(U_3078)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3079),U_3080)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3079,U_3078),U_3081),U_3080) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3078,U_3079,c_Groups_Otimes__class_Otimes(U_3078)),U_3081),c_Groups_Oone__class_Oone(U_3078)),U_3080)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3079),U_3080)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_3078) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

cnf(f_752_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3079,U_3078),U_3081),U_3080) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3078,U_3079,c_Groups_Otimes__class_Otimes(U_3078)),U_3081),c_Groups_Oone__class_Oone(U_3078)),U_3080)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3079),U_3080))
    | ~ class_Groups_Ocomm__monoid__mult(U_3078) ),
    inference(clausify,[status(thm)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3079,U_3078),U_3081),U_3080) = c_Groups_Oone__class_Oone(U_3078)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3079),U_3080))
    | ~ class_Groups_Ocomm__monoid__mult(U_3078) ),
    inference(clausify,[status(thm)],[f_752_2]) ).

fof(f_753_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_753_2,plain,
    ! [U_3085,U_3084,U_3083,U_3082] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3083,U_3082),U_3085),U_3084) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3082,U_3083,c_Groups_Otimes__class_Otimes(U_3082)),U_3085),c_Groups_Oone__class_Oone(U_3082)),U_3084)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
      | ~ class_Groups_Ocomm__monoid__mult(U_3082) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

cnf(f_753_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3083,U_3082),U_3085),U_3084) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3082,U_3083,c_Groups_Otimes__class_Otimes(U_3082)),U_3085),c_Groups_Oone__class_Oone(U_3082)),U_3084)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3083),U_3084))
    | ~ class_Groups_Ocomm__monoid__mult(U_3082) ),
    inference(clausify,[status(thm)],[f_753_2]) ).

fof(f_754_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_754_2,plain,
    ! [U_3090,U_3089,U_3088,U_3087,U_3086] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),U_3088)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),U_3089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3089))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088))
      | ~ class_Groups_Ocomm__monoid__mult(U_3086) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

cnf(f_754_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),U_3088)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),U_3089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3086),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3086,U_3087,c_Groups_Otimes__class_Otimes(U_3086)),U_3090),c_Groups_Oone__class_Oone(U_3086)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3089))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088))
    | ~ class_Groups_Ocomm__monoid__mult(U_3086) ),
    inference(clausify,[status(thm)],[f_754_2]) ).

fof(f_755_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_755_2,plain,
    ! [U_3097,U_3096,U_3095,U_3094,U_3093,U_3092,U_3091] :
      ( ( ( hAPP(hAPP(U_3095,U_3097),U_3096) = U_3094
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3096)) )
        & ( hAPP(hAPP(U_3095,U_3097),U_3096) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3091,U_3092,U_3093),U_3097),U_3094),U_3096)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3096)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_3091,U_3092,U_3093,U_3094,U_3095) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

cnf(f_755_3,plain,
    ( hAPP(hAPP(U_3095,U_3097),U_3096) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3091,U_3092,U_3093),U_3097),U_3094),U_3096)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3096))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_3091,U_3092,U_3093,U_3094,U_3095) ),
    inference(clausify,[status(thm)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hAPP(hAPP(U_3095,U_3097),U_3096) = U_3094
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3092),U_3096))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_3091,U_3092,U_3093,U_3094,U_3095) ),
    inference(clausify,[status(thm)],[f_755_2]) ).

fof(f_756_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_756_2,plain,
    ! [U_3103,U_3102,U_3101,U_3100,U_3099] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3099),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3101)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3102))
      | ? [U_3098] :
          ( hAPP(U_3103,U_3098) != c_Groups_Oone__class_Oone(U_3099)
          & hBOOL(hAPP(hAPP(c_member(U_3100),U_3098),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3102))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3101))
      | ~ class_Groups_Ocomm__monoid__mult(U_3099) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_3103,U_3102,U_3101,U_3100,U_3099] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3099),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3101)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3102))
      | ( hAPP(U_3103,sK51(U_3103,U_3102,U_3101,U_3100,U_3099)) != c_Groups_Oone__class_Oone(U_3099)
        & hBOOL(hAPP(hAPP(c_member(U_3100),sK51(U_3103,U_3102,U_3101,U_3100,U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3102))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3101))
      | ~ class_Groups_Ocomm__monoid__mult(U_3099) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3098,sK51(U_3103,U_3102,U_3101,U_3100,U_3099))],[f_756_2]) ).

cnf(f_756_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3100),sK51(U_3103,U_3102,U_3101,U_3100,U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102)))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3099),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3101)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3102))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3102))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3101))
    | ~ class_Groups_Ocomm__monoid__mult(U_3099) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

cnf(f_756_5,plain,
    ( hAPP(U_3103,sK51(U_3103,U_3102,U_3101,U_3100,U_3099)) != c_Groups_Oone__class_Oone(U_3099)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3100,tc_HOL_Obool)),U_3101),U_3102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3099),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3101)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3099,U_3100,c_Groups_Otimes__class_Otimes(U_3099)),U_3103),c_Groups_Oone__class_Oone(U_3099)),U_3102))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3102))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3100),U_3101))
    | ~ class_Groups_Ocomm__monoid__mult(U_3099) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_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_757_2,plain,
    ! [U_3109,U_3108,U_3107,U_3106,U_3105,U_3104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3108),U_3105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3109),U_3107))),U_3106))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3104),U_3108),U_3109) != c_Groups_Oone__class_Oone(U_3104)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3104),c_Groups_Ozero__class_Ozero(U_3104)),U_3109))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3104),c_Groups_Ozero__class_Ozero(U_3104)),U_3108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),U_3107),U_3106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),U_3105),U_3106))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_3104) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

cnf(f_757_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3108),U_3105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3109),U_3107))),U_3106))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3104),U_3108),U_3109) != c_Groups_Oone__class_Oone(U_3104)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3104),c_Groups_Ozero__class_Ozero(U_3104)),U_3109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3104),c_Groups_Ozero__class_Ozero(U_3104)),U_3108))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),U_3107),U_3106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3104),U_3105),U_3106))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_3104) ),
    inference(clausify,[status(thm)],[f_757_2]) ).

fof(f_758_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_758_2,plain,
    ! [U_3115,U_3114,U_3113] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
      | ? [U_3112] :
          ( ? [U_3111] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),U_3112),U_3111) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
              & U_3112 != U_3111
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3111),U_3114)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3112),U_3114)) )
      | ? [U_3110] :
          ( hAPP(c_Finite__Set_Ocard(U_3113),U_3110) != U_3115
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3110),U_3114)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_3115,U_3114,U_3113] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
      | ? [U_3112] :
          ( ? [U_3111] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),U_3112),U_3111) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
              & U_3112 != U_3111
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3111),U_3114)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3112),U_3114)) )
      | ( hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3110,sK52(U_3115,U_3114,U_3113))],[f_758_2]) ).

fof(f_758_4,plain,
    ! [U_3115,U_3114,U_3113] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
      | ( ? [U_3111] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),U_3111) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
            & sK53(U_3115,U_3114,U_3113) != U_3111
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),U_3111),U_3114)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),U_3114)) )
      | ( hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3112,sK53(U_3115,U_3114,U_3113))],[f_758_3]) ).

fof(f_758_5,plain,
    ! [U_3115,U_3114,U_3113] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),sK54(U_3115,U_3114,U_3113)) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
        & sK53(U_3115,U_3114,U_3113) != sK54(U_3115,U_3114,U_3113)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK54(U_3115,U_3114,U_3113)),U_3114))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),U_3114)) )
      | ( hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3111,sK54(U_3115,U_3114,U_3113))],[f_758_4]) ).

cnf(f_758_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),U_3114))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK54(U_3115,U_3114,U_3113)),U_3114))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_8,plain,
    ( sK53(U_3115,U_3114,U_3113) != sK54(U_3115,U_3114,U_3113)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),sK54(U_3115,U_3114,U_3113)) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK52(U_3115,U_3114,U_3113)),U_3114))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),U_3114))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3113,tc_HOL_Obool)),sK54(U_3115,U_3114,U_3113)),U_3114))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_12,plain,
    ( sK53(U_3115,U_3114,U_3113) != sK54(U_3115,U_3114,U_3113)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

cnf(f_758_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3113,tc_HOL_Obool)),sK53(U_3115,U_3114,U_3113)),sK54(U_3115,U_3114,U_3113)) != c_Orderings_Obot__class_Obot(tc_fun(U_3113,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),hAPP(c_Finite__Set_Ocard(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) = hAPP(c_Finite__Set_Ocard(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114))
    | hAPP(c_Finite__Set_Ocard(U_3113),sK52(U_3115,U_3114,U_3113)) != U_3115
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3113),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3113,tc_HOL_Obool),U_3114)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3113,tc_HOL_Obool)),U_3114)) ),
    inference(clausify,[status(thm)],[f_758_5]) ).

fof(f_759_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_759_2,plain,
    ! [U_3120,U_3119,U_3118,U_3117] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3117,U_3118,c_Groups_Otimes__class_Otimes(U_3117)),U_3120),c_Groups_Oone__class_Oone(U_3117)),U_3119) = c_Groups_Oone__class_Oone(U_3117)
      | ? [U_3116] :
          ( hAPP(U_3120,U_3116) != c_Groups_Oone__class_Oone(U_3117)
          & hBOOL(hAPP(hAPP(c_member(U_3118),U_3116),U_3119)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3118),U_3119))
      | ~ class_Groups_Ocomm__monoid__mult(U_3117) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_3120,U_3119,U_3118,U_3117] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3117,U_3118,c_Groups_Otimes__class_Otimes(U_3117)),U_3120),c_Groups_Oone__class_Oone(U_3117)),U_3119) = c_Groups_Oone__class_Oone(U_3117)
      | ( hAPP(U_3120,sK55(U_3120,U_3119,U_3118,U_3117)) != c_Groups_Oone__class_Oone(U_3117)
        & hBOOL(hAPP(hAPP(c_member(U_3118),sK55(U_3120,U_3119,U_3118,U_3117)),U_3119)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3118),U_3119))
      | ~ class_Groups_Ocomm__monoid__mult(U_3117) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3116,sK55(U_3120,U_3119,U_3118,U_3117))],[f_759_2]) ).

cnf(f_759_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3118),sK55(U_3120,U_3119,U_3118,U_3117)),U_3119))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3117,U_3118,c_Groups_Otimes__class_Otimes(U_3117)),U_3120),c_Groups_Oone__class_Oone(U_3117)),U_3119) = c_Groups_Oone__class_Oone(U_3117)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3118),U_3119))
    | ~ class_Groups_Ocomm__monoid__mult(U_3117) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

cnf(f_759_5,plain,
    ( hAPP(U_3120,sK55(U_3120,U_3119,U_3118,U_3117)) != c_Groups_Oone__class_Oone(U_3117)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3117,U_3118,c_Groups_Otimes__class_Otimes(U_3117)),U_3120),c_Groups_Oone__class_Oone(U_3117)),U_3119) = c_Groups_Oone__class_Oone(U_3117)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3118),U_3119))
    | ~ class_Groups_Ocomm__monoid__mult(U_3117) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_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_760_2,plain,
    ! [U_3124,U_3123,U_3122,U_3121] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3121,U_3123)),c_Sum__Type_OPlus(U_3121,U_3123,U_3122,U_3124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3121),U_3122)),hAPP(c_Finite__Set_Ocard(U_3123),U_3124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3123),U_3124))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3121),U_3122)) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

cnf(f_760_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3121,U_3123)),c_Sum__Type_OPlus(U_3121,U_3123,U_3122,U_3124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3121),U_3122)),hAPP(c_Finite__Set_Ocard(U_3123),U_3124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3123),U_3124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3121),U_3122)) ),
    inference(clausify,[status(thm)],[f_760_2]) ).

fof(f_761_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_761_2,plain,
    ! [U_3131,U_3130,U_3129,U_3128,U_3127,U_3126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3129),U_3131),U_3128) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3130),U_3131),U_3128)
      | ? [U_3125] :
          ( hAPP(U_3129,U_3125) != hAPP(U_3130,U_3125)
          & hBOOL(hAPP(hAPP(c_member(U_3127),U_3125),U_3128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3127),U_3128))
      | ~ class_Groups_Oab__semigroup__mult(U_3126) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_3131,U_3130,U_3129,U_3128,U_3127,U_3126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3129),U_3131),U_3128) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3130),U_3131),U_3128)
      | ( hAPP(U_3129,sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126)) != hAPP(U_3130,sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126))
        & hBOOL(hAPP(hAPP(c_member(U_3127),sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126)),U_3128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3127),U_3128))
      | ~ class_Groups_Oab__semigroup__mult(U_3126) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3125,sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126))],[f_761_2]) ).

cnf(f_761_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3127),sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126)),U_3128))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3129),U_3131),U_3128) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3130),U_3131),U_3128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3127),U_3128))
    | ~ class_Groups_Oab__semigroup__mult(U_3126) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

cnf(f_761_5,plain,
    ( hAPP(U_3129,sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126)) != hAPP(U_3130,sK56(U_3131,U_3130,U_3129,U_3128,U_3127,U_3126))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3129),U_3131),U_3128) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3126,U_3127,c_Groups_Otimes__class_Otimes(U_3126)),U_3130),U_3131),U_3128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3127),U_3128))
    | ~ class_Groups_Oab__semigroup__mult(U_3126) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_1,plain,
    ! [V_ca_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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_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_762_2,plain,
    ! [U_3136,U_3135,U_3134,U_3133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3133),U_3135),U_3136)),hAPP(hAPP(c_Finite__Set_Ofold(U_3133,U_3133,c_Lattices_Osemilattice__inf__class_Oinf(U_3133)),U_3136),U_3134)))
      | ? [U_3132] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),U_3132))
          & hBOOL(hAPP(hAPP(c_member(U_3133),U_3132),U_3134)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3133),U_3134))
      | ~ class_Lattices_Osemilattice__inf(U_3133) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ! [U_3136,U_3135,U_3134,U_3133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3133),U_3135),U_3136)),hAPP(hAPP(c_Finite__Set_Ofold(U_3133,U_3133,c_Lattices_Osemilattice__inf__class_Oinf(U_3133)),U_3136),U_3134)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),sK57(U_3136,U_3135,U_3134,U_3133)))
        & hBOOL(hAPP(hAPP(c_member(U_3133),sK57(U_3136,U_3135,U_3134,U_3133)),U_3134)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3133),U_3134))
      | ~ class_Lattices_Osemilattice__inf(U_3133) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_3132,sK57(U_3136,U_3135,U_3134,U_3133))],[f_762_2]) ).

cnf(f_762_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3133),sK57(U_3136,U_3135,U_3134,U_3133)),U_3134))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3133),U_3135),U_3136)),hAPP(hAPP(c_Finite__Set_Ofold(U_3133,U_3133,c_Lattices_Osemilattice__inf__class_Oinf(U_3133)),U_3136),U_3134)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3133),U_3134))
    | ~ class_Lattices_Osemilattice__inf(U_3133) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),sK57(U_3136,U_3135,U_3134,U_3133)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3133),U_3135),U_3136)),hAPP(hAPP(c_Finite__Set_Ofold(U_3133,U_3133,c_Lattices_Osemilattice__inf__class_Oinf(U_3133)),U_3136),U_3134)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3133),U_3134))
    | ~ class_Lattices_Osemilattice__inf(U_3133) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_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_763_2,plain,
    ! [U_3137] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3137),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

cnf(f_763_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3137),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_763_2]) ).

fof(f_764_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_764_2,plain,
    ! [U_3138] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3138)),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

cnf(f_764_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3138)),
    inference(clausify,[status(thm)],[f_764_2]) ).

fof(f_765_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_765_2,plain,
    ! [U_3139] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_3139))),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

cnf(f_765_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_3139))),
    inference(clausify,[status(thm)],[f_765_2]) ).

fof(f_766_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_766_2,plain,
    ! [U_3141,U_3140] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_3140) = U_3141
          | U_3141 != c_Groups_Ozero__class_Ozero(U_3140) )
        & ( U_3141 = c_Groups_Ozero__class_Ozero(U_3140)
          | c_Groups_Ozero__class_Ozero(U_3140) != U_3141 ) )
      | ~ class_Groups_Ozero(U_3140) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

cnf(f_766_3,plain,
    ( U_3141 = c_Groups_Ozero__class_Ozero(U_3140)
    | c_Groups_Ozero__class_Ozero(U_3140) != U_3141
    | ~ class_Groups_Ozero(U_3140) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

cnf(f_766_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_3140) = U_3141
    | U_3141 != c_Groups_Ozero__class_Ozero(U_3140)
    | ~ class_Groups_Ozero(U_3140) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

fof(f_767_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_767_2,plain,
    ! [U_3143,U_3142] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3142),U_3143),c_Groups_Ozero__class_Ozero(U_3142)) = U_3143
      | ~ class_Groups_Ocomm__monoid__add(U_3142) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

cnf(f_767_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3142),U_3143),c_Groups_Ozero__class_Ozero(U_3142)) = U_3143
    | ~ class_Groups_Ocomm__monoid__add(U_3142) ),
    inference(clausify,[status(thm)],[f_767_2]) ).

fof(f_768_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_768_2,plain,
    ! [U_3145,U_3144] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3144),U_3145),c_Groups_Ozero__class_Ozero(U_3144)) = U_3145
      | ~ class_Groups_Omonoid__add(U_3144) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

cnf(f_768_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3144),U_3145),c_Groups_Ozero__class_Ozero(U_3144)) = U_3145
    | ~ class_Groups_Omonoid__add(U_3144) ),
    inference(clausify,[status(thm)],[f_768_2]) ).

fof(f_769_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_769_2,plain,
    ! [U_3147,U_3146] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_3146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3146),U_3147),U_3147)
          | U_3147 != c_Groups_Ozero__class_Ozero(U_3146) )
        & ( U_3147 = c_Groups_Ozero__class_Ozero(U_3146)
          | c_Groups_Ozero__class_Ozero(U_3146) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3146),U_3147),U_3147) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3146) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

cnf(f_769_3,plain,
    ( U_3147 = c_Groups_Ozero__class_Ozero(U_3146)
    | c_Groups_Ozero__class_Ozero(U_3146) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3146),U_3147),U_3147)
    | ~ class_Groups_Olinordered__ab__group__add(U_3146) ),
    inference(clausify,[status(thm)],[f_769_2]) ).

cnf(f_769_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_3146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3146),U_3147),U_3147)
    | U_3147 != c_Groups_Ozero__class_Ozero(U_3146)
    | ~ class_Groups_Olinordered__ab__group__add(U_3146) ),
    inference(clausify,[status(thm)],[f_769_2]) ).

fof(f_770_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_770_2,plain,
    ! [U_3149,U_3148] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3148),c_Groups_Ozero__class_Ozero(U_3148)),U_3149) = U_3149
      | ~ class_Groups_Ocomm__monoid__add(U_3148) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

cnf(f_770_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3148),c_Groups_Ozero__class_Ozero(U_3148)),U_3149) = U_3149
    | ~ class_Groups_Ocomm__monoid__add(U_3148) ),
    inference(clausify,[status(thm)],[f_770_2]) ).

fof(f_771_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_771_2,plain,
    ! [U_3151,U_3150] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3150),c_Groups_Ozero__class_Ozero(U_3150)),U_3151) = U_3151
      | ~ class_Groups_Omonoid__add(U_3150) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

cnf(f_771_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3150),c_Groups_Ozero__class_Ozero(U_3150)),U_3151) = U_3151
    | ~ class_Groups_Omonoid__add(U_3150) ),
    inference(clausify,[status(thm)],[f_771_2]) ).

fof(f_772_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_772_2,plain,
    ! [U_3153,U_3152] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3152),c_Groups_Ozero__class_Ozero(U_3152)),U_3153) = U_3153
      | ~ class_Rings_Ocomm__semiring__1(U_3152) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

cnf(f_772_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3152),c_Groups_Ozero__class_Ozero(U_3152)),U_3153) = U_3153
    | ~ class_Rings_Ocomm__semiring__1(U_3152) ),
    inference(clausify,[status(thm)],[f_772_2]) ).

fof(f_773_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_773_2,plain,
    ! [U_3155,U_3154] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3154),U_3155),c_Groups_Ozero__class_Ozero(U_3154)) = U_3155
      | ~ class_Rings_Ocomm__semiring__1(U_3154) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

cnf(f_773_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3154),U_3155),c_Groups_Ozero__class_Ozero(U_3154)) = U_3155
    | ~ class_Rings_Ocomm__semiring__1(U_3154) ),
    inference(clausify,[status(thm)],[f_773_2]) ).

fof(f_774_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_774_2,plain,
    ! [U_3158,U_3157,U_3156] :
      ( ( ( U_3157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3156),U_3157),U_3158)
          | U_3158 != c_Groups_Ozero__class_Ozero(U_3156) )
        & ( U_3158 = c_Groups_Ozero__class_Ozero(U_3156)
          | U_3157 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3156),U_3157),U_3158) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3156) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

cnf(f_774_3,plain,
    ( U_3158 = c_Groups_Ozero__class_Ozero(U_3156)
    | U_3157 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3156),U_3157),U_3158)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3156) ),
    inference(clausify,[status(thm)],[f_774_2]) ).

cnf(f_774_4,plain,
    ( U_3157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3156),U_3157),U_3158)
    | U_3158 != c_Groups_Ozero__class_Ozero(U_3156)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3156) ),
    inference(clausify,[status(thm)],[f_774_2]) ).

fof(f_775_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_775_2,plain,
    ! [U_3160,U_3159] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3159),c_Groups_Ozero__class_Ozero(U_3159)),U_3160) = c_Groups_Ozero__class_Ozero(U_3159)
      | ~ class_Rings_Omult__zero(U_3159) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

cnf(f_775_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3159),c_Groups_Ozero__class_Ozero(U_3159)),U_3160) = c_Groups_Ozero__class_Ozero(U_3159)
    | ~ class_Rings_Omult__zero(U_3159) ),
    inference(clausify,[status(thm)],[f_775_2]) ).

fof(f_776_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_776_2,plain,
    ! [U_3162,U_3161] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3161),c_Groups_Ozero__class_Ozero(U_3161)),U_3162) = c_Groups_Ozero__class_Ozero(U_3161)
      | ~ class_Rings_Ocomm__semiring__1(U_3161) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

cnf(f_776_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3161),c_Groups_Ozero__class_Ozero(U_3161)),U_3162) = c_Groups_Ozero__class_Ozero(U_3161)
    | ~ class_Rings_Ocomm__semiring__1(U_3161) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

fof(f_777_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_777_2,plain,
    ! [U_3164,U_3163] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3163),U_3164),c_Groups_Ozero__class_Ozero(U_3163)) = c_Groups_Ozero__class_Ozero(U_3163)
      | ~ class_Rings_Omult__zero(U_3163) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

cnf(f_777_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3163),U_3164),c_Groups_Ozero__class_Ozero(U_3163)) = c_Groups_Ozero__class_Ozero(U_3163)
    | ~ class_Rings_Omult__zero(U_3163) ),
    inference(clausify,[status(thm)],[f_777_2]) ).

fof(f_778_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_778_2,plain,
    ! [U_3166,U_3165] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3165),U_3166),c_Groups_Ozero__class_Ozero(U_3165)) = c_Groups_Ozero__class_Ozero(U_3165)
      | ~ class_Rings_Ocomm__semiring__1(U_3165) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

cnf(f_778_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3165),U_3166),c_Groups_Ozero__class_Ozero(U_3165)) = c_Groups_Ozero__class_Ozero(U_3165)
    | ~ class_Rings_Ocomm__semiring__1(U_3165) ),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_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_779_2,plain,
    ! [U_3169,U_3168,U_3167] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3167),U_3168),U_3169) = c_Groups_Ozero__class_Ozero(U_3167)
          | ( U_3169 != c_Groups_Ozero__class_Ozero(U_3167)
            & U_3168 != c_Groups_Ozero__class_Ozero(U_3167) ) )
        & ( U_3169 = c_Groups_Ozero__class_Ozero(U_3167)
          | U_3168 = c_Groups_Ozero__class_Ozero(U_3167)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3167),U_3168),U_3169) != c_Groups_Ozero__class_Ozero(U_3167) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_3167) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

cnf(f_779_3,plain,
    ( U_3169 = c_Groups_Ozero__class_Ozero(U_3167)
    | U_3168 = c_Groups_Ozero__class_Ozero(U_3167)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3167),U_3168),U_3169) != c_Groups_Ozero__class_Ozero(U_3167)
    | ~ class_Rings_Oring__no__zero__divisors(U_3167) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( U_3168 != c_Groups_Ozero__class_Ozero(U_3167)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3167),U_3168),U_3169) = c_Groups_Ozero__class_Ozero(U_3167)
    | ~ class_Rings_Oring__no__zero__divisors(U_3167) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

cnf(f_779_5,plain,
    ( U_3169 != c_Groups_Ozero__class_Ozero(U_3167)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3167),U_3168),U_3169) = c_Groups_Ozero__class_Ozero(U_3167)
    | ~ class_Rings_Oring__no__zero__divisors(U_3167) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

fof(f_780_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_780_2,plain,
    ! [U_3172,U_3171,U_3170] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3170),U_3171),U_3172) != c_Groups_Ozero__class_Ozero(U_3170)
      | U_3172 = c_Groups_Ozero__class_Ozero(U_3170)
      | U_3171 = c_Groups_Ozero__class_Ozero(U_3170)
      | ~ class_Rings_Ono__zero__divisors(U_3170) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

cnf(f_780_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3170),U_3171),U_3172) != c_Groups_Ozero__class_Ozero(U_3170)
    | U_3172 = c_Groups_Ozero__class_Ozero(U_3170)
    | U_3171 = c_Groups_Ozero__class_Ozero(U_3170)
    | ~ class_Rings_Ono__zero__divisors(U_3170) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

fof(f_781_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_781_2,plain,
    ! [U_3175,U_3174,U_3173] :
      ( U_3175 = c_Groups_Ozero__class_Ozero(U_3173)
      | U_3174 = c_Groups_Ozero__class_Ozero(U_3173)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3173),U_3174),U_3175) != c_Groups_Ozero__class_Ozero(U_3173)
      | ~ class_Rings_Ono__zero__divisors(U_3173) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

cnf(f_781_3,plain,
    ( U_3175 = c_Groups_Ozero__class_Ozero(U_3173)
    | U_3174 = c_Groups_Ozero__class_Ozero(U_3173)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3173),U_3174),U_3175) != c_Groups_Ozero__class_Ozero(U_3173)
    | ~ class_Rings_Ono__zero__divisors(U_3173) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

fof(f_782_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_782_2,plain,
    ! [U_3177,U_3176] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),c_Groups_Ozero__class_Ozero(U_3176)) = U_3177
      | ~ class_Groups_Ogroup__add(U_3176) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

cnf(f_782_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3176),U_3177),c_Groups_Ozero__class_Ozero(U_3176)) = U_3177
    | ~ class_Groups_Ogroup__add(U_3176) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

fof(f_783_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_783_2,plain,
    ! [U_3179,U_3178] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3178),U_3179),U_3179) = c_Groups_Ozero__class_Ozero(U_3178)
      | ~ class_Groups_Ogroup__add(U_3178) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

cnf(f_783_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3178),U_3179),U_3179) = c_Groups_Ozero__class_Ozero(U_3178)
    | ~ class_Groups_Ogroup__add(U_3178) ),
    inference(clausify,[status(thm)],[f_783_2]) ).

fof(f_784_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_784_2,plain,
    ! [U_3182,U_3181,U_3180] :
      ( ( ( U_3181 = U_3182
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3180),U_3181),U_3182) != c_Groups_Ozero__class_Ozero(U_3180) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3180),U_3181),U_3182) = c_Groups_Ozero__class_Ozero(U_3180)
          | U_3181 != U_3182 ) )
      | ~ class_Groups_Oab__group__add(U_3180) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

cnf(f_784_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3180),U_3181),U_3182) = c_Groups_Ozero__class_Ozero(U_3180)
    | U_3181 != U_3182
    | ~ class_Groups_Oab__group__add(U_3180) ),
    inference(clausify,[status(thm)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( U_3181 = U_3182
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3180),U_3181),U_3182) != c_Groups_Ozero__class_Ozero(U_3180)
    | ~ class_Groups_Oab__group__add(U_3180) ),
    inference(clausify,[status(thm)],[f_784_2]) ).

fof(f_785_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_785_2,plain,
    ! [U_3185,U_3184,U_3183] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3183),U_3184),U_3185) = c_Groups_Ozero__class_Ozero(U_3183)
          | U_3184 != U_3185 )
        & ( U_3184 = U_3185
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3183),U_3184),U_3185) != c_Groups_Ozero__class_Ozero(U_3183) ) )
      | ~ class_Groups_Ogroup__add(U_3183) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

cnf(f_785_3,plain,
    ( U_3184 = U_3185
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3183),U_3184),U_3185) != c_Groups_Ozero__class_Ozero(U_3183)
    | ~ class_Groups_Ogroup__add(U_3183) ),
    inference(clausify,[status(thm)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3183),U_3184),U_3185) = c_Groups_Ozero__class_Ozero(U_3183)
    | U_3184 != U_3185
    | ~ class_Groups_Ogroup__add(U_3183) ),
    inference(clausify,[status(thm)],[f_785_2]) ).

fof(f_786_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_786_2,plain,
    ! [U_3186] :
      ( c_Groups_Ozero__class_Ozero(U_3186) != c_Groups_Oone__class_Oone(U_3186)
      | ~ class_Rings_Ozero__neq__one(U_3186) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

cnf(f_786_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_3186) != c_Groups_Oone__class_Oone(U_3186)
    | ~ class_Rings_Ozero__neq__one(U_3186) ),
    inference(clausify,[status(thm)],[f_786_2]) ).

fof(f_787_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_787_2,plain,
    ! [U_3187] :
      ( c_Groups_Oone__class_Oone(U_3187) != c_Groups_Ozero__class_Ozero(U_3187)
      | ~ class_Rings_Ozero__neq__one(U_3187) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

cnf(f_787_3,plain,
    ( c_Groups_Oone__class_Oone(U_3187) != c_Groups_Ozero__class_Ozero(U_3187)
    | ~ class_Rings_Ozero__neq__one(U_3187) ),
    inference(clausify,[status(thm)],[f_787_2]) ).

fof(f_788_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_788_2,plain,
    ! [U_3188] : hAPP(c_Nat_OSuc,U_3188) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

cnf(f_788_3,plain,
    hAPP(c_Nat_OSuc,U_3188) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_788_2]) ).

fof(f_789_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_789_2,plain,
    ! [U_3189] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3189),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

cnf(f_789_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3189),
    inference(clausify,[status(thm)],[f_789_2]) ).

fof(f_790_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_790_2,plain,
    ! [U_3190] : hAPP(c_Nat_OSuc,U_3190) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

cnf(f_790_3,plain,
    hAPP(c_Nat_OSuc,U_3190) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_790_2]) ).

fof(f_791_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_791_2,plain,
    ! [U_3191] : hAPP(c_Nat_OSuc,U_3191) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

cnf(f_791_3,plain,
    hAPP(c_Nat_OSuc,U_3191) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_791_2]) ).

fof(f_792_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_792_2,plain,
    ! [U_3192] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3192),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

cnf(f_792_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3192),
    inference(clausify,[status(thm)],[f_792_2]) ).

fof(f_793_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_793_2,plain,
    ! [U_3193] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3193),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

cnf(f_793_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_3193),
    inference(clausify,[status(thm)],[f_793_2]) ).

fof(f_794_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_794_2,plain,
    ! [U_3194] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3194),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

cnf(f_794_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3194),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_794_2]) ).

fof(f_795_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_795_2,plain,
    ! [U_3195] :
      ( ( U_3195 != 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_3195)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3195))
        | U_3195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ( ! [U_3197] :
        ( U_3197 != 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_3197)) )
    & ! [U_3196] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3196))
        | U_3196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3196))
    | U_3196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_5,plain,
    ( U_3197 != 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_3197)) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_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_796_2,plain,
    ! [U_3198] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3198),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

cnf(f_796_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3198),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_796_2]) ).

fof(f_797_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_797_2,plain,
    ! [U_3200,U_3199] :
      ( U_3200 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3199),U_3200)) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_3200] :
      ( ! [U_3199] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3199),U_3200))
      | U_3200 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3199),U_3200))
    | U_3200 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_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_798_2,plain,
    ! [U_3201] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3201))
      | U_3201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

cnf(f_798_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3201))
    | U_3201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_798_2]) ).

fof(f_799_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_799_2,plain,
    ! [U_3203,U_3202] :
      ( U_3203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3202),U_3203) != U_3202 ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_3203] :
      ( ! [U_3202] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3202),U_3203) != U_3202
      | U_3203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_799_2]) ).

cnf(f_799_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3202),U_3203) != U_3202
    | U_3203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

fof(f_800_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_800_2,plain,
    ! [U_3205,U_3204] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3204),U_3205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3205 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3204 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_3205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3204),U_3205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ( ! [U_3209,U_3207] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3207),U_3209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3208,U_3206] :
        ( ( U_3208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3206),U_3208) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_800_2]) ).

cnf(f_800_4,plain,
    ( U_3206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3206),U_3208) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

cnf(f_800_5,plain,
    ( U_3208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3206),U_3208) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

cnf(f_800_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3207),U_3209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_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_801_2,plain,
    ! [U_3210] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3210),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3210,
    inference(variable_rename,[status(thm)],[f_801_1]) ).

cnf(f_801_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3210),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3210,
    inference(clausify,[status(thm)],[f_801_2]) ).

fof(f_802_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_802_2,plain,
    ! [U_3211] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3211) = U_3211,
    inference(variable_rename,[status(thm)],[f_802_1]) ).

cnf(f_802_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3211) = U_3211,
    inference(clausify,[status(thm)],[f_802_2]) ).

fof(f_803_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_803_2,plain,
    ! [U_3212] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3212),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3212),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ( ! [U_3214] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3214),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3214 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3213] :
        ( U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3213),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_803_2]) ).

cnf(f_803_4,plain,
    ( U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3213),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3214),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3214 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_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_804_2,plain,
    ! [U_3215] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3215)),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

cnf(f_804_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3215)),
    inference(clausify,[status(thm)],[f_804_2]) ).

fof(f_805_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_805_2,plain,
    ! [U_3216] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3216) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

cnf(f_805_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3216) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_805_2]) ).

fof(f_806_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_806_2,plain,
    ! [U_3217] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3217,
    inference(variable_rename,[status(thm)],[f_806_1]) ).

cnf(f_806_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3217,
    inference(clausify,[status(thm)],[f_806_2]) ).

fof(f_807_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_807_2,plain,
    ! [U_3218] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3218),U_3218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

cnf(f_807_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3218),U_3218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_807_2]) ).

fof(f_808_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_808_2,plain,
    ! [U_3220,U_3219] :
      ( U_3219 = U_3220
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3220),U_3219) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3219),U_3220) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

cnf(f_808_3,plain,
    ( U_3219 = U_3220
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3220),U_3219) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3219),U_3220) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_808_2]) ).

fof(f_809_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_809_2,plain,
    ! [U_3223,U_3222,U_3221] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3221),U_3222) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3221),U_3223)
        | ( U_3222 != U_3223
          & U_3221 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_3222 = U_3223
        | U_3221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3221),U_3222) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3221),U_3223) ) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ( ! [U_3229,U_3227,U_3225] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3227) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3229)
        | ( U_3227 != U_3229
          & U_3225 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3228,U_3226,U_3224] :
        ( U_3226 = U_3228
        | U_3224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3224),U_3226) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3224),U_3228) ) ),
    inference(miniscope,[status(thm)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( U_3226 = U_3228
    | U_3224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3224),U_3226) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3224),U_3228) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

cnf(f_809_5,plain,
    ( U_3225 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3227) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3229) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

cnf(f_809_6,plain,
    ( U_3227 != U_3229
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3227) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3225),U_3229) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_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_810_2,plain,
    ! [U_3230] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3230) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

cnf(f_810_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3230) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_810_2]) ).

fof(f_811_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_811_2,plain,
    ! [U_3231] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3231),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

cnf(f_811_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3231),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_811_2]) ).

fof(f_812_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_812_2,plain,
    ! [U_3233,U_3232] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3232),U_3233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_3233 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_3233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3232),U_3233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ( ! [U_3237,U_3235] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),U_3237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_3237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3235 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3236,U_3234] :
        ( U_3236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3234),U_3236) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_812_2]) ).

cnf(f_812_4,plain,
    ( U_3236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3234),U_3236) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_5,plain,
    ( U_3235 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),U_3237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_6,plain,
    ( U_3237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),U_3237) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_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_813_2,plain,
    ! [U_3240,U_3239,U_3238] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3240)
        | ( U_3238 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3239 != U_3240 ) )
      & ( U_3238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3239 = U_3240
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3239) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3238),U_3240) ) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ( ! [U_3246,U_3244,U_3242] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3246)
        | ( U_3242 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3244 != U_3246 ) )
    & ! [U_3245,U_3243,U_3241] :
        ( U_3241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3243 = U_3245
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),U_3243) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),U_3245) ) ),
    inference(miniscope,[status(thm)],[f_813_2]) ).

cnf(f_813_4,plain,
    ( U_3241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3243 = U_3245
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),U_3243) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3241),U_3245) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_5,plain,
    ( U_3244 != U_3246
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3246) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_6,plain,
    ( U_3242 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3242),U_3246) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_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_814_2,plain,
    ! [U_3249,U_3248,U_3247] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),U_3248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3249),U_3248)
        | ( U_3248 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3247 != U_3249 ) )
      & ( U_3248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3247 = U_3249
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),U_3248) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3249),U_3248) ) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ( ! [U_3255,U_3253,U_3251] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3251),U_3253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3255),U_3253)
        | ( U_3253 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3251 != U_3255 ) )
    & ! [U_3254,U_3252,U_3250] :
        ( U_3252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3250 = U_3254
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3250),U_3252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3254),U_3252) ) ),
    inference(miniscope,[status(thm)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( U_3252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3250 = U_3254
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3250),U_3252) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3254),U_3252) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

cnf(f_814_5,plain,
    ( U_3251 != U_3255
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3251),U_3253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3255),U_3253) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

cnf(f_814_6,plain,
    ( U_3253 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3251),U_3253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3255),U_3253) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_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_815_2,plain,
    ! [U_3259,U_3258,U_3257,U_3256] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3257),U_3259))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3256,U_3257)),c_Sum__Type_OPlus(U_3256,U_3257,U_3258,U_3259))) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_3259,U_3258,U_3257] :
      ( ! [U_3256] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3256,U_3257)),c_Sum__Type_OPlus(U_3256,U_3257,U_3258,U_3259)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3257),U_3259)) ),
    inference(miniscope,[status(thm)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3256,U_3257)),c_Sum__Type_OPlus(U_3256,U_3257,U_3258,U_3259)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3257),U_3259)) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_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_816_2,plain,
    ! [U_3263,U_3262,U_3261,U_3260] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3262))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3260,U_3261)),c_Sum__Type_OPlus(U_3260,U_3261,U_3262,U_3263))) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

cnf(f_816_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3262))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3260,U_3261)),c_Sum__Type_OPlus(U_3260,U_3261,U_3262,U_3263))) ),
    inference(clausify,[status(thm)],[f_816_2]) ).

fof(f_817_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_817_2,plain,
    ! [U_3267,U_3266,U_3265,U_3264] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3264,U_3266)),c_Sum__Type_OPlus(U_3264,U_3266,U_3265,U_3267)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3267))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3264),U_3265)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

cnf(f_817_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3264,U_3266)),c_Sum__Type_OPlus(U_3264,U_3266,U_3265,U_3267)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3267))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3264),U_3265)) ),
    inference(clausify,[status(thm)],[f_817_2]) ).

fof(f_818_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_818_2,plain,
    ! [U_3271,U_3270,U_3269,U_3268] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3268,U_3269)),c_Sum__Type_OPlus(U_3268,U_3269,U_3270,U_3271)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3269),U_3271))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3268),U_3270)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3269),U_3271))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3268),U_3270)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3268,U_3269)),c_Sum__Type_OPlus(U_3268,U_3269,U_3270,U_3271))) ) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ( ! [U_3279,U_3277,U_3275,U_3273] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3273,U_3275)),c_Sum__Type_OPlus(U_3273,U_3275,U_3277,U_3279)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3275),U_3279))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3273),U_3277)) )
    & ! [U_3278,U_3276,U_3274,U_3272] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3274),U_3278))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3272),U_3276)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3272,U_3274)),c_Sum__Type_OPlus(U_3272,U_3274,U_3276,U_3278))) ) ),
    inference(miniscope,[status(thm)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3272),U_3276))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3272,U_3274)),c_Sum__Type_OPlus(U_3272,U_3274,U_3276,U_3278))) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

cnf(f_818_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3274),U_3278))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3272,U_3274)),c_Sum__Type_OPlus(U_3272,U_3274,U_3276,U_3278))) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

cnf(f_818_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3273,U_3275)),c_Sum__Type_OPlus(U_3273,U_3275,U_3277,U_3279)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3275),U_3279))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3273),U_3277)) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_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_819_2,plain,
    ! [U_3283,U_3282,U_3281,U_3280] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3280,U_3282)),c_Sum__Type_OPlus(U_3280,U_3282,U_3281,U_3283)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3282),U_3283))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3280),U_3281)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3280,U_3282)),c_Sum__Type_OPlus(U_3280,U_3282,U_3281,U_3283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3280),U_3281)),hAPP(c_Finite__Set_Ocard(U_3282),U_3283))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3282),U_3283))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3280),U_3281)) ) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ( ! [U_3291,U_3289,U_3287,U_3285] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3285,U_3289)),c_Sum__Type_OPlus(U_3285,U_3289,U_3287,U_3291)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3289),U_3291))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3285),U_3287)) ) )
    & ! [U_3290,U_3288,U_3286,U_3284] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3284,U_3288)),c_Sum__Type_OPlus(U_3284,U_3288,U_3286,U_3290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3284),U_3286)),hAPP(c_Finite__Set_Ocard(U_3288),U_3290))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3288),U_3290))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3284),U_3286)) ) ),
    inference(miniscope,[status(thm)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_3284,U_3288)),c_Sum__Type_OPlus(U_3284,U_3288,U_3286,U_3290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3284),U_3286)),hAPP(c_Finite__Set_Ocard(U_3288),U_3290))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3288),U_3290))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3284),U_3286)) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

cnf(f_819_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3285),U_3287))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_3285,U_3289)),c_Sum__Type_OPlus(U_3285,U_3289,U_3287,U_3291)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

cnf(f_819_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3289),U_3291))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_3285,U_3289)),c_Sum__Type_OPlus(U_3285,U_3289,U_3287,U_3291)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_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_820_2,plain,
    ! [U_3293,U_3292] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3292),U_3293),U_3293)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),U_3293)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),U_3293))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3292),U_3293),U_3293))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3292) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

cnf(f_820_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),U_3293))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3292),U_3293),U_3293)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3292) ),
    inference(clausify,[status(thm)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3292),U_3293),U_3293)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3292),c_Groups_Ozero__class_Ozero(U_3292)),U_3293))
    | ~ class_Groups_Olinordered__ab__group__add(U_3292) ),
    inference(clausify,[status(thm)],[f_820_2]) ).

fof(f_821_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_821_2,plain,
    ! [U_3295,U_3294] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3294),U_3295),U_3295)),c_Groups_Ozero__class_Ozero(U_3294)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),U_3295),c_Groups_Ozero__class_Ozero(U_3294))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),U_3295),c_Groups_Ozero__class_Ozero(U_3294)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3294),U_3295),U_3295)),c_Groups_Ozero__class_Ozero(U_3294))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3294) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

cnf(f_821_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),U_3295),c_Groups_Ozero__class_Ozero(U_3294)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3294),U_3295),U_3295)),c_Groups_Ozero__class_Ozero(U_3294)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3294) ),
    inference(clausify,[status(thm)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3294),U_3295),U_3295)),c_Groups_Ozero__class_Ozero(U_3294)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3294),U_3295),c_Groups_Ozero__class_Ozero(U_3294)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3294) ),
    inference(clausify,[status(thm)],[f_821_2]) ).

fof(f_822_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_822_2,plain,
    ! [U_3298,U_3297,U_3296] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3296),U_3297),U_3298)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),U_3298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),U_3297))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3296) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

cnf(f_822_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3296),U_3297),U_3298)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),U_3298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3296),c_Groups_Ozero__class_Ozero(U_3296)),U_3297))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3296) ),
    inference(clausify,[status(thm)],[f_822_2]) ).

fof(f_823_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_823_2,plain,
    ! [U_3301,U_3300,U_3299] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) = c_Groups_Ozero__class_Ozero(U_3299)
          | U_3301 != c_Groups_Ozero__class_Ozero(U_3299)
          | U_3300 != c_Groups_Ozero__class_Ozero(U_3299) )
        & ( ( U_3301 = c_Groups_Ozero__class_Ozero(U_3299)
            & U_3300 = c_Groups_Ozero__class_Ozero(U_3299) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != c_Groups_Ozero__class_Ozero(U_3299) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3300))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3299) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

cnf(f_823_3,plain,
    ( U_3300 = c_Groups_Ozero__class_Ozero(U_3299)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != c_Groups_Ozero__class_Ozero(U_3299)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3300))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3299) ),
    inference(clausify,[status(thm)],[f_823_2]) ).

cnf(f_823_4,plain,
    ( U_3301 = c_Groups_Ozero__class_Ozero(U_3299)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) != c_Groups_Ozero__class_Ozero(U_3299)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3300))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3299) ),
    inference(clausify,[status(thm)],[f_823_2]) ).

cnf(f_823_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3299),U_3300),U_3301) = c_Groups_Ozero__class_Ozero(U_3299)
    | U_3301 != c_Groups_Ozero__class_Ozero(U_3299)
    | U_3300 != c_Groups_Ozero__class_Ozero(U_3299)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3299),c_Groups_Ozero__class_Ozero(U_3299)),U_3300))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3299) ),
    inference(clausify,[status(thm)],[f_823_2]) ).

fof(f_824_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_824_2,plain,
    ! [U_3305,U_3304,U_3303,U_3302] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),U_3304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3302),U_3303),U_3305)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),U_3304),U_3305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),c_Groups_Ozero__class_Ozero(U_3302)),U_3303))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3302) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

cnf(f_824_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),U_3304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3302),U_3303),U_3305)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),U_3304),U_3305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3302),c_Groups_Ozero__class_Ozero(U_3302)),U_3303))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3302) ),
    inference(clausify,[status(thm)],[f_824_2]) ).

fof(f_825_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_825_2,plain,
    ! [U_3309,U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),U_3308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3306),U_3309),U_3307)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),U_3308),U_3309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),c_Groups_Ozero__class_Ozero(U_3306)),U_3307))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3306) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

cnf(f_825_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),U_3308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3306),U_3309),U_3307)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),U_3308),U_3309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3306),c_Groups_Ozero__class_Ozero(U_3306)),U_3307))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3306) ),
    inference(clausify,[status(thm)],[f_825_2]) ).

fof(f_826_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_826_2,plain,
    ! [U_3312,U_3311,U_3310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3310),U_3311),U_3312)),c_Groups_Ozero__class_Ozero(U_3310)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),U_3312),c_Groups_Ozero__class_Ozero(U_3310)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),U_3311),c_Groups_Ozero__class_Ozero(U_3310)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3310) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

cnf(f_826_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3310),U_3311),U_3312)),c_Groups_Ozero__class_Ozero(U_3310)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),U_3312),c_Groups_Ozero__class_Ozero(U_3310)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3310),U_3311),c_Groups_Ozero__class_Ozero(U_3310)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3310) ),
    inference(clausify,[status(thm)],[f_826_2]) ).

fof(f_827_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_827_2,plain,
    ! [U_3315,U_3314,U_3313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3313),U_3314),U_3315)),c_Groups_Ozero__class_Ozero(U_3313)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),c_Groups_Ozero__class_Ozero(U_3313)),U_3315))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),U_3314),c_Groups_Ozero__class_Ozero(U_3313))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),U_3315),c_Groups_Ozero__class_Ozero(U_3313)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),c_Groups_Ozero__class_Ozero(U_3313)),U_3314)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_3313) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

cnf(f_827_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),U_3315),c_Groups_Ozero__class_Ozero(U_3313)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),c_Groups_Ozero__class_Ozero(U_3313)),U_3314))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3313),U_3314),U_3315)),c_Groups_Ozero__class_Ozero(U_3313)))
    | ~ class_Rings_Oordered__cancel__semiring(U_3313) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

cnf(f_827_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),c_Groups_Ozero__class_Ozero(U_3313)),U_3315))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),U_3314),c_Groups_Ozero__class_Ozero(U_3313)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3313),U_3314),U_3315)),c_Groups_Ozero__class_Ozero(U_3313)))
    | ~ class_Rings_Oordered__cancel__semiring(U_3313) ),
    inference(clausify,[status(thm)],[f_827_2]) ).

fof(f_828_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_828_2,plain,
    ! [U_3318,U_3317,U_3316] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3316),U_3317),U_3318)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),U_3318),c_Groups_Ozero__class_Ozero(U_3316)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),U_3317),c_Groups_Ozero__class_Ozero(U_3316))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),U_3318))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),U_3317)) ) )
      | ~ class_Rings_Oordered__ring(U_3316) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

cnf(f_828_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),U_3318))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),U_3317))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3316),U_3317),U_3318)))
    | ~ class_Rings_Oordered__ring(U_3316) ),
    inference(clausify,[status(thm)],[f_828_2]) ).

cnf(f_828_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),U_3318),c_Groups_Ozero__class_Ozero(U_3316)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),U_3317),c_Groups_Ozero__class_Ozero(U_3316)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3316),c_Groups_Ozero__class_Ozero(U_3316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3316),U_3317),U_3318)))
    | ~ class_Rings_Oordered__ring(U_3316) ),
    inference(clausify,[status(thm)],[f_828_2]) ).

fof(f_829_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_829_2,plain,
    ! [U_3323,U_3322,U_3321,U_3320,U_3319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3319),U_3320),U_3322)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3319),U_3321),U_3323)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),c_Groups_Ozero__class_Ozero(U_3319)),U_3322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),c_Groups_Ozero__class_Ozero(U_3319)),U_3321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),U_3322),U_3323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),U_3320),U_3321))
      | ~ class_Rings_Oordered__semiring(U_3319) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

cnf(f_829_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3319),U_3320),U_3322)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3319),U_3321),U_3323)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),c_Groups_Ozero__class_Ozero(U_3319)),U_3322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),c_Groups_Ozero__class_Ozero(U_3319)),U_3321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),U_3322),U_3323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3319),U_3320),U_3321))
    | ~ class_Rings_Oordered__semiring(U_3319) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

fof(f_830_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_830_2,plain,
    ! [U_3328,U_3327,U_3326,U_3325,U_3324] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3324),U_3325),U_3327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3324),U_3326),U_3328)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),c_Groups_Ozero__class_Ozero(U_3324)),U_3327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),c_Groups_Ozero__class_Ozero(U_3324)),U_3325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),U_3327),U_3328))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),U_3325),U_3326))
      | ~ class_Rings_Oordered__semiring(U_3324) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

cnf(f_830_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3324),U_3325),U_3327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3324),U_3326),U_3328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),c_Groups_Ozero__class_Ozero(U_3324)),U_3327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),c_Groups_Ozero__class_Ozero(U_3324)),U_3325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),U_3327),U_3328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3324),U_3325),U_3326))
    | ~ class_Rings_Oordered__semiring(U_3324) ),
    inference(clausify,[status(thm)],[f_830_2]) ).

fof(f_831_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_831_2,plain,
    ! [U_3332,U_3331,U_3330,U_3329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3329),U_3332),U_3331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3329),U_3332),U_3330)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3332),c_Groups_Ozero__class_Ozero(U_3329)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3331))
      | ~ class_Rings_Oordered__ring(U_3329) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

cnf(f_831_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3329),U_3332),U_3331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3329),U_3332),U_3330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3332),c_Groups_Ozero__class_Ozero(U_3329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3331))
    | ~ class_Rings_Oordered__ring(U_3329) ),
    inference(clausify,[status(thm)],[f_831_2]) ).

fof(f_832_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_832_2,plain,
    ! [U_3336,U_3335,U_3334,U_3333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3333),U_3335),U_3336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3333),U_3334),U_3336)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3336),c_Groups_Ozero__class_Ozero(U_3333)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3334),U_3335))
      | ~ class_Rings_Oordered__ring(U_3333) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

cnf(f_832_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3333),U_3335),U_3336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3333),U_3334),U_3336)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3336),c_Groups_Ozero__class_Ozero(U_3333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3333),U_3334),U_3335))
    | ~ class_Rings_Oordered__ring(U_3333) ),
    inference(clausify,[status(thm)],[f_832_2]) ).

fof(f_833_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_833_2,plain,
    ! [U_3340,U_3339,U_3338,U_3337] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3337),U_3340),U_3338)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3337),U_3340),U_3339)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),c_Groups_Ozero__class_Ozero(U_3337)),U_3340))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),U_3338),U_3339))
      | ~ class_Rings_Oordered__comm__semiring(U_3337) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

cnf(f_833_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3337),U_3340),U_3338)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3337),U_3340),U_3339)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),c_Groups_Ozero__class_Ozero(U_3337)),U_3340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3337),U_3338),U_3339))
    | ~ class_Rings_Oordered__comm__semiring(U_3337) ),
    inference(clausify,[status(thm)],[f_833_2]) ).

fof(f_834_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_834_2,plain,
    ! [U_3344,U_3343,U_3342,U_3341] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3344),U_3342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3344),U_3343)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),c_Groups_Ozero__class_Ozero(U_3341)),U_3344))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),U_3342),U_3343))
      | ~ class_Rings_Oordered__semiring(U_3341) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

cnf(f_834_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3344),U_3342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3344),U_3343)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),c_Groups_Ozero__class_Ozero(U_3341)),U_3344))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3341),U_3342),U_3343))
    | ~ class_Rings_Oordered__semiring(U_3341) ),
    inference(clausify,[status(thm)],[f_834_2]) ).

fof(f_835_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_835_2,plain,
    ! [U_3348,U_3347,U_3346,U_3345] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3345),U_3346),U_3348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3345),U_3347),U_3348)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),c_Groups_Ozero__class_Ozero(U_3345)),U_3348))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),U_3346),U_3347))
      | ~ class_Rings_Oordered__semiring(U_3345) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

cnf(f_835_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3345),U_3346),U_3348)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3345),U_3347),U_3348)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),c_Groups_Ozero__class_Ozero(U_3345)),U_3348))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3345),U_3346),U_3347))
    | ~ class_Rings_Oordered__semiring(U_3345) ),
    inference(clausify,[status(thm)],[f_835_2]) ).

fof(f_836_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_836_2,plain,
    ! [U_3351,U_3350,U_3349] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),c_Groups_Ozero__class_Ozero(U_3349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3349),U_3350),U_3351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),U_3351),c_Groups_Ozero__class_Ozero(U_3349)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),U_3350),c_Groups_Ozero__class_Ozero(U_3349)))
      | ~ class_Rings_Oordered__ring(U_3349) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

cnf(f_836_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),c_Groups_Ozero__class_Ozero(U_3349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3349),U_3350),U_3351)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),U_3351),c_Groups_Ozero__class_Ozero(U_3349)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3349),U_3350),c_Groups_Ozero__class_Ozero(U_3349)))
    | ~ class_Rings_Oordered__ring(U_3349) ),
    inference(clausify,[status(thm)],[f_836_2]) ).

fof(f_837_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_837_2,plain,
    ! [U_3354,U_3353,U_3352] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3354)),c_Groups_Ozero__class_Ozero(U_3352)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),c_Groups_Ozero__class_Ozero(U_3352)),U_3354))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),U_3353),c_Groups_Ozero__class_Ozero(U_3352)))
      | ~ class_Rings_Oordered__cancel__semiring(U_3352) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

cnf(f_837_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3354)),c_Groups_Ozero__class_Ozero(U_3352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),c_Groups_Ozero__class_Ozero(U_3352)),U_3354))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3352),U_3353),c_Groups_Ozero__class_Ozero(U_3352)))
    | ~ class_Rings_Oordered__cancel__semiring(U_3352) ),
    inference(clausify,[status(thm)],[f_837_2]) ).

fof(f_838_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_838_2,plain,
    ! [U_3357,U_3356,U_3355] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3355),U_3357),U_3356)),c_Groups_Ozero__class_Ozero(U_3355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),U_3357),c_Groups_Ozero__class_Ozero(U_3355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),c_Groups_Ozero__class_Ozero(U_3355)),U_3356))
      | ~ class_Rings_Oordered__cancel__semiring(U_3355) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

cnf(f_838_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3355),U_3357),U_3356)),c_Groups_Ozero__class_Ozero(U_3355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),U_3357),c_Groups_Ozero__class_Ozero(U_3355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3355),c_Groups_Ozero__class_Ozero(U_3355)),U_3356))
    | ~ class_Rings_Oordered__cancel__semiring(U_3355) ),
    inference(clausify,[status(thm)],[f_838_2]) ).

fof(f_839_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_839_2,plain,
    ! [U_3360,U_3359,U_3358] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3358),U_3359),U_3360)),c_Groups_Ozero__class_Ozero(U_3358)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),U_3360),c_Groups_Ozero__class_Ozero(U_3358)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),c_Groups_Ozero__class_Ozero(U_3358)),U_3359))
      | ~ class_Rings_Oordered__cancel__semiring(U_3358) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

cnf(f_839_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3358),U_3359),U_3360)),c_Groups_Ozero__class_Ozero(U_3358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),U_3360),c_Groups_Ozero__class_Ozero(U_3358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3358),c_Groups_Ozero__class_Ozero(U_3358)),U_3359))
    | ~ class_Rings_Oordered__cancel__semiring(U_3358) ),
    inference(clausify,[status(thm)],[f_839_2]) ).

fof(f_840_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_840_2,plain,
    ! [U_3363,U_3362,U_3361] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3361),U_3362),U_3363)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),U_3363))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),U_3362))
      | ~ class_Rings_Oordered__cancel__semiring(U_3361) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

cnf(f_840_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3361),U_3362),U_3363)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),U_3363))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3361),c_Groups_Ozero__class_Ozero(U_3361)),U_3362))
    | ~ class_Rings_Oordered__cancel__semiring(U_3361) ),
    inference(clausify,[status(thm)],[f_840_2]) ).

fof(f_841_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_841_2,plain,
    ! [U_3366,U_3365,U_3364] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3366))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3365),c_Groups_Ozero__class_Ozero(U_3364))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3366),c_Groups_Ozero__class_Ozero(U_3364)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3365)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3366))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3365),c_Groups_Ozero__class_Ozero(U_3364))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3366),c_Groups_Ozero__class_Ozero(U_3364)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3365)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

cnf(f_841_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3365),c_Groups_Ozero__class_Ozero(U_3364)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3365))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

cnf(f_841_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3366))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3365))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

cnf(f_841_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3365),c_Groups_Ozero__class_Ozero(U_3364)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3366),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

cnf(f_841_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3366))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3366),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

cnf(f_841_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3366),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3365))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

cnf(f_841_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),c_Groups_Ozero__class_Ozero(U_3364)),U_3366))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),U_3365),c_Groups_Ozero__class_Ozero(U_3364)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3366)),c_Groups_Ozero__class_Ozero(U_3364)))
    | ~ class_Rings_Olinordered__ring__strict(U_3364) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

fof(f_842_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_842_2,plain,
    ! [U_3369,U_3368,U_3367] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3369),c_Groups_Ozero__class_Ozero(U_3367)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3368),c_Groups_Ozero__class_Ozero(U_3367))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3369))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3368)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3369),c_Groups_Ozero__class_Ozero(U_3367)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3368),c_Groups_Ozero__class_Ozero(U_3367))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3369))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3368)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

cnf(f_842_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3368),c_Groups_Ozero__class_Ozero(U_3367)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

cnf(f_842_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3369),c_Groups_Ozero__class_Ozero(U_3367)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

cnf(f_842_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3368),c_Groups_Ozero__class_Ozero(U_3367)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

cnf(f_842_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3369),c_Groups_Ozero__class_Ozero(U_3367)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

cnf(f_842_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),U_3368))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

cnf(f_842_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3369),c_Groups_Ozero__class_Ozero(U_3367)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),U_3368),c_Groups_Ozero__class_Ozero(U_3367)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3367),c_Groups_Ozero__class_Ozero(U_3367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3367),U_3368),U_3369)))
    | ~ class_Rings_Olinordered__ring__strict(U_3367) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

fof(f_843_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_843_2,plain,
    ! [U_3371,U_3370] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3370),c_Groups_Ozero__class_Ozero(U_3370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3370),U_3371),U_3371)))
      | ~ class_Rings_Olinordered__ring(U_3370) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

cnf(f_843_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3370),c_Groups_Ozero__class_Ozero(U_3370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3370),U_3371),U_3371)))
    | ~ class_Rings_Olinordered__ring(U_3370) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

fof(f_844_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_844_2,plain,
    ! [U_3373,U_3372] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3372),U_3373),U_3373)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),U_3373)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),U_3373))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3372),U_3373),U_3373))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3372) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

cnf(f_844_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),U_3373))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3372),U_3373),U_3373)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3372) ),
    inference(clausify,[status(thm)],[f_844_2]) ).

cnf(f_844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3372),U_3373),U_3373)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3372),c_Groups_Ozero__class_Ozero(U_3372)),U_3373))
    | ~ class_Groups_Olinordered__ab__group__add(U_3372) ),
    inference(clausify,[status(thm)],[f_844_2]) ).

fof(f_845_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_845_2,plain,
    ! [U_3375,U_3374] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3374),U_3375),U_3375)),c_Groups_Ozero__class_Ozero(U_3374)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),U_3375),c_Groups_Ozero__class_Ozero(U_3374))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),U_3375),c_Groups_Ozero__class_Ozero(U_3374)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3374),U_3375),U_3375)),c_Groups_Ozero__class_Ozero(U_3374))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3374) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

cnf(f_845_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),U_3375),c_Groups_Ozero__class_Ozero(U_3374)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3374),U_3375),U_3375)),c_Groups_Ozero__class_Ozero(U_3374)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3374) ),
    inference(clausify,[status(thm)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3374),U_3375),U_3375)),c_Groups_Ozero__class_Ozero(U_3374)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3374),U_3375),c_Groups_Ozero__class_Ozero(U_3374)))
    | ~ class_Groups_Olinordered__ab__group__add(U_3374) ),
    inference(clausify,[status(thm)],[f_845_2]) ).

fof(f_846_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_846_2,plain,
    ! [U_3378,U_3377,U_3376] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),U_3377),U_3378)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),U_3378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),U_3377))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3376) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

cnf(f_846_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),U_3377),U_3378)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),U_3378))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3376),c_Groups_Ozero__class_Ozero(U_3376)),U_3377))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3376) ),
    inference(clausify,[status(thm)],[f_846_2]) ).

fof(f_847_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_847_2,plain,
    ! [U_3381,U_3380,U_3379] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),c_Groups_Ozero__class_Ozero(U_3379)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3381),c_Groups_Ozero__class_Ozero(U_3379)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),c_Groups_Ozero__class_Ozero(U_3379)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3379) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

cnf(f_847_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3379),U_3380),U_3381)),c_Groups_Ozero__class_Ozero(U_3379)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3381),c_Groups_Ozero__class_Ozero(U_3379)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),U_3380),c_Groups_Ozero__class_Ozero(U_3379)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3379) ),
    inference(clausify,[status(thm)],[f_847_2]) ).

fof(f_848_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_848_2,plain,
    ! [U_3385,U_3384,U_3383,U_3382] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),U_3384),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3382),U_3383),U_3385)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),U_3384),U_3385))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),c_Groups_Ozero__class_Ozero(U_3382)),U_3383))
      | ~ class_Rings_Olinordered__semidom(U_3382) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

cnf(f_848_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),U_3384),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3382),U_3383),U_3385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),U_3384),U_3385))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3382),c_Groups_Ozero__class_Ozero(U_3382)),U_3383))
    | ~ class_Rings_Olinordered__semidom(U_3382) ),
    inference(clausify,[status(thm)],[f_848_2]) ).

fof(f_849_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_849_2,plain,
    ! [U_3387,U_3386] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),U_3387),U_3387)),c_Groups_Ozero__class_Ozero(U_3386)))
      | ~ class_Rings_Olinordered__ring(U_3386) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

cnf(f_849_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),U_3387),U_3387)),c_Groups_Ozero__class_Ozero(U_3386)))
    | ~ class_Rings_Olinordered__ring(U_3386) ),
    inference(clausify,[status(thm)],[f_849_2]) ).

fof(f_850_1,plain,
    ! [V_b_2,V_ca_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_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_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_ca_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_ca_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_ca_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_ca_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_850_2,plain,
    ! [U_3391,U_3390,U_3389,U_3388] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3391),U_3389))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3390),c_Groups_Ozero__class_Ozero(U_3388))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3389),U_3391))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3391),U_3389))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3390),c_Groups_Ozero__class_Ozero(U_3388))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3389),U_3391))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

cnf(f_850_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3390),c_Groups_Ozero__class_Ozero(U_3388)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3391),U_3389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

cnf(f_850_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3390),c_Groups_Ozero__class_Ozero(U_3388)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3389),U_3391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

cnf(f_850_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3391),U_3389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3389),U_3391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

cnf(f_850_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3389),U_3391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

cnf(f_850_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3391),U_3389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),U_3390),c_Groups_Ozero__class_Ozero(U_3388)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3389),U_3390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3388),U_3391),U_3390)))
    | ~ class_Rings_Olinordered__ring__strict(U_3388) ),
    inference(clausify,[status(thm)],[f_850_2]) ).

fof(f_851_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_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_ca_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_ca_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_ca_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_851_2,plain,
    ! [U_3395,U_3394,U_3393,U_3392] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3395),U_3394))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3393),c_Groups_Ozero__class_Ozero(U_3392))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3394),U_3395))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),c_Groups_Ozero__class_Ozero(U_3392)),U_3393)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3395),U_3394))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3393),c_Groups_Ozero__class_Ozero(U_3392))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3394),U_3395))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),c_Groups_Ozero__class_Ozero(U_3392)),U_3393)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

cnf(f_851_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3393),c_Groups_Ozero__class_Ozero(U_3392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),c_Groups_Ozero__class_Ozero(U_3392)),U_3393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3395),U_3394))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),c_Groups_Ozero__class_Ozero(U_3392)),U_3393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

cnf(f_851_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3393),c_Groups_Ozero__class_Ozero(U_3392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3394),U_3395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

cnf(f_851_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3395),U_3394))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3394),U_3395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

cnf(f_851_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3394),U_3395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),c_Groups_Ozero__class_Ozero(U_3392)),U_3393))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

cnf(f_851_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3395),U_3394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),U_3393),c_Groups_Ozero__class_Ozero(U_3392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3394)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3392),U_3393),U_3395)))
    | ~ class_Rings_Olinordered__ring__strict(U_3392) ),
    inference(clausify,[status(thm)],[f_851_2]) ).

fof(f_852_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_852_2,plain,
    ! [U_3399,U_3398,U_3397,U_3396] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3399)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),U_3398),U_3399)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),U_3398),U_3399))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3399))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),c_Groups_Ozero__class_Ozero(U_3396)),U_3397))
      | ~ class_Rings_Olinordered__ring__strict(U_3396) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

cnf(f_852_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),U_3398),U_3399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3399)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),c_Groups_Ozero__class_Ozero(U_3396)),U_3397))
    | ~ class_Rings_Olinordered__ring__strict(U_3396) ),
    inference(clausify,[status(thm)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3396),U_3397),U_3399)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),U_3398),U_3399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3396),c_Groups_Ozero__class_Ozero(U_3396)),U_3397))
    | ~ class_Rings_Olinordered__ring__strict(U_3396) ),
    inference(clausify,[status(thm)],[f_852_2]) ).

fof(f_853_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_853_2,plain,
    ! [U_3402,U_3401,U_3400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3400),U_3401),U_3402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),U_3402))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),U_3401))
      | ~ class_Rings_Olinordered__semiring__strict(U_3400) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

cnf(f_853_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3400),U_3401),U_3402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),U_3402))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3400),c_Groups_Ozero__class_Ozero(U_3400)),U_3401))
    | ~ class_Rings_Olinordered__semiring__strict(U_3400) ),
    inference(clausify,[status(thm)],[f_853_2]) ).

fof(f_854_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_854_2,plain,
    ! [U_3405,U_3404,U_3403] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3403),U_3404),U_3405)),c_Groups_Ozero__class_Ozero(U_3403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),U_3405),c_Groups_Ozero__class_Ozero(U_3403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),c_Groups_Ozero__class_Ozero(U_3403)),U_3404))
      | ~ class_Rings_Olinordered__semiring__strict(U_3403) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

cnf(f_854_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3403),U_3404),U_3405)),c_Groups_Ozero__class_Ozero(U_3403)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),U_3405),c_Groups_Ozero__class_Ozero(U_3403)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3403),c_Groups_Ozero__class_Ozero(U_3403)),U_3404))
    | ~ class_Rings_Olinordered__semiring__strict(U_3403) ),
    inference(clausify,[status(thm)],[f_854_2]) ).

fof(f_855_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_855_2,plain,
    ! [U_3408,U_3407,U_3406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3406),U_3408),U_3407)),c_Groups_Ozero__class_Ozero(U_3406)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),U_3408),c_Groups_Ozero__class_Ozero(U_3406)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),c_Groups_Ozero__class_Ozero(U_3406)),U_3407))
      | ~ class_Rings_Olinordered__semiring__strict(U_3406) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

cnf(f_855_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3406),U_3408),U_3407)),c_Groups_Ozero__class_Ozero(U_3406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),U_3408),c_Groups_Ozero__class_Ozero(U_3406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3406),c_Groups_Ozero__class_Ozero(U_3406)),U_3407))
    | ~ class_Rings_Olinordered__semiring__strict(U_3406) ),
    inference(clausify,[status(thm)],[f_855_2]) ).

fof(f_856_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_856_2,plain,
    ! [U_3411,U_3410,U_3409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),U_3411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),U_3410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3409),U_3410),U_3411)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3409) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),U_3411))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),U_3410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3409),c_Groups_Ozero__class_Ozero(U_3409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3409),U_3410),U_3411)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3409) ),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_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_857_2,plain,
    ! [U_3414,U_3413,U_3412] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),U_3413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),U_3414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3412),U_3413),U_3414)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3412) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

cnf(f_857_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),U_3413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),U_3414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),c_Groups_Ozero__class_Ozero(U_3412)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3412),U_3413),U_3414)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3412) ),
    inference(clausify,[status(thm)],[f_857_2]) ).

fof(f_858_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_858_2,plain,
    ! [U_3418,U_3417,U_3416,U_3415] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3418)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3418),U_3417)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3418),U_3417))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3418))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),c_Groups_Ozero__class_Ozero(U_3415)))
      | ~ class_Rings_Olinordered__ring__strict(U_3415) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3418),U_3417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),c_Groups_Ozero__class_Ozero(U_3415)))
    | ~ class_Rings_Olinordered__ring__strict(U_3415) ),
    inference(clausify,[status(thm)],[f_858_2]) ).

cnf(f_858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3415),U_3416),U_3418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3418),U_3417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3415),U_3416),c_Groups_Ozero__class_Ozero(U_3415)))
    | ~ class_Rings_Olinordered__ring__strict(U_3415) ),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_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_859_2,plain,
    ! [U_3421,U_3420,U_3419] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3419),U_3420),U_3421)),c_Groups_Ozero__class_Ozero(U_3419)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),c_Groups_Ozero__class_Ozero(U_3419)),U_3421))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),U_3420),c_Groups_Ozero__class_Ozero(U_3419)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3419) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

cnf(f_859_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3419),U_3420),U_3421)),c_Groups_Ozero__class_Ozero(U_3419)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),c_Groups_Ozero__class_Ozero(U_3419)),U_3421))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3419),U_3420),c_Groups_Ozero__class_Ozero(U_3419)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3419) ),
    inference(clausify,[status(thm)],[f_859_2]) ).

fof(f_860_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_860_2,plain,
    ! [U_3424,U_3423,U_3422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),c_Groups_Ozero__class_Ozero(U_3422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3422),U_3423),U_3424)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),U_3424),c_Groups_Ozero__class_Ozero(U_3422)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),U_3423),c_Groups_Ozero__class_Ozero(U_3422)))
      | ~ class_Rings_Olinordered__ring__strict(U_3422) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

cnf(f_860_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),c_Groups_Ozero__class_Ozero(U_3422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3422),U_3423),U_3424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),U_3424),c_Groups_Ozero__class_Ozero(U_3422)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3422),U_3423),c_Groups_Ozero__class_Ozero(U_3422)))
    | ~ class_Rings_Olinordered__ring__strict(U_3422) ),
    inference(clausify,[status(thm)],[f_860_2]) ).

fof(f_861_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_861_2,plain,
    ! [U_3428,U_3427,U_3426,U_3425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3425),U_3426),U_3428)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3425),U_3427),U_3428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),U_3426),U_3427))
      | ~ class_Rings_Olinordered__semiring__strict(U_3425) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

cnf(f_861_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3425),U_3426),U_3428)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3425),U_3427),U_3428)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),U_3426),U_3427))
    | ~ class_Rings_Olinordered__semiring__strict(U_3425) ),
    inference(clausify,[status(thm)],[f_861_2]) ).

fof(f_862_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_862_2,plain,
    ! [U_3432,U_3431,U_3430,U_3429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3429),U_3432),U_3430)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3429),U_3432),U_3431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),c_Groups_Ozero__class_Ozero(U_3429)),U_3432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),U_3430),U_3431))
      | ~ class_Rings_Olinordered__semiring__strict(U_3429) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

cnf(f_862_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3429),U_3432),U_3430)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3429),U_3432),U_3431)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),c_Groups_Ozero__class_Ozero(U_3429)),U_3432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3429),U_3430),U_3431))
    | ~ class_Rings_Olinordered__semiring__strict(U_3429) ),
    inference(clausify,[status(thm)],[f_862_2]) ).

fof(f_863_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_863_2,plain,
    ! [U_3436,U_3435,U_3434,U_3433] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3433),U_3436),U_3434)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3433),U_3436),U_3435)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),c_Groups_Ozero__class_Ozero(U_3433)),U_3436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),U_3434),U_3435))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_3433) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

cnf(f_863_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3433),U_3436),U_3434)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3433),U_3436),U_3435)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),c_Groups_Ozero__class_Ozero(U_3433)),U_3436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3433),U_3434),U_3435))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_3433) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

fof(f_864_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_864_2,plain,
    ! [U_3440,U_3439,U_3438,U_3437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3437),U_3439),U_3440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3437),U_3438),U_3440)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),U_3440),c_Groups_Ozero__class_Ozero(U_3437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),U_3438),U_3439))
      | ~ class_Rings_Olinordered__ring__strict(U_3437) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

cnf(f_864_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3437),U_3439),U_3440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3437),U_3438),U_3440)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),U_3440),c_Groups_Ozero__class_Ozero(U_3437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3437),U_3438),U_3439))
    | ~ class_Rings_Olinordered__ring__strict(U_3437) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

fof(f_865_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_865_2,plain,
    ! [U_3444,U_3443,U_3442,U_3441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3444),U_3443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3444),U_3442)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),U_3444),c_Groups_Ozero__class_Ozero(U_3441)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),U_3442),U_3443))
      | ~ class_Rings_Olinordered__ring__strict(U_3441) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3444),U_3443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3441),U_3444),U_3442)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),U_3444),c_Groups_Ozero__class_Ozero(U_3441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3441),U_3442),U_3443))
    | ~ class_Rings_Olinordered__ring__strict(U_3441) ),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_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_866_2,plain,
    ! [U_3447,U_3446,U_3445] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),U_3446),U_3447))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3445),U_3446),U_3447)),c_Groups_Ozero__class_Ozero(U_3445))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3445),U_3446),U_3447)),c_Groups_Ozero__class_Ozero(U_3445)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),U_3446),U_3447)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3445) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3445),U_3446),U_3447)),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),U_3446),U_3447))
    | ~ class_Groups_Oordered__ab__group__add(U_3445) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

cnf(f_866_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),U_3446),U_3447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3445),U_3446),U_3447)),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ class_Groups_Oordered__ab__group__add(U_3445) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_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_867_2,plain,
    ! [U_3450,U_3449,U_3448] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),U_3449),U_3450))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3448),U_3449),U_3450)),c_Groups_Ozero__class_Ozero(U_3448))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3448),U_3449),U_3450)),c_Groups_Ozero__class_Ozero(U_3448)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),U_3449),U_3450)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3448) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3448),U_3449),U_3450)),c_Groups_Ozero__class_Ozero(U_3448)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),U_3449),U_3450))
    | ~ class_Groups_Oordered__ab__group__add(U_3448) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),U_3449),U_3450))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3448),U_3449),U_3450)),c_Groups_Ozero__class_Ozero(U_3448)))
    | ~ class_Groups_Oordered__ab__group__add(U_3448) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_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_868_2,plain,
    ! [U_3456,U_3455,U_3454,U_3453,U_3452,U_3451] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3451),U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3451),U_3452),U_3455)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3451),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3451),U_3452),U_3456))
      | U_3455 = U_3456
      | U_3453 != U_3454
      | U_3452 = c_Groups_Ozero__class_Ozero(U_3451)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3451) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

cnf(f_868_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3451),U_3453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3451),U_3452),U_3455)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3451),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3451),U_3452),U_3456))
    | U_3455 = U_3456
    | U_3453 != U_3454
    | U_3452 = c_Groups_Ozero__class_Ozero(U_3451)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3451) ),
    inference(clausify,[status(thm)],[f_868_2]) ).

fof(f_869_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_869_2,plain,
    ! [U_3459,U_3458,U_3457] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3458),U_3458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3459),U_3459)) = c_Groups_Ozero__class_Ozero(U_3457)
          | U_3459 != c_Groups_Ozero__class_Ozero(U_3457)
          | U_3458 != c_Groups_Ozero__class_Ozero(U_3457) )
        & ( ( U_3459 = c_Groups_Ozero__class_Ozero(U_3457)
            & U_3458 = c_Groups_Ozero__class_Ozero(U_3457) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3458),U_3458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3459),U_3459)) != c_Groups_Ozero__class_Ozero(U_3457) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3457) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

cnf(f_869_3,plain,
    ( U_3458 = c_Groups_Ozero__class_Ozero(U_3457)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3458),U_3458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3459),U_3459)) != c_Groups_Ozero__class_Ozero(U_3457)
    | ~ class_Rings_Olinordered__ring__strict(U_3457) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

cnf(f_869_4,plain,
    ( U_3459 = c_Groups_Ozero__class_Ozero(U_3457)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3458),U_3458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3459),U_3459)) != c_Groups_Ozero__class_Ozero(U_3457)
    | ~ class_Rings_Olinordered__ring__strict(U_3457) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

cnf(f_869_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3458),U_3458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3457),U_3459),U_3459)) = c_Groups_Ozero__class_Ozero(U_3457)
    | U_3459 != c_Groups_Ozero__class_Ozero(U_3457)
    | U_3458 != c_Groups_Ozero__class_Ozero(U_3457)
    | ~ class_Rings_Olinordered__ring__strict(U_3457) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

fof(f_870_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_870_2,plain,
    ! [U_3460] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3460),c_Groups_Ozero__class_Ozero(U_3460)),c_Groups_Oone__class_Oone(U_3460)))
      | ~ class_Rings_Olinordered__semidom(U_3460) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3460),c_Groups_Ozero__class_Ozero(U_3460)),c_Groups_Oone__class_Oone(U_3460)))
    | ~ class_Rings_Olinordered__semidom(U_3460) ),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_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_871_2,plain,
    ! [U_3461] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3461),c_Groups_Oone__class_Oone(U_3461)),c_Groups_Ozero__class_Ozero(U_3461)))
      | ~ class_Rings_Olinordered__semidom(U_3461) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

cnf(f_871_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3461),c_Groups_Oone__class_Oone(U_3461)),c_Groups_Ozero__class_Ozero(U_3461)))
    | ~ class_Rings_Olinordered__semidom(U_3461) ),
    inference(clausify,[status(thm)],[f_871_2]) ).

fof(f_872_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_872_2,plain,
    ! [U_3462] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),c_Groups_Oone__class_Oone(U_3462)),c_Groups_Ozero__class_Ozero(U_3462)))
      | ~ class_Rings_Olinordered__semidom(U_3462) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

cnf(f_872_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),c_Groups_Oone__class_Oone(U_3462)),c_Groups_Ozero__class_Ozero(U_3462)))
    | ~ class_Rings_Olinordered__semidom(U_3462) ),
    inference(clausify,[status(thm)],[f_872_2]) ).

fof(f_873_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_873_2,plain,
    ! [U_3463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3463),c_Groups_Ozero__class_Ozero(U_3463)),c_Groups_Oone__class_Oone(U_3463)))
      | ~ class_Rings_Olinordered__semidom(U_3463) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

cnf(f_873_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3463),c_Groups_Ozero__class_Ozero(U_3463)),c_Groups_Oone__class_Oone(U_3463)))
    | ~ class_Rings_Olinordered__semidom(U_3463) ),
    inference(clausify,[status(thm)],[f_873_2]) ).

fof(f_874_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_874_2,plain,
    ! [U_3466,U_3465,U_3464] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,U_3464),U_3466),c_Orderings_Obot__class_Obot(tc_fun(U_3465,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3464)
      | ~ class_Groups_Ocomm__monoid__add(U_3464) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

cnf(f_874_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3465,U_3464),U_3466),c_Orderings_Obot__class_Obot(tc_fun(U_3465,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3464)
    | ~ class_Groups_Ocomm__monoid__add(U_3464) ),
    inference(clausify,[status(thm)],[f_874_2]) ).

fof(f_875_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_875_2,plain,
    ! [U_3469,U_3468,U_3467] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3468,U_3467),U_3469),c_Orderings_Obot__class_Obot(tc_fun(U_3468,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3467)
      | ~ class_Groups_Ocomm__monoid__add(U_3467) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

cnf(f_875_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3468,U_3467),U_3469),c_Orderings_Obot__class_Obot(tc_fun(U_3468,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_3467)
    | ~ class_Groups_Ocomm__monoid__add(U_3467) ),
    inference(clausify,[status(thm)],[f_875_2]) ).

fof(f_876_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_876_2,plain,
    ! [U_3473,U_3472,U_3471,U_3470] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472) = c_Groups_Ozero__class_Ozero(U_3470)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
      | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472) = c_Groups_Ozero__class_Ozero(U_3470)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
    | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_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_877_2,plain,
    ! [U_3477,U_3476,U_3475,U_3474] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3477),U_3476) = c_Groups_Ozero__class_Ozero(U_3474)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3475),U_3476))
      | ~ class_Groups_Ocomm__monoid__add(U_3474) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

cnf(f_877_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3475,U_3474),U_3477),U_3476) = c_Groups_Ozero__class_Ozero(U_3474)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3475),U_3476))
    | ~ class_Groups_Ocomm__monoid__add(U_3474) ),
    inference(clausify,[status(thm)],[f_877_2]) ).

fof(f_878_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_878_2,plain,
    ! [U_3483,U_3482,U_3481,U_3480] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) = c_Groups_Ozero__class_Ozero(U_3480)
          | ! [U_3479] :
              ( hAPP(U_3483,U_3479) != c_Groups_Ozero__class_Ozero(U_3480)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3479),U_3482)) ) )
        & ( ? [U_3478] :
              ( hAPP(U_3483,U_3478) = c_Groups_Ozero__class_Ozero(U_3480)
              & hBOOL(hAPP(hAPP(c_member(U_3481),U_3478),U_3482)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) != c_Groups_Ozero__class_Ozero(U_3480) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
      | ~ class_Rings_Ono__zero__divisors(U_3480)
      | ~ class_Rings_Ocomm__semiring__1(U_3480) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_3483,U_3482,U_3481,U_3480] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) = c_Groups_Ozero__class_Ozero(U_3480)
          | ! [U_3479] :
              ( hAPP(U_3483,U_3479) != c_Groups_Ozero__class_Ozero(U_3480)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3479),U_3482)) ) )
        & ( ( hAPP(U_3483,sK58(U_3483,U_3482,U_3481,U_3480)) = c_Groups_Ozero__class_Ozero(U_3480)
            & hBOOL(hAPP(hAPP(c_member(U_3481),sK58(U_3483,U_3482,U_3481,U_3480)),U_3482)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) != c_Groups_Ozero__class_Ozero(U_3480) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
      | ~ class_Rings_Ono__zero__divisors(U_3480)
      | ~ class_Rings_Ocomm__semiring__1(U_3480) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_3478,sK58(U_3483,U_3482,U_3481,U_3480))],[f_878_2]) ).

cnf(f_878_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3481),sK58(U_3483,U_3482,U_3481,U_3480)),U_3482))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) != c_Groups_Ozero__class_Ozero(U_3480)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Rings_Ono__zero__divisors(U_3480)
    | ~ class_Rings_Ocomm__semiring__1(U_3480) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

cnf(f_878_5,plain,
    ( hAPP(U_3483,sK58(U_3483,U_3482,U_3481,U_3480)) = c_Groups_Ozero__class_Ozero(U_3480)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) != c_Groups_Ozero__class_Ozero(U_3480)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Rings_Ono__zero__divisors(U_3480)
    | ~ class_Rings_Ocomm__semiring__1(U_3480) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

cnf(f_878_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3481,U_3480),U_3483),U_3482) = c_Groups_Ozero__class_Ozero(U_3480)
    | hAPP(U_3483,U_3479) != c_Groups_Ozero__class_Ozero(U_3480)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3479),U_3482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Rings_Ono__zero__divisors(U_3480)
    | ~ class_Rings_Ocomm__semiring__1(U_3480) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_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_879_2,plain,
    ! [U_3488,U_3487,U_3486,U_3485] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3486,U_3485),U_3488),U_3487) = c_Groups_Ozero__class_Ozero(U_3485)
      | ! [U_3484] :
          ( hAPP(U_3488,U_3484) != c_Groups_Ozero__class_Ozero(U_3485)
          | ~ hBOOL(hAPP(hAPP(c_member(U_3486),U_3484),U_3487)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3486),U_3487))
      | ~ class_Rings_Ocomm__semiring__1(U_3485) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3486,U_3485),U_3488),U_3487) = c_Groups_Ozero__class_Ozero(U_3485)
    | hAPP(U_3488,U_3484) != c_Groups_Ozero__class_Ozero(U_3485)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3486),U_3484),U_3487))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3486),U_3487))
    | ~ class_Rings_Ocomm__semiring__1(U_3485) ),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_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_880_2,plain,
    ! [U_3492,U_3491] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3491),hAPP(c_Nat_OSuc,U_3492)))
        | ( ! [U_3490] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3490),U_3492))
              | U_3491 != hAPP(c_Nat_OSuc,U_3490) )
          & U_3491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_3489] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3489),U_3492))
            & U_3491 = hAPP(c_Nat_OSuc,U_3489) )
        | U_3491 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3491),hAPP(c_Nat_OSuc,U_3492))) ) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ( ! [U_3496,U_3494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3494),hAPP(c_Nat_OSuc,U_3496)))
        | ( ! [U_3490] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3490),U_3496))
              | U_3494 != hAPP(c_Nat_OSuc,U_3490) )
          & U_3494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3495,U_3493] :
        ( ? [U_3489] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3489),U_3495))
            & U_3493 = hAPP(c_Nat_OSuc,U_3489) )
        | U_3493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3493),hAPP(c_Nat_OSuc,U_3495))) ) ),
    inference(miniscope,[status(thm)],[f_880_2]) ).

fof(f_880_4,plain,
    ( ! [U_3496,U_3494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3494),hAPP(c_Nat_OSuc,U_3496)))
        | ( ! [U_3490] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3490),U_3496))
              | U_3494 != hAPP(c_Nat_OSuc,U_3490) )
          & U_3494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3495,U_3493] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK59(U_3495,U_3493)),U_3495))
          & U_3493 = hAPP(c_Nat_OSuc,sK59(U_3495,U_3493)) )
        | U_3493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3493),hAPP(c_Nat_OSuc,U_3495))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3489,sK59(U_3495,U_3493))],[f_880_3]) ).

cnf(f_880_5,plain,
    ( U_3493 = hAPP(c_Nat_OSuc,sK59(U_3495,U_3493))
    | U_3493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3493),hAPP(c_Nat_OSuc,U_3495))) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK59(U_3495,U_3493)),U_3495))
    | U_3493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3493),hAPP(c_Nat_OSuc,U_3495))) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_7,plain,
    ( U_3494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3494),hAPP(c_Nat_OSuc,U_3496))) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3490),U_3496))
    | U_3494 != hAPP(c_Nat_OSuc,U_3490)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3494),hAPP(c_Nat_OSuc,U_3496))) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

fof(f_881_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_881_2,plain,
    ! [U_3497] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3497),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_3497 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_3497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3497),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ( ! [U_3499] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3499),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_3499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3498] :
        ( U_3498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3498),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_881_2]) ).

cnf(f_881_4,plain,
    ( U_3498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3498),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_881_3]) ).

cnf(f_881_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3499),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_3499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_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_882_2,plain,
    ! [U_3502] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3502))
        | ! [U_3501] : U_3502 != hAPP(c_Nat_OSuc,U_3501) )
      & ( ? [U_3500] : U_3502 = hAPP(c_Nat_OSuc,U_3500)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3502)) ) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ( ! [U_3504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3504))
        | ! [U_3501] : U_3504 != hAPP(c_Nat_OSuc,U_3501) )
    & ! [U_3503] :
        ( ? [U_3500] : U_3503 = hAPP(c_Nat_OSuc,U_3500)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3503)) ) ),
    inference(miniscope,[status(thm)],[f_882_2]) ).

fof(f_882_4,plain,
    ( ! [U_3504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3504))
        | ! [U_3501] : U_3504 != hAPP(c_Nat_OSuc,U_3501) )
    & ! [U_3503] :
        ( U_3503 = hAPP(c_Nat_OSuc,sK60(U_3503))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3503)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3500,sK60(U_3503))],[f_882_3]) ).

cnf(f_882_5,plain,
    ( U_3503 = hAPP(c_Nat_OSuc,sK60(U_3503))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3503)) ),
    inference(clausify,[status(thm)],[f_882_4]) ).

cnf(f_882_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3504))
    | U_3504 != hAPP(c_Nat_OSuc,U_3501) ),
    inference(clausify,[status(thm)],[f_882_4]) ).

fof(f_883_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_883_2,plain,
    ! [U_3506,U_3505] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3505),U_3506) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_3506 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_3505 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_3506 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_3505 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_3506 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_3506 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3505 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3505),U_3506) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ( ! [U_3510,U_3508] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3508),U_3510) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_3510 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_3508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_3510 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_3508 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_3509,U_3507] :
        ( ( U_3509 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3507 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3507),U_3509) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_883_2]) ).

cnf(f_883_4,plain,
    ( U_3507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3507 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3507),U_3509) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_5,plain,
    ( U_3509 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3507 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3507),U_3509) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_6,plain,
    ( U_3507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3507),U_3509) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_7,plain,
    ( U_3509 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3507),U_3509) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_8,plain,
    ( U_3510 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3508 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3508),U_3510) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_9,plain,
    ( U_3510 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3508),U_3510) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_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_884_2,plain,
    ! [U_3512,U_3511] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3511),U_3512)
        | ( ( U_3512 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_3511 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_3512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_3511 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_3512 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_3512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3511 = 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_3511),U_3512) ) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ( ! [U_3516,U_3514] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3514),U_3516)
        | ( ( U_3516 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_3514 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_3516 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_3514 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_3515,U_3513] :
        ( ( U_3515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_3515 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_3513 = 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_3513),U_3515) ) ),
    inference(miniscope,[status(thm)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( U_3513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3513 = 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_3513),U_3515) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_5,plain,
    ( U_3515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3513 = 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_3513),U_3515) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_6,plain,
    ( U_3513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3515 = 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_3513),U_3515) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_7,plain,
    ( U_3515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3515 = 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_3513),U_3515) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_8,plain,
    ( U_3516 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3514 != 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_3514),U_3516) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_9,plain,
    ( U_3516 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3514 != 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_3514),U_3516) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_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_885_2,plain,
    ! [U_3518,U_3517] :
      ( ( 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_3517),U_3518)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3518))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3517)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3518))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3517))
        | ~ 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_3517),U_3518))) ) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ( ! [U_3522,U_3520] :
        ( 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_3520),U_3522)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3522))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3520)) ) )
    & ! [U_3521,U_3519] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3521))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3519))
        | ~ 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_3519),U_3521))) ) ),
    inference(miniscope,[status(thm)],[f_885_2]) ).

cnf(f_885_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3521))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3519))
    | ~ 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_3519),U_3521))) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

cnf(f_885_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3520))
    | 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_3520),U_3522))) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

cnf(f_885_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3522))
    | 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_3520),U_3522))) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_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_886_2,plain,
    ! [U_3523] : hAPP(c_Finite__Set_Ocard(U_3523),c_Orderings_Obot__class_Obot(tc_fun(U_3523,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

cnf(f_886_3,plain,
    hAPP(c_Finite__Set_Ocard(U_3523),c_Orderings_Obot__class_Obot(tc_fun(U_3523,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_886_2]) ).

fof(f_887_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_887_2,plain,
    ! [U_3525,U_3524] :
      ( hAPP(c_Finite__Set_Ocard(U_3524),U_3525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3524),U_3525)) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

cnf(f_887_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3524),U_3525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3524),U_3525)) ),
    inference(clausify,[status(thm)],[f_887_2]) ).

fof(f_888_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_888_2,plain,
    ! [U_3527,U_3526] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3526),U_3527) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_3527 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_3526 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_3527 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3526 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3526),U_3527) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ( ! [U_3531,U_3529] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3531) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_3531 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_3529 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_3530,U_3528] :
        ( ( U_3530 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_3528 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( U_3528 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_5,plain,
    ( U_3530 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3528),U_3530) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

cnf(f_888_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3529),U_3531) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3531 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_3529 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_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_889_2,plain,
    ! [U_3533,U_3532] :
      ( ( 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_3532),U_3533)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),U_3532)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),U_3532))
        | ~ 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_3532),U_3533))) ) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ( ! [U_3537,U_3535] :
        ( 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_3535),U_3537)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3537),U_3535)) )
    & ! [U_3536,U_3534] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3534))
        | ~ 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_3534),U_3536))) ) ),
    inference(miniscope,[status(thm)],[f_889_2]) ).

cnf(f_889_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3534))
    | ~ 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_3534),U_3536))) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

cnf(f_889_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_3535),U_3537)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3537),U_3535)) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_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_890_2,plain,
    ! [U_3539,U_3538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3539),U_3538)),U_3539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3538)) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

cnf(f_890_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3539),U_3538)),U_3539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3538)) ),
    inference(clausify,[status(thm)],[f_890_2]) ).

fof(f_891_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_891_2,plain,
    ! [U_3542,U_3541,U_3540] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3542),U_3540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3542),U_3541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3542))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3540),U_3541)) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

cnf(f_891_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3542),U_3540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3542),U_3541)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3542))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3540),U_3541)) ),
    inference(clausify,[status(thm)],[f_891_2]) ).

fof(f_892_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_892_2,plain,
    ! [U_3545,U_3544,U_3543] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3543),U_3544)) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

cnf(f_892_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3543),U_3545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3544),U_3545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3543),U_3544)) ),
    inference(clausify,[status(thm)],[f_892_2]) ).

fof(f_893_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_893_2,plain,
    ! [U_3548,U_3547,U_3546] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3547)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3546),U_3548))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3547)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3546),U_3548))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3547)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3547))) ) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ( ! [U_3554,U_3552,U_3550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),U_3552)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3550),U_3554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3552)) )
    & ! [U_3553,U_3551,U_3549] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3549),U_3553))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3551)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3549),U_3551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3551))) ) ),
    inference(miniscope,[status(thm)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3549),U_3551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3551))) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

cnf(f_893_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3549),U_3553))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3549),U_3551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3551))) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

cnf(f_893_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),U_3552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3550),U_3554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3552)) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_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_894_2,plain,
    ! [U_3557,U_3556,U_3555] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3555),U_3556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3555),U_3557)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3556),U_3557))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3555)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3556),U_3557))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3555)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3555),U_3556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3555),U_3557))) ) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ( ! [U_3563,U_3561,U_3559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3563)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3563))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3559)) )
    & ! [U_3562,U_3560,U_3558] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3560),U_3562))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3558)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3562))) ) ),
    inference(miniscope,[status(thm)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3558))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3562))) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

cnf(f_894_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3560),U_3562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3558),U_3562))) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

cnf(f_894_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3563)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3559)) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_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_895_2,plain,
    ! [U_3565,U_3564] :
      ( ( 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_3564),U_3565)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3565))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3564)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3565))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3564)) )
        | ~ 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_3564),U_3565))) ) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ( ! [U_3569,U_3567] :
        ( 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_3567),U_3569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3567)) )
    & ! [U_3568,U_3566] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3568))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3566)) )
        | ~ 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_3566),U_3568))) ) ),
    inference(miniscope,[status(thm)],[f_895_2]) ).

cnf(f_895_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3566))
    | ~ 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_3566),U_3568))) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

cnf(f_895_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3568))
    | ~ 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_3566),U_3568))) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

cnf(f_895_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_3567),U_3569)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3567)) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_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_896_2,plain,
    ! [U_3572,U_3571,U_3570] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3572)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3571),U_3572)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3571),U_3572))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3572))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3570)) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

cnf(f_896_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3571),U_3572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3570)) ),
    inference(clausify,[status(thm)],[f_896_2]) ).

cnf(f_896_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3571)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3570),U_3572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3571),U_3572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3570)) ),
    inference(clausify,[status(thm)],[f_896_2]) ).

fof(f_897_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_897_2,plain,
    ! [U_3575,U_3574,U_3573] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3575)
          | U_3574 != U_3575 )
        & ( U_3574 = U_3575
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3574) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3575) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3573)) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

cnf(f_897_3,plain,
    ( U_3574 = U_3575
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3574) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3575)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3573)) ),
    inference(clausify,[status(thm)],[f_897_2]) ).

cnf(f_897_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3573),U_3575)
    | U_3574 != U_3575
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3573)) ),
    inference(clausify,[status(thm)],[f_897_2]) ).

fof(f_898_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_898_2,plain,
    ! [U_3577,U_3576] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3576),U_3577)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

cnf(f_898_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3576),U_3577)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_898_2]) ).

fof(f_899_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_899_2,plain,
    ! [U_3579,U_3578] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3578),U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3578),U_3579)) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

cnf(f_899_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3578),U_3579) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3578),U_3579)) ),
    inference(clausify,[status(thm)],[f_899_2]) ).

fof(f_900_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_900_2,plain,
    ! [U_3581,U_3580] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3580),U_3581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3580),U_3581)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3580),U_3581))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3580),U_3581) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ( ! [U_3585,U_3583] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3583),U_3585) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3583),U_3585)) )
    & ! [U_3584,U_3582] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3582),U_3584))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3582),U_3584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_900_2]) ).

cnf(f_900_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3582),U_3584))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3582),U_3584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

cnf(f_900_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3583),U_3585) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3583),U_3585)) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_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_901_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_901_1]) ).

fof(f_902_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_902_2,plain,
    ! [U_3587,U_3586] :
      ( U_3586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_3587 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_3586 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3586),U_3587) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

cnf(f_902_3,plain,
    ( U_3586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3587 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_3586 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3586),U_3587) ),
    inference(clausify,[status(thm)],[f_902_2]) ).

fof(f_903_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_903_2,plain,
    ! [U_3592,U_3591,U_3590] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_3589] :
              ( hAPP(U_3592,U_3589) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_3590),U_3589),U_3591)) ) )
        & ( ! [U_3588] :
              ( hAPP(U_3592,U_3588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3588),U_3591)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591)) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_3592,U_3591,U_3590] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_3592,sK61(U_3592,U_3591,U_3590)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3590),sK61(U_3592,U_3591,U_3590)),U_3591)) ) )
        & ( ! [U_3588] :
              ( hAPP(U_3592,U_3588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3588),U_3591)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3589,sK61(U_3592,U_3591,U_3590))],[f_903_2]) ).

cnf(f_903_4,plain,
    ( hAPP(U_3592,U_3588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3588),U_3591))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591)) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

cnf(f_903_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3590),sK61(U_3592,U_3591,U_3590)),U_3591))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591)) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

cnf(f_903_6,plain,
    ( hAPP(U_3592,sK61(U_3592,U_3591,U_3590)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3590,tc_Nat_Onat),U_3592),U_3591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591)) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_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_904_2,plain,
    ! [U_3595,U_3594,U_3593] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3593),U_3594),U_3595)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),U_3595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),U_3594))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3593) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

cnf(f_904_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3593),U_3594),U_3595)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),U_3595))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3593),c_Groups_Ozero__class_Ozero(U_3593)),U_3594))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3593) ),
    inference(clausify,[status(thm)],[f_904_2]) ).

fof(f_905_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_905_2,plain,
    ! [U_3598,U_3597,U_3596] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3596),U_3597),U_3598)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),U_3598))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),U_3597))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3596) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

cnf(f_905_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3596),U_3597),U_3598)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),U_3598))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3596),c_Groups_Ozero__class_Ozero(U_3596)),U_3597))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3596) ),
    inference(clausify,[status(thm)],[f_905_2]) ).

fof(f_906_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_906_2,plain,
    ! [U_3602,U_3601,U_3600,U_3599] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3599),U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3599),U_3600),U_3602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3601),U_3602))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3599),c_Groups_Ozero__class_Ozero(U_3599)),U_3600))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3599) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

cnf(f_906_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3599),U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3599),U_3600),U_3602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3599),U_3601),U_3602))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3599),c_Groups_Ozero__class_Ozero(U_3599)),U_3600))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3599) ),
    inference(clausify,[status(thm)],[f_906_2]) ).

fof(f_907_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_907_2,plain,
    ! [U_3606,U_3605,U_3604,U_3603] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3603),U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3603),U_3604),U_3606)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3603),U_3605),U_3606))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3603),c_Groups_Ozero__class_Ozero(U_3603)),U_3604))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3603) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

cnf(f_907_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3603),U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3603),U_3604),U_3606)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3603),U_3605),U_3606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3603),c_Groups_Ozero__class_Ozero(U_3603)),U_3604))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3603) ),
    inference(clausify,[status(thm)],[f_907_2]) ).

fof(f_908_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_908_2,plain,
    ! [U_3609,U_3608,U_3607] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3607),U_3608),U_3609)),c_Groups_Ozero__class_Ozero(U_3607)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3607),U_3609),c_Groups_Ozero__class_Ozero(U_3607)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3607),U_3608),c_Groups_Ozero__class_Ozero(U_3607)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3607) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

cnf(f_908_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3607),U_3608),U_3609)),c_Groups_Ozero__class_Ozero(U_3607)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3607),U_3609),c_Groups_Ozero__class_Ozero(U_3607)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3607),U_3608),c_Groups_Ozero__class_Ozero(U_3607)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3607) ),
    inference(clausify,[status(thm)],[f_908_2]) ).

fof(f_909_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_909_2,plain,
    ! [U_3612,U_3611,U_3610] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3610),U_3611),U_3612)),c_Groups_Ozero__class_Ozero(U_3610)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3610),U_3612),c_Groups_Ozero__class_Ozero(U_3610)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3610),U_3611),c_Groups_Ozero__class_Ozero(U_3610)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3610) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

cnf(f_909_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3610),U_3611),U_3612)),c_Groups_Ozero__class_Ozero(U_3610)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3610),U_3612),c_Groups_Ozero__class_Ozero(U_3610)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3610),U_3611),c_Groups_Ozero__class_Ozero(U_3610)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3610) ),
    inference(clausify,[status(thm)],[f_909_2]) ).

fof(f_910_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_910_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_Otimes__class_Otimes(U_3613),U_3614),U_3615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3616)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3615),U_3616)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3615),U_3616))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3616))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3613),c_Groups_Ozero__class_Ozero(U_3613)),U_3614))
      | ~ class_Rings_Olinordered__ring__strict(U_3613) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

cnf(f_910_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3615),U_3616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3613),c_Groups_Ozero__class_Ozero(U_3613)),U_3614))
    | ~ class_Rings_Olinordered__ring__strict(U_3613) ),
    inference(clausify,[status(thm)],[f_910_2]) ).

cnf(f_910_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3613),U_3614),U_3616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3615),U_3616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3613),c_Groups_Ozero__class_Ozero(U_3613)),U_3614))
    | ~ class_Rings_Olinordered__ring__strict(U_3613) ),
    inference(clausify,[status(thm)],[f_910_2]) ).

fof(f_911_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_911_2,plain,
    ! [U_3620,U_3619,U_3618,U_3617] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3620)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3619)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3619))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3620))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3617),U_3618),c_Groups_Ozero__class_Ozero(U_3617)))
      | ~ class_Rings_Olinordered__ring__strict(U_3617) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

cnf(f_911_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3619))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3617),U_3618),c_Groups_Ozero__class_Ozero(U_3617)))
    | ~ class_Rings_Olinordered__ring__strict(U_3617) ),
    inference(clausify,[status(thm)],[f_911_2]) ).

cnf(f_911_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3617),U_3618),U_3620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3619))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3617),U_3618),c_Groups_Ozero__class_Ozero(U_3617)))
    | ~ class_Rings_Olinordered__ring__strict(U_3617) ),
    inference(clausify,[status(thm)],[f_911_2]) ).

fof(f_912_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_912_2,plain,
    ! [U_3625,U_3624,U_3623,U_3622,U_3621] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3621),U_3622),U_3624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3621),U_3623),U_3625)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3621),c_Groups_Ozero__class_Ozero(U_3621)),U_3624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),c_Groups_Ozero__class_Ozero(U_3621)),U_3623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),U_3624),U_3625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),U_3622),U_3623))
      | ~ class_Rings_Olinordered__semiring__strict(U_3621) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

cnf(f_912_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3621),U_3622),U_3624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3621),U_3623),U_3625)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3621),c_Groups_Ozero__class_Ozero(U_3621)),U_3624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),c_Groups_Ozero__class_Ozero(U_3621)),U_3623))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),U_3624),U_3625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3621),U_3622),U_3623))
    | ~ class_Rings_Olinordered__semiring__strict(U_3621) ),
    inference(clausify,[status(thm)],[f_912_2]) ).

fof(f_913_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_913_2,plain,
    ! [U_3630,U_3629,U_3628,U_3627,U_3626] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3626),U_3627),U_3629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3626),U_3628),U_3630)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3627))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),U_3629),U_3630))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),U_3627),U_3628))
      | ~ class_Rings_Olinordered__semiring__strict(U_3626) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

cnf(f_913_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3626),U_3627),U_3629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3626),U_3628),U_3630)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3627))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),U_3629),U_3630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3626),U_3627),U_3628))
    | ~ class_Rings_Olinordered__semiring__strict(U_3626) ),
    inference(clausify,[status(thm)],[f_913_2]) ).

fof(f_914_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_914_2,plain,
    ! [U_3635,U_3634,U_3633,U_3632,U_3631] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3631),U_3632),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3631),U_3633),U_3635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),c_Groups_Ozero__class_Ozero(U_3631)),U_3634))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3631),c_Groups_Ozero__class_Ozero(U_3631)),U_3632))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3631),U_3634),U_3635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),U_3632),U_3633))
      | ~ class_Rings_Olinordered__semiring__strict(U_3631) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

cnf(f_914_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3631),U_3632),U_3634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3631),U_3633),U_3635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),c_Groups_Ozero__class_Ozero(U_3631)),U_3634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3631),c_Groups_Ozero__class_Ozero(U_3631)),U_3632))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3631),U_3634),U_3635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3631),U_3632),U_3633))
    | ~ class_Rings_Olinordered__semiring__strict(U_3631) ),
    inference(clausify,[status(thm)],[f_914_2]) ).

fof(f_915_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_915_2,plain,
    ! [U_3640,U_3639,U_3638,U_3637,U_3636] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3636),U_3637),U_3639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3636),U_3638),U_3640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3636),c_Groups_Ozero__class_Ozero(U_3636)),U_3639))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),c_Groups_Ozero__class_Ozero(U_3636)),U_3637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),U_3639),U_3640))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3636),U_3637),U_3638))
      | ~ class_Rings_Olinordered__semiring__strict(U_3636) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

cnf(f_915_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3636),U_3637),U_3639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3636),U_3638),U_3640)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3636),c_Groups_Ozero__class_Ozero(U_3636)),U_3639))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),c_Groups_Ozero__class_Ozero(U_3636)),U_3637))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3636),U_3639),U_3640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3636),U_3637),U_3638))
    | ~ class_Rings_Olinordered__semiring__strict(U_3636) ),
    inference(clausify,[status(thm)],[f_915_2]) ).

fof(f_916_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_916_2,plain,
    ! [U_3644,U_3643,U_3642,U_3641] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3641),U_3642),U_3644))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3641),c_Groups_Ozero__class_Ozero(U_3641)),U_3643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3641),U_3642),U_3643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3641),U_3644),U_3643)))
      | ~ class_Rings_Olinordered__semiring(U_3641) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

cnf(f_916_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3641),U_3642),U_3644))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3641),c_Groups_Ozero__class_Ozero(U_3641)),U_3643))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3641),U_3642),U_3643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3641),U_3644),U_3643)))
    | ~ class_Rings_Olinordered__semiring(U_3641) ),
    inference(clausify,[status(thm)],[f_916_2]) ).

fof(f_917_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_917_2,plain,
    ! [U_3648,U_3647,U_3646,U_3645] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3645),U_3646),U_3648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3645),c_Groups_Ozero__class_Ozero(U_3645)),U_3647))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3645),U_3646),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3645),U_3648),U_3647)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3645) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

cnf(f_917_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3645),U_3646),U_3648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3645),c_Groups_Ozero__class_Ozero(U_3645)),U_3647))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3645),U_3646),U_3647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3645),U_3648),U_3647)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3645) ),
    inference(clausify,[status(thm)],[f_917_2]) ).

fof(f_918_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_918_2,plain,
    ! [U_3652,U_3651,U_3650,U_3649] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3649),U_3651),U_3652))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3649),c_Groups_Ozero__class_Ozero(U_3649)),U_3650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3650),U_3651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3650),U_3652)))
      | ~ class_Rings_Olinordered__semiring(U_3649) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

cnf(f_918_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3649),U_3651),U_3652))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3649),c_Groups_Ozero__class_Ozero(U_3649)),U_3650))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3650),U_3651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3650),U_3652)))
    | ~ class_Rings_Olinordered__semiring(U_3649) ),
    inference(clausify,[status(thm)],[f_918_2]) ).

fof(f_919_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_919_2,plain,
    ! [U_3656,U_3655,U_3654,U_3653] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3653),U_3655),U_3656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3653),c_Groups_Ozero__class_Ozero(U_3653)),U_3654))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3653),U_3654),U_3655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3653),U_3654),U_3656)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3653) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

cnf(f_919_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3653),U_3655),U_3656))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3653),c_Groups_Ozero__class_Ozero(U_3653)),U_3654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3653),U_3654),U_3655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3653),U_3654),U_3656)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3653) ),
    inference(clausify,[status(thm)],[f_919_2]) ).

fof(f_920_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_920_2,plain,
    ! [U_3660,U_3659,U_3658,U_3657] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3657),U_3658),U_3660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3657),c_Groups_Ozero__class_Ozero(U_3657)),U_3659))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3657),U_3658),U_3659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3657),U_3660),U_3659)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3657) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

cnf(f_920_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3657),U_3658),U_3660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3657),c_Groups_Ozero__class_Ozero(U_3657)),U_3659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3657),U_3658),U_3659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3657),U_3660),U_3659)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3657) ),
    inference(clausify,[status(thm)],[f_920_2]) ).

fof(f_921_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_921_2,plain,
    ! [U_3664,U_3663,U_3662,U_3661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3661),U_3663),U_3664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3661),c_Groups_Ozero__class_Ozero(U_3661)),U_3662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3661),U_3662),U_3663)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3661),U_3662),U_3664)))
      | ~ class_Rings_Olinordered__semiring__strict(U_3661) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

cnf(f_921_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3661),U_3663),U_3664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3661),c_Groups_Ozero__class_Ozero(U_3661)),U_3662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3661),U_3662),U_3663)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3661),U_3662),U_3664)))
    | ~ class_Rings_Olinordered__semiring__strict(U_3661) ),
    inference(clausify,[status(thm)],[f_921_2]) ).

fof(f_922_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_922_2,plain,
    ! [U_3667,U_3666,U_3665] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3666),U_3666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3667),U_3667))),c_Groups_Ozero__class_Ozero(U_3665)))
          | U_3667 != c_Groups_Ozero__class_Ozero(U_3665)
          | U_3666 != c_Groups_Ozero__class_Ozero(U_3665) )
        & ( ( U_3667 = c_Groups_Ozero__class_Ozero(U_3665)
            & U_3666 = c_Groups_Ozero__class_Ozero(U_3665) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3666),U_3666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3667),U_3667))),c_Groups_Ozero__class_Ozero(U_3665))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3665) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

cnf(f_922_3,plain,
    ( U_3666 = c_Groups_Ozero__class_Ozero(U_3665)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3666),U_3666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3667),U_3667))),c_Groups_Ozero__class_Ozero(U_3665)))
    | ~ class_Rings_Olinordered__ring__strict(U_3665) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

cnf(f_922_4,plain,
    ( U_3667 = c_Groups_Ozero__class_Ozero(U_3665)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3666),U_3666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3667),U_3667))),c_Groups_Ozero__class_Ozero(U_3665)))
    | ~ class_Rings_Olinordered__ring__strict(U_3665) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

cnf(f_922_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3666),U_3666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3665),U_3667),U_3667))),c_Groups_Ozero__class_Ozero(U_3665)))
    | U_3667 != c_Groups_Ozero__class_Ozero(U_3665)
    | U_3666 != c_Groups_Ozero__class_Ozero(U_3665)
    | ~ class_Rings_Olinordered__ring__strict(U_3665) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

fof(f_923_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_923_2,plain,
    ! [U_3670,U_3669,U_3668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3668),c_Groups_Ozero__class_Ozero(U_3668)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3668),U_3669),U_3669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3668),U_3670),U_3670))))
      | ~ class_Rings_Olinordered__ring(U_3668) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

cnf(f_923_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3668),c_Groups_Ozero__class_Ozero(U_3668)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3668),U_3669),U_3669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3668),U_3670),U_3670))))
    | ~ class_Rings_Olinordered__ring(U_3668) ),
    inference(clausify,[status(thm)],[f_923_2]) ).

fof(f_924_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_924_2,plain,
    ! [U_3673,U_3672,U_3671] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3671),U_3672),U_3672)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3671),U_3673),U_3673))),c_Groups_Ozero__class_Ozero(U_3671)))
      | ~ class_Rings_Olinordered__ring(U_3671) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

cnf(f_924_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3671),U_3672),U_3672)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3671),U_3673),U_3673))),c_Groups_Ozero__class_Ozero(U_3671)))
    | ~ class_Rings_Olinordered__ring(U_3671) ),
    inference(clausify,[status(thm)],[f_924_2]) ).

fof(f_925_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_925_2,plain,
    ! [U_3676,U_3675,U_3674] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3674),c_Groups_Ozero__class_Ozero(U_3674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3675),U_3675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3676),U_3676))))
          | ( U_3676 = c_Groups_Ozero__class_Ozero(U_3674)
            & U_3675 = c_Groups_Ozero__class_Ozero(U_3674) ) )
        & ( U_3676 != c_Groups_Ozero__class_Ozero(U_3674)
          | U_3675 != c_Groups_Ozero__class_Ozero(U_3674)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3674),c_Groups_Ozero__class_Ozero(U_3674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3675),U_3675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3676),U_3676)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_3674) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

cnf(f_925_3,plain,
    ( U_3676 != c_Groups_Ozero__class_Ozero(U_3674)
    | U_3675 != c_Groups_Ozero__class_Ozero(U_3674)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3674),c_Groups_Ozero__class_Ozero(U_3674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3675),U_3675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3676),U_3676))))
    | ~ class_Rings_Olinordered__ring__strict(U_3674) ),
    inference(clausify,[status(thm)],[f_925_2]) ).

cnf(f_925_4,plain,
    ( U_3675 = c_Groups_Ozero__class_Ozero(U_3674)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3674),c_Groups_Ozero__class_Ozero(U_3674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3675),U_3675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3676),U_3676))))
    | ~ class_Rings_Olinordered__ring__strict(U_3674) ),
    inference(clausify,[status(thm)],[f_925_2]) ).

cnf(f_925_5,plain,
    ( U_3676 = c_Groups_Ozero__class_Ozero(U_3674)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3674),c_Groups_Ozero__class_Ozero(U_3674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3675),U_3675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3674),U_3676),U_3676))))
    | ~ class_Rings_Olinordered__ring__strict(U_3674) ),
    inference(clausify,[status(thm)],[f_925_2]) ).

fof(f_926_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_926_2,plain,
    ! [U_3679,U_3678,U_3677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3678)),U_3678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),U_3679),c_Groups_Oone__class_Oone(U_3677)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),c_Groups_Ozero__class_Ozero(U_3677)),U_3679))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),c_Groups_Ozero__class_Ozero(U_3677)),U_3678))
      | ~ class_Rings_Olinordered__idom(U_3677) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

cnf(f_926_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3678)),U_3678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),U_3679),c_Groups_Oone__class_Oone(U_3677)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),c_Groups_Ozero__class_Ozero(U_3677)),U_3679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3677),c_Groups_Ozero__class_Ozero(U_3677)),U_3678))
    | ~ class_Rings_Olinordered__idom(U_3677) ),
    inference(clausify,[status(thm)],[f_926_2]) ).

fof(f_927_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_927_2,plain,
    ! [U_3682,U_3681,U_3680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),U_3681),U_3682)),U_3681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),U_3682),c_Groups_Oone__class_Oone(U_3680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),c_Groups_Ozero__class_Ozero(U_3680)),U_3682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),c_Groups_Ozero__class_Ozero(U_3680)),U_3681))
      | ~ class_Rings_Olinordered__idom(U_3680) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

cnf(f_927_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),U_3681),U_3682)),U_3681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),U_3682),c_Groups_Oone__class_Oone(U_3680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),c_Groups_Ozero__class_Ozero(U_3680)),U_3682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3680),c_Groups_Ozero__class_Ozero(U_3680)),U_3681))
    | ~ class_Rings_Olinordered__idom(U_3680) ),
    inference(clausify,[status(thm)],[f_927_2]) ).

fof(f_928_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_928_2,plain,
    ! [U_3683] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3683),c_Groups_Ozero__class_Ozero(U_3683)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),c_Groups_Oone__class_Oone(U_3683)),c_Groups_Oone__class_Oone(U_3683))))
      | ~ class_Rings_Olinordered__semidom(U_3683) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

cnf(f_928_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3683),c_Groups_Ozero__class_Ozero(U_3683)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3683),c_Groups_Oone__class_Oone(U_3683)),c_Groups_Oone__class_Oone(U_3683))))
    | ~ class_Rings_Olinordered__semidom(U_3683) ),
    inference(clausify,[status(thm)],[f_928_2]) ).

fof(f_929_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_929_2,plain,
    ! [U_3685,U_3684] :
      ( ( hAPP(c_Finite__Set_Ocard(U_3684),U_3685) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3684),U_3685))
          & U_3685 != c_Orderings_Obot__class_Obot(tc_fun(U_3684,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3684),U_3685))
        | U_3685 = c_Orderings_Obot__class_Obot(tc_fun(U_3684,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_3684),U_3685) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ( ! [U_3689,U_3687] :
        ( hAPP(c_Finite__Set_Ocard(U_3687),U_3689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3687),U_3689))
          & U_3689 != c_Orderings_Obot__class_Obot(tc_fun(U_3687,tc_HOL_Obool)) ) )
    & ! [U_3688,U_3686] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3688))
        | U_3688 = c_Orderings_Obot__class_Obot(tc_fun(U_3686,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_3686),U_3688) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_929_2]) ).

cnf(f_929_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3688))
    | U_3688 = c_Orderings_Obot__class_Obot(tc_fun(U_3686,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3686),U_3688) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_5,plain,
    ( U_3689 != c_Orderings_Obot__class_Obot(tc_fun(U_3687,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3687),U_3689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

cnf(f_929_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3687),U_3689))
    | hAPP(c_Finite__Set_Ocard(U_3687),U_3689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_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_930_2,plain,
    ! [U_3691,U_3690] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3691))
      | ~ 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_3690),U_3691))) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

cnf(f_930_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3691))
    | ~ 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_3690),U_3691))) ),
    inference(clausify,[status(thm)],[f_930_2]) ).

fof(f_931_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_931_2,plain,
    ! [U_3693,U_3692] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3692),hAPP(c_Nat_OSuc,U_3693))),U_3692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3692)) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

cnf(f_931_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3692),hAPP(c_Nat_OSuc,U_3693))),U_3692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3692)) ),
    inference(clausify,[status(thm)],[f_931_2]) ).

fof(f_932_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_932_2,plain,
    ! [U_3694] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3694
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3694)) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

cnf(f_932_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3694
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3694)) ),
    inference(clausify,[status(thm)],[f_932_2]) ).

fof(f_933_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_933_2,plain,
    ! [U_3696,U_3695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3696),U_3695)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3696))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3695)) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

cnf(f_933_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3696),U_3695)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3695)) ),
    inference(clausify,[status(thm)],[f_933_2]) ).

fof(f_934_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_934_2,plain,
    ! [U_3698,U_3697] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3697),U_3698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3697)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

cnf(f_934_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3697),U_3698)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3697)) ),
    inference(clausify,[status(thm)],[f_934_2]) ).

fof(f_935_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_935_2,plain,
    ! [U_3700,U_3699] :
      ( 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_3700),U_3699)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3699)) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

cnf(f_935_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_3700),U_3699)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3700))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3699)) ),
    inference(clausify,[status(thm)],[f_935_2]) ).

fof(f_936_1,plain,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_Pa_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_Pa_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_936_2,plain,
    ! [U_3705,U_3704,U_3703] :
      ( ( hBOOL(hAPP(U_3703,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3704),U_3705)))
        | ? [U_3702] :
            ( ~ hBOOL(hAPP(U_3703,U_3702))
            & U_3704 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),U_3702) )
        | ( ~ hBOOL(hAPP(U_3703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3704),U_3705)) ) )
      & ( ( ! [U_3701] :
              ( hBOOL(hAPP(U_3703,U_3701))
              | U_3704 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3705),U_3701) )
          & ( hBOOL(hAPP(U_3703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3704),U_3705)) ) )
        | ~ hBOOL(hAPP(U_3703,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3704),U_3705))) ) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ( ! [U_3711,U_3709,U_3707] :
        ( hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711)))
        | ? [U_3702] :
            ( ~ hBOOL(hAPP(U_3707,U_3702))
            & U_3709 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),U_3702) )
        | ( ~ hBOOL(hAPP(U_3707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3709),U_3711)) ) )
    & ! [U_3710,U_3708,U_3706] :
        ( ( ! [U_3701] :
              ( hBOOL(hAPP(U_3706,U_3701))
              | U_3708 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3701) )
          & ( hBOOL(hAPP(U_3706,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3708),U_3710)) ) )
        | ~ hBOOL(hAPP(U_3706,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3710))) ) ),
    inference(miniscope,[status(thm)],[f_936_2]) ).

fof(f_936_4,plain,
    ( ! [U_3711,U_3709,U_3707] :
        ( hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711)))
        | ( ~ hBOOL(hAPP(U_3707,sK62(U_3711,U_3709,U_3707)))
          & U_3709 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),sK62(U_3711,U_3709,U_3707)) )
        | ( ~ hBOOL(hAPP(U_3707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3709),U_3711)) ) )
    & ! [U_3710,U_3708,U_3706] :
        ( ( ! [U_3701] :
              ( hBOOL(hAPP(U_3706,U_3701))
              | U_3708 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3701) )
          & ( hBOOL(hAPP(U_3706,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3708),U_3710)) ) )
        | ~ hBOOL(hAPP(U_3706,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3710))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3702,sK62(U_3711,U_3709,U_3707))],[f_936_3]) ).

cnf(f_936_5,plain,
    ( hBOOL(hAPP(U_3706,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3708),U_3710))
    | ~ hBOOL(hAPP(U_3706,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3710))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_6,plain,
    ( hBOOL(hAPP(U_3706,U_3701))
    | U_3708 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3710),U_3701)
    | ~ hBOOL(hAPP(U_3706,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3710))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_7,plain,
    ( U_3709 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),sK62(U_3711,U_3709,U_3707))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3709),U_3711))
    | hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_8,plain,
    ( ~ hBOOL(hAPP(U_3707,sK62(U_3711,U_3709,U_3707)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3709),U_3711))
    | hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_9,plain,
    ( U_3709 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),sK62(U_3711,U_3709,U_3707))
    | ~ hBOOL(hAPP(U_3707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

cnf(f_936_10,plain,
    ( ~ hBOOL(hAPP(U_3707,sK62(U_3711,U_3709,U_3707)))
    | ~ hBOOL(hAPP(U_3707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_3707,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3709),U_3711))) ),
    inference(clausify,[status(thm)],[f_936_4]) ).

fof(f_937_1,plain,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_Pa_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_Pa_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_937_2,plain,
    ! [U_3716,U_3715,U_3714] :
      ( ( hBOOL(hAPP(U_3714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3715),U_3716)))
        | ? [U_3713] :
            ( ~ hBOOL(hAPP(U_3714,U_3713))
            & U_3715 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3716),U_3713) )
        | ( ~ hBOOL(hAPP(U_3714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3715),U_3716)) ) )
      & ( ( ! [U_3712] :
              ( hBOOL(hAPP(U_3714,U_3712))
              | U_3715 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3716),U_3712) )
          & ( hBOOL(hAPP(U_3714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3715),U_3716)) ) )
        | ~ hBOOL(hAPP(U_3714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3715),U_3716))) ) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ( ! [U_3722,U_3720,U_3718] :
        ( hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722)))
        | ? [U_3713] :
            ( ~ hBOOL(hAPP(U_3718,U_3713))
            & U_3720 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),U_3713) )
        | ( ~ hBOOL(hAPP(U_3718,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3720),U_3722)) ) )
    & ! [U_3721,U_3719,U_3717] :
        ( ( ! [U_3712] :
              ( hBOOL(hAPP(U_3717,U_3712))
              | U_3719 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3721),U_3712) )
          & ( hBOOL(hAPP(U_3717,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3719),U_3721)) ) )
        | ~ hBOOL(hAPP(U_3717,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3719),U_3721))) ) ),
    inference(miniscope,[status(thm)],[f_937_2]) ).

fof(f_937_4,plain,
    ( ! [U_3722,U_3720,U_3718] :
        ( hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722)))
        | ( ~ hBOOL(hAPP(U_3718,sK63(U_3722,U_3720,U_3718)))
          & U_3720 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),sK63(U_3722,U_3720,U_3718)) )
        | ( ~ hBOOL(hAPP(U_3718,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3720),U_3722)) ) )
    & ! [U_3721,U_3719,U_3717] :
        ( ( ! [U_3712] :
              ( hBOOL(hAPP(U_3717,U_3712))
              | U_3719 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3721),U_3712) )
          & ( hBOOL(hAPP(U_3717,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3719),U_3721)) ) )
        | ~ hBOOL(hAPP(U_3717,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3719),U_3721))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3713,sK63(U_3722,U_3720,U_3718))],[f_937_3]) ).

cnf(f_937_5,plain,
    ( hBOOL(hAPP(U_3717,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3719),U_3721))
    | ~ hBOOL(hAPP(U_3717,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3719),U_3721))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_6,plain,
    ( hBOOL(hAPP(U_3717,U_3712))
    | U_3719 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3721),U_3712)
    | ~ hBOOL(hAPP(U_3717,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3719),U_3721))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_7,plain,
    ( U_3720 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),sK63(U_3722,U_3720,U_3718))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3720),U_3722))
    | hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_8,plain,
    ( ~ hBOOL(hAPP(U_3718,sK63(U_3722,U_3720,U_3718)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3720),U_3722))
    | hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_9,plain,
    ( U_3720 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3722),sK63(U_3722,U_3720,U_3718))
    | ~ hBOOL(hAPP(U_3718,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

cnf(f_937_10,plain,
    ( ~ hBOOL(hAPP(U_3718,sK63(U_3722,U_3720,U_3718)))
    | ~ hBOOL(hAPP(U_3718,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_3718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3722))) ),
    inference(clausify,[status(thm)],[f_937_4]) ).

fof(f_938_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_938_2,plain,
    ! [U_3724,U_3723] :
      ( ( 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_3723),U_3724)))
        | ~ 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_3724))
        | ~ 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_3723)) )
      & ( ( 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_3724))
          & 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_3723)) )
        | ~ 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_3723),U_3724))) ) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ( ! [U_3728,U_3726] :
        ( 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_3726),U_3728)))
        | ~ 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_3728))
        | ~ 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_3726)) )
    & ! [U_3727,U_3725] :
        ( ( 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_3727))
          & 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_3725)) )
        | ~ 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_3725),U_3727))) ) ),
    inference(miniscope,[status(thm)],[f_938_2]) ).

cnf(f_938_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_3725))
    | ~ 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_3725),U_3727))) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

cnf(f_938_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_3727))
    | ~ 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_3725),U_3727))) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

cnf(f_938_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_3726),U_3728)))
    | ~ 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_3728))
    | ~ 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_3726)) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_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_939_2,plain,
    ! [U_3731,U_3730,U_3729] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3731),U_3730)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3731))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3730)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3731))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3731),U_3730))) ) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ( ! [U_3737,U_3735,U_3733] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3733),U_3735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3737),U_3735)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3737))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3735)) ) )
    & ! [U_3736,U_3734,U_3732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3732),U_3736))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3732),U_3734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3736),U_3734))) ) ),
    inference(miniscope,[status(thm)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3732),U_3736))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3734))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3732),U_3734)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3736),U_3734))) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

cnf(f_939_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3735))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3733),U_3735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3737),U_3735))) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

cnf(f_939_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3737))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3733),U_3735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3737),U_3735))) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_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_940_2,plain,
    ! [U_3740,U_3739,U_3738] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3739),U_3740))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3738)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3739),U_3740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3738))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740))) ) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ( ! [U_3746,U_3744,U_3742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3746)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3744),U_3746))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3742)) ) )
    & ! [U_3745,U_3743,U_3741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3743),U_3745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3741))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3743)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3745))) ) ),
    inference(miniscope,[status(thm)],[f_940_2]) ).

cnf(f_940_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3743),U_3745))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3743)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3741),U_3745))) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3742))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3746))) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3744),U_3746))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3742),U_3746))) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_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_941_2,plain,
    ! [U_3749,U_3748,U_3747] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3749)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3748),U_3749)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3748),U_3749))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3749))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3747)) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

cnf(f_941_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3748),U_3749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3749)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3747)) ),
    inference(clausify,[status(thm)],[f_941_2]) ).

cnf(f_941_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_3747),U_3748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3749)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3748),U_3749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3747)) ),
    inference(clausify,[status(thm)],[f_941_2]) ).

fof(f_942_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_942_2,plain,
    ! [U_3756,U_3755,U_3754] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_3753] :
              ( ? [U_3752] :
                  ( hAPP(U_3756,U_3752) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3753 != U_3752
                  & hBOOL(hAPP(hAPP(c_member(U_3754),U_3752),U_3755)) )
              | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755)) ) )
        & ( ? [U_3751] :
              ( ! [U_3750] :
                  ( hAPP(U_3756,U_3750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_3751 = U_3750
                  | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3750),U_3755)) )
              & hAPP(U_3756,U_3751) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_3754),U_3751),U_3755)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_3756,U_3755,U_3754] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_3753] :
              ( ? [U_3752] :
                  ( hAPP(U_3756,U_3752) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3753 != U_3752
                  & hBOOL(hAPP(hAPP(c_member(U_3754),U_3752),U_3755)) )
              | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755)) ) )
        & ( ( ! [U_3750] :
                ( hAPP(U_3756,U_3750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK64(U_3756,U_3755,U_3754) = U_3750
                | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3750),U_3755)) )
            & hAPP(U_3756,sK64(U_3756,U_3755,U_3754)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_3754),sK64(U_3756,U_3755,U_3754)),U_3755)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3751,sK64(U_3756,U_3755,U_3754))],[f_942_2]) ).

fof(f_942_4,plain,
    ! [U_3756,U_3755,U_3754] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_3753] :
              ( ( hAPP(U_3756,sK65(U_3756,U_3755,U_3754,U_3753)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_3753 != sK65(U_3756,U_3755,U_3754,U_3753)
                & hBOOL(hAPP(hAPP(c_member(U_3754),sK65(U_3756,U_3755,U_3754,U_3753)),U_3755)) )
              | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755)) ) )
        & ( ( ! [U_3750] :
                ( hAPP(U_3756,U_3750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK64(U_3756,U_3755,U_3754) = U_3750
                | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3750),U_3755)) )
            & hAPP(U_3756,sK64(U_3756,U_3755,U_3754)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_3754),sK64(U_3756,U_3755,U_3754)),U_3755)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3752,sK65(U_3756,U_3755,U_3754,U_3753))],[f_942_3]) ).

cnf(f_942_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3754),sK64(U_3756,U_3755,U_3754)),U_3755))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_6,plain,
    ( hAPP(U_3756,sK64(U_3756,U_3755,U_3754)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_7,plain,
    ( hAPP(U_3756,U_3750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK64(U_3756,U_3755,U_3754) = U_3750
    | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3750),U_3755))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3754),sK65(U_3756,U_3755,U_3754,U_3753)),U_3755))
    | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_9,plain,
    ( U_3753 != sK65(U_3756,U_3755,U_3754,U_3753)
    | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_10,plain,
    ( hAPP(U_3756,sK65(U_3756,U_3755,U_3754,U_3753)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_3756,U_3753) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3754),U_3753),U_3755))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3754,tc_Nat_Onat),U_3756),U_3755) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

fof(f_943_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_943_2,plain,
    ! [U_3763,U_3762,U_3761] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3760] :
              ( ? [U_3759] :
                  ( hAPP(U_3763,U_3759) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3760 != U_3759
                  & hBOOL(hAPP(hAPP(c_member(U_3761),U_3759),U_3762)) )
              | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762)) ) )
        & ( ? [U_3758] :
              ( ! [U_3757] :
                  ( hAPP(U_3763,U_3757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_3758 = U_3757
                  | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3757),U_3762)) )
              & hAPP(U_3763,U_3758) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_3761),U_3758),U_3762)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_3763,U_3762,U_3761] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3760] :
              ( ? [U_3759] :
                  ( hAPP(U_3763,U_3759) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_3760 != U_3759
                  & hBOOL(hAPP(hAPP(c_member(U_3761),U_3759),U_3762)) )
              | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762)) ) )
        & ( ( ! [U_3757] :
                ( hAPP(U_3763,U_3757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK66(U_3763,U_3762,U_3761) = U_3757
                | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3757),U_3762)) )
            & hAPP(U_3763,sK66(U_3763,U_3762,U_3761)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3761),sK66(U_3763,U_3762,U_3761)),U_3762)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3758,sK66(U_3763,U_3762,U_3761))],[f_943_2]) ).

fof(f_943_4,plain,
    ! [U_3763,U_3762,U_3761] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_3760] :
              ( ( hAPP(U_3763,sK67(U_3763,U_3762,U_3761,U_3760)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_3760 != sK67(U_3763,U_3762,U_3761,U_3760)
                & hBOOL(hAPP(hAPP(c_member(U_3761),sK67(U_3763,U_3762,U_3761,U_3760)),U_3762)) )
              | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762)) ) )
        & ( ( ! [U_3757] :
                ( hAPP(U_3763,U_3757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK66(U_3763,U_3762,U_3761) = U_3757
                | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3757),U_3762)) )
            & hAPP(U_3763,sK66(U_3763,U_3762,U_3761)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_3761),sK66(U_3763,U_3762,U_3761)),U_3762)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3759,sK67(U_3763,U_3762,U_3761,U_3760))],[f_943_3]) ).

cnf(f_943_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3761),sK66(U_3763,U_3762,U_3761)),U_3762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_6,plain,
    ( hAPP(U_3763,sK66(U_3763,U_3762,U_3761)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_7,plain,
    ( hAPP(U_3763,U_3757) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK66(U_3763,U_3762,U_3761) = U_3757
    | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3757),U_3762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3761),sK67(U_3763,U_3762,U_3761,U_3760)),U_3762))
    | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_9,plain,
    ( U_3760 != sK67(U_3763,U_3762,U_3761,U_3760)
    | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_10,plain,
    ( hAPP(U_3763,sK67(U_3763,U_3762,U_3761,U_3760)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_3763,U_3760) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3761),U_3760),U_3762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3761,tc_Nat_Onat),U_3763),U_3762) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

fof(f_944_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_944_2,plain,
    ! [U_3768,U_3767,U_3766] :
      ( ( ( 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_3766,tc_Nat_Onat),U_3768),U_3767)))
          | ? [U_3765] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,U_3765)))
              & hBOOL(hAPP(hAPP(c_member(U_3766),U_3765),U_3767)) ) )
        & ( ! [U_3764] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,U_3764)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3766),U_3764),U_3767)) )
          | ~ 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_3766,tc_Nat_Onat),U_3768),U_3767))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),U_3767)) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_3768,U_3767,U_3766] :
      ( ( ( 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_3766,tc_Nat_Onat),U_3768),U_3767)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,sK68(U_3768,U_3767,U_3766))))
            & hBOOL(hAPP(hAPP(c_member(U_3766),sK68(U_3768,U_3767,U_3766)),U_3767)) ) )
        & ( ! [U_3764] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,U_3764)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3766),U_3764),U_3767)) )
          | ~ 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_3766,tc_Nat_Onat),U_3768),U_3767))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),U_3767)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3765,sK68(U_3768,U_3767,U_3766))],[f_944_2]) ).

cnf(f_944_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,U_3764)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3766),U_3764),U_3767))
    | ~ 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_3766,tc_Nat_Onat),U_3768),U_3767)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),U_3767)) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

cnf(f_944_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3766),sK68(U_3768,U_3767,U_3766)),U_3767))
    | 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_3766,tc_Nat_Onat),U_3768),U_3767)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),U_3767)) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

cnf(f_944_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3768,sK68(U_3768,U_3767,U_3766))))
    | 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_3766,tc_Nat_Onat),U_3768),U_3767)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),U_3767)) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_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_945_2,plain,
    ! [U_3774,U_3773,U_3772,U_3771,U_3770,U_3769] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3769),U_3773),U_3770)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3769),U_3774),U_3772))),U_3771))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3769),U_3773),U_3774) != c_Groups_Oone__class_Oone(U_3769)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),c_Groups_Ozero__class_Ozero(U_3769)),U_3774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),c_Groups_Ozero__class_Ozero(U_3769)),U_3773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),U_3772),U_3771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),U_3770),U_3771))
      | ~ class_Rings_Olinordered__semiring__1(U_3769) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

cnf(f_945_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3769),U_3773),U_3770)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3769),U_3774),U_3772))),U_3771))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3769),U_3773),U_3774) != c_Groups_Oone__class_Oone(U_3769)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),c_Groups_Ozero__class_Ozero(U_3769)),U_3774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),c_Groups_Ozero__class_Ozero(U_3769)),U_3773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),U_3772),U_3771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3769),U_3770),U_3771))
    | ~ class_Rings_Olinordered__semiring__1(U_3769) ),
    inference(clausify,[status(thm)],[f_945_2]) ).

fof(f_946_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_946_2,plain,
    ! [U_3776,U_3775] :
      ( ( 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_3775),U_3776)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3775),U_3776))
        | U_3776 = c_Orderings_Obot__class_Obot(tc_fun(U_3775,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3775),U_3776))
          & U_3776 != c_Orderings_Obot__class_Obot(tc_fun(U_3775,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_3775),U_3776))) ) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ( ! [U_3780,U_3778] :
        ( 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_3778),U_3780)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3778),U_3780))
        | U_3780 = c_Orderings_Obot__class_Obot(tc_fun(U_3778,tc_HOL_Obool)) )
    & ! [U_3779,U_3777] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3777),U_3779))
          & U_3779 != c_Orderings_Obot__class_Obot(tc_fun(U_3777,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_3777),U_3779))) ) ),
    inference(miniscope,[status(thm)],[f_946_2]) ).

cnf(f_946_4,plain,
    ( U_3779 != c_Orderings_Obot__class_Obot(tc_fun(U_3777,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_3777),U_3779))) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

cnf(f_946_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3777),U_3779))
    | ~ 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_3777),U_3779))) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

cnf(f_946_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_3778),U_3780)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3778),U_3780))
    | U_3780 = c_Orderings_Obot__class_Obot(tc_fun(U_3778,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_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_947_2,plain,
    ! [U_3784,U_3783,U_3782,U_3781] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3782,U_3781),U_3784),U_3783) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3781,U_3782,c_Groups_Oplus__class_Oplus(U_3781)),U_3784),c_Groups_Ozero__class_Ozero(U_3781)),U_3783)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),U_3783))
      | ~ class_Groups_Ocomm__monoid__add(U_3781) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

cnf(f_947_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3782,U_3781),U_3784),U_3783) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3781,U_3782,c_Groups_Oplus__class_Oplus(U_3781)),U_3784),c_Groups_Ozero__class_Ozero(U_3781)),U_3783)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),U_3783))
    | ~ class_Groups_Ocomm__monoid__add(U_3781) ),
    inference(clausify,[status(thm)],[f_947_2]) ).

fof(f_948_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_948_2,plain,
    ! [U_3788,U_3787,U_3786,U_3785] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3786,U_3785),U_3788),U_3787) = c_Groups_Ozero__class_Ozero(U_3785)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3786,U_3785),U_3788),U_3787) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3785,U_3786,c_Groups_Oplus__class_Oplus(U_3785)),U_3788),c_Groups_Ozero__class_Ozero(U_3785)),U_3787)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_3785) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

cnf(f_948_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3786,U_3785),U_3788),U_3787) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3785,U_3786,c_Groups_Oplus__class_Oplus(U_3785)),U_3788),c_Groups_Ozero__class_Ozero(U_3785)),U_3787)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787))
    | ~ class_Groups_Ocomm__monoid__add(U_3785) ),
    inference(clausify,[status(thm)],[f_948_2]) ).

cnf(f_948_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3786,U_3785),U_3788),U_3787) = c_Groups_Ozero__class_Ozero(U_3785)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787))
    | ~ class_Groups_Ocomm__monoid__add(U_3785) ),
    inference(clausify,[status(thm)],[f_948_2]) ).

fof(f_949_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_949_2,plain,
    ! [U_3789] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3789),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3789
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3789)) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

cnf(f_949_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3789),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3789
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3789)) ),
    inference(clausify,[status(thm)],[f_949_2]) ).

fof(f_950_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_950_2,plain,
    ! [U_3790] :
      ( U_3790 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3790),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_3790)) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

cnf(f_950_3,plain,
    ( U_3790 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3790),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_3790)) ),
    inference(clausify,[status(thm)],[f_950_2]) ).

fof(f_951_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_951_2,plain,
    ! [U_3792,U_3791] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3791),U_3792) = 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_3791),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3792))
        | U_3791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3791),U_3792) = U_3792
        | U_3791 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ( ! [U_3796,U_3794] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3794),U_3796) = 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_3794),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3796))
        | U_3794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3795,U_3793] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3793),U_3795) = U_3795
        | U_3793 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3793),U_3795) = U_3795
    | U_3793 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

cnf(f_951_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3794),U_3796) = 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_3794),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3796))
    | U_3794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_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_952_2,plain,
    ! [U_3798,U_3797] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3797),U_3798) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3798),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3797),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3798))
        | U_3797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3797),U_3798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3797 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ( ! [U_3802,U_3800] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3800),U_3802) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3800),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3802))
        | U_3800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3801,U_3799] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3799),U_3801) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3799 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3799),U_3801) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3799 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

cnf(f_952_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3800),U_3802) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3800),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3802))
    | U_3800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_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_953_2,plain,
    ! [U_3809,U_3808,U_3807,U_3806,U_3805,U_3804,U_3803] :
      ( hAPP(hAPP(U_3807,U_3809),U_3808) = U_3806
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3804),U_3808))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_3803,U_3804,U_3805,U_3806,U_3807) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_3809,U_3808,U_3807,U_3806,U_3805,U_3804] :
      ( ! [U_3803] : ~ c_Big__Operators_Ocomm__monoid__big(U_3803,U_3804,U_3805,U_3806,U_3807)
      | hAPP(hAPP(U_3807,U_3809),U_3808) = U_3806
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3804),U_3808)) ),
    inference(miniscope,[status(thm)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_3803,U_3804,U_3805,U_3806,U_3807)
    | hAPP(hAPP(U_3807,U_3809),U_3808) = U_3806
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_3804),U_3808)) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_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_954_2,plain,
    ! [U_3811,U_3810] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),U_3811),U_3811)),c_Groups_Ozero__class_Ozero(U_3810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),U_3811),c_Groups_Ozero__class_Ozero(U_3810))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),U_3811),c_Groups_Ozero__class_Ozero(U_3810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),U_3811),U_3811)),c_Groups_Ozero__class_Ozero(U_3810))) ) )
      | ~ class_Rings_Olinordered__idom(U_3810) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

cnf(f_954_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),U_3811),c_Groups_Ozero__class_Ozero(U_3810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),U_3811),U_3811)),c_Groups_Ozero__class_Ozero(U_3810)))
    | ~ class_Rings_Olinordered__idom(U_3810) ),
    inference(clausify,[status(thm)],[f_954_2]) ).

cnf(f_954_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),U_3811),U_3811)),c_Groups_Ozero__class_Ozero(U_3810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3810),U_3811),c_Groups_Ozero__class_Ozero(U_3810)))
    | ~ class_Rings_Olinordered__idom(U_3810) ),
    inference(clausify,[status(thm)],[f_954_2]) ).

fof(f_955_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_triple_Osize_I1_J]) ).

fof(f_955_2,plain,
    ! [U_3816,U_3815,U_3814,U_3813,U_3812] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_3812,U_3813,c_Hoare__Mirabelle_Otriple_Otriple(U_3812,U_3814,U_3815,U_3816)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

cnf(f_955_3,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(U_3812,U_3813,c_Hoare__Mirabelle_Otriple_Otriple(U_3812,U_3814,U_3815,U_3816)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_955_2]) ).

fof(f_956_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_956_2,plain,
    ! [U_3822,U_3821,U_3820,U_3819,U_3818] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3821)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3820)))
      | ? [U_3817] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),c_Groups_Ozero__class_Ozero(U_3818)),hAPP(U_3822,U_3817)))
          & hBOOL(hAPP(hAPP(c_member(U_3819),U_3817),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3819,tc_HOL_Obool)),U_3820),U_3821))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3819,tc_HOL_Obool)),U_3821),U_3820))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3819),U_3820))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3818) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_3822,U_3821,U_3820,U_3819,U_3818] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3821)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3820)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),c_Groups_Ozero__class_Ozero(U_3818)),hAPP(U_3822,sK69(U_3822,U_3821,U_3820,U_3819,U_3818))))
        & hBOOL(hAPP(hAPP(c_member(U_3819),sK69(U_3822,U_3821,U_3820,U_3819,U_3818)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3819,tc_HOL_Obool)),U_3820),U_3821))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3819,tc_HOL_Obool)),U_3821),U_3820))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3819),U_3820))
      | ~ class_Groups_Oordered__comm__monoid__add(U_3818) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3817,sK69(U_3822,U_3821,U_3820,U_3819,U_3818))],[f_956_2]) ).

cnf(f_956_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3819),sK69(U_3822,U_3821,U_3820,U_3819,U_3818)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3819,tc_HOL_Obool)),U_3820),U_3821)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3821)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3819,tc_HOL_Obool)),U_3821),U_3820))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3819),U_3820))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3818) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

cnf(f_956_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),c_Groups_Ozero__class_Ozero(U_3818)),hAPP(U_3822,sK69(U_3822,U_3821,U_3820,U_3819,U_3818))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3818),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3821)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3819,U_3818),U_3822),U_3820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3819,tc_HOL_Obool)),U_3821),U_3820))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3819),U_3820))
    | ~ class_Groups_Oordered__comm__monoid__add(U_3818) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_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_957_2,plain,
    ! [U_3826,U_3825,U_3824,U_3823] :
      ( ( c_Sum__Type_OPlus(U_3823,U_3824,U_3825,U_3826) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3823,U_3824),tc_HOL_Obool))
        | U_3826 != c_Orderings_Obot__class_Obot(tc_fun(U_3824,tc_HOL_Obool))
        | U_3825 != c_Orderings_Obot__class_Obot(tc_fun(U_3823,tc_HOL_Obool)) )
      & ( ( U_3826 = c_Orderings_Obot__class_Obot(tc_fun(U_3824,tc_HOL_Obool))
          & U_3825 = c_Orderings_Obot__class_Obot(tc_fun(U_3823,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_3823,U_3824,U_3825,U_3826) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3823,U_3824),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ( ! [U_3834,U_3832,U_3830,U_3828] :
        ( c_Sum__Type_OPlus(U_3828,U_3830,U_3832,U_3834) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3828,U_3830),tc_HOL_Obool))
        | U_3834 != c_Orderings_Obot__class_Obot(tc_fun(U_3830,tc_HOL_Obool))
        | U_3832 != c_Orderings_Obot__class_Obot(tc_fun(U_3828,tc_HOL_Obool)) )
    & ! [U_3833,U_3831,U_3829,U_3827] :
        ( ( U_3833 = c_Orderings_Obot__class_Obot(tc_fun(U_3829,tc_HOL_Obool))
          & U_3831 = c_Orderings_Obot__class_Obot(tc_fun(U_3827,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_3827,U_3829,U_3831,U_3833) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3827,U_3829),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_957_2]) ).

cnf(f_957_4,plain,
    ( U_3831 = c_Orderings_Obot__class_Obot(tc_fun(U_3827,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_3827,U_3829,U_3831,U_3833) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3827,U_3829),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_957_3]) ).

cnf(f_957_5,plain,
    ( U_3833 = c_Orderings_Obot__class_Obot(tc_fun(U_3829,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_3827,U_3829,U_3831,U_3833) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3827,U_3829),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_957_3]) ).

cnf(f_957_6,plain,
    ( c_Sum__Type_OPlus(U_3828,U_3830,U_3832,U_3834) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_3828,U_3830),tc_HOL_Obool))
    | U_3834 != c_Orderings_Obot__class_Obot(tc_fun(U_3830,tc_HOL_Obool))
    | U_3832 != c_Orderings_Obot__class_Obot(tc_fun(U_3828,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_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_958_2,plain,
    ! [U_3838,U_3837,U_3836] :
      ( hAPP(c_Finite__Set_Ocard(U_3836),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3836),U_3837)),hAPP(c_Finite__Set_Ocard(U_3836),U_3838))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_3835] : hBOOL(hAPP(hAPP(c_member(U_3836),U_3835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3838))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3837)) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_3838,U_3837,U_3836] :
      ( hAPP(c_Finite__Set_Ocard(U_3836),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3836),U_3837)),hAPP(c_Finite__Set_Ocard(U_3836),U_3838))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_3836),sK70(U_3838,U_3837,U_3836)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3838))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3837)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3835,sK70(U_3838,U_3837,U_3836))],[f_958_2]) ).

cnf(f_958_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3836),sK70(U_3838,U_3837,U_3836)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838)))
    | hAPP(c_Finite__Set_Ocard(U_3836),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3836),U_3837)),hAPP(c_Finite__Set_Ocard(U_3836),U_3838))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3838))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3837)) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

cnf(f_958_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_3836),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3836,tc_HOL_Obool)),U_3837),U_3838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3836),U_3837)),hAPP(c_Finite__Set_Ocard(U_3836),U_3838))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3838))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3836),U_3837)) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_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_959_2,plain,
    ! [U_3844,U_3843,U_3842,U_3841,U_3840] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3842)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3843))
      | ? [U_3839] :
          ( hAPP(U_3844,U_3839) != c_Groups_Ozero__class_Ozero(U_3840)
          & hBOOL(hAPP(hAPP(c_member(U_3841),U_3839),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3843))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3842))
      | ~ class_Groups_Ocomm__monoid__add(U_3840) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_3844,U_3843,U_3842,U_3841,U_3840] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3842)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3843))
      | ( hAPP(U_3844,sK71(U_3844,U_3843,U_3842,U_3841,U_3840)) != c_Groups_Ozero__class_Ozero(U_3840)
        & hBOOL(hAPP(hAPP(c_member(U_3841),sK71(U_3844,U_3843,U_3842,U_3841,U_3840)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3843))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3842))
      | ~ class_Groups_Ocomm__monoid__add(U_3840) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3839,sK71(U_3844,U_3843,U_3842,U_3841,U_3840))],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3841),sK71(U_3844,U_3843,U_3842,U_3841,U_3840)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3842)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3843))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3843))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3842))
    | ~ class_Groups_Ocomm__monoid__add(U_3840) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

cnf(f_959_5,plain,
    ( hAPP(U_3844,sK71(U_3844,U_3843,U_3842,U_3841,U_3840)) != c_Groups_Ozero__class_Ozero(U_3840)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3841,tc_HOL_Obool)),U_3842),U_3843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3842)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3841,U_3840),U_3844),U_3843))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3843))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3841),U_3842))
    | ~ class_Groups_Ocomm__monoid__add(U_3840) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_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_960_2,plain,
    ! [U_3850,U_3849,U_3848,U_3847,U_3846] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3848)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3849))
      | ? [U_3845] :
          ( hAPP(U_3850,U_3845) != c_Groups_Ozero__class_Ozero(U_3846)
          & hBOOL(hAPP(hAPP(c_member(U_3847),U_3845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3848))
      | ~ class_Groups_Ocomm__monoid__add(U_3846) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_3850,U_3849,U_3848,U_3847,U_3846] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3848)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3849))
      | ( hAPP(U_3850,sK72(U_3850,U_3849,U_3848,U_3847,U_3846)) != c_Groups_Ozero__class_Ozero(U_3846)
        & hBOOL(hAPP(hAPP(c_member(U_3847),sK72(U_3850,U_3849,U_3848,U_3847,U_3846)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3848))
      | ~ class_Groups_Ocomm__monoid__add(U_3846) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3845,sK72(U_3850,U_3849,U_3848,U_3847,U_3846))],[f_960_2]) ).

cnf(f_960_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3847),sK72(U_3850,U_3849,U_3848,U_3847,U_3846)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3848)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3848))
    | ~ class_Groups_Ocomm__monoid__add(U_3846) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

cnf(f_960_5,plain,
    ( hAPP(U_3850,sK72(U_3850,U_3849,U_3848,U_3847,U_3846)) != c_Groups_Ozero__class_Ozero(U_3846)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3847,tc_HOL_Obool)),U_3848),U_3849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3848)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3847,U_3846),U_3850),U_3849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3847),U_3848))
    | ~ class_Groups_Ocomm__monoid__add(U_3846) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

fof(f_961_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_961_2,plain,
    ! [U_3856,U_3855,U_3854,U_3853,U_3852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3854)))
      | ? [U_3851] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),c_Groups_Ozero__class_Ozero(U_3852)),hAPP(U_3856,U_3851)))
          & hBOOL(hAPP(hAPP(c_member(U_3853),U_3851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3853,tc_HOL_Obool)),U_3854),U_3855))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3853,tc_HOL_Obool)),U_3855),U_3854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3853),U_3854))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_3852)
      | ~ class_Groups_Ocomm__monoid__add(U_3852) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_3856,U_3855,U_3854,U_3853,U_3852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3854)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),c_Groups_Ozero__class_Ozero(U_3852)),hAPP(U_3856,sK73(U_3856,U_3855,U_3854,U_3853,U_3852))))
        & hBOOL(hAPP(hAPP(c_member(U_3853),sK73(U_3856,U_3855,U_3854,U_3853,U_3852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3853,tc_HOL_Obool)),U_3854),U_3855))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3853,tc_HOL_Obool)),U_3855),U_3854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3853),U_3854))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_3852)
      | ~ class_Groups_Ocomm__monoid__add(U_3852) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3851,sK73(U_3856,U_3855,U_3854,U_3853,U_3852))],[f_961_2]) ).

cnf(f_961_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3853),sK73(U_3856,U_3855,U_3854,U_3853,U_3852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3853,tc_HOL_Obool)),U_3854),U_3855)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3854)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3853,tc_HOL_Obool)),U_3855),U_3854))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3853),U_3854))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_3852)
    | ~ class_Groups_Ocomm__monoid__add(U_3852) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

cnf(f_961_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),c_Groups_Ozero__class_Ozero(U_3852)),hAPP(U_3856,sK73(U_3856,U_3855,U_3854,U_3853,U_3852))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3852),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3853,U_3852),U_3856),U_3854)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3853,tc_HOL_Obool)),U_3855),U_3854))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3853),U_3854))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_3852)
    | ~ class_Groups_Ocomm__monoid__add(U_3852) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_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_962_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_962_1]) ).

fof(f_963_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_963_2,plain,
    ! [U_3858,U_3857] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3857),U_3858),U_3858) = c_Groups_Ozero__class_Ozero(U_3857)
          | U_3858 != c_Groups_Ozero__class_Ozero(U_3857) )
        & ( U_3858 = c_Groups_Ozero__class_Ozero(U_3857)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3857),U_3858),U_3858) != c_Groups_Ozero__class_Ozero(U_3857) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_3857) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

cnf(f_963_3,plain,
    ( U_3858 = c_Groups_Ozero__class_Ozero(U_3857)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3857),U_3858),U_3858) != c_Groups_Ozero__class_Ozero(U_3857)
    | ~ class_Groups_Olinordered__ab__group__add(U_3857) ),
    inference(clausify,[status(thm)],[f_963_2]) ).

cnf(f_963_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3857),U_3858),U_3858) = c_Groups_Ozero__class_Ozero(U_3857)
    | U_3858 != c_Groups_Ozero__class_Ozero(U_3857)
    | ~ class_Groups_Olinordered__ab__group__add(U_3857) ),
    inference(clausify,[status(thm)],[f_963_2]) ).

fof(f_964_1,plain,
    ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_triple_Osize_I2_J]) ).

fof(f_964_2,plain,
    ! [U_3862,U_3861,U_3860,U_3859] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_3859)),c_Hoare__Mirabelle_Otriple_Otriple(U_3859,U_3860,U_3861,U_3862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

cnf(f_964_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_3859)),c_Hoare__Mirabelle_Otriple_Otriple(U_3859,U_3860,U_3861,U_3862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_964_2]) ).

fof(f_965_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_965_2,plain,
    ! [U_3869,U_3868,U_3867] :
      ( ( hAPP(c_Finite__Set_Ocard(U_3867),U_3868) = hAPP(c_Nat_OSuc,U_3869)
        | ! [U_3866,U_3865] :
            ( ( U_3865 != c_Orderings_Obot__class_Obot(tc_fun(U_3867,tc_HOL_Obool))
              & U_3869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_3867),U_3865) != U_3869
            | hBOOL(hAPP(hAPP(c_member(U_3867),U_3866),U_3865))
            | U_3868 != hAPP(hAPP(c_Set_Oinsert(U_3867),U_3866),U_3865) ) )
      & ( ? [U_3864,U_3863] :
            ( ( U_3863 = c_Orderings_Obot__class_Obot(tc_fun(U_3867,tc_HOL_Obool))
              | U_3869 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_3867),U_3863) = U_3869
            & ~ hBOOL(hAPP(hAPP(c_member(U_3867),U_3864),U_3863))
            & U_3868 = hAPP(hAPP(c_Set_Oinsert(U_3867),U_3864),U_3863) )
        | hAPP(c_Finite__Set_Ocard(U_3867),U_3868) != hAPP(c_Nat_OSuc,U_3869) ) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ( ! [U_3875,U_3873,U_3871] :
        ( hAPP(c_Finite__Set_Ocard(U_3871),U_3873) = hAPP(c_Nat_OSuc,U_3875)
        | ! [U_3866,U_3865] :
            ( ( U_3865 != c_Orderings_Obot__class_Obot(tc_fun(U_3871,tc_HOL_Obool))
              & U_3875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_3871),U_3865) != U_3875
            | hBOOL(hAPP(hAPP(c_member(U_3871),U_3866),U_3865))
            | U_3873 != hAPP(hAPP(c_Set_Oinsert(U_3871),U_3866),U_3865) ) )
    & ! [U_3874,U_3872,U_3870] :
        ( ? [U_3864,U_3863] :
            ( ( U_3863 = c_Orderings_Obot__class_Obot(tc_fun(U_3870,tc_HOL_Obool))
              | U_3874 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_3870),U_3863) = U_3874
            & ~ hBOOL(hAPP(hAPP(c_member(U_3870),U_3864),U_3863))
            & U_3872 = hAPP(hAPP(c_Set_Oinsert(U_3870),U_3864),U_3863) )
        | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ) ),
    inference(miniscope,[status(thm)],[f_965_2]) ).

fof(f_965_4,plain,
    ( ! [U_3875,U_3873,U_3871] :
        ( hAPP(c_Finite__Set_Ocard(U_3871),U_3873) = hAPP(c_Nat_OSuc,U_3875)
        | ! [U_3866,U_3865] :
            ( ( U_3865 != c_Orderings_Obot__class_Obot(tc_fun(U_3871,tc_HOL_Obool))
              & U_3875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_3871),U_3865) != U_3875
            | hBOOL(hAPP(hAPP(c_member(U_3871),U_3866),U_3865))
            | U_3873 != hAPP(hAPP(c_Set_Oinsert(U_3871),U_3866),U_3865) ) )
    & ! [U_3874,U_3872,U_3870] :
        ( ? [U_3863] :
            ( ( U_3863 = c_Orderings_Obot__class_Obot(tc_fun(U_3870,tc_HOL_Obool))
              | U_3874 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_3870),U_3863) = U_3874
            & ~ hBOOL(hAPP(hAPP(c_member(U_3870),sK74(U_3874,U_3872,U_3870)),U_3863))
            & U_3872 = hAPP(hAPP(c_Set_Oinsert(U_3870),sK74(U_3874,U_3872,U_3870)),U_3863) )
        | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3864,sK74(U_3874,U_3872,U_3870))],[f_965_3]) ).

fof(f_965_5,plain,
    ( ! [U_3875,U_3873,U_3871] :
        ( hAPP(c_Finite__Set_Ocard(U_3871),U_3873) = hAPP(c_Nat_OSuc,U_3875)
        | ! [U_3866,U_3865] :
            ( ( U_3865 != c_Orderings_Obot__class_Obot(tc_fun(U_3871,tc_HOL_Obool))
              & U_3875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_3871),U_3865) != U_3875
            | hBOOL(hAPP(hAPP(c_member(U_3871),U_3866),U_3865))
            | U_3873 != hAPP(hAPP(c_Set_Oinsert(U_3871),U_3866),U_3865) ) )
    & ! [U_3874,U_3872,U_3870] :
        ( ( ( sK75(U_3874,U_3872,U_3870) = c_Orderings_Obot__class_Obot(tc_fun(U_3870,tc_HOL_Obool))
            | U_3874 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_3870),sK75(U_3874,U_3872,U_3870)) = U_3874
          & ~ hBOOL(hAPP(hAPP(c_member(U_3870),sK74(U_3874,U_3872,U_3870)),sK75(U_3874,U_3872,U_3870)))
          & U_3872 = hAPP(hAPP(c_Set_Oinsert(U_3870),sK74(U_3874,U_3872,U_3870)),sK75(U_3874,U_3872,U_3870)) )
        | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3863,sK75(U_3874,U_3872,U_3870))],[f_965_4]) ).

cnf(f_965_6,plain,
    ( U_3872 = hAPP(hAPP(c_Set_Oinsert(U_3870),sK74(U_3874,U_3872,U_3870)),sK75(U_3874,U_3872,U_3870))
    | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

cnf(f_965_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3870),sK74(U_3874,U_3872,U_3870)),sK75(U_3874,U_3872,U_3870)))
    | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

cnf(f_965_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_3870),sK75(U_3874,U_3872,U_3870)) = U_3874
    | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

cnf(f_965_9,plain,
    ( sK75(U_3874,U_3872,U_3870) = c_Orderings_Obot__class_Obot(tc_fun(U_3870,tc_HOL_Obool))
    | U_3874 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_3870),U_3872) != hAPP(c_Nat_OSuc,U_3874) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

cnf(f_965_10,plain,
    ( U_3875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_3871),U_3865) != U_3875
    | hBOOL(hAPP(hAPP(c_member(U_3871),U_3866),U_3865))
    | U_3873 != hAPP(hAPP(c_Set_Oinsert(U_3871),U_3866),U_3865)
    | hAPP(c_Finite__Set_Ocard(U_3871),U_3873) = hAPP(c_Nat_OSuc,U_3875) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

cnf(f_965_11,plain,
    ( U_3865 != c_Orderings_Obot__class_Obot(tc_fun(U_3871,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_3871),U_3865) != U_3875
    | hBOOL(hAPP(hAPP(c_member(U_3871),U_3866),U_3865))
    | U_3873 != hAPP(hAPP(c_Set_Oinsert(U_3871),U_3866),U_3865)
    | hAPP(c_Finite__Set_Ocard(U_3871),U_3873) = hAPP(c_Nat_OSuc,U_3875) ),
    inference(clausify,[status(thm)],[f_965_5]) ).

fof(f_966_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_966_2,plain,
    ! [U_3877,U_3876] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),c_Groups_Oone__class_Oone(U_3876)),U_3877)),U_3877)),c_Groups_Ozero__class_Ozero(U_3876)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),U_3877),c_Groups_Ozero__class_Ozero(U_3876))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),U_3877),c_Groups_Ozero__class_Ozero(U_3876)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),c_Groups_Oone__class_Oone(U_3876)),U_3877)),U_3877)),c_Groups_Ozero__class_Ozero(U_3876))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_3876),U_3877),c_Int_Oring__1__class_OInts(U_3876)))
      | ~ class_Rings_Olinordered__idom(U_3876) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

cnf(f_966_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),U_3877),c_Groups_Ozero__class_Ozero(U_3876)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),c_Groups_Oone__class_Oone(U_3876)),U_3877)),U_3877)),c_Groups_Ozero__class_Ozero(U_3876)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3876),U_3877),c_Int_Oring__1__class_OInts(U_3876)))
    | ~ class_Rings_Olinordered__idom(U_3876) ),
    inference(clausify,[status(thm)],[f_966_2]) ).

cnf(f_966_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3876),c_Groups_Oone__class_Oone(U_3876)),U_3877)),U_3877)),c_Groups_Ozero__class_Ozero(U_3876)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3876),U_3877),c_Groups_Ozero__class_Ozero(U_3876)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3876),U_3877),c_Int_Oring__1__class_OInts(U_3876)))
    | ~ class_Rings_Olinordered__idom(U_3876) ),
    inference(clausify,[status(thm)],[f_966_2]) ).

fof(f_967_1,plain,
    ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I4_J]) ).

fof(f_967_2,plain,
    ! [U_3879,U_3878] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_3878,U_3879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_3878)),c_Com_Ocom_Ocom__size(U_3879))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

cnf(f_967_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_3878,U_3879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_3878)),c_Com_Ocom_Ocom__size(U_3879))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_967_2]) ).

fof(f_968_1,plain,
    ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I12_J]) ).

fof(f_968_2,plain,
    ! [U_3881,U_3880] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_3880,U_3881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3880)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3881))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

cnf(f_968_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_3880,U_3881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3880)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3881))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_968_2]) ).

fof(f_969_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_969_2,plain,
    ! [U_3886,U_3885,U_3884,U_3883,U_3882] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3883,tc_HOL_Obool)),U_3884),hAPP(hAPP(c_Set_Oinsert(U_3883),U_3886),c_Orderings_Obot__class_Obot(tc_fun(U_3883,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),U_3884)
          | hBOOL(hAPP(hAPP(c_member(U_3883),U_3886),U_3884)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3883,tc_HOL_Obool)),U_3884),hAPP(hAPP(c_Set_Oinsert(U_3883),U_3886),c_Orderings_Obot__class_Obot(tc_fun(U_3883,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3882),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),U_3884)),hAPP(U_3885,U_3886))
          | ~ hBOOL(hAPP(hAPP(c_member(U_3883),U_3886),U_3884)) ) )
      | hAPP(U_3885,U_3886) = c_Groups_Ozero__class_Ozero(U_3882)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3883),U_3884))
      | ~ class_Fields_Ofield(U_3882) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

cnf(f_969_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3883,tc_HOL_Obool)),U_3884),hAPP(hAPP(c_Set_Oinsert(U_3883),U_3886),c_Orderings_Obot__class_Obot(tc_fun(U_3883,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3882),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),U_3884)),hAPP(U_3885,U_3886))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3883),U_3886),U_3884))
    | hAPP(U_3885,U_3886) = c_Groups_Ozero__class_Ozero(U_3882)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3883),U_3884))
    | ~ class_Fields_Ofield(U_3882) ),
    inference(clausify,[status(thm)],[f_969_2]) ).

cnf(f_969_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3883,tc_HOL_Obool)),U_3884),hAPP(hAPP(c_Set_Oinsert(U_3883),U_3886),c_Orderings_Obot__class_Obot(tc_fun(U_3883,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3883,U_3882),U_3885),U_3884)
    | hBOOL(hAPP(hAPP(c_member(U_3883),U_3886),U_3884))
    | hAPP(U_3885,U_3886) = c_Groups_Ozero__class_Ozero(U_3882)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3883),U_3884))
    | ~ class_Fields_Ofield(U_3882) ),
    inference(clausify,[status(thm)],[f_969_2]) ).

fof(f_970_1,plain,
    ! [V_n_2,V_Pa_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
      | hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_970_2,plain,
    ! [U_3890,U_3889] :
      ( ? [U_3888] :
          ( hBOOL(hAPP(U_3889,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3888),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_3887] :
              ( ~ hBOOL(hAPP(U_3889,U_3887))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),U_3888)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3888),U_3890)) )
      | ~ hBOOL(hAPP(U_3889,U_3890))
      | hBOOL(hAPP(U_3889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_3890,U_3889] :
      ( ( hBOOL(hAPP(U_3889,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK76(U_3890,U_3889)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_3887] :
            ( ~ hBOOL(hAPP(U_3889,U_3887))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),sK76(U_3890,U_3889))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK76(U_3890,U_3889)),U_3890)) )
      | ~ hBOOL(hAPP(U_3889,U_3890))
      | hBOOL(hAPP(U_3889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3888,sK76(U_3890,U_3889))],[f_970_2]) ).

cnf(f_970_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK76(U_3890,U_3889)),U_3890))
    | ~ hBOOL(hAPP(U_3889,U_3890))
    | hBOOL(hAPP(U_3889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_5,plain,
    ( ~ hBOOL(hAPP(U_3889,U_3887))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3887),sK76(U_3890,U_3889)))
    | ~ hBOOL(hAPP(U_3889,U_3890))
    | hBOOL(hAPP(U_3889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_6,plain,
    ( hBOOL(hAPP(U_3889,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK76(U_3890,U_3889)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(U_3889,U_3890))
    | hBOOL(hAPP(U_3889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_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_971_2,plain,
    ! [U_3896,U_3895,U_3894,U_3893,U_3892] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3894) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3895)
      | ? [U_3891] :
          ( hAPP(U_3896,U_3891) != c_Groups_Ozero__class_Ozero(U_3892)
          & hBOOL(hAPP(hAPP(c_member(U_3893),U_3891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3893,tc_HOL_Obool)),U_3894),U_3895))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3893,tc_HOL_Obool)),U_3895),U_3894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3893),U_3894))
      | ~ class_Groups_Ocomm__monoid__add(U_3892) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3896,U_3895,U_3894,U_3893,U_3892] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3894) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3895)
      | ( hAPP(U_3896,sK77(U_3896,U_3895,U_3894,U_3893,U_3892)) != c_Groups_Ozero__class_Ozero(U_3892)
        & hBOOL(hAPP(hAPP(c_member(U_3893),sK77(U_3896,U_3895,U_3894,U_3893,U_3892)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3893,tc_HOL_Obool)),U_3894),U_3895))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3893,tc_HOL_Obool)),U_3895),U_3894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3893),U_3894))
      | ~ class_Groups_Ocomm__monoid__add(U_3892) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3891,sK77(U_3896,U_3895,U_3894,U_3893,U_3892))],[f_971_2]) ).

cnf(f_971_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3893),sK77(U_3896,U_3895,U_3894,U_3893,U_3892)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3893,tc_HOL_Obool)),U_3894),U_3895)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3894) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3895)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3893,tc_HOL_Obool)),U_3895),U_3894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3893),U_3894))
    | ~ class_Groups_Ocomm__monoid__add(U_3892) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_5,plain,
    ( hAPP(U_3896,sK77(U_3896,U_3895,U_3894,U_3893,U_3892)) != c_Groups_Ozero__class_Ozero(U_3892)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3894) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3893,U_3892),U_3896),U_3895)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3893,tc_HOL_Obool)),U_3895),U_3894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3893),U_3894))
    | ~ class_Groups_Ocomm__monoid__add(U_3892) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_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_972_2,plain,
    ! [U_3898,U_3897] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3897),U_3898),c_Groups_Ozero__class_Ozero(U_3897)) = c_Groups_Ozero__class_Ozero(U_3897)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_3897) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

cnf(f_972_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3897),U_3898),c_Groups_Ozero__class_Ozero(U_3897)) = c_Groups_Ozero__class_Ozero(U_3897)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_3897) ),
    inference(clausify,[status(thm)],[f_972_2]) ).

fof(f_973_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_973_2,plain,
    ! [U_3900,U_3899] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3899),c_Groups_Ozero__class_Ozero(U_3899)),U_3900) = c_Groups_Ozero__class_Ozero(U_3899)
      | ~ class_Rings_Odivision__ring(U_3899) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

cnf(f_973_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3899),c_Groups_Ozero__class_Ozero(U_3899)),U_3900) = c_Groups_Ozero__class_Ozero(U_3899)
    | ~ class_Rings_Odivision__ring(U_3899) ),
    inference(clausify,[status(thm)],[f_973_2]) ).

fof(f_974_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_974_2,plain,
    ! [U_3904,U_3903,U_3902,U_3901] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3901),U_3902),U_3903)),U_3904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),U_3902),U_3904)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),U_3903),U_3904))
      | ~ class_Rings_Odivision__ring(U_3901) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

cnf(f_974_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3901),U_3902),U_3903)),U_3904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),U_3902),U_3904)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3901),U_3903),U_3904))
    | ~ class_Rings_Odivision__ring(U_3901) ),
    inference(clausify,[status(thm)],[f_974_2]) ).

fof(f_975_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_975_2,plain,
    ! [U_3908,U_3907,U_3906,U_3905] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3905),U_3906),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3905),U_3907),U_3908)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3905),U_3906),U_3907)),U_3908)
      | ~ class_Rings_Odivision__ring(U_3905) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

cnf(f_975_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3905),U_3906),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3905),U_3907),U_3908)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3905),U_3906),U_3907)),U_3908)
    | ~ class_Rings_Odivision__ring(U_3905) ),
    inference(clausify,[status(thm)],[f_975_2]) ).

fof(f_976_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_976_2,plain,
    ! [U_3912,U_3911,U_3910,U_3909] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3909),U_3910),U_3911)),U_3912) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3909),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),U_3910),U_3912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),U_3911),U_3912))
      | ~ class_Rings_Odivision__ring(U_3909) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

cnf(f_976_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3909),U_3910),U_3911)),U_3912) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3909),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),U_3910),U_3912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3909),U_3911),U_3912))
    | ~ class_Rings_Odivision__ring(U_3909) ),
    inference(clausify,[status(thm)],[f_976_2]) ).

fof(f_977_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_977_2,plain,
    ! [U_3914,U_3913] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3913),U_3914),c_Groups_Oone__class_Oone(U_3913)) = U_3914
      | ~ class_Rings_Odivision__ring(U_3913) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

cnf(f_977_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3913),U_3914),c_Groups_Oone__class_Oone(U_3913)) = U_3914
    | ~ class_Rings_Odivision__ring(U_3913) ),
    inference(clausify,[status(thm)],[f_977_2]) ).

fof(f_978_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_978_2,plain,
    ! [U_3918,U_3917,U_3916,U_3915] :
      ( U_3917 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3915),U_3918),U_3916)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3915),U_3917),U_3916) != U_3918
      | U_3916 = c_Groups_Ozero__class_Ozero(U_3915)
      | ~ class_Rings_Odivision__ring(U_3915) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

cnf(f_978_3,plain,
    ( U_3917 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3915),U_3918),U_3916)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3915),U_3917),U_3916) != U_3918
    | U_3916 = c_Groups_Ozero__class_Ozero(U_3915)
    | ~ class_Rings_Odivision__ring(U_3915) ),
    inference(clausify,[status(thm)],[f_978_2]) ).

fof(f_979_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_979_2,plain,
    ! [U_3922,U_3921,U_3920,U_3919] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3919),U_3921),U_3920) = U_3922
      | U_3921 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3919),U_3922),U_3920)
      | U_3920 = c_Groups_Ozero__class_Ozero(U_3919)
      | ~ class_Rings_Odivision__ring(U_3919) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

cnf(f_979_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3919),U_3921),U_3920) = U_3922
    | U_3921 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3919),U_3922),U_3920)
    | U_3920 = c_Groups_Ozero__class_Ozero(U_3919)
    | ~ class_Rings_Odivision__ring(U_3919) ),
    inference(clausify,[status(thm)],[f_979_2]) ).

fof(f_980_1,plain,
    ! [V_a_2,V_b_2,V_ca_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) != V_a_2 ) )
      | V_ca_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_980_2,plain,
    ! [U_3926,U_3925,U_3924,U_3923] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3923),U_3925),U_3924) = U_3926
          | U_3925 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3926),U_3924) )
        & ( U_3925 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3926),U_3924)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3923),U_3925),U_3924) != U_3926 ) )
      | U_3924 = c_Groups_Ozero__class_Ozero(U_3923)
      | ~ class_Rings_Odivision__ring(U_3923) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

cnf(f_980_3,plain,
    ( U_3925 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3926),U_3924)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3923),U_3925),U_3924) != U_3926
    | U_3924 = c_Groups_Ozero__class_Ozero(U_3923)
    | ~ class_Rings_Odivision__ring(U_3923) ),
    inference(clausify,[status(thm)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3923),U_3925),U_3924) = U_3926
    | U_3925 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3923),U_3926),U_3924)
    | U_3924 = c_Groups_Ozero__class_Ozero(U_3923)
    | ~ class_Rings_Odivision__ring(U_3923) ),
    inference(clausify,[status(thm)],[f_980_2]) ).

fof(f_981_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) != V_b_2 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) ) )
      | V_ca_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_981_2,plain,
    ! [U_3930,U_3929,U_3928,U_3927] :
      ( ( ( U_3929 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3927),U_3930),U_3928)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3929),U_3928) != U_3930 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3929),U_3928) = U_3930
          | U_3929 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3927),U_3930),U_3928) ) )
      | U_3928 = c_Groups_Ozero__class_Ozero(U_3927)
      | ~ class_Rings_Odivision__ring(U_3927) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

cnf(f_981_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3929),U_3928) = U_3930
    | U_3929 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3927),U_3930),U_3928)
    | U_3928 = c_Groups_Ozero__class_Ozero(U_3927)
    | ~ class_Rings_Odivision__ring(U_3927) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( U_3929 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3927),U_3930),U_3928)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3929),U_3928) != U_3930
    | U_3928 = c_Groups_Ozero__class_Ozero(U_3927)
    | ~ class_Rings_Odivision__ring(U_3927) ),
    inference(clausify,[status(thm)],[f_981_2]) ).

fof(f_982_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_982_2,plain,
    ! [U_3933,U_3932,U_3931] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3931),U_3933),U_3932) = c_Groups_Oone__class_Oone(U_3931)
          | U_3933 != U_3932 )
        & ( U_3933 = U_3932
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3931),U_3933),U_3932) != c_Groups_Oone__class_Oone(U_3931) ) )
      | U_3932 = c_Groups_Ozero__class_Ozero(U_3931)
      | ~ class_Rings_Odivision__ring(U_3931) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

cnf(f_982_3,plain,
    ( U_3933 = U_3932
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3931),U_3933),U_3932) != c_Groups_Oone__class_Oone(U_3931)
    | U_3932 = c_Groups_Ozero__class_Ozero(U_3931)
    | ~ class_Rings_Odivision__ring(U_3931) ),
    inference(clausify,[status(thm)],[f_982_2]) ).

cnf(f_982_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3931),U_3933),U_3932) = c_Groups_Oone__class_Oone(U_3931)
    | U_3933 != U_3932
    | U_3932 = c_Groups_Ozero__class_Ozero(U_3931)
    | ~ class_Rings_Odivision__ring(U_3931) ),
    inference(clausify,[status(thm)],[f_982_2]) ).

fof(f_983_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_983_2,plain,
    ! [U_3935,U_3934] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3934),U_3935),U_3935) = c_Groups_Oone__class_Oone(U_3934)
      | U_3935 = c_Groups_Ozero__class_Ozero(U_3934)
      | ~ class_Rings_Odivision__ring(U_3934) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

cnf(f_983_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3934),U_3935),U_3935) = c_Groups_Oone__class_Oone(U_3934)
    | U_3935 = c_Groups_Ozero__class_Ozero(U_3934)
    | ~ class_Rings_Odivision__ring(U_3934) ),
    inference(clausify,[status(thm)],[f_983_2]) ).

fof(f_984_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_984_2,plain,
    ! [U_3937,U_3936] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3936),U_3937),U_3937) = c_Groups_Oone__class_Oone(U_3936)
          | U_3937 = c_Groups_Ozero__class_Ozero(U_3936) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3936),U_3937),U_3937) = c_Groups_Ozero__class_Ozero(U_3936)
          | U_3937 != c_Groups_Ozero__class_Ozero(U_3936) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_3936) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

cnf(f_984_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3936),U_3937),U_3937) = c_Groups_Ozero__class_Ozero(U_3936)
    | U_3937 != c_Groups_Ozero__class_Ozero(U_3936)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_3936) ),
    inference(clausify,[status(thm)],[f_984_2]) ).

cnf(f_984_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3936),U_3937),U_3937) = c_Groups_Oone__class_Oone(U_3936)
    | U_3937 = c_Groups_Ozero__class_Ozero(U_3936)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_3936) ),
    inference(clausify,[status(thm)],[f_984_2]) ).

fof(f_985_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_985_2,plain,
    ! [U_3938] :
      ( hBOOL(hAPP(hAPP(c_member(U_3938),c_Groups_Ozero__class_Ozero(U_3938)),c_Int_Oring__1__class_OInts(U_3938)))
      | ~ class_Rings_Oring__1(U_3938) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

cnf(f_985_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3938),c_Groups_Ozero__class_Ozero(U_3938)),c_Int_Oring__1__class_OInts(U_3938)))
    | ~ class_Rings_Oring__1(U_3938) ),
    inference(clausify,[status(thm)],[f_985_2]) ).

fof(f_986_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_986_2,plain,
    ! [U_3941,U_3940,U_3939] :
      ( hBOOL(hAPP(hAPP(c_member(U_3939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3939),U_3940),U_3941)),c_Int_Oring__1__class_OInts(U_3939)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3939),U_3941),c_Int_Oring__1__class_OInts(U_3939)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3939),U_3940),c_Int_Oring__1__class_OInts(U_3939)))
      | ~ class_Rings_Oring__1(U_3939) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

cnf(f_986_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3939),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3939),U_3940),U_3941)),c_Int_Oring__1__class_OInts(U_3939)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3939),U_3941),c_Int_Oring__1__class_OInts(U_3939)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3939),U_3940),c_Int_Oring__1__class_OInts(U_3939)))
    | ~ class_Rings_Oring__1(U_3939) ),
    inference(clausify,[status(thm)],[f_986_2]) ).

fof(f_987_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_987_2,plain,
    ! [U_3944,U_3943,U_3942] :
      ( hBOOL(hAPP(hAPP(c_member(U_3942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3942),U_3943),U_3944)),c_Int_Oring__1__class_OInts(U_3942)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3944),c_Int_Oring__1__class_OInts(U_3942)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3943),c_Int_Oring__1__class_OInts(U_3942)))
      | ~ class_Rings_Oring__1(U_3942) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

cnf(f_987_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3942),U_3943),U_3944)),c_Int_Oring__1__class_OInts(U_3942)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3944),c_Int_Oring__1__class_OInts(U_3942)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3942),U_3943),c_Int_Oring__1__class_OInts(U_3942)))
    | ~ class_Rings_Oring__1(U_3942) ),
    inference(clausify,[status(thm)],[f_987_2]) ).

fof(f_988_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_988_2,plain,
    ! [U_3947,U_3946,U_3945] :
      ( hBOOL(hAPP(hAPP(c_member(U_3945),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3945),U_3946),U_3947)),c_Int_Oring__1__class_OInts(U_3945)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3945),U_3947),c_Int_Oring__1__class_OInts(U_3945)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3945),U_3946),c_Int_Oring__1__class_OInts(U_3945)))
      | ~ class_Rings_Oring__1(U_3945) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

cnf(f_988_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3945),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3945),U_3946),U_3947)),c_Int_Oring__1__class_OInts(U_3945)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3945),U_3947),c_Int_Oring__1__class_OInts(U_3945)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3945),U_3946),c_Int_Oring__1__class_OInts(U_3945)))
    | ~ class_Rings_Oring__1(U_3945) ),
    inference(clausify,[status(thm)],[f_988_2]) ).

fof(f_989_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_989_2,plain,
    ! [U_3948] :
      ( hBOOL(hAPP(hAPP(c_member(U_3948),c_Groups_Oone__class_Oone(U_3948)),c_Int_Oring__1__class_OInts(U_3948)))
      | ~ class_Rings_Oring__1(U_3948) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

cnf(f_989_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3948),c_Groups_Oone__class_Oone(U_3948)),c_Int_Oring__1__class_OInts(U_3948)))
    | ~ class_Rings_Oring__1(U_3948) ),
    inference(clausify,[status(thm)],[f_989_2]) ).

fof(f_990_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I9_J]) ).

cnf(f_990_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_990_1]) ).

fof(f_991_1,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I1_J]) ).

cnf(f_991_2,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_991_1]) ).

fof(f_992_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_992_2,plain,
    ! [U_3950,U_3949] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),U_3950),U_3950) = c_Groups_Ozero__class_Ozero(U_3949)
          | U_3950 != c_Groups_Ozero__class_Ozero(U_3949) )
        & ( U_3950 = c_Groups_Ozero__class_Ozero(U_3949)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),U_3950),U_3950) != c_Groups_Ozero__class_Ozero(U_3949) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_3949),U_3950),c_Int_Oring__1__class_OInts(U_3949)))
      | ~ class_Int_Oring__char__0(U_3949) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

cnf(f_992_3,plain,
    ( U_3950 = c_Groups_Ozero__class_Ozero(U_3949)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),U_3950),U_3950) != c_Groups_Ozero__class_Ozero(U_3949)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3949),U_3950),c_Int_Oring__1__class_OInts(U_3949)))
    | ~ class_Int_Oring__char__0(U_3949) ),
    inference(clausify,[status(thm)],[f_992_2]) ).

cnf(f_992_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3949),U_3950),U_3950) = c_Groups_Ozero__class_Ozero(U_3949)
    | U_3950 != c_Groups_Ozero__class_Ozero(U_3949)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3949),U_3950),c_Int_Oring__1__class_OInts(U_3949)))
    | ~ class_Int_Oring__char__0(U_3949) ),
    inference(clausify,[status(thm)],[f_992_2]) ).

fof(f_993_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_993_2,plain,
    ! [U_3952,U_3951] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3951),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3951),c_Groups_Oone__class_Oone(U_3951)),U_3952)),U_3952) != c_Groups_Ozero__class_Ozero(U_3951)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3951),U_3952),c_Int_Oring__1__class_OInts(U_3951)))
      | ~ class_Int_Oring__char__0(U_3951) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

cnf(f_993_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3951),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3951),c_Groups_Oone__class_Oone(U_3951)),U_3952)),U_3952) != c_Groups_Ozero__class_Ozero(U_3951)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3951),U_3952),c_Int_Oring__1__class_OInts(U_3951)))
    | ~ class_Int_Oring__char__0(U_3951) ),
    inference(clausify,[status(thm)],[f_993_2]) ).

fof(f_994_1,plain,
    ! [V_ca_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_ca_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_ca_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_ca_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).

fof(f_994_2,plain,
    ! [U_3956,U_3955,U_3954,U_3953] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

cnf(f_994_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),c_Groups_Ozero__class_Ozero(U_3953)),U_3956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3953),U_3956),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

cnf(f_994_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),c_Groups_Ozero__class_Ozero(U_3953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3953),U_3954),U_3956)),U_3955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3953),U_3954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3953),U_3955),U_3956)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3953) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

fof(f_995_1,plain,
    ! [V_a_2,V_ca_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_ca_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_ca_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_ca_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).

fof(f_995_2,plain,
    ! [U_3960,U_3959,U_3958,U_3957] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

cnf(f_995_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3957),U_3959),c_Groups_Ozero__class_Ozero(U_3957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

cnf(f_995_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)),U_3958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3957),U_3960),U_3959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3957),U_3958),U_3959)),U_3960))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3957) ),
    inference(clausify,[status(thm)],[f_995_2]) ).

fof(f_996_1,plain,
    ! [V_b_2,V_a_2,V_ca_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_ca_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_ca_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_ca_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_ca_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).

fof(f_996_2,plain,
    ! [U_3964,U_3963,U_3962,U_3961] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),U_3963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3961),U_3964),U_3962)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3961),U_3963),U_3962)),U_3964)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3961),U_3963),U_3962)),U_3964))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),U_3963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3961),U_3964),U_3962))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3961),c_Groups_Ozero__class_Ozero(U_3961)),U_3962))
      | ~ class_Fields_Olinordered__field(U_3961) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

cnf(f_996_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3961),U_3963),U_3962)),U_3964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),U_3963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3961),U_3964),U_3962)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3961),c_Groups_Ozero__class_Ozero(U_3961)),U_3962))
    | ~ class_Fields_Olinordered__field(U_3961) ),
    inference(clausify,[status(thm)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),U_3963),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3961),U_3964),U_3962)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3961),U_3963),U_3962)),U_3964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3961),c_Groups_Ozero__class_Ozero(U_3961)),U_3962))
    | ~ class_Fields_Olinordered__field(U_3961) ),
    inference(clausify,[status(thm)],[f_996_2]) ).

fof(f_997_1,plain,
    ! [V_a_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).

fof(f_997_2,plain,
    ! [U_3968,U_3967,U_3966,U_3965] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3965),U_3967),U_3966)),U_3968))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),U_3967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3965),U_3968),U_3966))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),U_3967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3965),U_3968),U_3966)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3965),U_3967),U_3966)),U_3968)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
      | ~ class_Fields_Olinordered__field(U_3965) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

cnf(f_997_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),U_3967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3965),U_3968),U_3966)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3965),U_3967),U_3966)),U_3968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
    | ~ class_Fields_Olinordered__field(U_3965) ),
    inference(clausify,[status(thm)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3965),U_3967),U_3966)),U_3968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3965),U_3967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3965),U_3968),U_3966)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),U_3966))
    | ~ class_Fields_Olinordered__field(U_3965) ),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_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_998_2,plain,
    ! [U_3972,U_3971,U_3970,U_3969] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3969),U_3971),U_3970)),U_3972))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),U_3971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3969),U_3972),U_3970)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3969),c_Groups_Ozero__class_Ozero(U_3969)),U_3970))
      | ~ class_Fields_Olinordered__field(U_3969) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

cnf(f_998_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3969),U_3971),U_3970)),U_3972))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3969),U_3971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3969),U_3972),U_3970)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3969),c_Groups_Ozero__class_Ozero(U_3969)),U_3970))
    | ~ class_Fields_Olinordered__field(U_3969) ),
    inference(clausify,[status(thm)],[f_998_2]) ).

fof(f_999_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_999_2,plain,
    ! [U_3976,U_3975,U_3974,U_3973] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3973),U_3975),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3973),U_3976),U_3974)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3973),U_3975),U_3974)),U_3976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),U_3974))
      | ~ class_Fields_Olinordered__field(U_3973) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

cnf(f_999_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3973),U_3975),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3973),U_3976),U_3974)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3973),U_3975),U_3974)),U_3976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3973),c_Groups_Ozero__class_Ozero(U_3973)),U_3974))
    | ~ class_Fields_Olinordered__field(U_3973) ),
    inference(clausify,[status(thm)],[f_999_2]) ).

fof(f_1000_1,plain,
    ! [V_b_2,V_a_2,V_ca_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_ca_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_ca_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_ca_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_ca_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_1000_2,plain,
    ! [U_3980,U_3979,U_3978,U_3977] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3977),U_3980),U_3978)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3977),U_3979),U_3978))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3977),U_3979),U_3978)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3977),U_3980),U_3978))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3977),U_3978),c_Groups_Ozero__class_Ozero(U_3977)))
      | ~ class_Fields_Olinordered__field(U_3977) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3977),U_3979),U_3978)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3977),U_3980),U_3978)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3977),U_3978),c_Groups_Ozero__class_Ozero(U_3977)))
    | ~ class_Fields_Olinordered__field(U_3977) ),
    inference(clausify,[status(thm)],[f_1000_2]) ).

cnf(f_1000_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3977),U_3980),U_3978)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3977),U_3979),U_3978)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3977),U_3978),c_Groups_Ozero__class_Ozero(U_3977)))
    | ~ class_Fields_Olinordered__field(U_3977) ),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_1,plain,
    ! [V_a_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_1001_2,plain,
    ! [U_3984,U_3983,U_3982,U_3981] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3981),U_3983),U_3982)),U_3984))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3981),U_3984),U_3982)),U_3983)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3981),U_3984),U_3982)),U_3983))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3981),U_3983),U_3982)),U_3984)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),U_3982),c_Groups_Ozero__class_Ozero(U_3981)))
      | ~ class_Fields_Olinordered__field(U_3981) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

cnf(f_1001_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3981),U_3984),U_3982)),U_3983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3981),U_3983),U_3982)),U_3984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),U_3982),c_Groups_Ozero__class_Ozero(U_3981)))
    | ~ class_Fields_Olinordered__field(U_3981) ),
    inference(clausify,[status(thm)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3981),U_3983),U_3982)),U_3984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3981),U_3984),U_3982)),U_3983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),U_3982),c_Groups_Ozero__class_Ozero(U_3981)))
    | ~ class_Fields_Olinordered__field(U_3981) ),
    inference(clausify,[status(thm)],[f_1001_2]) ).

fof(f_1002_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_1002_2,plain,
    ! [U_3989,U_3988,U_3987,U_3986,U_3985] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),U_3986),U_3987)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),U_3988),U_3989)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3987),U_3989))
      | ~ class_Fields_Ofield__inverse__zero(U_3985) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

cnf(f_1002_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),U_3986),U_3987)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),U_3988),U_3989)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3987),U_3989))
    | ~ class_Fields_Ofield__inverse__zero(U_3985) ),
    inference(clausify,[status(thm)],[f_1002_2]) ).

fof(f_1003_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_1003_2,plain,
    ! [U_3993,U_3992,U_3991,U_3990] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3990),U_3992),U_3993)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3990),U_3991),U_3993)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),U_3993),c_Groups_Ozero__class_Ozero(U_3990)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),U_3991),U_3992))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3990) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

cnf(f_1003_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3990),U_3992),U_3993)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3990),U_3991),U_3993)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),U_3993),c_Groups_Ozero__class_Ozero(U_3990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3990),U_3991),U_3992))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3990) ),
    inference(clausify,[status(thm)],[f_1003_2]) ).

fof(f_1004_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_1004_2,plain,
    ! [U_3997,U_3996,U_3995,U_3994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3994),U_3995),U_3997)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3994),U_3996),U_3997)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),c_Groups_Ozero__class_Ozero(U_3994)),U_3997))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),U_3995),U_3996))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3994) ),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3994),U_3995),U_3997)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3994),U_3996),U_3997)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),c_Groups_Ozero__class_Ozero(U_3994)),U_3997))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3994),U_3995),U_3996))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3994) ),
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_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_1005_2,plain,
    ! [U_4000,U_3999,U_3998] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_4000))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_3999),c_Groups_Ozero__class_Ozero(U_3998))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_4000),c_Groups_Ozero__class_Ozero(U_3998)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_3999)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_4000))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_3999),c_Groups_Ozero__class_Ozero(U_3998))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_4000),c_Groups_Ozero__class_Ozero(U_3998)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_3999)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

cnf(f_1005_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_3999),c_Groups_Ozero__class_Ozero(U_3998)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_3999))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

cnf(f_1005_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_4000))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_3999))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

cnf(f_1005_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_3999),c_Groups_Ozero__class_Ozero(U_3998)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_4000),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

cnf(f_1005_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_4000))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_4000),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

cnf(f_1005_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_4000),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_3999))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

cnf(f_1005_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),c_Groups_Ozero__class_Ozero(U_3998)),U_4000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),U_3999),c_Groups_Ozero__class_Ozero(U_3998)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3998),U_3999),U_4000)),c_Groups_Ozero__class_Ozero(U_3998)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3998) ),
    inference(clausify,[status(thm)],[f_1005_2]) ).

fof(f_1006_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_1006_2,plain,
    ! [U_4003,U_4002,U_4001] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4003),c_Groups_Ozero__class_Ozero(U_4001)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4002),c_Groups_Ozero__class_Ozero(U_4001))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4003))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4002)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4003),c_Groups_Ozero__class_Ozero(U_4001)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4002),c_Groups_Ozero__class_Ozero(U_4001))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4003))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4002)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

cnf(f_1006_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4002),c_Groups_Ozero__class_Ozero(U_4001)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4002))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4003),c_Groups_Ozero__class_Ozero(U_4001)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4002))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

cnf(f_1006_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4002),c_Groups_Ozero__class_Ozero(U_4001)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

cnf(f_1006_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4003),c_Groups_Ozero__class_Ozero(U_4001)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

cnf(f_1006_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),U_4002))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

cnf(f_1006_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4003),c_Groups_Ozero__class_Ozero(U_4001)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),U_4002),c_Groups_Ozero__class_Ozero(U_4001)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4001),c_Groups_Ozero__class_Ozero(U_4001)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4001),U_4002),U_4003)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4001) ),
    inference(clausify,[status(thm)],[f_1006_2]) ).

fof(f_1007_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_1007_2,plain,
    ! [U_4006,U_4005,U_4004] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4006),c_Groups_Ozero__class_Ozero(U_4004)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4005),c_Groups_Ozero__class_Ozero(U_4004))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4006))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4005)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4006),c_Groups_Ozero__class_Ozero(U_4004)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4005),c_Groups_Ozero__class_Ozero(U_4004))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4006))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4005)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4005),c_Groups_Ozero__class_Ozero(U_4004)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

cnf(f_1007_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4006),c_Groups_Ozero__class_Ozero(U_4004)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

cnf(f_1007_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4005),c_Groups_Ozero__class_Ozero(U_4004)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4006))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

cnf(f_1007_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4006),c_Groups_Ozero__class_Ozero(U_4004)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4006))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

cnf(f_1007_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4006))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),U_4005))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

cnf(f_1007_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4006),c_Groups_Ozero__class_Ozero(U_4004)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),U_4005),c_Groups_Ozero__class_Ozero(U_4004)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4004),c_Groups_Ozero__class_Ozero(U_4004)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4004),U_4005),U_4006)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4004) ),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_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_1008_2,plain,
    ! [U_4009,U_4008,U_4007] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4009))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4008),c_Groups_Ozero__class_Ozero(U_4007))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4009),c_Groups_Ozero__class_Ozero(U_4007)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4008)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4009))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4008),c_Groups_Ozero__class_Ozero(U_4007))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4009),c_Groups_Ozero__class_Ozero(U_4007)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4008)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4008),c_Groups_Ozero__class_Ozero(U_4007)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

cnf(f_1008_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4009))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

cnf(f_1008_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4008),c_Groups_Ozero__class_Ozero(U_4007)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4009),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

cnf(f_1008_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4009))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4009),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

cnf(f_1008_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4009),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4008))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

cnf(f_1008_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),c_Groups_Ozero__class_Ozero(U_4007)),U_4009))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),U_4008),c_Groups_Ozero__class_Ozero(U_4007)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4007),U_4008),U_4009)),c_Groups_Ozero__class_Ozero(U_4007)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4007) ),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_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_1009_2,plain,
    ! [U_4012,U_4011,U_4010] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4010),U_4011),U_4012)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),U_4012))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),U_4011))
      | ~ class_Fields_Olinordered__field(U_4010) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4010),U_4011),U_4012)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),U_4012))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4010),c_Groups_Ozero__class_Ozero(U_4010)),U_4011))
    | ~ class_Fields_Olinordered__field(U_4010) ),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_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_1010_2,plain,
    ! [U_4015,U_4014,U_4013] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4013),U_4014),U_4015)),c_Groups_Ozero__class_Ozero(U_4013)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),U_4015),c_Groups_Ozero__class_Ozero(U_4013)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),c_Groups_Ozero__class_Ozero(U_4013)),U_4014))
      | ~ class_Fields_Olinordered__field(U_4013) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4013),U_4014),U_4015)),c_Groups_Ozero__class_Ozero(U_4013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),U_4015),c_Groups_Ozero__class_Ozero(U_4013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4013),c_Groups_Ozero__class_Ozero(U_4013)),U_4014))
    | ~ class_Fields_Olinordered__field(U_4013) ),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_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_1011_2,plain,
    ! [U_4018,U_4017,U_4016] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4016),U_4017),U_4018)),c_Groups_Ozero__class_Ozero(U_4016)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),c_Groups_Ozero__class_Ozero(U_4016)),U_4018))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),U_4017),c_Groups_Ozero__class_Ozero(U_4016)))
      | ~ class_Fields_Olinordered__field(U_4016) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

cnf(f_1011_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4016),U_4017),U_4018)),c_Groups_Ozero__class_Ozero(U_4016)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),c_Groups_Ozero__class_Ozero(U_4016)),U_4018))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4016),U_4017),c_Groups_Ozero__class_Ozero(U_4016)))
    | ~ class_Fields_Olinordered__field(U_4016) ),
    inference(clausify,[status(thm)],[f_1011_2]) ).

fof(f_1012_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_1012_2,plain,
    ! [U_4021,U_4020,U_4019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),c_Groups_Ozero__class_Ozero(U_4019)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4019),U_4020),U_4021)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),U_4021),c_Groups_Ozero__class_Ozero(U_4019)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),U_4020),c_Groups_Ozero__class_Ozero(U_4019)))
      | ~ class_Fields_Olinordered__field(U_4019) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

cnf(f_1012_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),c_Groups_Ozero__class_Ozero(U_4019)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4019),U_4020),U_4021)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),U_4021),c_Groups_Ozero__class_Ozero(U_4019)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4019),U_4020),c_Groups_Ozero__class_Ozero(U_4019)))
    | ~ class_Fields_Olinordered__field(U_4019) ),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_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_1013_2,plain,
    ! [U_4025,U_4024,U_4023,U_4022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4022),U_4023),U_4025)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4022),U_4024),U_4025)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),c_Groups_Ozero__class_Ozero(U_4022)),U_4025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),U_4023),U_4024))
      | ~ class_Fields_Olinordered__field(U_4022) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

cnf(f_1013_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4022),U_4023),U_4025)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4022),U_4024),U_4025)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),c_Groups_Ozero__class_Ozero(U_4022)),U_4025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4022),U_4023),U_4024))
    | ~ class_Fields_Olinordered__field(U_4022) ),
    inference(clausify,[status(thm)],[f_1013_2]) ).

fof(f_1014_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_1014_2,plain,
    ! [U_4029,U_4028,U_4027,U_4026] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4026),U_4028),U_4029)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4026),U_4027),U_4029)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4029),c_Groups_Ozero__class_Ozero(U_4026)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4027),U_4028))
      | ~ class_Fields_Olinordered__field(U_4026) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

cnf(f_1014_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4026),U_4028),U_4029)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4026),U_4027),U_4029)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4029),c_Groups_Ozero__class_Ozero(U_4026)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4027),U_4028))
    | ~ class_Fields_Olinordered__field(U_4026) ),
    inference(clausify,[status(thm)],[f_1014_2]) ).

fof(f_1015_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_1015_2,plain,
    ! [U_4034,U_4033,U_4032,U_4031,U_4030] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4033),U_4031) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4034),U_4032)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4033),U_4032) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4034),U_4031) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4033),U_4032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4034),U_4031)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4033),U_4031) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4034),U_4032) ) )
      | U_4032 = c_Groups_Ozero__class_Ozero(U_4030)
      | U_4031 = c_Groups_Ozero__class_Ozero(U_4030)
      | ~ class_Fields_Ofield(U_4030) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

cnf(f_1015_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4033),U_4032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4034),U_4031)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4033),U_4031) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4034),U_4032)
    | U_4032 = c_Groups_Ozero__class_Ozero(U_4030)
    | U_4031 = c_Groups_Ozero__class_Ozero(U_4030)
    | ~ class_Fields_Ofield(U_4030) ),
    inference(clausify,[status(thm)],[f_1015_2]) ).

cnf(f_1015_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4033),U_4031) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4030),U_4034),U_4032)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4033),U_4032) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4030),U_4034),U_4031)
    | U_4032 = c_Groups_Ozero__class_Ozero(U_4030)
    | U_4031 = c_Groups_Ozero__class_Ozero(U_4030)
    | ~ class_Fields_Ofield(U_4030) ),
    inference(clausify,[status(thm)],[f_1015_2]) ).

fof(f_1016_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_1016_2,plain,
    ! [U_4038,U_4037,U_4036,U_4035] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4035),U_4036),U_4037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4035),U_4036),U_4038)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4035),U_4037),U_4038)
      | U_4036 = c_Groups_Ozero__class_Ozero(U_4035)
      | ~ class_Fields_Ofield__inverse__zero(U_4035) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

cnf(f_1016_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4035),U_4036),U_4037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4035),U_4036),U_4038)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4035),U_4037),U_4038)
    | U_4036 = c_Groups_Ozero__class_Ozero(U_4035)
    | ~ class_Fields_Ofield__inverse__zero(U_4035) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

fof(f_1017_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_1017_2,plain,
    ! [U_4042,U_4041,U_4040,U_4039] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4039),U_4041),U_4040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4039),U_4042),U_4040)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4039),U_4041),U_4042)
      | U_4040 = c_Groups_Ozero__class_Ozero(U_4039)
      | ~ class_Fields_Ofield__inverse__zero(U_4039) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4039),U_4041),U_4040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4039),U_4042),U_4040)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4039),U_4041),U_4042)
    | U_4040 = c_Groups_Ozero__class_Ozero(U_4039)
    | ~ class_Fields_Ofield__inverse__zero(U_4039) ),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_1,plain,
    ! [V_a_2,V_ca_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
            & V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)
              | V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) != V_a_2 ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).

fof(f_1018_2,plain,
    ! [U_4046,U_4045,U_4044,U_4043] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) = U_4046
          | ( U_4046 != c_Groups_Ozero__class_Ozero(U_4043)
            & U_4045 = c_Groups_Ozero__class_Ozero(U_4043) )
          | ( U_4044 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4043),U_4046),U_4045)
            & U_4045 != c_Groups_Ozero__class_Ozero(U_4043) ) )
        & ( ( ( U_4046 = c_Groups_Ozero__class_Ozero(U_4043)
              | U_4045 != c_Groups_Ozero__class_Ozero(U_4043) )
            & ( U_4044 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4043),U_4046),U_4045)
              | U_4045 = c_Groups_Ozero__class_Ozero(U_4043) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) != U_4046 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

cnf(f_1018_3,plain,
    ( U_4044 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4043),U_4046),U_4045)
    | U_4045 = c_Groups_Ozero__class_Ozero(U_4043)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) != U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( U_4046 = c_Groups_Ozero__class_Ozero(U_4043)
    | U_4045 != c_Groups_Ozero__class_Ozero(U_4043)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) != U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_5,plain,
    ( U_4045 = c_Groups_Ozero__class_Ozero(U_4043)
    | U_4045 != c_Groups_Ozero__class_Ozero(U_4043)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) = U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_6,plain,
    ( U_4046 != c_Groups_Ozero__class_Ozero(U_4043)
    | U_4045 != c_Groups_Ozero__class_Ozero(U_4043)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) = U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_7,plain,
    ( U_4045 = c_Groups_Ozero__class_Ozero(U_4043)
    | U_4044 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4043),U_4046),U_4045)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) = U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_8,plain,
    ( U_4046 != c_Groups_Ozero__class_Ozero(U_4043)
    | U_4044 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4043),U_4046),U_4045)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4043),U_4044),U_4045) = U_4046
    | ~ class_Fields_Ofield__inverse__zero(U_4043) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

fof(f_1019_1,plain,
    ! [V_ca_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_ca_2)
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) != V_b_2
            & V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2
              | V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).

fof(f_1019_2,plain,
    ! [U_4050,U_4049,U_4048,U_4047] :
      ( ( ( U_4048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
          | ( U_4048 != c_Groups_Ozero__class_Ozero(U_4047)
            & U_4050 = c_Groups_Ozero__class_Ozero(U_4047) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4047),U_4048),U_4050) != U_4049
            & U_4050 != c_Groups_Ozero__class_Ozero(U_4047) ) )
        & ( ( ( U_4048 = c_Groups_Ozero__class_Ozero(U_4047)
              | U_4050 != c_Groups_Ozero__class_Ozero(U_4047) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4047),U_4048),U_4050) = U_4049
              | U_4050 = c_Groups_Ozero__class_Ozero(U_4047) ) )
          | U_4048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

cnf(f_1019_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4047),U_4048),U_4050) = U_4049
    | U_4050 = c_Groups_Ozero__class_Ozero(U_4047)
    | U_4048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

cnf(f_1019_4,plain,
    ( U_4048 = c_Groups_Ozero__class_Ozero(U_4047)
    | U_4050 != c_Groups_Ozero__class_Ozero(U_4047)
    | U_4048 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

cnf(f_1019_5,plain,
    ( U_4050 = c_Groups_Ozero__class_Ozero(U_4047)
    | U_4050 != c_Groups_Ozero__class_Ozero(U_4047)
    | U_4048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

cnf(f_1019_6,plain,
    ( U_4048 != c_Groups_Ozero__class_Ozero(U_4047)
    | U_4050 != c_Groups_Ozero__class_Ozero(U_4047)
    | U_4048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

cnf(f_1019_7,plain,
    ( U_4050 = c_Groups_Ozero__class_Ozero(U_4047)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4047),U_4048),U_4050) != U_4049
    | U_4048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

cnf(f_1019_8,plain,
    ( U_4048 != c_Groups_Ozero__class_Ozero(U_4047)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4047),U_4048),U_4050) != U_4049
    | U_4048 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4047),U_4049),U_4050)
    | ~ class_Fields_Ofield__inverse__zero(U_4047) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

fof(f_1020_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_1020_2,plain,
    ! [U_4053,U_4052,U_4051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4051),c_Groups_Ozero__class_Ozero(U_4051)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4051),U_4052),U_4053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4051),U_4053),c_Groups_Ozero__class_Ozero(U_4051)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4051),U_4052),c_Groups_Ozero__class_Ozero(U_4051)))
      | ~ class_Fields_Olinordered__field(U_4051) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4051),c_Groups_Ozero__class_Ozero(U_4051)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4051),U_4052),U_4053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4051),U_4053),c_Groups_Ozero__class_Ozero(U_4051)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4051),U_4052),c_Groups_Ozero__class_Ozero(U_4051)))
    | ~ class_Fields_Olinordered__field(U_4051) ),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_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_1021_2,plain,
    ! [U_4056,U_4055,U_4054] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4054),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4054),U_4055),U_4056)),c_Groups_Ozero__class_Ozero(U_4054)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4054),c_Groups_Ozero__class_Ozero(U_4054)),U_4056))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4054),U_4055),c_Groups_Ozero__class_Ozero(U_4054)))
      | ~ class_Fields_Olinordered__field(U_4054) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4054),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4054),U_4055),U_4056)),c_Groups_Ozero__class_Ozero(U_4054)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4054),c_Groups_Ozero__class_Ozero(U_4054)),U_4056))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4054),U_4055),c_Groups_Ozero__class_Ozero(U_4054)))
    | ~ class_Fields_Olinordered__field(U_4054) ),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_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_1022_2,plain,
    ! [U_4061,U_4060,U_4059,U_4058,U_4057] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4057),U_4058),U_4061)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4057),U_4059),U_4060)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),U_4060),U_4061))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4057),c_Groups_Ozero__class_Ozero(U_4057)),U_4060))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),U_4058),U_4059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),c_Groups_Ozero__class_Ozero(U_4057)),U_4058))
      | ~ class_Fields_Olinordered__field(U_4057) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4057),U_4058),U_4061)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4057),U_4059),U_4060)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),U_4060),U_4061))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4057),c_Groups_Ozero__class_Ozero(U_4057)),U_4060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),U_4058),U_4059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4057),c_Groups_Ozero__class_Ozero(U_4057)),U_4058))
    | ~ class_Fields_Olinordered__field(U_4057) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_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_1023_2,plain,
    ! [U_4066,U_4065,U_4064,U_4063,U_4062] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4062),U_4063),U_4066)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4062),U_4064),U_4065)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4062),U_4065),U_4066))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),c_Groups_Ozero__class_Ozero(U_4062)),U_4065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),U_4063),U_4064))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4062),c_Groups_Ozero__class_Ozero(U_4062)),U_4063))
      | ~ class_Fields_Olinordered__field(U_4062) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4062),U_4063),U_4066)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4062),U_4064),U_4065)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4062),U_4065),U_4066))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),c_Groups_Ozero__class_Ozero(U_4062)),U_4065))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4062),U_4063),U_4064))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4062),c_Groups_Ozero__class_Ozero(U_4062)),U_4063))
    | ~ class_Fields_Olinordered__field(U_4062) ),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_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_1024_2,plain,
    ! [U_4071,U_4070,U_4069,U_4068,U_4067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4067),U_4068),U_4071)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4067),U_4069),U_4070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),U_4070),U_4071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4070))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4067),U_4068),U_4069))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4068))
      | ~ class_Fields_Olinordered__field(U_4067) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

cnf(f_1024_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4067),U_4068),U_4071)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4067),U_4069),U_4070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),U_4070),U_4071))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4070))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4067),U_4068),U_4069))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4068))
    | ~ class_Fields_Olinordered__field(U_4067) ),
    inference(clausify,[status(thm)],[f_1024_2]) ).

fof(f_1025_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_1025_2,plain,
    ! [U_4074,U_4073,U_4072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4072),U_4073),U_4074)),c_Groups_Ozero__class_Ozero(U_4072)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4072),U_4074),c_Groups_Ozero__class_Ozero(U_4072)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4072),c_Groups_Ozero__class_Ozero(U_4072)),U_4073))
      | ~ class_Fields_Olinordered__field(U_4072) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4072),U_4073),U_4074)),c_Groups_Ozero__class_Ozero(U_4072)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4072),U_4074),c_Groups_Ozero__class_Ozero(U_4072)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4072),c_Groups_Ozero__class_Ozero(U_4072)),U_4073))
    | ~ class_Fields_Olinordered__field(U_4072) ),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_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_1026_2,plain,
    ! [U_4077,U_4076,U_4075] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4075),U_4076),U_4077)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),U_4077))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),U_4076))
      | ~ class_Fields_Olinordered__field(U_4075) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4075),U_4076),U_4077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),U_4077))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),c_Groups_Ozero__class_Ozero(U_4075)),U_4076))
    | ~ class_Fields_Olinordered__field(U_4075) ),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_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_1027_2,plain,
    ! [U_4081,U_4080,U_4079,U_4078] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4078),U_4081),U_4079)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4078),U_4081),U_4080)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),c_Groups_Ozero__class_Ozero(U_4078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),U_4079),U_4080)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),U_4081),c_Groups_Ozero__class_Ozero(U_4078)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),U_4079),U_4080))
      | ~ class_Fields_Olinordered__field(U_4078) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4078),U_4081),U_4079)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4078),U_4081),U_4080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),c_Groups_Ozero__class_Ozero(U_4078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),U_4079),U_4080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),U_4081),c_Groups_Ozero__class_Ozero(U_4078)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),U_4079),U_4080))
    | ~ class_Fields_Olinordered__field(U_4078) ),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_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_1028_2,plain,
    ! [U_4085,U_4084,U_4083,U_4082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4082),U_4085),U_4084)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4082),U_4085),U_4083)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),c_Groups_Ozero__class_Ozero(U_4082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4082),U_4084),U_4083)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),c_Groups_Ozero__class_Ozero(U_4082)),U_4085))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),U_4083),U_4084))
      | ~ class_Fields_Olinordered__field(U_4082) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4082),U_4085),U_4084)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4082),U_4085),U_4083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),c_Groups_Ozero__class_Ozero(U_4082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4082),U_4084),U_4083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),c_Groups_Ozero__class_Ozero(U_4082)),U_4085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4082),U_4083),U_4084))
    | ~ class_Fields_Olinordered__field(U_4082) ),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_1,plain,
    ! [V_a_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_1029_2,plain,
    ! [U_4089,U_4088,U_4087,U_4086] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4086),U_4088),U_4087)),U_4089))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4089),U_4087)),U_4088)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4089),U_4087)),U_4088))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4086),U_4088),U_4087)),U_4089)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),U_4087),c_Groups_Ozero__class_Ozero(U_4086)))
      | ~ class_Fields_Olinordered__field(U_4086) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4089),U_4087)),U_4088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4086),U_4088),U_4087)),U_4089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),U_4087),c_Groups_Ozero__class_Ozero(U_4086)))
    | ~ class_Fields_Olinordered__field(U_4086) ),
    inference(clausify,[status(thm)],[f_1029_2]) ).

cnf(f_1029_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4086),U_4088),U_4087)),U_4089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4086),U_4089),U_4087)),U_4088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4086),U_4087),c_Groups_Ozero__class_Ozero(U_4086)))
    | ~ class_Fields_Olinordered__field(U_4086) ),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    ! [V_b_2,V_a_2,V_ca_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_ca_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_ca_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_ca_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_ca_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_1030_2,plain,
    ! [U_4093,U_4092,U_4091,U_4090] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4092),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4090),U_4093),U_4091)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4092),U_4091))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4092),U_4091)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4092),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4090),U_4093),U_4091))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4091),c_Groups_Ozero__class_Ozero(U_4090)))
      | ~ class_Fields_Olinordered__field(U_4090) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4092),U_4091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4092),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4090),U_4093),U_4091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4091),c_Groups_Ozero__class_Ozero(U_4090)))
    | ~ class_Fields_Olinordered__field(U_4090) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

cnf(f_1030_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4092),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4090),U_4093),U_4091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4090),U_4092),U_4091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4090),U_4091),c_Groups_Ozero__class_Ozero(U_4090)))
    | ~ class_Fields_Olinordered__field(U_4090) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_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_1031_2,plain,
    ! [U_4097,U_4096,U_4095,U_4094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),U_4096),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4094),U_4097),U_4095)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4094),U_4096),U_4095)),U_4097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),c_Groups_Ozero__class_Ozero(U_4094)),U_4095))
      | ~ class_Fields_Olinordered__field(U_4094) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),U_4096),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4094),U_4097),U_4095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4094),U_4096),U_4095)),U_4097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4094),c_Groups_Ozero__class_Ozero(U_4094)),U_4095))
    | ~ class_Fields_Olinordered__field(U_4094) ),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_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_1032_2,plain,
    ! [U_4101,U_4100,U_4099,U_4098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4098),U_4100),U_4099)),U_4101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),U_4100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4098),U_4101),U_4099)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),c_Groups_Ozero__class_Ozero(U_4098)),U_4099))
      | ~ class_Fields_Olinordered__field(U_4098) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4098),U_4100),U_4099)),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),U_4100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4098),U_4101),U_4099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4098),c_Groups_Ozero__class_Ozero(U_4098)),U_4099))
    | ~ class_Fields_Olinordered__field(U_4098) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_1,plain,
    ! [V_a_2,V_b_2,V_ca_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_ca_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_ca_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_ca_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).

fof(f_1033_2,plain,
    ! [U_4105,U_4104,U_4103,U_4102] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4102),U_4104),U_4103)),U_4105))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4102),U_4105),U_4103))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4102),U_4105),U_4103)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4102),U_4104),U_4103)),U_4105)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),c_Groups_Ozero__class_Ozero(U_4102)),U_4103))
      | ~ class_Fields_Olinordered__field(U_4102) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4102),U_4105),U_4103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4102),U_4104),U_4103)),U_4105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),c_Groups_Ozero__class_Ozero(U_4102)),U_4103))
    | ~ class_Fields_Olinordered__field(U_4102) ),
    inference(clausify,[status(thm)],[f_1033_2]) ).

cnf(f_1033_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4102),U_4104),U_4103)),U_4105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4102),U_4105),U_4103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4102),c_Groups_Ozero__class_Ozero(U_4102)),U_4103))
    | ~ class_Fields_Olinordered__field(U_4102) ),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_1,plain,
    ! [V_b_2,V_a_2,V_ca_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_ca_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_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_ca_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_ca_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).

fof(f_1034_2,plain,
    ! [U_4109,U_4108,U_4107,U_4106] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4106),U_4109),U_4107)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4106),U_4108),U_4107)),U_4109)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4106),U_4108),U_4107)),U_4109))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4106),U_4109),U_4107))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),c_Groups_Ozero__class_Ozero(U_4106)),U_4107))
      | ~ class_Fields_Olinordered__field(U_4106) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4106),U_4108),U_4107)),U_4109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4106),U_4109),U_4107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),c_Groups_Ozero__class_Ozero(U_4106)),U_4107))
    | ~ class_Fields_Olinordered__field(U_4106) ),
    inference(clausify,[status(thm)],[f_1034_2]) ).

cnf(f_1034_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),U_4108),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4106),U_4109),U_4107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4106),U_4108),U_4107)),U_4109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),c_Groups_Ozero__class_Ozero(U_4106)),U_4107))
    | ~ class_Fields_Olinordered__field(U_4106) ),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    ! [V_a_2,V_ca_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_ca_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_ca_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_ca_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).

fof(f_1035_2,plain,
    ! [U_4113,U_4112,U_4111,U_4110] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4112),c_Groups_Ozero__class_Ozero(U_4110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

cnf(f_1035_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),c_Groups_Ozero__class_Ozero(U_4110)),U_4113))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)),U_4111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),U_4111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4113),U_4112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4110),U_4111),U_4112)),U_4113))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4110) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_1,plain,
    ! [V_ca_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_ca_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_ca_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_ca_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).

fof(f_1036_2,plain,
    ! [U_4117,U_4116,U_4115,U_4114] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),c_Groups_Ozero__class_Ozero(U_4114)),U_4117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4117),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),c_Groups_Ozero__class_Ozero(U_4114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4114),U_4115),U_4117)),U_4116))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4114),U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4114),U_4116),U_4117)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4114) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_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_1037_2,plain,
    ! [U_4121,U_4120,U_4119,U_4118] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4118),U_4120),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4118),U_4121),U_4119)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4118),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4118),U_4121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),U_4120),U_4119))),U_4119)
      | U_4119 = c_Groups_Ozero__class_Ozero(U_4118)
      | ~ class_Fields_Ofield__inverse__zero(U_4118) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4118),U_4120),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4118),U_4121),U_4119)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4118),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4118),U_4121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4118),U_4120),U_4119))),U_4119)
    | U_4119 = c_Groups_Ozero__class_Ozero(U_4118)
    | ~ class_Fields_Ofield__inverse__zero(U_4118) ),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_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_1038_2,plain,
    ! [U_4125,U_4124,U_4123,U_4122] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),U_4124),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4122),U_4125),U_4123)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),U_4123)
      | U_4123 = c_Groups_Ozero__class_Ozero(U_4122)
      | ~ class_Fields_Ofield(U_4122) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),U_4124),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4122),U_4125),U_4123)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),U_4123)
    | U_4123 = c_Groups_Ozero__class_Ozero(U_4122)
    | ~ class_Fields_Ofield(U_4122) ),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_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_1039_2,plain,
    ! [U_4129,U_4128,U_4127,U_4126] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),U_4128),U_4127)),U_4129) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),U_4129),U_4127))),U_4127)
      | U_4127 = c_Groups_Ozero__class_Ozero(U_4126)
      | ~ class_Fields_Ofield__inverse__zero(U_4126) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),U_4128),U_4127)),U_4129) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4126),U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),U_4129),U_4127))),U_4127)
    | U_4127 = c_Groups_Ozero__class_Ozero(U_4126)
    | ~ class_Fields_Ofield__inverse__zero(U_4126) ),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_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_1040_2,plain,
    ! [U_4133,U_4132,U_4131,U_4130] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4130),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4130),U_4132),U_4131)),U_4133) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4130),U_4132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4131),U_4133))),U_4131)
      | U_4131 = c_Groups_Ozero__class_Ozero(U_4130)
      | ~ class_Fields_Ofield(U_4130) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4130),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4130),U_4132),U_4131)),U_4133) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4130),U_4132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4131),U_4133))),U_4131)
    | U_4131 = c_Groups_Ozero__class_Ozero(U_4130)
    | ~ class_Fields_Ofield(U_4130) ),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_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_1041_2,plain,
    ! [U_4138,U_4137,U_4136,U_4135,U_4134] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4134),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),U_4137),U_4135)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),U_4138),U_4136)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4137),U_4136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4138),U_4135))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4135),U_4136))
      | U_4136 = c_Groups_Ozero__class_Ozero(U_4134)
      | U_4135 = c_Groups_Ozero__class_Ozero(U_4134)
      | ~ class_Fields_Ofield(U_4134) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4134),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),U_4137),U_4135)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),U_4138),U_4136)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4137),U_4136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4138),U_4135))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4134),U_4135),U_4136))
    | U_4136 = c_Groups_Ozero__class_Ozero(U_4134)
    | U_4135 = c_Groups_Ozero__class_Ozero(U_4134)
    | ~ class_Fields_Ofield(U_4134) ),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_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_1042_2,plain,
    ! [U_4143,U_4142,U_4141,U_4140,U_4139] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),U_4142),U_4140)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),U_4143),U_4141)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4142),U_4141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4143),U_4140))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4140),U_4141))
      | U_4141 = c_Groups_Ozero__class_Ozero(U_4139)
      | U_4140 = c_Groups_Ozero__class_Ozero(U_4139)
      | ~ class_Fields_Ofield(U_4139) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),U_4142),U_4140)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),U_4143),U_4141)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4139),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4142),U_4141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4143),U_4140))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),U_4140),U_4141))
    | U_4141 = c_Groups_Ozero__class_Ozero(U_4139)
    | U_4140 = c_Groups_Ozero__class_Ozero(U_4139)
    | ~ class_Fields_Ofield(U_4139) ),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_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_1043_2,plain,
    ! [U_4147,U_4146,U_4145,U_4144] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4144),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4144),U_4146),U_4145)),U_4147) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4144),U_4146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147))),U_4145)
      | U_4145 = c_Groups_Ozero__class_Ozero(U_4144)
      | ~ class_Fields_Ofield(U_4144) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4144),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4144),U_4146),U_4145)),U_4147) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4144),U_4146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4144),U_4145),U_4147))),U_4145)
    | U_4145 = c_Groups_Ozero__class_Ozero(U_4144)
    | ~ class_Fields_Ofield(U_4144) ),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_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_1044_2,plain,
    ! [U_4151,U_4150,U_4149,U_4148] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4148),U_4150),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4148),U_4151),U_4149)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4148),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4148),U_4149),U_4150)),U_4151)),U_4149)
      | U_4149 = c_Groups_Ozero__class_Ozero(U_4148)
      | ~ class_Fields_Ofield(U_4148) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4148),U_4150),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4148),U_4151),U_4149)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4148),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4148),U_4149),U_4150)),U_4151)),U_4149)
    | U_4149 = c_Groups_Ozero__class_Ozero(U_4148)
    | ~ class_Fields_Ofield(U_4148) ),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_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_1045_2,plain,
    ! [U_4154,U_4153,U_4152] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4152),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4152),U_4153),U_4154)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4152),c_Groups_Oone__class_Oone(U_4152)),c_Groups_Oone__class_Oone(U_4152)))),U_4154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4152),U_4153),U_4154))
      | ~ class_Fields_Olinordered__field(U_4152) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4152),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4152),U_4153),U_4154)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4152),c_Groups_Oone__class_Oone(U_4152)),c_Groups_Oone__class_Oone(U_4152)))),U_4154))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4152),U_4153),U_4154))
    | ~ class_Fields_Olinordered__field(U_4152) ),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_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_1046_2,plain,
    ! [U_4157,U_4156,U_4155] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4155),U_4156),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4155),U_4156),U_4157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4155),c_Groups_Oone__class_Oone(U_4155)),c_Groups_Oone__class_Oone(U_4155)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4155),U_4156),U_4157))
      | ~ class_Fields_Olinordered__field(U_4155) ),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4155),U_4156),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4155),U_4156),U_4157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4155),c_Groups_Oone__class_Oone(U_4155)),c_Groups_Oone__class_Oone(U_4155)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4155),U_4156),U_4157))
    | ~ class_Fields_Olinordered__field(U_4155) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_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_1047_2,plain,
    ! [U_4161,U_4160,U_4159,U_4158] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4158),U_4161),U_4159)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4158),U_4161),U_4160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4158),c_Groups_Ozero__class_Ozero(U_4158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),U_4159),U_4160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),U_4161),c_Groups_Ozero__class_Ozero(U_4158)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),U_4159),U_4160))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4158) ),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4158),U_4161),U_4159)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4158),U_4161),U_4160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4158),c_Groups_Ozero__class_Ozero(U_4158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),U_4159),U_4160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),U_4161),c_Groups_Ozero__class_Ozero(U_4158)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4158),U_4159),U_4160))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4158) ),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_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_1048_2,plain,
    ! [U_4165,U_4164,U_4163,U_4162] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4162),U_4165),U_4164)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4162),U_4165),U_4163)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4162),c_Groups_Ozero__class_Ozero(U_4162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4162),U_4164),U_4163)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),c_Groups_Ozero__class_Ozero(U_4162)),U_4165))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),U_4163),U_4164))
      | ~ class_Fields_Olinordered__field(U_4162) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4162),U_4165),U_4164)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4162),U_4165),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4162),c_Groups_Ozero__class_Ozero(U_4162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4162),U_4164),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),c_Groups_Ozero__class_Ozero(U_4162)),U_4165))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4162),U_4163),U_4164))
    | ~ class_Fields_Olinordered__field(U_4162) ),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_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_1049_2,plain,
    ! [U_4171,U_4170,U_4169,U_4168,U_4167] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4167),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4169)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4170))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)))
      | ? [U_4166] :
          ( hAPP(U_4171,U_4166) = c_Groups_Ozero__class_Ozero(U_4167)
          & hBOOL(hAPP(hAPP(c_member(U_4168),U_4166),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4170))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4169))
      | ~ class_Fields_Ofield(U_4167) ),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_4171,U_4170,U_4169,U_4168,U_4167] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4167),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4169)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4170))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)))
      | ( hAPP(U_4171,sK78(U_4171,U_4170,U_4169,U_4168,U_4167)) = c_Groups_Ozero__class_Ozero(U_4167)
        & hBOOL(hAPP(hAPP(c_member(U_4168),sK78(U_4171,U_4170,U_4169,U_4168,U_4167)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4170))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4169))
      | ~ class_Fields_Ofield(U_4167) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_4166,sK78(U_4171,U_4170,U_4169,U_4168,U_4167))],[f_1049_2]) ).

cnf(f_1049_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4168),sK78(U_4171,U_4170,U_4169,U_4168,U_4167)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4167),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4169)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4170))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4170))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4169))
    | ~ class_Fields_Ofield(U_4167) ),
    inference(clausify,[status(thm)],[f_1049_3]) ).

cnf(f_1049_5,plain,
    ( hAPP(U_4171,sK78(U_4171,U_4170,U_4169,U_4168,U_4167)) = c_Groups_Ozero__class_Ozero(U_4167)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4167),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4169)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),U_4170))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4168,U_4167),U_4171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,tc_HOL_Obool)),U_4169),U_4170)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4170))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4168),U_4169))
    | ~ class_Fields_Ofield(U_4167) ),
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_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_1050_2,plain,
    ! [U_4177,U_4176,U_4175,U_4174,U_4173] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4175)
      | ? [U_4172] :
          ( hAPP(U_4177,U_4172) != c_Groups_Ozero__class_Ozero(U_4173)
          & hBOOL(hAPP(hAPP(c_member(U_4174),U_4172),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4174,tc_HOL_Obool)),U_4175),U_4176))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4174,tc_HOL_Obool)),U_4176),U_4175))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4174),U_4175))
      | ~ class_Groups_Ocomm__monoid__add(U_4173) ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ! [U_4177,U_4176,U_4175,U_4174,U_4173] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4175)
      | ( hAPP(U_4177,sK79(U_4177,U_4176,U_4175,U_4174,U_4173)) != c_Groups_Ozero__class_Ozero(U_4173)
        & hBOOL(hAPP(hAPP(c_member(U_4174),sK79(U_4177,U_4176,U_4175,U_4174,U_4173)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4174,tc_HOL_Obool)),U_4175),U_4176))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4174,tc_HOL_Obool)),U_4176),U_4175))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4174),U_4175))
      | ~ class_Groups_Ocomm__monoid__add(U_4173) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_4172,sK79(U_4177,U_4176,U_4175,U_4174,U_4173))],[f_1050_2]) ).

cnf(f_1050_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4174),sK79(U_4177,U_4176,U_4175,U_4174,U_4173)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4174,tc_HOL_Obool)),U_4175),U_4176)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4175)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4174,tc_HOL_Obool)),U_4176),U_4175))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4174),U_4175))
    | ~ class_Groups_Ocomm__monoid__add(U_4173) ),
    inference(clausify,[status(thm)],[f_1050_3]) ).

cnf(f_1050_5,plain,
    ( hAPP(U_4177,sK79(U_4177,U_4176,U_4175,U_4174,U_4173)) != c_Groups_Ozero__class_Ozero(U_4173)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4174,U_4173),U_4177),U_4175)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4174,tc_HOL_Obool)),U_4176),U_4175))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4174),U_4175))
    | ~ class_Groups_Ocomm__monoid__add(U_4173) ),
    inference(clausify,[status(thm)],[f_1050_3]) ).

fof(f_1051_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_1051_2,plain,
    ! [U_4181,U_4180,U_4179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),U_4180),U_4181))
      | ? [U_4178] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4179),U_4178),U_4180)),U_4181))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),U_4178),c_Groups_Oone__class_Oone(U_4179)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),c_Groups_Ozero__class_Ozero(U_4179)),U_4178)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4179) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_4181,U_4180,U_4179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),U_4180),U_4181))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4179),sK80(U_4181,U_4180,U_4179)),U_4180)),U_4181))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),sK80(U_4181,U_4180,U_4179)),c_Groups_Oone__class_Oone(U_4179)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),c_Groups_Ozero__class_Ozero(U_4179)),sK80(U_4181,U_4180,U_4179))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4179) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_4178,sK80(U_4181,U_4180,U_4179))],[f_1051_2]) ).

cnf(f_1051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),c_Groups_Ozero__class_Ozero(U_4179)),sK80(U_4181,U_4180,U_4179)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),U_4180),U_4181))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4179) ),
    inference(clausify,[status(thm)],[f_1051_3]) ).

cnf(f_1051_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4179),sK80(U_4181,U_4180,U_4179)),c_Groups_Oone__class_Oone(U_4179)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),U_4180),U_4181))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4179) ),
    inference(clausify,[status(thm)],[f_1051_3]) ).

cnf(f_1051_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4179),sK80(U_4181,U_4180,U_4179)),U_4180)),U_4181))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4179),U_4180),U_4181))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4179) ),
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_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_1052_2,plain,
    ! [U_4185,U_4184,U_4183] :
      ( 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_4183,tc_Nat_Onat),U_4185),U_4184)))
      | ? [U_4182] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4185,U_4182)))
          & hBOOL(hAPP(hAPP(c_member(U_4183),U_4182),U_4184)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4183),U_4184)) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ! [U_4185,U_4184,U_4183] :
      ( 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_4183,tc_Nat_Onat),U_4185),U_4184)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4185,sK81(U_4185,U_4184,U_4183))))
        & hBOOL(hAPP(hAPP(c_member(U_4183),sK81(U_4185,U_4184,U_4183)),U_4184)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4183),U_4184)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_4182,sK81(U_4185,U_4184,U_4183))],[f_1052_2]) ).

cnf(f_1052_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4183),sK81(U_4185,U_4184,U_4183)),U_4184))
    | 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_4183,tc_Nat_Onat),U_4185),U_4184)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4183),U_4184)) ),
    inference(clausify,[status(thm)],[f_1052_3]) ).

cnf(f_1052_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4185,sK81(U_4185,U_4184,U_4183))))
    | 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_4183,tc_Nat_Onat),U_4185),U_4184)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4183),U_4184)) ),
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_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_1053_2,plain,
    ! [U_4190,U_4189,U_4188,U_4187] :
      ( ? [U_4186] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4188,U_4186)))
          & hBOOL(hAPP(hAPP(c_member(U_4187),U_4186),U_4189)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,tc_Nat_Onat),U_4188),U_4189) != hAPP(c_Nat_OSuc,U_4190) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ! [U_4190,U_4189,U_4188,U_4187] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4188,sK82(U_4190,U_4189,U_4188,U_4187))))
        & hBOOL(hAPP(hAPP(c_member(U_4187),sK82(U_4190,U_4189,U_4188,U_4187)),U_4189)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,tc_Nat_Onat),U_4188),U_4189) != hAPP(c_Nat_OSuc,U_4190) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_4186,sK82(U_4190,U_4189,U_4188,U_4187))],[f_1053_2]) ).

cnf(f_1053_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4187),sK82(U_4190,U_4189,U_4188,U_4187)),U_4189))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,tc_Nat_Onat),U_4188),U_4189) != hAPP(c_Nat_OSuc,U_4190) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

cnf(f_1053_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_4188,sK82(U_4190,U_4189,U_4188,U_4187))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,tc_Nat_Onat),U_4188),U_4189) != hAPP(c_Nat_OSuc,U_4190) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I5_J]) ).

fof(f_1054_2,plain,
    ! [U_4193,U_4192,U_4191] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_4191,U_4192,U_4193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4192)),c_Com_Ocom_Ocom__size(U_4193))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_4191,U_4192,U_4193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4192)),c_Com_Ocom_Ocom__size(U_4193))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I13_J]) ).

fof(f_1055_2,plain,
    ! [U_4196,U_4195,U_4194] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_4194,U_4195,U_4196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4195)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4196))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

cnf(f_1055_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_4194,U_4195,U_4196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4195)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4196))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1055_2]) ).

fof(f_1056_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_1056_2,plain,
    ! [U_4199,U_4198] :
      ( hAPP(c_Finite__Set_Ocard(U_4198),U_4199) = 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_4197] : hBOOL(hAPP(hAPP(c_member(U_4198),U_4197),U_4199)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4198),U_4199)) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

fof(f_1056_3,plain,
    ! [U_4199,U_4198] :
      ( hAPP(c_Finite__Set_Ocard(U_4198),U_4199) = 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_4198),sK83(U_4199,U_4198)),U_4199)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4198),U_4199)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_4197,sK83(U_4199,U_4198))],[f_1056_2]) ).

cnf(f_1056_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4198),sK83(U_4199,U_4198)),U_4199))
    | hAPP(c_Finite__Set_Ocard(U_4198),U_4199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4198),U_4199)) ),
    inference(clausify,[status(thm)],[f_1056_3]) ).

cnf(f_1056_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_4198),U_4199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4198),U_4199)) ),
    inference(clausify,[status(thm)],[f_1056_3]) ).

fof(f_1057_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
      ( ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
        | V_com2_2 != V_com2_H_2
        | V_com1_2 != V_com1_H_2
        | V_fun_2 != V_fun_H_2 )
      & ( ( V_com2_2 = V_com2_H_2
          & V_com1_2 = V_com1_H_2
          & V_fun_2 = V_fun_H_2 )
        | c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J]) ).

fof(f_1057_2,plain,
    ! [U_4205,U_4204,U_4203,U_4202,U_4201,U_4200] :
      ( ( c_Com_Ocom_OCond(U_4200,U_4201,U_4202) = c_Com_Ocom_OCond(U_4203,U_4204,U_4205)
        | U_4202 != U_4205
        | U_4201 != U_4204
        | U_4200 != U_4203 )
      & ( ( U_4202 = U_4205
          & U_4201 = U_4204
          & U_4200 = U_4203 )
        | c_Com_Ocom_OCond(U_4200,U_4201,U_4202) != c_Com_Ocom_OCond(U_4203,U_4204,U_4205) ) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ( ! [U_4217,U_4215,U_4213,U_4211,U_4209,U_4207] :
        ( c_Com_Ocom_OCond(U_4207,U_4209,U_4211) = c_Com_Ocom_OCond(U_4213,U_4215,U_4217)
        | U_4211 != U_4217
        | U_4209 != U_4215
        | U_4207 != U_4213 )
    & ! [U_4216,U_4214,U_4212,U_4210,U_4208,U_4206] :
        ( ( U_4210 = U_4216
          & U_4208 = U_4214
          & U_4206 = U_4212 )
        | c_Com_Ocom_OCond(U_4206,U_4208,U_4210) != c_Com_Ocom_OCond(U_4212,U_4214,U_4216) ) ),
    inference(miniscope,[status(thm)],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( U_4206 = U_4212
    | c_Com_Ocom_OCond(U_4206,U_4208,U_4210) != c_Com_Ocom_OCond(U_4212,U_4214,U_4216) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

cnf(f_1057_5,plain,
    ( U_4208 = U_4214
    | c_Com_Ocom_OCond(U_4206,U_4208,U_4210) != c_Com_Ocom_OCond(U_4212,U_4214,U_4216) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

cnf(f_1057_6,plain,
    ( U_4210 = U_4216
    | c_Com_Ocom_OCond(U_4206,U_4208,U_4210) != c_Com_Ocom_OCond(U_4212,U_4214,U_4216) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

cnf(f_1057_7,plain,
    ( c_Com_Ocom_OCond(U_4207,U_4209,U_4211) = c_Com_Ocom_OCond(U_4213,U_4215,U_4217)
    | U_4211 != U_4217
    | U_4209 != U_4215
    | U_4207 != U_4213 ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

fof(f_1058_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I44_J]) ).

fof(f_1058_2,plain,
    ! [U_4222,U_4221,U_4220,U_4219,U_4218] : c_Com_Ocom_OSemi(U_4218,U_4219) != c_Com_Ocom_OCond(U_4220,U_4221,U_4222),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    c_Com_Ocom_OSemi(U_4218,U_4219) != c_Com_Ocom_OCond(U_4220,U_4221,U_4222),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I45_J]) ).

fof(f_1059_2,plain,
    ! [U_4227,U_4226,U_4225,U_4224,U_4223] : c_Com_Ocom_OCond(U_4223,U_4224,U_4225) != c_Com_Ocom_OSemi(U_4226,U_4227),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    c_Com_Ocom_OCond(U_4223,U_4224,U_4225) != c_Com_Ocom_OSemi(U_4226,U_4227),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I14_J]) ).

fof(f_1060_2,plain,
    ! [U_4230,U_4229,U_4228] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_4228,U_4229,U_4230),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_4228,U_4229,U_4230),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I15_J]) ).

fof(f_1061_2,plain,
    ! [U_4233,U_4232,U_4231] : c_Com_Ocom_OCond(U_4231,U_4232,U_4233) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    c_Com_Ocom_OCond(U_4231,U_4232,U_4233) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    ! [V_ca_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_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_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_1062_2,plain,
    ! [U_4238,U_4237,U_4236,U_4235] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),hAPP(hAPP(c_Finite__Set_Ofold(U_4235,U_4235,c_Lattices_Osemilattice__sup__class_Osup(U_4235)),U_4238),U_4236)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4235),U_4237),U_4238)))
      | ? [U_4234] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),U_4234),U_4237))
          & hBOOL(hAPP(hAPP(c_member(U_4235),U_4234),U_4236)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4235),U_4236))
      | ~ class_Lattices_Osemilattice__sup(U_4235) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ! [U_4238,U_4237,U_4236,U_4235] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),hAPP(hAPP(c_Finite__Set_Ofold(U_4235,U_4235,c_Lattices_Osemilattice__sup__class_Osup(U_4235)),U_4238),U_4236)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4235),U_4237),U_4238)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),sK84(U_4238,U_4237,U_4236,U_4235)),U_4237))
        & hBOOL(hAPP(hAPP(c_member(U_4235),sK84(U_4238,U_4237,U_4236,U_4235)),U_4236)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4235),U_4236))
      | ~ class_Lattices_Osemilattice__sup(U_4235) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4234,sK84(U_4238,U_4237,U_4236,U_4235))],[f_1062_2]) ).

cnf(f_1062_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4235),sK84(U_4238,U_4237,U_4236,U_4235)),U_4236))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),hAPP(hAPP(c_Finite__Set_Ofold(U_4235,U_4235,c_Lattices_Osemilattice__sup__class_Osup(U_4235)),U_4238),U_4236)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4235),U_4237),U_4238)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4235),U_4236))
    | ~ class_Lattices_Osemilattice__sup(U_4235) ),
    inference(clausify,[status(thm)],[f_1062_3]) ).

cnf(f_1062_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),sK84(U_4238,U_4237,U_4236,U_4235)),U_4237))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4235),hAPP(hAPP(c_Finite__Set_Ofold(U_4235,U_4235,c_Lattices_Osemilattice__sup__class_Osup(U_4235)),U_4238),U_4236)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4235),U_4237),U_4238)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4235),U_4236))
    | ~ class_Lattices_Osemilattice__sup(U_4235) ),
    inference(clausify,[status(thm)],[f_1062_3]) ).

fof(f_1063_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_1063_2,plain,
    ! [U_4239] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4239) = 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_4239)),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_4239))) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4239) = 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_4239)),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_4239))) ),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I11_J]) ).

fof(f_1064_2,plain,
    ! [U_4242,U_4241,U_4240] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_4240,U_4241,U_4242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4242)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_4240,U_4241,U_4242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4242)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I3_J]) ).

fof(f_1065_2,plain,
    ! [U_4245,U_4244,U_4243] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_4243,U_4244,U_4245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4245)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_4243,U_4244,U_4245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4245)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_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_1066_2,plain,
    ! [U_4249,U_4248,U_4247] :
      ( ? [U_4246] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4247,tc_HOL_Obool)),U_4246),U_4249))
          & hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),U_4246)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4247,tc_HOL_Obool),U_4249))) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ! [U_4249,U_4248,U_4247] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4247,tc_HOL_Obool)),sK85(U_4249,U_4248,U_4247)),U_4249))
        & hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),sK85(U_4249,U_4248,U_4247))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4247,tc_HOL_Obool),U_4249))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_4246,sK85(U_4249,U_4248,U_4247))],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),sK85(U_4249,U_4248,U_4247)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4247,tc_HOL_Obool),U_4249))) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

cnf(f_1066_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4247,tc_HOL_Obool)),sK85(U_4249,U_4248,U_4247)),U_4249))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4247),U_4248),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4247,tc_HOL_Obool),U_4249))) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_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_1067_2,plain,
    ! [U_4254,U_4253,U_4252,U_4251] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4252,U_4251),U_4254),U_4253)))
      | ? [U_4250] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(U_4254,U_4250)))
          & hBOOL(hAPP(hAPP(c_member(U_4252),U_4250),U_4253)) )
      | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ! [U_4254,U_4253,U_4252,U_4251] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4252,U_4251),U_4254),U_4253)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(U_4254,sK86(U_4254,U_4253,U_4252,U_4251))))
        & hBOOL(hAPP(hAPP(c_member(U_4252),sK86(U_4254,U_4253,U_4252,U_4251)),U_4253)) )
      | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_4250,sK86(U_4254,U_4253,U_4252,U_4251))],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4252),sK86(U_4254,U_4253,U_4252,U_4251)),U_4253))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4252,U_4251),U_4254),U_4253)))
    | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(U_4254,sK86(U_4254,U_4253,U_4252,U_4251))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4251),c_Groups_Ozero__class_Ozero(U_4251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4252,U_4251),U_4254),U_4253)))
    | ~ class_Rings_Olinordered__semidom(U_4251) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_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_1068_2,plain,
    ! [U_4259,U_4258,U_4257,U_4256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4257,U_4256),U_4259),U_4258)))
      | ? [U_4255] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(U_4259,U_4255)))
          & hBOOL(hAPP(hAPP(c_member(U_4257),U_4255),U_4258)) )
      | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ! [U_4259,U_4258,U_4257,U_4256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4257,U_4256),U_4259),U_4258)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(U_4259,sK87(U_4259,U_4258,U_4257,U_4256))))
        & hBOOL(hAPP(hAPP(c_member(U_4257),sK87(U_4259,U_4258,U_4257,U_4256)),U_4258)) )
      | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_4255,sK87(U_4259,U_4258,U_4257,U_4256))],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4257),sK87(U_4259,U_4258,U_4257,U_4256)),U_4258))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4257,U_4256),U_4259),U_4258)))
    | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

cnf(f_1068_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(U_4259,sK87(U_4259,U_4258,U_4257,U_4256))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4257,U_4256),U_4259),U_4258)))
    | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

fof(f_1069_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
      ( ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
        | V_com_2 != V_com_H_2
        | V_fun_2 != V_fun_H_2
        | V_loc_2 != V_loc_H_2 )
      & ( ( V_com_2 = V_com_H_2
          & V_fun_2 = V_fun_H_2
          & V_loc_2 = V_loc_H_2 )
        | c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J]) ).

fof(f_1069_2,plain,
    ! [U_4265,U_4264,U_4263,U_4262,U_4261,U_4260] :
      ( ( c_Com_Ocom_OLocal(U_4260,U_4261,U_4262) = c_Com_Ocom_OLocal(U_4263,U_4264,U_4265)
        | U_4262 != U_4265
        | U_4261 != U_4264
        | U_4260 != U_4263 )
      & ( ( U_4262 = U_4265
          & U_4261 = U_4264
          & U_4260 = U_4263 )
        | c_Com_Ocom_OLocal(U_4260,U_4261,U_4262) != c_Com_Ocom_OLocal(U_4263,U_4264,U_4265) ) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ( ! [U_4277,U_4275,U_4273,U_4271,U_4269,U_4267] :
        ( c_Com_Ocom_OLocal(U_4267,U_4269,U_4271) = c_Com_Ocom_OLocal(U_4273,U_4275,U_4277)
        | U_4271 != U_4277
        | U_4269 != U_4275
        | U_4267 != U_4273 )
    & ! [U_4276,U_4274,U_4272,U_4270,U_4268,U_4266] :
        ( ( U_4270 = U_4276
          & U_4268 = U_4274
          & U_4266 = U_4272 )
        | c_Com_Ocom_OLocal(U_4266,U_4268,U_4270) != c_Com_Ocom_OLocal(U_4272,U_4274,U_4276) ) ),
    inference(miniscope,[status(thm)],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( U_4266 = U_4272
    | c_Com_Ocom_OLocal(U_4266,U_4268,U_4270) != c_Com_Ocom_OLocal(U_4272,U_4274,U_4276) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_5,plain,
    ( U_4268 = U_4274
    | c_Com_Ocom_OLocal(U_4266,U_4268,U_4270) != c_Com_Ocom_OLocal(U_4272,U_4274,U_4276) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_6,plain,
    ( U_4270 = U_4276
    | c_Com_Ocom_OLocal(U_4266,U_4268,U_4270) != c_Com_Ocom_OLocal(U_4272,U_4274,U_4276) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_7,plain,
    ( c_Com_Ocom_OLocal(U_4267,U_4269,U_4271) = c_Com_Ocom_OLocal(U_4273,U_4275,U_4277)
    | U_4271 != U_4277
    | U_4269 != U_4275
    | U_4267 != U_4273 ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

fof(f_1070_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_1070_2,plain,
    ! [U_4280,U_4279,U_4278] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279) = U_4280
          | U_4280 != hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279) )
        & ( U_4280 = hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279) != U_4280 ) )
      | ~ class_Int_Onumber(U_4278) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    ( U_4280 = hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279) != U_4280
    | ~ class_Int_Onumber(U_4278) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279) = U_4280
    | U_4280 != hAPP(c_Int_Onumber__class_Onumber__of(U_4278),U_4279)
    | ~ class_Int_Onumber(U_4278) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_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_1071_2,plain,
    ! [U_4283,U_4282,U_4281] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282) = hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4283)
          | U_4282 != U_4283 )
        & ( U_4282 = U_4283
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282) != hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4283) ) )
      | ~ class_Int_Oring__char__0(U_4281)
      | ~ class_Int_Onumber__ring(U_4281) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    ( U_4282 = U_4283
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282) != hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4283)
    | ~ class_Int_Oring__char__0(U_4281)
    | ~ class_Int_Onumber__ring(U_4281) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

cnf(f_1071_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282) = hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4283)
    | U_4282 != U_4283
    | ~ class_Int_Oring__char__0(U_4281)
    | ~ class_Int_Onumber__ring(U_4281) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_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_1072_2,plain,
    ! [U_4286,U_4285,U_4284] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4284),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4285)),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4286)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4285),U_4286)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4285),U_4286))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4284),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4285)),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4286))) ) )
      | ~ class_Rings_Olinordered__idom(U_4284)
      | ~ class_Int_Onumber__ring(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_Int_Oint),U_4285),U_4286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4284),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4285)),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4286)))
    | ~ class_Rings_Olinordered__idom(U_4284)
    | ~ class_Int_Onumber__ring(U_4284) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

cnf(f_1072_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4284),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4285)),hAPP(c_Int_Onumber__class_Onumber__of(U_4284),U_4286)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4285),U_4286))
    | ~ class_Rings_Olinordered__idom(U_4284)
    | ~ class_Int_Onumber__ring(U_4284) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_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_1073_2,plain,
    ! [U_4289,U_4288,U_4287] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4287),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4288)),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4289)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4288),U_4289)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4288),U_4289))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4287),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4288)),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4289))) ) )
      | ~ class_Rings_Olinordered__idom(U_4287)
      | ~ class_Int_Onumber__ring(U_4287) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4288),U_4289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4287),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4288)),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4289)))
    | ~ class_Rings_Olinordered__idom(U_4287)
    | ~ class_Int_Onumber__ring(U_4287) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

cnf(f_1073_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4287),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4288)),hAPP(c_Int_Onumber__class_Onumber__of(U_4287),U_4289)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4288),U_4289))
    | ~ class_Rings_Olinordered__idom(U_4287)
    | ~ class_Int_Onumber__ring(U_4287) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_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_1074_2,plain,
    ! [U_4292,U_4291,U_4290] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4291),U_4292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4290),hAPP(c_Int_Onumber__class_Onumber__of(U_4290),U_4291)),hAPP(c_Int_Onumber__class_Onumber__of(U_4290),U_4292))
      | ~ class_Int_Onumber__ring(U_4290) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4291),U_4292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4290),hAPP(c_Int_Onumber__class_Onumber__of(U_4290),U_4291)),hAPP(c_Int_Onumber__class_Onumber__of(U_4290),U_4292))
    | ~ class_Int_Onumber__ring(U_4290) ),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_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_1075_2,plain,
    ! [U_4295,U_4294,U_4293] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4293),hAPP(c_Int_Onumber__class_Onumber__of(U_4293),U_4294)),hAPP(c_Int_Onumber__class_Onumber__of(U_4293),U_4295)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4293),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4294),U_4295))
      | ~ class_Int_Onumber__ring(U_4293) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4293),hAPP(c_Int_Onumber__class_Onumber__of(U_4293),U_4294)),hAPP(c_Int_Onumber__class_Onumber__of(U_4293),U_4295)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4293),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4294),U_4295))
    | ~ class_Int_Onumber__ring(U_4293) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_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_1076_2,plain,
    ! [U_4299,U_4298,U_4297,U_4296] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),U_4297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),U_4298)),U_4299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4297),U_4298))),U_4299)
      | ~ class_Int_Onumber__ring(U_4296) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),U_4297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),U_4298)),U_4299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Int_Onumber__class_Onumber__of(U_4296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4297),U_4298))),U_4299)
    | ~ class_Int_Onumber__ring(U_4296) ),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_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_1077_2,plain,
    ! [U_4303,U_4302,U_4301,U_4300] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),U_4301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),U_4302)),U_4303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4301),U_4302))),U_4303)
      | ~ class_Int_Onumber__ring(U_4300) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),U_4301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),U_4302)),U_4303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(c_Int_Onumber__class_Onumber__of(U_4300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4301),U_4302))),U_4303)
    | ~ class_Int_Onumber__ring(U_4300) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_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_1078_2,plain,
    ! [U_4306,U_4305,U_4304] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4304),hAPP(c_Int_Onumber__class_Onumber__of(U_4304),U_4305)),hAPP(c_Int_Onumber__class_Onumber__of(U_4304),U_4306)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4305),U_4306))
      | ~ class_Int_Onumber__ring(U_4304) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4304),hAPP(c_Int_Onumber__class_Onumber__of(U_4304),U_4305)),hAPP(c_Int_Onumber__class_Onumber__of(U_4304),U_4306)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4305),U_4306))
    | ~ class_Int_Onumber__ring(U_4304) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_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_1079_2,plain,
    ! [U_4309,U_4308,U_4307] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4308),U_4309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4308)),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4309))
      | ~ class_Int_Onumber__ring(U_4307) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4308),U_4309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4308)),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4309))
    | ~ class_Int_Onumber__ring(U_4307) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_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_1080_2,plain,
    ! [U_4312,U_4311,U_4310] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4311),U_4312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4310),hAPP(c_Int_Onumber__class_Onumber__of(U_4310),U_4311)),hAPP(c_Int_Onumber__class_Onumber__of(U_4310),U_4312))
      | ~ class_Int_Onumber__ring(U_4310) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4311),U_4312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4310),hAPP(c_Int_Onumber__class_Onumber__of(U_4310),U_4311)),hAPP(c_Int_Onumber__class_Onumber__of(U_4310),U_4312))
    | ~ class_Int_Onumber__ring(U_4310) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I37_J]) ).

fof(f_1081_2,plain,
    ! [U_4318,U_4317,U_4316,U_4315,U_4314,U_4313] : c_Com_Ocom_OCond(U_4313,U_4314,U_4315) != c_Com_Ocom_OLocal(U_4316,U_4317,U_4318),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    c_Com_Ocom_OCond(U_4313,U_4314,U_4315) != c_Com_Ocom_OLocal(U_4316,U_4317,U_4318),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I36_J]) ).

fof(f_1082_2,plain,
    ! [U_4324,U_4323,U_4322,U_4321,U_4320,U_4319] : c_Com_Ocom_OLocal(U_4319,U_4320,U_4321) != c_Com_Ocom_OCond(U_4322,U_4323,U_4324),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    c_Com_Ocom_OLocal(U_4319,U_4320,U_4321) != c_Com_Ocom_OCond(U_4322,U_4323,U_4324),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I34_J]) ).

fof(f_1083_2,plain,
    ! [U_4329,U_4328,U_4327,U_4326,U_4325] : c_Com_Ocom_OLocal(U_4325,U_4326,U_4327) != c_Com_Ocom_OSemi(U_4328,U_4329),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    c_Com_Ocom_OLocal(U_4325,U_4326,U_4327) != c_Com_Ocom_OSemi(U_4328,U_4329),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I35_J]) ).

fof(f_1084_2,plain,
    ! [U_4334,U_4333,U_4332,U_4331,U_4330] : c_Com_Ocom_OSemi(U_4330,U_4331) != c_Com_Ocom_OLocal(U_4332,U_4333,U_4334),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    c_Com_Ocom_OSemi(U_4330,U_4331) != c_Com_Ocom_OLocal(U_4332,U_4333,U_4334),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I11_J]) ).

fof(f_1085_2,plain,
    ! [U_4337,U_4336,U_4335] : c_Com_Ocom_OLocal(U_4335,U_4336,U_4337) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    c_Com_Ocom_OLocal(U_4335,U_4336,U_4337) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I10_J]) ).

fof(f_1086_2,plain,
    ! [U_4340,U_4339,U_4338] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_4338,U_4339,U_4340),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_4338,U_4339,U_4340),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_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_1087_2,plain,
    ! [U_4343,U_4342,U_4341] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343))) ) )
      | ~ class_Orderings_Olinorder(U_4341)
      | ~ class_Int_Onumber(U_4341) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)))
    | ~ class_Orderings_Olinorder(U_4341)
    | ~ class_Int_Onumber(U_4341) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

cnf(f_1087_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4341),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4343)),hAPP(c_Int_Onumber__class_Onumber__of(U_4341),U_4342)))
    | ~ class_Orderings_Olinorder(U_4341)
    | ~ class_Int_Onumber(U_4341) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_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_1088_2,plain,
    ! [U_4347,U_4346,U_4345,U_4344] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4344),U_4346),U_4347)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),U_4346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),U_4347))
      | ~ class_Rings_Osemiring(U_4344)
      | ~ class_Int_Onumber(U_4344) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4344),U_4346),U_4347)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),U_4346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),hAPP(c_Int_Onumber__class_Onumber__of(U_4344),U_4345)),U_4347))
    | ~ class_Rings_Osemiring(U_4344)
    | ~ class_Int_Onumber(U_4344) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_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_1089_2,plain,
    ! [U_4351,U_4350,U_4349,U_4348] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4348),U_4349),U_4350)),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4349),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4350),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351)))
      | ~ class_Rings_Osemiring(U_4348)
      | ~ class_Int_Onumber(U_4348) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4348),U_4349),U_4350)),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4349),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4350),hAPP(c_Int_Onumber__class_Onumber__of(U_4348),U_4351)))
    | ~ class_Rings_Osemiring(U_4348)
    | ~ class_Int_Onumber(U_4348) ),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_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_1090_2,plain,
    ! [U_4355,U_4354,U_4353,U_4352] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),U_4353)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),U_4354)),U_4355)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4353),U_4354))),U_4355)
      | ~ class_Int_Onumber__ring(U_4352) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),U_4353)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),U_4354)),U_4355)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4352),hAPP(c_Int_Onumber__class_Onumber__of(U_4352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4353),U_4354))),U_4355)
    | ~ class_Int_Onumber__ring(U_4352) ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_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_1091_2,plain,
    ! [U_4359,U_4358,U_4357,U_4356] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4356),U_4357),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359)))
      | ~ class_Rings_Oring(U_4356)
      | ~ class_Int_Onumber(U_4356) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4356),U_4357),U_4358)),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4357),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),hAPP(c_Int_Onumber__class_Onumber__of(U_4356),U_4359)))
    | ~ class_Rings_Oring(U_4356)
    | ~ class_Int_Onumber(U_4356) ),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_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_1092_2,plain,
    ! [U_4363,U_4362,U_4361,U_4360] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4360),U_4362),U_4363)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),U_4362)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),U_4363))
      | ~ class_Rings_Oring(U_4360)
      | ~ class_Int_Onumber(U_4360) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4360),U_4362),U_4363)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),U_4362)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),hAPP(c_Int_Onumber__class_Onumber__of(U_4360),U_4361)),U_4363))
    | ~ class_Rings_Oring(U_4360)
    | ~ class_Int_Onumber(U_4360) ),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_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_1093_2,plain,
    ! [U_4365,U_4364] :
      ( hBOOL(hAPP(hAPP(c_member(U_4364),hAPP(c_Int_Onumber__class_Onumber__of(U_4364),U_4365)),c_Int_Oring__1__class_OInts(U_4364)))
      | ~ class_Int_Onumber__ring(U_4364) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4364),hAPP(c_Int_Onumber__class_Onumber__of(U_4364),U_4365)),c_Int_Oring__1__class_OInts(U_4364)))
    | ~ class_Int_Onumber__ring(U_4364) ),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_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_1094_2,plain,
    ! [U_4369,U_4368,U_4367,U_4366] :
      ( ( ( U_4367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
          | ( U_4367 != c_Groups_Ozero__class_Ozero(U_4366)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) = c_Groups_Ozero__class_Ozero(U_4366) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),U_4367),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) != U_4368
            & hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) != c_Groups_Ozero__class_Ozero(U_4366) ) )
        & ( ( ( U_4367 = c_Groups_Ozero__class_Ozero(U_4366)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) != c_Groups_Ozero__class_Ozero(U_4366) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),U_4367),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) = U_4368
              | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) = c_Groups_Ozero__class_Ozero(U_4366) ) )
          | U_4367 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) ) )
      | ~ class_Int_Onumber(U_4366)
      | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),U_4367),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) = U_4368
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) = c_Groups_Ozero__class_Ozero(U_4366)
    | U_4367 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

cnf(f_1094_4,plain,
    ( U_4367 = c_Groups_Ozero__class_Ozero(U_4366)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) != c_Groups_Ozero__class_Ozero(U_4366)
    | U_4367 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

cnf(f_1094_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) = c_Groups_Ozero__class_Ozero(U_4366)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) != c_Groups_Ozero__class_Ozero(U_4366)
    | U_4367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

cnf(f_1094_6,plain,
    ( U_4367 != c_Groups_Ozero__class_Ozero(U_4366)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) != c_Groups_Ozero__class_Ozero(U_4366)
    | U_4367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

cnf(f_1094_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369) = c_Groups_Ozero__class_Ozero(U_4366)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),U_4367),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) != U_4368
    | U_4367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

cnf(f_1094_8,plain,
    ( U_4367 != c_Groups_Ozero__class_Ozero(U_4366)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),U_4367),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369)) != U_4368
    | U_4367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4366),U_4368),hAPP(c_Int_Onumber__class_Onumber__of(U_4366),U_4369))
    | ~ class_Int_Onumber(U_4366)
    | ~ class_Fields_Ofield__inverse__zero(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ! [V_ca_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_ca_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
            & V_ca_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_ca_2) != V_b_2
            & V_ca_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_ca_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_ca_2) = V_b_2
              | V_ca_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_ca_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_1095_2,plain,
    ! [U_4373,U_4372,U_4371,U_4370] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != c_Groups_Ozero__class_Ozero(U_4370)
            & U_4373 = c_Groups_Ozero__class_Ozero(U_4370) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4370),hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371)),U_4373) != U_4372
            & U_4373 != c_Groups_Ozero__class_Ozero(U_4370) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = c_Groups_Ozero__class_Ozero(U_4370)
              | U_4373 != c_Groups_Ozero__class_Ozero(U_4370) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4370),hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371)),U_4373) = U_4372
              | U_4373 = c_Groups_Ozero__class_Ozero(U_4370) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373) ) )
      | ~ class_Int_Onumber(U_4370)
      | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4370),hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371)),U_4373) = U_4372
    | U_4373 = c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = c_Groups_Ozero__class_Ozero(U_4370)
    | U_4373 != c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_5,plain,
    ( U_4373 = c_Groups_Ozero__class_Ozero(U_4370)
    | U_4373 != c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != c_Groups_Ozero__class_Ozero(U_4370)
    | U_4373 != c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_7,plain,
    ( U_4373 = c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4370),hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371)),U_4373) != U_4372
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

cnf(f_1095_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) != c_Groups_Ozero__class_Ozero(U_4370)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4370),hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371)),U_4373) != U_4372
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4370),U_4371) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4370),U_4372),U_4373)
    | ~ class_Int_Onumber(U_4370)
    | ~ class_Fields_Ofield__inverse__zero(U_4370) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ! [V_w_2,V_ca_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_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_ca_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_ca_2)
            & V_ca_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_ca_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_ca_2)
              | V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_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_1096_2,plain,
    ! [U_4377,U_4376,U_4375,U_4374] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) = hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) != c_Groups_Ozero__class_Ozero(U_4374)
            & U_4376 = c_Groups_Ozero__class_Ozero(U_4374) )
          | ( U_4375 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)),U_4376)
            & U_4376 != c_Groups_Ozero__class_Ozero(U_4374) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) = c_Groups_Ozero__class_Ozero(U_4374)
              | U_4376 != c_Groups_Ozero__class_Ozero(U_4374) )
            & ( U_4375 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)),U_4376)
              | U_4376 = c_Groups_Ozero__class_Ozero(U_4374) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) != hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) ) )
      | ~ class_Int_Onumber(U_4374)
      | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    ( U_4375 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)),U_4376)
    | U_4376 = c_Groups_Ozero__class_Ozero(U_4374)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) != hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

cnf(f_1096_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) = c_Groups_Ozero__class_Ozero(U_4374)
    | U_4376 != c_Groups_Ozero__class_Ozero(U_4374)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) != hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

cnf(f_1096_5,plain,
    ( U_4376 = c_Groups_Ozero__class_Ozero(U_4374)
    | U_4376 != c_Groups_Ozero__class_Ozero(U_4374)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) = hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

cnf(f_1096_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) != c_Groups_Ozero__class_Ozero(U_4374)
    | U_4376 != c_Groups_Ozero__class_Ozero(U_4374)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) = hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

cnf(f_1096_7,plain,
    ( U_4376 = c_Groups_Ozero__class_Ozero(U_4374)
    | U_4375 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)),U_4376)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) = hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

cnf(f_1096_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377) != c_Groups_Ozero__class_Ozero(U_4374)
    | U_4375 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)),U_4376)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4374),U_4375),U_4376) = hAPP(c_Int_Onumber__class_Onumber__of(U_4374),U_4377)
    | ~ class_Int_Onumber(U_4374)
    | ~ class_Fields_Ofield__inverse__zero(U_4374) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_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_1097_2,plain,
    ! [U_4381,U_4380,U_4379,U_4378] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) = U_4381
          | ( U_4381 != c_Groups_Ozero__class_Ozero(U_4378)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) = c_Groups_Ozero__class_Ozero(U_4378) )
          | ( U_4379 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4378),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) != c_Groups_Ozero__class_Ozero(U_4378) ) )
        & ( ( ( U_4381 = c_Groups_Ozero__class_Ozero(U_4378)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) != c_Groups_Ozero__class_Ozero(U_4378) )
            & ( U_4379 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4378),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) = c_Groups_Ozero__class_Ozero(U_4378) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) != U_4381 ) )
      | ~ class_Int_Onumber(U_4378)
      | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    ( U_4379 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4378),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) = c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) != U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_4,plain,
    ( U_4381 = c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) != c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) != U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) = c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) != c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) = U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_6,plain,
    ( U_4381 != c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) != c_Groups_Ozero__class_Ozero(U_4378)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) = U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380) = c_Groups_Ozero__class_Ozero(U_4378)
    | U_4379 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4378),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) = U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

cnf(f_1097_8,plain,
    ( U_4381 != c_Groups_Ozero__class_Ozero(U_4378)
    | U_4379 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4378),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4378),U_4379),hAPP(c_Int_Onumber__class_Onumber__of(U_4378),U_4380)) = U_4381
    | ~ class_Int_Onumber(U_4378)
    | ~ class_Fields_Ofield__inverse__zero(U_4378) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_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_1098_2,plain,
    ! [U_4385,U_4384,U_4383,U_4382] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))) ) )
      | ~ class_Int_Onumber(U_4382)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),c_Groups_Ozero__class_Ozero(U_4382)),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385)),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

cnf(f_1098_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),c_Groups_Ozero__class_Ozero(U_4382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4382),U_4383),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))),U_4384))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4382),U_4383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4382),U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4382),U_4385))))
    | ~ class_Int_Onumber(U_4382)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4382) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    ! [V_ca_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_ca_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_ca_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_ca_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_1099_2,plain,
    ! [U_4389,U_4388,U_4387,U_4386] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389))) ) )
      | ~ class_Int_Onumber(U_4386)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),c_Groups_Ozero__class_Ozero(U_4386)),U_4389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4389),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

cnf(f_1099_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),c_Groups_Ozero__class_Ozero(U_4386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),U_4389)),U_4388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4386),hAPP(c_Int_Onumber__class_Onumber__of(U_4386),U_4387)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4386),U_4388),U_4389)))
    | ~ class_Int_Onumber(U_4386)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4386) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    ! [V_w_2,V_ca_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_ca_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_ca_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_ca_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_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_1100_2,plain,
    ! [U_4393,U_4392,U_4391,U_4390] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393))) ) )
      | ~ class_Int_Onumber(U_4390)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),U_4392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4392),c_Groups_Ozero__class_Ozero(U_4390)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

cnf(f_1100_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),c_Groups_Ozero__class_Ozero(U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)),U_4391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4390),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)),U_4392)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4390),U_4391),U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4390),U_4393)))
    | ~ class_Int_Onumber(U_4390)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_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_1101_2,plain,
    ! [U_4397,U_4396,U_4395,U_4394] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397)) ) )
      | ~ class_Int_Onumber(U_4394)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396)),c_Groups_Ozero__class_Ozero(U_4394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

cnf(f_1101_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),U_4395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4394),U_4397),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4394),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4394),U_4396))),U_4397))
    | ~ class_Int_Onumber(U_4394)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4394) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_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_1102_2,plain,
    ! [U_4401,U_4400,U_4399,U_4398] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401)) ) )
      | ~ class_Int_Onumber(U_4398)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400)),c_Groups_Ozero__class_Ozero(U_4398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

cnf(f_1102_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),c_Groups_Ozero__class_Ozero(U_4398)),U_4401))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),U_4399),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4401),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4398),U_4399),hAPP(c_Int_Onumber__class_Onumber__of(U_4398),U_4400))),U_4401))
    | ~ class_Int_Onumber(U_4398)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4398) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_1,plain,
    ! [V_w_2,V_ca_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_ca_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_ca_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_ca_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_1103_2,plain,
    ! [U_4405,U_4404,U_4403,U_4402] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405))) ) )
      | ~ class_Int_Onumber(U_4402)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),U_4404),c_Groups_Ozero__class_Ozero(U_4402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

cnf(f_1103_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)),U_4403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)),U_4404)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),U_4404)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4405)))
    | ~ class_Int_Onumber(U_4402)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    ! [V_ca_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_ca_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_ca_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_ca_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_ca_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_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_ca_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_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_ca_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_1104_2,plain,
    ! [U_4409,U_4408,U_4407,U_4406] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409))) ) )
      | ~ class_Int_Onumber(U_4406)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4409),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

cnf(f_1104_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),c_Groups_Ozero__class_Ozero(U_4406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),U_4409)),U_4408))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4408),U_4409)))
    | ~ class_Int_Onumber(U_4406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_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_1105_2,plain,
    ! [U_4413,U_4412,U_4411,U_4410] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))) ) )
      | ~ class_Int_Onumber(U_4410)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413)),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

cnf(f_1105_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),c_Groups_Ozero__class_Ozero(U_4410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),U_4411),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))),U_4412))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4413))))
    | ~ class_Int_Onumber(U_4410)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    ! [V_Pa_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_F_2))
      | ? [B_x,B_F] :
          ( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F)))
          & hBOOL(hAPP(V_Pa_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_Pa_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_1106_2,plain,
    ! [U_4418,U_4417,U_4416] :
      ( hBOOL(hAPP(U_4418,U_4417))
      | ? [U_4415,U_4414] :
          ( ~ hBOOL(hAPP(U_4418,hAPP(hAPP(c_Set_Oinsert(U_4416),U_4415),U_4414)))
          & hBOOL(hAPP(U_4418,U_4414))
          & ~ hBOOL(hAPP(hAPP(c_member(U_4416),U_4415),U_4414))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4414)) )
      | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

fof(f_1106_3,plain,
    ! [U_4418,U_4417,U_4416] :
      ( hBOOL(hAPP(U_4418,U_4417))
      | ? [U_4414] :
          ( ~ hBOOL(hAPP(U_4418,hAPP(hAPP(c_Set_Oinsert(U_4416),sK88(U_4418,U_4417,U_4416)),U_4414)))
          & hBOOL(hAPP(U_4418,U_4414))
          & ~ hBOOL(hAPP(hAPP(c_member(U_4416),sK88(U_4418,U_4417,U_4416)),U_4414))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4414)) )
      | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4415,sK88(U_4418,U_4417,U_4416))],[f_1106_2]) ).

fof(f_1106_4,plain,
    ! [U_4418,U_4417,U_4416] :
      ( hBOOL(hAPP(U_4418,U_4417))
      | ( ~ hBOOL(hAPP(U_4418,hAPP(hAPP(c_Set_Oinsert(U_4416),sK88(U_4418,U_4417,U_4416)),sK89(U_4418,U_4417,U_4416))))
        & hBOOL(hAPP(U_4418,sK89(U_4418,U_4417,U_4416)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_4416),sK88(U_4418,U_4417,U_4416)),sK89(U_4418,U_4417,U_4416)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),sK89(U_4418,U_4417,U_4416))) )
      | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4414,sK89(U_4418,U_4417,U_4416))],[f_1106_3]) ).

cnf(f_1106_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),sK89(U_4418,U_4417,U_4416)))
    | hBOOL(hAPP(U_4418,U_4417))
    | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

cnf(f_1106_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4416),sK88(U_4418,U_4417,U_4416)),sK89(U_4418,U_4417,U_4416)))
    | hBOOL(hAPP(U_4418,U_4417))
    | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

cnf(f_1106_7,plain,
    ( hBOOL(hAPP(U_4418,sK89(U_4418,U_4417,U_4416)))
    | hBOOL(hAPP(U_4418,U_4417))
    | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

cnf(f_1106_8,plain,
    ( ~ hBOOL(hAPP(U_4418,hAPP(hAPP(c_Set_Oinsert(U_4416),sK88(U_4418,U_4417,U_4416)),sK89(U_4418,U_4417,U_4416))))
    | hBOOL(hAPP(U_4418,U_4417))
    | ~ hBOOL(hAPP(U_4418,c_Orderings_Obot__class_Obot(tc_fun(U_4416,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4417)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

fof(f_1107_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_1107_2,plain,
    ! [U_4421,U_4420,U_4419] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4419),hAPP(c_Finite__Set_Ofold1(U_4419,c_Orderings_Oord__class_Omin(U_4419)),U_4421)),hAPP(c_Finite__Set_Ofold1(U_4419,c_Orderings_Oord__class_Omin(U_4419)),U_4420)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4419),U_4421))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4419,tc_HOL_Obool)),U_4420),U_4421))
      | U_4420 = c_Orderings_Obot__class_Obot(tc_fun(U_4419,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_4419) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4419),hAPP(c_Finite__Set_Ofold1(U_4419,c_Orderings_Oord__class_Omin(U_4419)),U_4421)),hAPP(c_Finite__Set_Ofold1(U_4419,c_Orderings_Oord__class_Omin(U_4419)),U_4420)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4419),U_4421))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4419,tc_HOL_Obool)),U_4420),U_4421))
    | U_4420 = c_Orderings_Obot__class_Obot(tc_fun(U_4419,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_4419) ),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I6_J]) ).

fof(f_1108_2,plain,
    ! [U_4423,U_4422] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_4422,U_4423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4423)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_4422,U_4423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_4423)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_1,plain,
    ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_com_Osize_I14_J]) ).

fof(f_1109_2,plain,
    ! [U_4425,U_4424] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_4424,U_4425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4425)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_4424,U_4425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_4425)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_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_1110_2,plain,
    ! [U_4427,U_4426] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4426),c_Int_Osucc(U_4427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4426),c_Groups_Oone__class_Oone(U_4426)),hAPP(c_Int_Onumber__class_Onumber__of(U_4426),U_4427))
      | ~ class_Int_Onumber__ring(U_4426) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4426),c_Int_Osucc(U_4427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4426),c_Groups_Oone__class_Oone(U_4426)),hAPP(c_Int_Onumber__class_Onumber__of(U_4426),U_4427))
    | ~ class_Int_Onumber__ring(U_4426) ),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_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_1111_2,plain,
    ! [U_4431,U_4430,U_4429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),U_4431))
      | ? [U_4428] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4429),U_4431),U_4428)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4429),c_Groups_Ozero__class_Ozero(U_4429)),U_4428)) )
      | ~ class_Fields_Olinordered__field(U_4429) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ! [U_4431,U_4430,U_4429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),U_4431))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4429),U_4431),sK90(U_4431,U_4430,U_4429))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4429),c_Groups_Ozero__class_Ozero(U_4429)),sK90(U_4431,U_4430,U_4429))) )
      | ~ class_Fields_Olinordered__field(U_4429) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4428,sK90(U_4431,U_4430,U_4429))],[f_1111_2]) ).

cnf(f_1111_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4429),c_Groups_Ozero__class_Ozero(U_4429)),sK90(U_4431,U_4430,U_4429)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),U_4431))
    | ~ class_Fields_Olinordered__field(U_4429) ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

cnf(f_1111_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4429),U_4431),sK90(U_4431,U_4430,U_4429))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4429),U_4430),U_4431))
    | ~ class_Fields_Olinordered__field(U_4429) ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_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_1112_2,plain,
    ! [U_4437,U_4436,U_4435,U_4434,U_4433,U_4432] : c_Nitpick_Opair__box_Opair__box__size(U_4432,U_4433,U_4434,U_4435,c_Nitpick_Opair__box_OPairBox(U_4432,U_4433,U_4436,U_4437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_4434,U_4436)),hAPP(U_4435,U_4437))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    c_Nitpick_Opair__box_Opair__box__size(U_4432,U_4433,U_4434,U_4435,c_Nitpick_Opair__box_OPairBox(U_4432,U_4433,U_4436,U_4437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_4434,U_4436)),hAPP(U_4435,U_4437))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_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_1113_2,plain,
    ! [U_4439,U_4438] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4439)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4438),U_4439)),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4439)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4438),U_4439)),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_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_1114_2,plain,
    ! [U_4441,U_4440] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4440)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4441)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4440),U_4441)),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4440)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4441)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4440),U_4441)),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_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_1115_2,plain,
    ! [U_4443,U_4442] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4443)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4442),U_4443)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4442),U_4443))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4442)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4443))) ) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ( ! [U_4447,U_4445] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4445)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4445),U_4447)) )
    & ! [U_4446,U_4444] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4444),U_4446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4446))) ) ),
    inference(miniscope,[status(thm)],[f_1115_2]) ).

cnf(f_1115_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4444),U_4446))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4446))) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

cnf(f_1115_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4445)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4447)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4445),U_4447)) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

fof(f_1116_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_1116_2,plain,
    ! [U_4449,U_4448] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4448)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4449)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4448),U_4449)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4448),U_4449))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4448)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4449))) ) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ( ! [U_4453,U_4451] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4451)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4453)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4451),U_4453)) )
    & ! [U_4452,U_4450] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4450),U_4452))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4450)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4452))) ) ),
    inference(miniscope,[status(thm)],[f_1116_2]) ).

cnf(f_1116_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4450),U_4452))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4450)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4452))) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

cnf(f_1116_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_4451)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4453)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4451),U_4453)) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_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_1117_2,plain,
    ! [U_4455,U_4454] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4454),U_4455) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_4455 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_4454 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_4455 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_4454 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4454),U_4455) != 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_4454)) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    ( U_4454 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4454),U_4455) != 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_4454)) ),
    inference(clausify,[status(thm)],[f_1117_2]) ).

cnf(f_1117_4,plain,
    ( U_4455 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4454),U_4455) != 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_4454)) ),
    inference(clausify,[status(thm)],[f_1117_2]) ).

cnf(f_1117_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4454),U_4455) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4455 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4454 != 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_4454)) ),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_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_1118_2,plain,
    ! [U_4456] : 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_4456)),U_4456) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

cnf(f_1118_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_4456)),U_4456) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_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_1119_2,plain,
    ! [U_4457] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4457))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4457)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4457))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4457)) ) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ( ! [U_4459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4459)) )
    & ! [U_4458] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4458))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4458)) ) ),
    inference(miniscope,[status(thm)],[f_1119_2]) ).

cnf(f_1119_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4458)) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

cnf(f_1119_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4459)) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

fof(f_1120_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_1120_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_1120_1]) ).

fof(f_1121_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_1121_2,plain,
    ! [U_4460] :
      ( 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_4460)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4460)) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

cnf(f_1121_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_4460)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4460)) ),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_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_1122_2,plain,
    ! [U_4461] :
      ( ( 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_4461)),U_4461)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4461),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4461),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_4461)),U_4461)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

fof(f_1122_3,plain,
    ( ! [U_4463] :
        ( 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_4463)),U_4463)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4463),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4462] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4462),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_4462)),U_4462)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1122_2]) ).

cnf(f_1122_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4462),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_4462)),U_4462)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

cnf(f_1122_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_4463)),U_4463)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4463),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

fof(f_1123_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_1123_2,plain,
    ! [U_4466,U_4465,U_4464] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4466),U_4464)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4466),U_4465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4466))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4464),U_4465)) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4466),U_4464)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4466),U_4465)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4466))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4464),U_4465)) ),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_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_1124_2,plain,
    ! [U_4467] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4467) = U_4467,
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4467) = U_4467,
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_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_1125_2,plain,
    ! [U_4468] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4468),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_4468,
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4468),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_4468,
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_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_1126_2,plain,
    ! [U_4470,U_4469] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4469),U_4470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4469),U_4470)),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_4469),U_4470)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4469),U_4470)) ) ),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

fof(f_1126_3,plain,
    ( ! [U_4474,U_4472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4472),U_4474))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4472),U_4474)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4473,U_4471] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4471),U_4473)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4471),U_4473)) ) ),
    inference(miniscope,[status(thm)],[f_1126_2]) ).

cnf(f_1126_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4471),U_4473)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4471),U_4473)) ),
    inference(clausify,[status(thm)],[f_1126_3]) ).

cnf(f_1126_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4472),U_4474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4472),U_4474)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1126_3]) ).

fof(f_1127_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_1127_2,plain,
    ! [U_4477,U_4476,U_4475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4477),U_4475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4477),U_4476)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4475),U_4476)) ),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

cnf(f_1127_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_4477),U_4475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4477),U_4476)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4475),U_4476)) ),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_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_1128_2,plain,
    ! [U_4480,U_4479,U_4478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4478),U_4480)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),U_4480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4478),U_4479)) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4478),U_4480)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4479),U_4480)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4478),U_4479)) ),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_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_1129_2,plain,
    ! [U_4484,U_4483,U_4482,U_4481] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4481),U_4483)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4482),U_4484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4483),U_4484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4481),U_4482)) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

cnf(f_1129_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4481),U_4483)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4482),U_4484)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4483),U_4484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4481),U_4482)) ),
    inference(clausify,[status(thm)],[f_1129_2]) ).

fof(f_1130_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_1130_2,plain,
    ! [U_4486,U_4485] :
      ( U_4485 = U_4486
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4486),U_4485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4485),U_4486)) ),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    ( U_4485 = U_4486
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4486),U_4485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4485),U_4486)) ),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_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_1131_2,plain,
    ! [U_4489,U_4488,U_4487] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4487),U_4489))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4488),U_4489))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4487),U_4488)) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4487),U_4489))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4488),U_4489))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4487),U_4488)) ),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_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_1132_2,plain,
    ! [U_4491,U_4490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4491),U_4490))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4490),U_4491)) ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4491),U_4490))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4490),U_4491)) ),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_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_1133_2,plain,
    ! [U_4492] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4492),U_4492)),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4492),U_4492)),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_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_1134_2,plain,
    ! [U_4494,U_4493] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4494),U_4493))
      | U_4493 = U_4494
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4493),U_4494)) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4494),U_4493))
    | U_4493 = U_4494
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4493),U_4494)) ),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_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_1135_2,plain,
    ! [U_4496,U_4495] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4495),U_4496))
        | U_4495 = U_4496
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4495),U_4496)) )
      & ( ( U_4495 != U_4496
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4495),U_4496)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4495),U_4496)) ) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

fof(f_1135_3,plain,
    ( ! [U_4500,U_4498] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4498),U_4500))
        | U_4498 = U_4500
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4498),U_4500)) )
    & ! [U_4499,U_4497] :
        ( ( U_4497 != U_4499
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4497),U_4499)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4497),U_4499)) ) ),
    inference(miniscope,[status(thm)],[f_1135_2]) ).

cnf(f_1135_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4497),U_4499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4497),U_4499)) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

cnf(f_1135_5,plain,
    ( U_4497 != U_4499
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4497),U_4499)) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

cnf(f_1135_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4498),U_4500))
    | U_4498 = U_4500
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4498),U_4500)) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

fof(f_1136_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_1136_2,plain,
    ! [U_4503,U_4502,U_4501] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4501),U_4502)),U_4503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4502),U_4503)),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4501),U_4502)),U_4503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4502),U_4503)),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_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_1137_2,plain,
    ! [U_4506,U_4505,U_4504] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4504),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4505),U_4506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4504),U_4506)),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4504),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4505),U_4506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4504),U_4506)),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_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_1138_2,plain,
    ! [U_4508,U_4507] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4507),U_4508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4508),U_4507),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

cnf(f_1138_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4507),U_4508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4508),U_4507),
    inference(clausify,[status(thm)],[f_1138_2]) ).

fof(f_1139_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_1139_2,plain,
    ! [U_4511,U_4510,U_4509] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4509),U_4510)),U_4511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4509),U_4511)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4510),U_4511)),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4509),U_4510)),U_4511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4509),U_4511)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4510),U_4511)),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_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_1140_2,plain,
    ! [U_4514,U_4513,U_4512] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4513),U_4514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),U_4513)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),U_4514)),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4513),U_4514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),U_4513)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4512),U_4514)),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_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_1141_2,plain,
    ! [U_4517,U_4516,U_4515] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4515),U_4516)),U_4517) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4515),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4516),U_4517)),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4515),U_4516)),U_4517) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4515),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4516),U_4517)),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_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_1142_2,plain,
    ! [U_4519,U_4518] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4518),U_4519) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4519),U_4518),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4518),U_4519) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4519),U_4518),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_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_1143_2,plain,
    ! [U_4522,U_4521,U_4520] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4521),U_4522)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),U_4521)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),U_4522)),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4521),U_4522)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),U_4521)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4520),U_4522)),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_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_1144_2,plain,
    ! [U_4525,U_4524,U_4523] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4523),U_4524)),U_4525) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4523),U_4525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4524),U_4525)),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4523),U_4524)),U_4525) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4523),U_4525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4524),U_4525)),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_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_1145_2,plain,
    ! [U_4527,U_4526] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4527),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_4526 != U_4527
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4526),U_4527)) ) )
      & ( U_4526 = U_4527
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4526),U_4527))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4527),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ( ! [U_4531,U_4529] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4531),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_4529 != U_4531
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4529),U_4531)) ) )
    & ! [U_4530,U_4528] :
        ( U_4528 = U_4530
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),U_4530))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4530),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( U_4528 = U_4530
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),U_4530))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4530),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4529),U_4531))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4531),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_6,plain,
    ( U_4529 != U_4531
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4531),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_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_1146_2,plain,
    ! [U_4533,U_4532] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4533),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4532),U_4533)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4532),U_4533))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4533),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ( ! [U_4537,U_4535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4535),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4537),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4535),U_4537)) )
    & ! [U_4536,U_4534] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4534),U_4536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4536),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1146_2]) ).

cnf(f_1146_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4534),U_4536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4536),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

cnf(f_1146_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4535),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4537),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4535),U_4537)) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

fof(f_1147_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_1147_2,plain,
    ! [U_4539,U_4538] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4538),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4538),U_4539)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4538),U_4539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4538),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4539)) ) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

fof(f_1147_3,plain,
    ( ! [U_4543,U_4541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4541),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4541),U_4543)) )
    & ! [U_4542,U_4540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4540),U_4542))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4540),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4542)) ) ),
    inference(miniscope,[status(thm)],[f_1147_2]) ).

cnf(f_1147_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4540),U_4542))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4540),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4542)) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

cnf(f_1147_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_4541),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4541),U_4543)) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

fof(f_1148_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_1148_2,plain,
    ! [U_4545,U_4544] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4544),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4544),U_4545)) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

cnf(f_1148_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_4544),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4544),U_4545)) ),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_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_1149_2,plain,
    ! [U_4547,U_4546] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4546),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4547),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4546),U_4547)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4546),U_4547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4546),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4547),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

fof(f_1149_3,plain,
    ( ! [U_4551,U_4549] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4549),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4551),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4549),U_4551)) )
    & ! [U_4550,U_4548] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4548),U_4550))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4548),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4550),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1149_2]) ).

cnf(f_1149_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4548),U_4550))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4548),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4550),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1149_3]) ).

cnf(f_1149_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4549),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4551),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4549),U_4551)) ),
    inference(clausify,[status(thm)],[f_1149_3]) ).

fof(f_1150_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_1150_2,plain,
    ! [U_4552] : c_Int_Osucc(U_4552) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4552),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    c_Int_Osucc(U_4552) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4552),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_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_1151_2,plain,
    ! [U_4553] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4553),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_4553,
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4553),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_4553,
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_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_1152_2,plain,
    ! [U_4554] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4554) = U_4554,
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4554) = U_4554,
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_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_1153_2,plain,
    ! [U_4560,U_4559,U_4558,U_4557,U_4556,U_4555] :
      ( ( c_Nitpick_Opair__box_OPairBox(U_4555,U_4556,U_4557,U_4558) = c_Nitpick_Opair__box_OPairBox(U_4555,U_4556,U_4559,U_4560)
        | U_4558 != U_4560
        | U_4557 != U_4559 )
      & ( ( U_4558 = U_4560
          & U_4557 = U_4559 )
        | c_Nitpick_Opair__box_OPairBox(U_4555,U_4556,U_4557,U_4558) != c_Nitpick_Opair__box_OPairBox(U_4555,U_4556,U_4559,U_4560) ) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ( ! [U_4572,U_4570,U_4568,U_4566] :
        ( ! [U_4564,U_4562] : c_Nitpick_Opair__box_OPairBox(U_4562,U_4564,U_4566,U_4568) = c_Nitpick_Opair__box_OPairBox(U_4562,U_4564,U_4570,U_4572)
        | U_4568 != U_4572
        | U_4566 != U_4570 )
    & ! [U_4571,U_4569,U_4567,U_4565] :
        ( ! [U_4563,U_4561] : c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4565,U_4567) != c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4569,U_4571)
        | ( U_4567 = U_4571
          & U_4565 = U_4569 ) ) ),
    inference(miniscope,[status(thm)],[f_1153_2]) ).

cnf(f_1153_4,plain,
    ( U_4565 = U_4569
    | c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4565,U_4567) != c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4569,U_4571) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

cnf(f_1153_5,plain,
    ( U_4567 = U_4571
    | c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4565,U_4567) != c_Nitpick_Opair__box_OPairBox(U_4561,U_4563,U_4569,U_4571) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

cnf(f_1153_6,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_4562,U_4564,U_4566,U_4568) = c_Nitpick_Opair__box_OPairBox(U_4562,U_4564,U_4570,U_4572)
    | U_4568 != U_4572
    | U_4566 != U_4570 ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_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_1154_2,plain,
    ! [U_4574,U_4573] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4573),U_4574),U_4574) = U_4574
      | ~ class_Orderings_Olinorder(U_4573) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4573),U_4574),U_4574) = U_4574
    | ~ class_Orderings_Olinorder(U_4573) ),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
      ( ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
        | V_com_2 != V_com_H_2
        | V_fun_2 != V_fun_H_2 )
      & ( ( V_com_2 = V_com_H_2
          & V_fun_2 = V_fun_H_2 )
        | c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J]) ).

fof(f_1155_2,plain,
    ! [U_4578,U_4577,U_4576,U_4575] :
      ( ( c_Com_Ocom_OWhile(U_4575,U_4576) = c_Com_Ocom_OWhile(U_4577,U_4578)
        | U_4576 != U_4578
        | U_4575 != U_4577 )
      & ( ( U_4576 = U_4578
          & U_4575 = U_4577 )
        | c_Com_Ocom_OWhile(U_4575,U_4576) != c_Com_Ocom_OWhile(U_4577,U_4578) ) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

fof(f_1155_3,plain,
    ( ! [U_4586,U_4584,U_4582,U_4580] :
        ( c_Com_Ocom_OWhile(U_4580,U_4582) = c_Com_Ocom_OWhile(U_4584,U_4586)
        | U_4582 != U_4586
        | U_4580 != U_4584 )
    & ! [U_4585,U_4583,U_4581,U_4579] :
        ( ( U_4581 = U_4585
          & U_4579 = U_4583 )
        | c_Com_Ocom_OWhile(U_4579,U_4581) != c_Com_Ocom_OWhile(U_4583,U_4585) ) ),
    inference(miniscope,[status(thm)],[f_1155_2]) ).

cnf(f_1155_4,plain,
    ( U_4579 = U_4583
    | c_Com_Ocom_OWhile(U_4579,U_4581) != c_Com_Ocom_OWhile(U_4583,U_4585) ),
    inference(clausify,[status(thm)],[f_1155_3]) ).

cnf(f_1155_5,plain,
    ( U_4581 = U_4585
    | c_Com_Ocom_OWhile(U_4579,U_4581) != c_Com_Ocom_OWhile(U_4583,U_4585) ),
    inference(clausify,[status(thm)],[f_1155_3]) ).

cnf(f_1155_6,plain,
    ( c_Com_Ocom_OWhile(U_4580,U_4582) = c_Com_Ocom_OWhile(U_4584,U_4586)
    | U_4582 != U_4586
    | U_4580 != U_4584 ),
    inference(clausify,[status(thm)],[f_1155_3]) ).

fof(f_1156_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_1156_2,plain,
    ! [U_4590,U_4589,U_4588,U_4587] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4588),U_4589)),U_4590) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4588),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4589),U_4590))
      | ~ class_Orderings_Olinorder(U_4587) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4588),U_4589)),U_4590) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4588),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4587),U_4589),U_4590))
    | ~ class_Orderings_Olinorder(U_4587) ),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_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_1157_2,plain,
    ! [U_4594,U_4593,U_4592,U_4591] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4592),U_4593)),U_4594) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4592),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4593),U_4594))
      | ~ class_Orderings_Olinorder(U_4591) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4592),U_4593)),U_4594) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4592),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4591),U_4593),U_4594))
    | ~ class_Orderings_Olinorder(U_4591) ),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_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_1158_2,plain,
    ! [U_4598,U_4597,U_4596,U_4595] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4596),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4597),U_4598)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4597),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4596),U_4598))
      | ~ class_Orderings_Olinorder(U_4595) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4596),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4597),U_4598)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4597),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4595),U_4596),U_4598))
    | ~ class_Orderings_Olinorder(U_4595) ),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_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_1159_2,plain,
    ! [U_4602,U_4601,U_4600,U_4599] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4600),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4601),U_4602)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4601),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4600),U_4602))
      | ~ class_Orderings_Olinorder(U_4599) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4600),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4601),U_4602)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4601),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4599),U_4600),U_4602))
    | ~ class_Orderings_Olinorder(U_4599) ),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_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_1160_2,plain,
    ! [U_4605,U_4604,U_4603] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),U_4605)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),U_4605)
      | ~ class_Orderings_Olinorder(U_4603) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),U_4605)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4603),U_4604),U_4605)
    | ~ class_Orderings_Olinorder(U_4603) ),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_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_1161_2,plain,
    ! [U_4608,U_4607,U_4606] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),U_4608)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),U_4608)
      | ~ class_Orderings_Olinorder(U_4606) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

cnf(f_1161_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),U_4608)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4606),U_4607),U_4608)
    | ~ class_Orderings_Olinorder(U_4606) ),
    inference(clausify,[status(thm)],[f_1161_2]) ).

fof(f_1162_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_1162_2,plain,
    ! [U_4611,U_4610,U_4609] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4609),U_4610),U_4611) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4609),U_4611),U_4610)
      | ~ class_Orderings_Olinorder(U_4609) ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4609),U_4610),U_4611) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4609),U_4611),U_4610)
    | ~ class_Orderings_Olinorder(U_4609) ),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_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_1163_2,plain,
    ! [U_4614,U_4613,U_4612] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4612),U_4613),U_4614) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4612),U_4614),U_4613)
      | ~ class_Orderings_Olinorder(U_4612) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

cnf(f_1163_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4612),U_4613),U_4614) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4612),U_4614),U_4613)
    | ~ class_Orderings_Olinorder(U_4612) ),
    inference(clausify,[status(thm)],[f_1163_2]) ).

fof(f_1164_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_1164_2,plain,
    ! [U_4616,U_4615] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4615),U_4616),U_4616) = U_4616
      | ~ class_Orderings_Olinorder(U_4615) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4615),U_4616),U_4616) = U_4616
    | ~ class_Orderings_Olinorder(U_4615) ),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_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_1165_2,plain,
    ! [U_4619,U_4618,U_4617] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4617),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4617),U_4618),U_4619)),U_4618))
      | ~ class_Orderings_Olinorder(U_4617) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4617),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4617),U_4618),U_4619)),U_4618))
    | ~ class_Orderings_Olinorder(U_4617) ),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_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_1166_2,plain,
    ! [U_4622,U_4621,U_4620] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4620),U_4621),U_4622)),U_4622))
      | ~ class_Orderings_Olinorder(U_4620) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4620),U_4621),U_4622)),U_4622))
    | ~ class_Orderings_Olinorder(U_4620) ),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_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_1167_2,plain,
    ! [U_4625,U_4624,U_4623] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4623),U_4624),U_4625) != U_4624 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4623),U_4624),U_4625) = U_4624
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625)) ) )
      | ~ class_Orderings_Olinorder(U_4623) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4623),U_4624),U_4625) = U_4624
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
    | ~ class_Orderings_Olinorder(U_4623) ),
    inference(clausify,[status(thm)],[f_1167_2]) ).

cnf(f_1167_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4623),U_4624),U_4625) != U_4624
    | ~ class_Orderings_Olinorder(U_4623) ),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_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_1168_2,plain,
    ! [U_4629,U_4628,U_4627,U_4626] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4626),U_4628),U_4629)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4629))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4628)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4629))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4628)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4626),U_4628),U_4629))) ) )
      | ~ class_Orderings_Olinorder(U_4626) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

cnf(f_1168_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4628))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4626),U_4628),U_4629)))
    | ~ class_Orderings_Olinorder(U_4626) ),
    inference(clausify,[status(thm)],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4626),U_4628),U_4629)))
    | ~ class_Orderings_Olinorder(U_4626) ),
    inference(clausify,[status(thm)],[f_1168_2]) ).

cnf(f_1168_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4626),U_4628),U_4629)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4626),U_4627),U_4628))
    | ~ class_Orderings_Olinorder(U_4626) ),
    inference(clausify,[status(thm)],[f_1168_2]) ).

fof(f_1169_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_1169_2,plain,
    ! [U_4633,U_4632,U_4631,U_4630] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4630),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4630),U_4631),U_4633)),U_4632))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4630),U_4631),U_4632))
      | ~ class_Orderings_Olinorder(U_4630) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4630),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4630),U_4631),U_4633)),U_4632))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4630),U_4631),U_4632))
    | ~ class_Orderings_Olinorder(U_4630) ),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_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_1170_2,plain,
    ! [U_4637,U_4636,U_4635,U_4634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4634),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4634),U_4637),U_4635)),U_4636))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4634),U_4635),U_4636))
      | ~ class_Orderings_Olinorder(U_4634) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4634),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4634),U_4637),U_4635)),U_4636))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4634),U_4635),U_4636))
    | ~ class_Orderings_Olinorder(U_4634) ),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_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_1171_2,plain,
    ! [U_4640,U_4639,U_4638] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4638),U_4639),U_4640) = U_4639
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4638),U_4639),U_4640))
      | ~ class_Orderings_Olinorder(U_4638) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

cnf(f_1171_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4638),U_4639),U_4640) = U_4639
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4638),U_4639),U_4640))
    | ~ class_Orderings_Olinorder(U_4638) ),
    inference(clausify,[status(thm)],[f_1171_2]) ).

fof(f_1172_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_1172_2,plain,
    ! [U_4643,U_4642,U_4641] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4641),U_4643),U_4642) = U_4642
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4641),U_4642),U_4643))
      | ~ class_Orderings_Olinorder(U_4641) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

cnf(f_1172_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4641),U_4643),U_4642) = U_4642
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4641),U_4642),U_4643))
    | ~ class_Orderings_Olinorder(U_4641) ),
    inference(clausify,[status(thm)],[f_1172_2]) ).

fof(f_1173_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_1173_2,plain,
    ! [U_4647,U_4646,U_4645,U_4644] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4644),U_4646),U_4647)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),U_4647))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),U_4646))
      | ~ class_Orderings_Olinorder(U_4644) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

cnf(f_1173_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4644),U_4646),U_4647)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),U_4647))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4644),U_4645),U_4646))
    | ~ class_Orderings_Olinorder(U_4644) ),
    inference(clausify,[status(thm)],[f_1173_2]) ).

fof(f_1174_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_1174_2,plain,
    ! [U_4651,U_4650,U_4649,U_4648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4648),U_4650),U_4651)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),U_4651))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),U_4650))
      | ~ class_Orderings_Olinorder(U_4648) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

cnf(f_1174_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4648),U_4650),U_4651)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),U_4651))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4648),U_4649),U_4650))
    | ~ class_Orderings_Olinorder(U_4648) ),
    inference(clausify,[status(thm)],[f_1174_2]) ).

fof(f_1175_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_1175_2,plain,
    ! [U_4656,U_4655,U_4654,U_4653,U_4652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4652),U_4653),U_4655)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4652),U_4654),U_4656)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),U_4655),U_4656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),U_4653),U_4654))
      | ~ class_Orderings_Olinorder(U_4652) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

cnf(f_1175_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4652),U_4653),U_4655)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4652),U_4654),U_4656)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),U_4655),U_4656))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4652),U_4653),U_4654))
    | ~ class_Orderings_Olinorder(U_4652) ),
    inference(clausify,[status(thm)],[f_1175_2]) ).

fof(f_1176_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_1176_2,plain,
    ! [U_4660,U_4659,U_4658,U_4657] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),U_4660))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),U_4659)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4657),U_4659),U_4660)))
      | ~ class_Orderings_Olinorder(U_4657) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

cnf(f_1176_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),U_4659))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4657),U_4659),U_4660)))
    | ~ class_Orderings_Olinorder(U_4657) ),
    inference(clausify,[status(thm)],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),U_4660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),U_4658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4657),U_4659),U_4660)))
    | ~ class_Orderings_Olinorder(U_4657) ),
    inference(clausify,[status(thm)],[f_1176_2]) ).

fof(f_1177_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_1177_2,plain,
    ! [U_4664,U_4663,U_4662,U_4661] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4661),U_4662),U_4663)),U_4664))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4663),U_4664))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4663),U_4664))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4661),U_4662),U_4663)),U_4664)) ) )
      | ~ class_Orderings_Olinorder(U_4661) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

cnf(f_1177_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4663),U_4664))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4661),U_4662),U_4663)),U_4664))
    | ~ class_Orderings_Olinorder(U_4661) ),
    inference(clausify,[status(thm)],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4661),U_4662),U_4663)),U_4664))
    | ~ class_Orderings_Olinorder(U_4661) ),
    inference(clausify,[status(thm)],[f_1177_2]) ).

cnf(f_1177_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4663),U_4664))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4661),U_4662),U_4663)),U_4664))
    | ~ class_Orderings_Olinorder(U_4661) ),
    inference(clausify,[status(thm)],[f_1177_2]) ).

fof(f_1178_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_1178_2,plain,
    ! [U_4668,U_4667,U_4666,U_4665] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4665),U_4666),U_4667)),U_4668))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4667),U_4668))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4666),U_4668)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4667),U_4668))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4666),U_4668))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4665),U_4666),U_4667)),U_4668)) ) )
      | ~ class_Orderings_Olinorder(U_4665) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

cnf(f_1178_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4667),U_4668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4666),U_4668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4665),U_4666),U_4667)),U_4668))
    | ~ class_Orderings_Olinorder(U_4665) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4666),U_4668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4665),U_4666),U_4667)),U_4668))
    | ~ class_Orderings_Olinorder(U_4665) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

cnf(f_1178_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),U_4667),U_4668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4665),U_4666),U_4667)),U_4668))
    | ~ class_Orderings_Olinorder(U_4665) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

fof(f_1179_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_1179_2,plain,
    ! [U_4672,U_4671,U_4670,U_4669] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4669),U_4671),U_4672)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4672))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4671)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4672))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4671)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4669),U_4671),U_4672))) ) )
      | ~ class_Orderings_Olinorder(U_4669) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4669),U_4671),U_4672)))
    | ~ class_Orderings_Olinorder(U_4669) ),
    inference(clausify,[status(thm)],[f_1179_2]) ).

cnf(f_1179_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4669),U_4671),U_4672)))
    | ~ class_Orderings_Olinorder(U_4669) ),
    inference(clausify,[status(thm)],[f_1179_2]) ).

cnf(f_1179_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4669),U_4671),U_4672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),U_4670),U_4671))
    | ~ class_Orderings_Olinorder(U_4669) ),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_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_1180_2,plain,
    ! [U_4676,U_4675,U_4674,U_4673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4673),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4673),U_4676),U_4674)),U_4675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4673),U_4674),U_4675))
      | ~ class_Orderings_Olinorder(U_4673) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4673),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4673),U_4676),U_4674)),U_4675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4673),U_4674),U_4675))
    | ~ class_Orderings_Olinorder(U_4673) ),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_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_1181_2,plain,
    ! [U_4680,U_4679,U_4678,U_4677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4677),U_4678),U_4680)),U_4679))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),U_4678),U_4679))
      | ~ class_Orderings_Olinorder(U_4677) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4677),U_4678),U_4680)),U_4679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),U_4678),U_4679))
    | ~ class_Orderings_Olinorder(U_4677) ),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_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_1182_2,plain,
    ! [U_4684,U_4683,U_4682,U_4681] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4681),U_4682),U_4683)),U_4684) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),U_4682),U_4684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),U_4683),U_4684))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4681) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

cnf(f_1182_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4681),U_4682),U_4683)),U_4684) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),U_4682),U_4684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4681),U_4683),U_4684))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_4681) ),
    inference(clausify,[status(thm)],[f_1182_2]) ).

fof(f_1183_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_1183_2,plain,
    ! [U_4688,U_4687,U_4686,U_4685] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4685),U_4686),U_4687)),U_4688) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4685),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),U_4686),U_4688)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),U_4687),U_4688))
      | ~ class_Groups_Oordered__ab__group__add(U_4685) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4685),U_4686),U_4687)),U_4688) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4685),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),U_4686),U_4688)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4685),U_4687),U_4688))
    | ~ class_Groups_Oordered__ab__group__add(U_4685) ),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_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_1184_2,plain,
    ! [U_4689] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_4689) = c_Orderings_Oord__class_Omin(U_4689)
      | ~ class_Orderings_Olinorder(U_4689)
      | ~ class_Lattices_Osemilattice__inf(U_4689) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_4689) = c_Orderings_Oord__class_Omin(U_4689)
    | ~ class_Orderings_Olinorder(U_4689)
    | ~ class_Lattices_Osemilattice__inf(U_4689) ),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_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_1185_2,plain,
    ! [U_4690] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4690) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

cnf(f_1185_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4690) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1185_2]) ).

fof(f_1186_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_1186_2,plain,
    ! [U_4691] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4691),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

cnf(f_1186_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4691),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1186_2]) ).

fof(f_1187_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_1187_2,plain,
    ! [U_4693,U_4692] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4692)),hAPP(c_Nat_OSuc,U_4693)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4692),U_4693)),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

cnf(f_1187_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4692)),hAPP(c_Nat_OSuc,U_4693)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4692),U_4693)),
    inference(clausify,[status(thm)],[f_1187_2]) ).

fof(f_1188_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_1188_2,plain,
    ! [U_4696,U_4695,U_4694] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4694),U_4695)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4696),U_4695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4694),U_4696)),U_4695),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4694),U_4695)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4696),U_4695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4694),U_4696)),U_4695),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_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_1189_2,plain,
    ! [U_4697] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_4697,U_4697,c_Orderings_Oord__class_Omin(U_4697))
      | ~ class_Orderings_Olinorder(U_4697) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_4697,U_4697,c_Orderings_Oord__class_Omin(U_4697))
    | ~ class_Orderings_Olinorder(U_4697) ),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I52_J]) ).

fof(f_1190_2,plain,
    ! [U_4702,U_4701,U_4700,U_4699,U_4698] : c_Com_Ocom_OCond(U_4698,U_4699,U_4700) != c_Com_Ocom_OWhile(U_4701,U_4702),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

cnf(f_1190_3,plain,
    c_Com_Ocom_OCond(U_4698,U_4699,U_4700) != c_Com_Ocom_OWhile(U_4701,U_4702),
    inference(clausify,[status(thm)],[f_1190_2]) ).

fof(f_1191_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I53_J]) ).

fof(f_1191_2,plain,
    ! [U_4707,U_4706,U_4705,U_4704,U_4703] : c_Com_Ocom_OWhile(U_4703,U_4704) != c_Com_Ocom_OCond(U_4705,U_4706,U_4707),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    c_Com_Ocom_OWhile(U_4703,U_4704) != c_Com_Ocom_OCond(U_4705,U_4706,U_4707),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I46_J]) ).

fof(f_1192_2,plain,
    ! [U_4711,U_4710,U_4709,U_4708] : c_Com_Ocom_OSemi(U_4708,U_4709) != c_Com_Ocom_OWhile(U_4710,U_4711),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

cnf(f_1192_3,plain,
    c_Com_Ocom_OSemi(U_4708,U_4709) != c_Com_Ocom_OWhile(U_4710,U_4711),
    inference(clausify,[status(thm)],[f_1192_2]) ).

fof(f_1193_1,plain,
    ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I47_J]) ).

fof(f_1193_2,plain,
    ! [U_4715,U_4714,U_4713,U_4712] : c_Com_Ocom_OWhile(U_4712,U_4713) != c_Com_Ocom_OSemi(U_4714,U_4715),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    c_Com_Ocom_OWhile(U_4712,U_4713) != c_Com_Ocom_OSemi(U_4714,U_4715),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_1,plain,
    ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I38_J]) ).

fof(f_1194_2,plain,
    ! [U_4720,U_4719,U_4718,U_4717,U_4716] : c_Com_Ocom_OLocal(U_4716,U_4717,U_4718) != c_Com_Ocom_OWhile(U_4719,U_4720),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

cnf(f_1194_3,plain,
    c_Com_Ocom_OLocal(U_4716,U_4717,U_4718) != c_Com_Ocom_OWhile(U_4719,U_4720),
    inference(clausify,[status(thm)],[f_1194_2]) ).

fof(f_1195_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I39_J]) ).

fof(f_1195_2,plain,
    ! [U_4725,U_4724,U_4723,U_4722,U_4721] : c_Com_Ocom_OWhile(U_4721,U_4722) != c_Com_Ocom_OLocal(U_4723,U_4724,U_4725),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

cnf(f_1195_3,plain,
    c_Com_Ocom_OWhile(U_4721,U_4722) != c_Com_Ocom_OLocal(U_4723,U_4724,U_4725),
    inference(clausify,[status(thm)],[f_1195_2]) ).

fof(f_1196_1,plain,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I16_J]) ).

fof(f_1196_2,plain,
    ! [U_4727,U_4726] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_4726,U_4727),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

cnf(f_1196_3,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_4726,U_4727),
    inference(clausify,[status(thm)],[f_1196_2]) ).

fof(f_1197_1,plain,
    ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I17_J]) ).

fof(f_1197_2,plain,
    ! [U_4729,U_4728] : c_Com_Ocom_OWhile(U_4728,U_4729) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

cnf(f_1197_3,plain,
    c_Com_Ocom_OWhile(U_4728,U_4729) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_1197_2]) ).

fof(f_1198_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_1198_2,plain,
    ! [U_4732,U_4731,U_4730] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732))) ) )
      | ~ class_Orderings_Oord(U_4730)
      | ~ class_Int_Onumber(U_4730) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

cnf(f_1198_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)))
    | ~ class_Orderings_Oord(U_4730)
    | ~ class_Int_Onumber(U_4730) ),
    inference(clausify,[status(thm)],[f_1198_2]) ).

cnf(f_1198_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4730),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4731)),hAPP(c_Int_Onumber__class_Onumber__of(U_4730),U_4732)))
    | ~ class_Orderings_Oord(U_4730)
    | ~ class_Int_Onumber(U_4730) ),
    inference(clausify,[status(thm)],[f_1198_2]) ).

fof(f_1199_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_1199_2,plain,
    ! [U_4736,U_4735,U_4734,U_4733] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4733,U_4733,c_Orderings_Oord__class_Omin(U_4733)),U_4735),hAPP(hAPP(c_Set_Oinsert(U_4733),U_4736),U_4734)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4733),U_4736),hAPP(hAPP(c_Finite__Set_Ofold(U_4733,U_4733,c_Orderings_Oord__class_Omin(U_4733)),U_4735),U_4734))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4733),U_4734))
      | ~ class_Orderings_Olinorder(U_4733) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

cnf(f_1199_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4733,U_4733,c_Orderings_Oord__class_Omin(U_4733)),U_4735),hAPP(hAPP(c_Set_Oinsert(U_4733),U_4736),U_4734)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4733),U_4736),hAPP(hAPP(c_Finite__Set_Ofold(U_4733,U_4733,c_Orderings_Oord__class_Omin(U_4733)),U_4735),U_4734))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4733),U_4734))
    | ~ class_Orderings_Olinorder(U_4733) ),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_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_1200_2,plain,
    ! [U_4740,U_4739,U_4738,U_4737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4737),hAPP(hAPP(c_Finite__Set_Ofold(U_4737,U_4737,c_Orderings_Oord__class_Omin(U_4737)),U_4740),U_4738)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4737),U_4739),U_4740)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4737),U_4739),U_4738))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4737),U_4738))
      | ~ class_Orderings_Olinorder(U_4737) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

cnf(f_1200_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4737),hAPP(hAPP(c_Finite__Set_Ofold(U_4737,U_4737,c_Orderings_Oord__class_Omin(U_4737)),U_4740),U_4738)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4737),U_4739),U_4740)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4737),U_4739),U_4738))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4737),U_4738))
    | ~ class_Orderings_Olinorder(U_4737) ),
    inference(clausify,[status(thm)],[f_1200_2]) ).

fof(f_1201_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_1201_2,plain,
    ! [U_4743,U_4742,U_4741] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4741),hAPP(c_Finite__Set_Ofold1(U_4741,c_Orderings_Oord__class_Omin(U_4741)),U_4742)),U_4743))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4741),U_4743),U_4742))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4741),U_4742))
      | ~ class_Orderings_Olinorder(U_4741) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

cnf(f_1201_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4741),hAPP(c_Finite__Set_Ofold1(U_4741,c_Orderings_Oord__class_Omin(U_4741)),U_4742)),U_4743))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4741),U_4743),U_4742))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4741),U_4742))
    | ~ class_Orderings_Olinorder(U_4741) ),
    inference(clausify,[status(thm)],[f_1201_2]) ).

fof(f_1202_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_1202_2,plain,
    ! [U_4748,U_4747,U_4746] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747)))
          | ? [U_4745] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),U_4745))
              & hBOOL(hAPP(hAPP(c_member(U_4746),U_4745),U_4747)) ) )
        & ( ! [U_4744] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),U_4744))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4746),U_4744),U_4747)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747))) ) )
      | U_4747 = c_Orderings_Obot__class_Obot(tc_fun(U_4746,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4746),U_4747))
      | ~ class_Orderings_Olinorder(U_4746) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ! [U_4748,U_4747,U_4746] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),sK91(U_4748,U_4747,U_4746)))
            & hBOOL(hAPP(hAPP(c_member(U_4746),sK91(U_4748,U_4747,U_4746)),U_4747)) ) )
        & ( ! [U_4744] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),U_4744))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4746),U_4744),U_4747)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747))) ) )
      | U_4747 = c_Orderings_Obot__class_Obot(tc_fun(U_4746,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4746),U_4747))
      | ~ class_Orderings_Olinorder(U_4746) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4745,sK91(U_4748,U_4747,U_4746))],[f_1202_2]) ).

cnf(f_1202_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),U_4744))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4746),U_4744),U_4747))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747)))
    | U_4747 = c_Orderings_Obot__class_Obot(tc_fun(U_4746,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4746),U_4747))
    | ~ class_Orderings_Olinorder(U_4746) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

cnf(f_1202_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4746),sK91(U_4748,U_4747,U_4746)),U_4747))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747)))
    | U_4747 = c_Orderings_Obot__class_Obot(tc_fun(U_4746,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4746),U_4747))
    | ~ class_Orderings_Olinorder(U_4746) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

cnf(f_1202_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),sK91(U_4748,U_4747,U_4746)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4746),U_4748),hAPP(c_Finite__Set_Ofold1(U_4746,c_Orderings_Oord__class_Omin(U_4746)),U_4747)))
    | U_4747 = c_Orderings_Obot__class_Obot(tc_fun(U_4746,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4746),U_4747))
    | ~ class_Orderings_Olinorder(U_4746) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

fof(f_1203_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_1203_2,plain,
    ! [U_4753,U_4752,U_4751] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753))
          | ! [U_4750] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),U_4750),U_4753))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4751),U_4750),U_4752)) ) )
        & ( ? [U_4749] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),U_4749),U_4753))
              & hBOOL(hAPP(hAPP(c_member(U_4751),U_4749),U_4752)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753)) ) )
      | U_4752 = c_Orderings_Obot__class_Obot(tc_fun(U_4751,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4751),U_4752))
      | ~ class_Orderings_Olinorder(U_4751) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_4753,U_4752,U_4751] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753))
          | ! [U_4750] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),U_4750),U_4753))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4751),U_4750),U_4752)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),sK92(U_4753,U_4752,U_4751)),U_4753))
            & hBOOL(hAPP(hAPP(c_member(U_4751),sK92(U_4753,U_4752,U_4751)),U_4752)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753)) ) )
      | U_4752 = c_Orderings_Obot__class_Obot(tc_fun(U_4751,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4751),U_4752))
      | ~ class_Orderings_Olinorder(U_4751) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4749,sK92(U_4753,U_4752,U_4751))],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4751),sK92(U_4753,U_4752,U_4751)),U_4752))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753))
    | U_4752 = c_Orderings_Obot__class_Obot(tc_fun(U_4751,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4751),U_4752))
    | ~ class_Orderings_Olinorder(U_4751) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

cnf(f_1203_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),sK92(U_4753,U_4752,U_4751)),U_4753))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753))
    | U_4752 = c_Orderings_Obot__class_Obot(tc_fun(U_4751,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4751),U_4752))
    | ~ class_Orderings_Olinorder(U_4751) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

cnf(f_1203_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),hAPP(c_Finite__Set_Ofold1(U_4751,c_Orderings_Oord__class_Omin(U_4751)),U_4752)),U_4753))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4751),U_4750),U_4753))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4751),U_4750),U_4752))
    | U_4752 = c_Orderings_Obot__class_Obot(tc_fun(U_4751,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4751),U_4752))
    | ~ class_Orderings_Olinorder(U_4751) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_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_1204_2,plain,
    ! [U_4758,U_4757,U_4756] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758))
          | ! [U_4755] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),U_4755),U_4758))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4756),U_4755),U_4757)) ) )
        & ( ? [U_4754] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),U_4754),U_4758))
              & hBOOL(hAPP(hAPP(c_member(U_4756),U_4754),U_4757)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758)) ) )
      | U_4757 = c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4756),U_4757))
      | ~ class_Orderings_Olinorder(U_4756) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_4758,U_4757,U_4756] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758))
          | ! [U_4755] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),U_4755),U_4758))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4756),U_4755),U_4757)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),sK93(U_4758,U_4757,U_4756)),U_4758))
            & hBOOL(hAPP(hAPP(c_member(U_4756),sK93(U_4758,U_4757,U_4756)),U_4757)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758)) ) )
      | U_4757 = c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4756),U_4757))
      | ~ class_Orderings_Olinorder(U_4756) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_4754,sK93(U_4758,U_4757,U_4756))],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4756),sK93(U_4758,U_4757,U_4756)),U_4757))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758))
    | U_4757 = c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4756),U_4757))
    | ~ class_Orderings_Olinorder(U_4756) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

cnf(f_1204_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),sK93(U_4758,U_4757,U_4756)),U_4758))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758))
    | U_4757 = c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4756),U_4757))
    | ~ class_Orderings_Olinorder(U_4756) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

cnf(f_1204_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),hAPP(c_Finite__Set_Ofold1(U_4756,c_Orderings_Oord__class_Omin(U_4756)),U_4757)),U_4758))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4756),U_4755),U_4758))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4756),U_4755),U_4757))
    | U_4757 = c_Orderings_Obot__class_Obot(tc_fun(U_4756,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4756),U_4757))
    | ~ class_Orderings_Olinorder(U_4756) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_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_1205_2,plain,
    ! [U_4763,U_4762,U_4761] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762)))
          | ? [U_4760] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),U_4760))
              & hBOOL(hAPP(hAPP(c_member(U_4761),U_4760),U_4762)) ) )
        & ( ! [U_4759] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),U_4759))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4761),U_4759),U_4762)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762))) ) )
      | U_4762 = c_Orderings_Obot__class_Obot(tc_fun(U_4761,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4761),U_4762))
      | ~ class_Orderings_Olinorder(U_4761) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

fof(f_1205_3,plain,
    ! [U_4763,U_4762,U_4761] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),sK94(U_4763,U_4762,U_4761)))
            & hBOOL(hAPP(hAPP(c_member(U_4761),sK94(U_4763,U_4762,U_4761)),U_4762)) ) )
        & ( ! [U_4759] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),U_4759))
              | ~ hBOOL(hAPP(hAPP(c_member(U_4761),U_4759),U_4762)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762))) ) )
      | U_4762 = c_Orderings_Obot__class_Obot(tc_fun(U_4761,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4761),U_4762))
      | ~ class_Orderings_Olinorder(U_4761) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_4760,sK94(U_4763,U_4762,U_4761))],[f_1205_2]) ).

cnf(f_1205_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),U_4759))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4761),U_4759),U_4762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762)))
    | U_4762 = c_Orderings_Obot__class_Obot(tc_fun(U_4761,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4761),U_4762))
    | ~ class_Orderings_Olinorder(U_4761) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

cnf(f_1205_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4761),sK94(U_4763,U_4762,U_4761)),U_4762))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762)))
    | U_4762 = c_Orderings_Obot__class_Obot(tc_fun(U_4761,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4761),U_4762))
    | ~ class_Orderings_Olinorder(U_4761) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

cnf(f_1205_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),sK94(U_4763,U_4762,U_4761)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4761),U_4763),hAPP(c_Finite__Set_Ofold1(U_4761,c_Orderings_Oord__class_Omin(U_4761)),U_4762)))
    | U_4762 = c_Orderings_Obot__class_Obot(tc_fun(U_4761,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4761),U_4762))
    | ~ class_Orderings_Olinorder(U_4761) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

fof(f_1206_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_1206_2,plain,
    ! [U_4766,U_4765,U_4764] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4766))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4765),U_4764))
      | U_4764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4764),U_4766))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4764)) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4766))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4765),U_4764))
    | U_4764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4764),U_4766))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4764)) ),
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_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_1207_2,plain,
    ! [U_4769,U_4768,U_4767] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4769),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_4768))
      | U_4767 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4767),U_4769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4767)) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

cnf(f_1207_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4769),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_4768))
    | U_4767 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4767),U_4769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4767)) ),
    inference(clausify,[status(thm)],[f_1207_2]) ).

fof(f_1208_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_1208_2,plain,
    ! [U_4775,U_4774,U_4773,U_4772,U_4771,U_4770] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4774),U_4771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4773),U_4770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4772),U_4770))
      | ~ 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_4773),U_4774)),U_4775)),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_4770),U_4771)),U_4772) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4773),U_4774)),U_4775) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

cnf(f_1208_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4774),U_4771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4773),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4772),U_4770))
    | ~ 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_4773),U_4774)),U_4775)),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_4770),U_4771)),U_4772) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4773),U_4774)),U_4775) ),
    inference(clausify,[status(thm)],[f_1208_2]) ).

fof(f_1209_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_1209_2,plain,
    ! [U_4780,U_4779,U_4778,U_4777,U_4776] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4779),U_4777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4776),U_4778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4776),U_4780))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4780),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_4776),U_4777)),U_4778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4776),U_4779)),U_4780))) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

cnf(f_1209_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4779),U_4777))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4776),U_4778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4776),U_4780))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4780),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_4776),U_4777)),U_4778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4776),U_4779)),U_4780))) ),
    inference(clausify,[status(thm)],[f_1209_2]) ).

fof(f_1210_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_1210_2,plain,
    ! [U_4786,U_4785,U_4784,U_4783,U_4782,U_4781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4782),U_4785))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4784),U_4781))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4786),U_4784))
      | ~ 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_4784),U_4785)),U_4786)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4781),U_4782)),U_4783) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4784),U_4785)),U_4786) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

cnf(f_1210_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4782),U_4785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4784),U_4781))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4786),U_4784))
    | ~ 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_4784),U_4785)),U_4786)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4781),U_4782)),U_4783) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4784),U_4785)),U_4786) ),
    inference(clausify,[status(thm)],[f_1210_2]) ).

fof(f_1211_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_1211_2,plain,
    ! [U_4791,U_4790,U_4789,U_4788,U_4787] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4788),U_4790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4791),U_4787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4789),U_4787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4789))
      | ~ 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_4787),U_4788)),U_4789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4787),U_4790)),U_4791))) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

cnf(f_1211_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4788),U_4790))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4791),U_4787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4789),U_4787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4789))
    | ~ 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_4787),U_4788)),U_4789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4787),U_4790)),U_4791))) ),
    inference(clausify,[status(thm)],[f_1211_2]) ).

fof(f_1212_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_1212_2,plain,
    ! [U_4794,U_4793,U_4792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4793),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_4792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4794))
      | ~ 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_4792),U_4793)),U_4794)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

cnf(f_1212_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4793),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_4792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4794))
    | ~ 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_4792),U_4793)),U_4794)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

fof(f_1213_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_1213_2,plain,
    ! [U_4795] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4795) = U_4795,
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

cnf(f_1213_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4795) = U_4795,
    inference(clausify,[status(thm)],[f_1213_2]) ).

fof(f_1214_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_1214_2,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1214_1]) ).

fof(f_1215_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_1215_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1215_1]) ).

fof(f_1216_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_1216_2,plain,
    ! [U_4798,U_4797,U_4796] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4798),U_4796))
      | ~ 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_4796),U_4797)),U_4798))) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

cnf(f_1216_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4797))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4798),U_4796))
    | ~ 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_4796),U_4797)),U_4798))) ),
    inference(clausify,[status(thm)],[f_1216_2]) ).

fof(f_1217_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_1217_2,plain,
    ! [U_4800,U_4799] :
      ( 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_4799),U_4800)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4799)) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

cnf(f_1217_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_4799),U_4800)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4800))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4799)) ),
    inference(clausify,[status(thm)],[f_1217_2]) ).

fof(f_1218_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_1218_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_1218_1]) ).

fof(f_1219_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_1219_2,plain,
    ! [U_4802,U_4801] :
      ( 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_4801),U_4802)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

cnf(f_1219_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_4801),U_4802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ),
    inference(clausify,[status(thm)],[f_1219_2]) ).

fof(f_1220_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_1220_2,plain,
    ! [U_4806,U_4805,U_4804,U_4803] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_4803,U_4804)),c_Nitpick_Opair__box_OPairBox(U_4803,U_4804,U_4805,U_4806)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

cnf(f_1220_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_4803,U_4804)),c_Nitpick_Opair__box_OPairBox(U_4803,U_4804,U_4805,U_4806)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1220_2]) ).

fof(f_1221_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_1221_2,plain,
    ! [U_4812,U_4811,U_4810,U_4809,U_4808,U_4807] : c_Nitpick_Opair__box_Opair__box__rec(U_4807,U_4808,U_4809,U_4810,c_Nitpick_Opair__box_OPairBox(U_4807,U_4808,U_4811,U_4812)) = hAPP(hAPP(U_4810,U_4811),U_4812),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

cnf(f_1221_3,plain,
    c_Nitpick_Opair__box_Opair__box__rec(U_4807,U_4808,U_4809,U_4810,c_Nitpick_Opair__box_OPairBox(U_4807,U_4808,U_4811,U_4812)) = hAPP(hAPP(U_4810,U_4811),U_4812),
    inference(clausify,[status(thm)],[f_1221_2]) ).

fof(f_1222_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_1222_2,plain,
    ! [U_4818,U_4817,U_4816,U_4815,U_4814,U_4813] : c_Nitpick_Opair__box_Opair__box__case(U_4813,U_4814,U_4815,U_4816,c_Nitpick_Opair__box_OPairBox(U_4813,U_4814,U_4817,U_4818)) = hAPP(hAPP(U_4816,U_4817),U_4818),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

cnf(f_1222_3,plain,
    c_Nitpick_Opair__box_Opair__box__case(U_4813,U_4814,U_4815,U_4816,c_Nitpick_Opair__box_OPairBox(U_4813,U_4814,U_4817,U_4818)) = hAPP(hAPP(U_4816,U_4817),U_4818),
    inference(clausify,[status(thm)],[f_1222_2]) ).

fof(f_1223_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_1223_2,plain,
    ! [U_4819] :
      ( c_Orderings_Oord__class_Omin(U_4819) = c_Orderings_Oord_Omin(U_4819,c_Orderings_Oord__class_Oless__eq(U_4819))
      | ~ class_Orderings_Oord(U_4819) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

cnf(f_1223_3,plain,
    ( c_Orderings_Oord__class_Omin(U_4819) = c_Orderings_Oord_Omin(U_4819,c_Orderings_Oord__class_Oless__eq(U_4819))
    | ~ class_Orderings_Oord(U_4819) ),
    inference(clausify,[status(thm)],[f_1223_2]) ).

fof(f_1224_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_1224_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_1224_1]) ).

fof(f_1225_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_1225_2,plain,
    ! [U_4821,U_4820] :
      ( ( 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_4820)),U_4821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4820))),U_4821)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4820))) )
      & ( 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_4820)),U_4821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4821)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4820))) ) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ( ! [U_4825,U_4823] :
        ( 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_4823)),U_4825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4823))),U_4825)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4823))) )
    & ! [U_4824,U_4822] :
        ( 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_4822)),U_4824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4824)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4822))) ) ),
    inference(miniscope,[status(thm)],[f_1225_2]) ).

cnf(f_1225_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_4822)),U_4824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4824)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4822))) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

cnf(f_1225_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_4823)),U_4825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4823))),U_4825)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4823))) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_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_1226_2,plain,
    ! [U_4827,U_4826] :
      ( ( c_Nat__Transfer_Otsub(U_4827,U_4826) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4826),U_4827)) )
      & ( c_Nat__Transfer_Otsub(U_4827,U_4826) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4827),U_4826)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4826),U_4827)) ) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ( ! [U_4831,U_4829] :
        ( c_Nat__Transfer_Otsub(U_4831,U_4829) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4829),U_4831)) )
    & ! [U_4830,U_4828] :
        ( c_Nat__Transfer_Otsub(U_4830,U_4828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4830),U_4828)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4828),U_4830)) ) ),
    inference(miniscope,[status(thm)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( c_Nat__Transfer_Otsub(U_4830,U_4828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4830),U_4828)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4828),U_4830)) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

cnf(f_1226_5,plain,
    ( c_Nat__Transfer_Otsub(U_4831,U_4829) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4829),U_4831)) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_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_1227_2,plain,
    ! [U_4834,U_4833,U_4832] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_4832,U_4833) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4832),U_4834),c_Big__Operators_Olinorder__class_OMin(U_4832,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_4832,U_4833) = U_4834
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4832),U_4834),U_4833))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4832),U_4833))
      | ~ class_Orderings_Olinorder(U_4832) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

cnf(f_1227_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4832,U_4833) = U_4834
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4832),U_4834),U_4833))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4832),U_4833))
    | ~ class_Orderings_Olinorder(U_4832) ),
    inference(clausify,[status(thm)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4832,U_4833) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4832),U_4834),c_Big__Operators_Olinorder__class_OMin(U_4832,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4832,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_Set_Oinsert(U_4832),U_4834),c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4832,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4832),U_4834),U_4833))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4832),U_4833))
    | ~ class_Orderings_Olinorder(U_4832) ),
    inference(clausify,[status(thm)],[f_1227_2]) ).

fof(f_1228_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_1228_2,plain,
    ! [U_4837,U_4836,U_4835] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),U_4836) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4835),U_4837),c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),U_4836) = U_4837
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4835),U_4837),U_4836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4835),U_4836))
      | ~ class_Orderings_Olinorder(U_4835) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

cnf(f_1228_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),U_4836) = U_4837
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4835),U_4837),U_4836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4835),U_4836))
    | ~ class_Orderings_Olinorder(U_4835) ),
    inference(clausify,[status(thm)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),U_4836) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4835),U_4837),c_Big__Operators_Olattice_OInf__fin(U_4835,c_Orderings_Oord__class_Omin(U_4835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4835,tc_HOL_Obool)),U_4836),hAPP(hAPP(c_Set_Oinsert(U_4835),U_4837),c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4835,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4835),U_4837),U_4836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4835),U_4836))
    | ~ class_Orderings_Olinorder(U_4835) ),
    inference(clausify,[status(thm)],[f_1228_2]) ).

fof(f_1229_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_1229_2,plain,
    ! [U_4838] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4838)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4838))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4838))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4838)) = 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_4838))) ) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ( ! [U_4840] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4840)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4840))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4840))) )
    & ! [U_4839] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4839)) = 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_4839))) ) ),
    inference(miniscope,[status(thm)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4839)) = 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_4839))) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

cnf(f_1229_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4840)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4840))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4840))) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_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_1230_2,plain,
    ! [U_4842,U_4841] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)) = c_Groups_Ozero__class_Ozero(U_4841)
          | 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_4842))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4841),U_4842)
          | ~ 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_4842))) ) )
      | ~ class_Int_Onumber__ring(U_4841) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

cnf(f_1230_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4841),U_4842)
    | ~ 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_4842)))
    | ~ class_Int_Onumber__ring(U_4841) ),
    inference(clausify,[status(thm)],[f_1230_2]) ).

cnf(f_1230_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)) = c_Groups_Ozero__class_Ozero(U_4841)
    | 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_4842)))
    | ~ class_Int_Onumber__ring(U_4841) ),
    inference(clausify,[status(thm)],[f_1230_2]) ).

fof(f_1231_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_1231_2,plain,
    ! [U_4845,U_4844,U_4843] :
      ( c_Big__Operators_Olinorder__class_OMin(U_4843,hAPP(hAPP(c_Set_Oinsert(U_4843),U_4845),U_4844)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4843,c_Orderings_Oord__class_Omin(U_4843)),U_4845),U_4844)
      | hBOOL(hAPP(hAPP(c_member(U_4843),U_4845),U_4844))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4843),U_4844))
      | ~ class_Orderings_Olinorder(U_4843) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

cnf(f_1231_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4843,hAPP(hAPP(c_Set_Oinsert(U_4843),U_4845),U_4844)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4843,c_Orderings_Oord__class_Omin(U_4843)),U_4845),U_4844)
    | hBOOL(hAPP(hAPP(c_member(U_4843),U_4845),U_4844))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4843),U_4844))
    | ~ class_Orderings_Olinorder(U_4843) ),
    inference(clausify,[status(thm)],[f_1231_2]) ).

fof(f_1232_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_1232_2,plain,
    ! [U_4847,U_4846] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4847)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4846),U_4847)),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

cnf(f_1232_3,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4847)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4846),U_4847)),
    inference(clausify,[status(thm)],[f_1232_2]) ).

fof(f_1233_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_1233_2,plain,
    ! [U_4850,U_4849,U_4848] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4849) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4850)
          | U_4849 != U_4850 )
        & ( U_4849 = U_4850
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4849) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4850) ) )
      | ~ class_Nat_Osemiring__char__0(U_4848) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

cnf(f_1233_3,plain,
    ( U_4849 = U_4850
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4849) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4850)
    | ~ class_Nat_Osemiring__char__0(U_4848) ),
    inference(clausify,[status(thm)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4849) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4848),U_4850)
    | U_4849 != U_4850
    | ~ class_Nat_Osemiring__char__0(U_4848) ),
    inference(clausify,[status(thm)],[f_1233_2]) ).

fof(f_1234_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_1234_2,plain,
    ! [U_4851] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4851))),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

cnf(f_1234_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4851))),
    inference(clausify,[status(thm)],[f_1234_2]) ).

fof(f_1235_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_1235_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1235_1]) ).

fof(f_1236_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_1236_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1236_1]) ).

fof(f_1237_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_1237_2,plain,
    ! [U_4852] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4852)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4852)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4852))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4852)) = 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_4852))) ) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ( ! [U_4854] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4854)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4854)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4854))) )
    & ! [U_4853] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4853)) = 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_4853))) ) ),
    inference(miniscope,[status(thm)],[f_1237_2]) ).

cnf(f_1237_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4853)) = 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_4853))) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

cnf(f_1237_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4854)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4854)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4854))) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_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_1238_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_1238_1]) ).

fof(f_1239_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_1239_2,plain,
    ! [U_4855] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4855) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_4855 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_4855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4855) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ( ! [U_4857] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4857) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_4857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4856] :
        ( U_4856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4856) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    ( U_4856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4856) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

cnf(f_1239_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4857) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_4857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_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_1240_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_1240_1]) ).

fof(f_1241_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_1241_2,plain,
    ! [U_4858] : 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_4858))),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

cnf(f_1241_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_4858))),
    inference(clausify,[status(thm)],[f_1241_2]) ).

fof(f_1242_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_1242_2,plain,
    ! [U_4859] : 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_4859))),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

cnf(f_1242_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_4859))),
    inference(clausify,[status(thm)],[f_1242_2]) ).

fof(f_1243_1,plain,
    ! [V_Pa_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_1243_2,plain,
    ! [U_4864] :
      ( ( ? [U_4863] :
            ( hBOOL(hAPP(U_4864,U_4863))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4863)) )
        | ! [U_4862] : ~ hBOOL(hAPP(U_4864,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) )
      & ( ? [U_4861] : hBOOL(hAPP(U_4864,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4861)))
        | ! [U_4860] :
            ( ~ hBOOL(hAPP(U_4864,U_4860))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4860)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ( ! [U_4866] :
        ( ? [U_4863] :
            ( hBOOL(hAPP(U_4866,U_4863))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4863)) )
        | ! [U_4862] : ~ hBOOL(hAPP(U_4866,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) )
    & ! [U_4865] :
        ( ? [U_4861] : hBOOL(hAPP(U_4865,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4861)))
        | ! [U_4860] :
            ( ~ hBOOL(hAPP(U_4865,U_4860))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4860)) ) ) ),
    inference(miniscope,[status(thm)],[f_1243_2]) ).

fof(f_1243_4,plain,
    ( ! [U_4866] :
        ( ? [U_4863] :
            ( hBOOL(hAPP(U_4866,U_4863))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4863)) )
        | ! [U_4862] : ~ hBOOL(hAPP(U_4866,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) )
    & ! [U_4865] :
        ( hBOOL(hAPP(U_4865,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK95(U_4865))))
        | ! [U_4860] :
            ( ~ hBOOL(hAPP(U_4865,U_4860))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4860)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_4861,sK95(U_4865))],[f_1243_3]) ).

fof(f_1243_5,plain,
    ( ! [U_4866] :
        ( ( hBOOL(hAPP(U_4866,sK96(U_4866)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK96(U_4866))) )
        | ! [U_4862] : ~ hBOOL(hAPP(U_4866,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) )
    & ! [U_4865] :
        ( hBOOL(hAPP(U_4865,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK95(U_4865))))
        | ! [U_4860] :
            ( ~ hBOOL(hAPP(U_4865,U_4860))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4860)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_4863,sK96(U_4866))],[f_1243_4]) ).

cnf(f_1243_6,plain,
    ( hBOOL(hAPP(U_4865,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK95(U_4865))))
    | ~ hBOOL(hAPP(U_4865,U_4860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4860)) ),
    inference(clausify,[status(thm)],[f_1243_5]) ).

cnf(f_1243_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK96(U_4866)))
    | ~ hBOOL(hAPP(U_4866,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) ),
    inference(clausify,[status(thm)],[f_1243_5]) ).

cnf(f_1243_8,plain,
    ( hBOOL(hAPP(U_4866,sK96(U_4866)))
    | ~ hBOOL(hAPP(U_4866,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4862))) ),
    inference(clausify,[status(thm)],[f_1243_5]) ).

fof(f_1244_1,plain,
    ! [V_Pa_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_1244_2,plain,
    ! [U_4871] :
      ( ( ! [U_4870] :
            ( hBOOL(hAPP(U_4871,U_4870))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4870)) )
        | ? [U_4869] : ~ hBOOL(hAPP(U_4871,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4869))) )
      & ( ! [U_4868] : hBOOL(hAPP(U_4871,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868)))
        | ? [U_4867] :
            ( ~ hBOOL(hAPP(U_4871,U_4867))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4867)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ( ! [U_4873] :
        ( ! [U_4870] :
            ( hBOOL(hAPP(U_4873,U_4870))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4870)) )
        | ? [U_4869] : ~ hBOOL(hAPP(U_4873,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4869))) )
    & ! [U_4872] :
        ( ! [U_4868] : hBOOL(hAPP(U_4872,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868)))
        | ? [U_4867] :
            ( ~ hBOOL(hAPP(U_4872,U_4867))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4867)) ) ) ),
    inference(miniscope,[status(thm)],[f_1244_2]) ).

fof(f_1244_4,plain,
    ( ! [U_4873] :
        ( ! [U_4870] :
            ( hBOOL(hAPP(U_4873,U_4870))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4870)) )
        | ? [U_4869] : ~ hBOOL(hAPP(U_4873,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4869))) )
    & ! [U_4872] :
        ( ! [U_4868] : hBOOL(hAPP(U_4872,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868)))
        | ( ~ hBOOL(hAPP(U_4872,sK97(U_4872)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK97(U_4872))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_4867,sK97(U_4872))],[f_1244_3]) ).

fof(f_1244_5,plain,
    ( ! [U_4873] :
        ( ! [U_4870] :
            ( hBOOL(hAPP(U_4873,U_4870))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4870)) )
        | ~ hBOOL(hAPP(U_4873,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK98(U_4873)))) )
    & ! [U_4872] :
        ( ! [U_4868] : hBOOL(hAPP(U_4872,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868)))
        | ( ~ hBOOL(hAPP(U_4872,sK97(U_4872)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK97(U_4872))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_4869,sK98(U_4873))],[f_1244_4]) ).

cnf(f_1244_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK97(U_4872)))
    | hBOOL(hAPP(U_4872,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868))) ),
    inference(clausify,[status(thm)],[f_1244_5]) ).

cnf(f_1244_7,plain,
    ( ~ hBOOL(hAPP(U_4872,sK97(U_4872)))
    | hBOOL(hAPP(U_4872,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4868))) ),
    inference(clausify,[status(thm)],[f_1244_5]) ).

cnf(f_1244_8,plain,
    ( hBOOL(hAPP(U_4873,U_4870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4870))
    | ~ hBOOL(hAPP(U_4873,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK98(U_4873)))) ),
    inference(clausify,[status(thm)],[f_1244_5]) ).

fof(f_1245_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_1245_2,plain,
    ! [U_4874] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4874)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

cnf(f_1245_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_4874)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1245_2]) ).

fof(f_1246_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_1246_2,plain,
    ! [U_4876,U_4875] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4875)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4876)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4875),U_4876)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4875),U_4876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4875)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4876))) ) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ( ! [U_4880,U_4878] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4878)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4880)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4878),U_4880)) )
    & ! [U_4879,U_4877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4877),U_4879))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4877)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4879))) ) ),
    inference(miniscope,[status(thm)],[f_1246_2]) ).

cnf(f_1246_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4877),U_4879))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4877)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4879))) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

cnf(f_1246_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_4878)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4880)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4878),U_4880)) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_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_1247_2,plain,
    ! [U_4882,U_4881] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4881)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4881),U_4882)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4881),U_4882))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4881)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4882))) ) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ( ! [U_4886,U_4884] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4884)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4886)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4884),U_4886)) )
    & ! [U_4885,U_4883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4883),U_4885))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4883)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4885))) ) ),
    inference(miniscope,[status(thm)],[f_1247_2]) ).

cnf(f_1247_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4883),U_4885))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4883)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4885))) ),
    inference(clausify,[status(thm)],[f_1247_3]) ).

cnf(f_1247_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_4884)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4884),U_4886)) ),
    inference(clausify,[status(thm)],[f_1247_3]) ).

fof(f_1248_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_1248_2,plain,
    ! [U_4888,U_4887] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4887)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4888)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4887),U_4888)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4887),U_4888))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4887)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4888))) ) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ( ! [U_4892,U_4890] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4890)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4892)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4890),U_4892)) )
    & ! [U_4891,U_4889] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4889),U_4891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4889)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4891))) ) ),
    inference(miniscope,[status(thm)],[f_1248_2]) ).

cnf(f_1248_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4889),U_4891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4889)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4891))) ),
    inference(clausify,[status(thm)],[f_1248_3]) ).

cnf(f_1248_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_4890)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4890),U_4892)) ),
    inference(clausify,[status(thm)],[f_1248_3]) ).

fof(f_1249_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_1249_2,plain,
    ! [U_4894,U_4893] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4893)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4894)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4893),U_4894)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4893),U_4894))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4893)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4894))) ) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ( ! [U_4898,U_4896] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4896)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4898)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4896),U_4898)) )
    & ! [U_4897,U_4895] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4895),U_4897))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4895)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4897))) ) ),
    inference(miniscope,[status(thm)],[f_1249_2]) ).

cnf(f_1249_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4895),U_4897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4895)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4897))) ),
    inference(clausify,[status(thm)],[f_1249_3]) ).

cnf(f_1249_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_4896)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4898)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4896),U_4898)) ),
    inference(clausify,[status(thm)],[f_1249_3]) ).

fof(f_1250_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_1250_2,plain,
    ! [U_4901,U_4900,U_4899] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4900)),U_4901)) = 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_4899),U_4900))),U_4901),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

cnf(f_1250_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4900)),U_4901)) = 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_4899),U_4900))),U_4901),
    inference(clausify,[status(thm)],[f_1250_2]) ).

fof(f_1251_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_1251_2,plain,
    ! [U_4903,U_4902] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4902)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4903)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4902),U_4903)),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

cnf(f_1251_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4902)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4903)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4902),U_4903)),
    inference(clausify,[status(thm)],[f_1251_2]) ).

fof(f_1252_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_1252_2,plain,
    ! [U_4905,U_4904] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4904)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4905)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4904),U_4905)),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

cnf(f_1252_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4904)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4905)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4904),U_4905)),
    inference(clausify,[status(thm)],[f_1252_2]) ).

fof(f_1253_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_1253_2,plain,
    ! [U_4909,U_4908] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4908),U_4909))
        | ! [U_4907] : U_4909 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4908),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4907)) )
      & ( ? [U_4906] : U_4909 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4908),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4906))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4908),U_4909)) ) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ( ! [U_4913,U_4911] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4911),U_4913))
        | ! [U_4907] : U_4913 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4911),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4907)) )
    & ! [U_4912,U_4910] :
        ( ? [U_4906] : U_4912 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4906))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),U_4912)) ) ),
    inference(miniscope,[status(thm)],[f_1253_2]) ).

fof(f_1253_4,plain,
    ( ! [U_4913,U_4911] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4911),U_4913))
        | ! [U_4907] : U_4913 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4911),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4907)) )
    & ! [U_4912,U_4910] :
        ( U_4912 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK99(U_4912,U_4910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),U_4912)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_4906,sK99(U_4912,U_4910))],[f_1253_3]) ).

cnf(f_1253_5,plain,
    ( U_4912 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK99(U_4912,U_4910)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),U_4912)) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

cnf(f_1253_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4911),U_4913))
    | U_4913 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4911),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4907)) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

fof(f_1254_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_1254_2,plain,
    ! [U_4915,U_4914] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4914),c_Groups_Ozero__class_Ozero(U_4914)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4914),U_4915)))
      | ~ class_Rings_Olinordered__semidom(U_4914) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

cnf(f_1254_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4914),c_Groups_Ozero__class_Ozero(U_4914)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4914),U_4915)))
    | ~ class_Rings_Olinordered__semidom(U_4914) ),
    inference(clausify,[status(thm)],[f_1254_2]) ).

fof(f_1255_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_1255_2,plain,
    ! [U_4917,U_4916] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4916),U_4917)))
      | ~ class_Rings_Olinordered__semidom(U_4916) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

cnf(f_1255_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4916),U_4917)))
    | ~ class_Rings_Olinordered__semidom(U_4916) ),
    inference(clausify,[status(thm)],[f_1255_2]) ).

fof(f_1256_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_1256_2,plain,
    ! [U_4919,U_4918] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4918),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4918),U_4919)),c_Groups_Ozero__class_Ozero(U_4918)))
      | ~ class_Rings_Olinordered__semidom(U_4918) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

cnf(f_1256_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4918),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4918),U_4919)),c_Groups_Ozero__class_Ozero(U_4918)))
    | ~ class_Rings_Olinordered__semidom(U_4918) ),
    inference(clausify,[status(thm)],[f_1256_2]) ).

fof(f_1257_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_1257_2,plain,
    ! [U_4921,U_4920] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4920),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4921)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4920),U_4921)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4921))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4920),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4921)) = c_Groups_Ozero__class_Ozero(U_4920)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4921))) ) )
      | ~ class_Int_Onumber__ring(U_4920) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

cnf(f_1257_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4920),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4921)) = c_Groups_Ozero__class_Ozero(U_4920)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4921)))
    | ~ class_Int_Onumber__ring(U_4920) ),
    inference(clausify,[status(thm)],[f_1257_2]) ).

cnf(f_1257_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4920),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4921)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4920),U_4921)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4921)))
    | ~ class_Int_Onumber__ring(U_4920) ),
    inference(clausify,[status(thm)],[f_1257_2]) ).

fof(f_1258_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_1258_2,plain,
    ! [U_4923,U_4922] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4922)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4923)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4922),U_4923)),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

cnf(f_1258_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4922)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4923)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4922),U_4923)),
    inference(clausify,[status(thm)],[f_1258_2]) ).

fof(f_1259_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_1259_2,plain,
    ! [U_4925,U_4924] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4924),U_4925)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4924)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4925)),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

cnf(f_1259_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4924),U_4925)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4924)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4925)),
    inference(clausify,[status(thm)],[f_1259_2]) ).

fof(f_1260_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_1260_2,plain,
    ! [U_4927,U_4926] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4926)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4927)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4927)),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

cnf(f_1260_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4926)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4927)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4927)),
    inference(clausify,[status(thm)],[f_1260_2]) ).

fof(f_1261_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_1261_2,plain,
    ! [U_4928] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4928),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_4928)
      | ~ class_Rings_Osemiring__1(U_4928) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

cnf(f_1261_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4928),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_4928)
    | ~ class_Rings_Osemiring__1(U_4928) ),
    inference(clausify,[status(thm)],[f_1261_2]) ).

fof(f_1262_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_1262_2,plain,
    ! [U_4931,U_4930,U_4929] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4930),U_4931))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4929),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4929),U_4930)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4929),U_4931)))
      | ~ class_Rings_Olinordered__semidom(U_4929) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

cnf(f_1262_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4930),U_4931))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4929),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4929),U_4930)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4929),U_4931)))
    | ~ class_Rings_Olinordered__semidom(U_4929) ),
    inference(clausify,[status(thm)],[f_1262_2]) ).

fof(f_1263_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_1263_2,plain,
    ! [U_4934,U_4933,U_4932] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4932),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4932),U_4933)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4932),U_4934)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4933),U_4934))
      | ~ class_Rings_Olinordered__semidom(U_4932) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

cnf(f_1263_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4932),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4932),U_4933)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4932),U_4934)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4933),U_4934))
    | ~ class_Rings_Olinordered__semidom(U_4932) ),
    inference(clausify,[status(thm)],[f_1263_2]) ).

fof(f_1264_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_1264_2,plain,
    ! [U_4937,U_4936,U_4935] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4935),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4937)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4936),U_4937)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4936),U_4937))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4935),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4937))) ) )
      | ~ class_Rings_Olinordered__semidom(U_4935) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

cnf(f_1264_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4936),U_4937))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4935),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4937)))
    | ~ class_Rings_Olinordered__semidom(U_4935) ),
    inference(clausify,[status(thm)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4935),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4935),U_4937)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4936),U_4937))
    | ~ class_Rings_Olinordered__semidom(U_4935) ),
    inference(clausify,[status(thm)],[f_1264_2]) ).

fof(f_1265_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_1265_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_1265_1]) ).

fof(f_1266_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_1266_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_1266_1]) ).

fof(f_1267_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_1267_2,plain,
    ! [U_4940,U_4939,U_4938] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4939)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4940)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4939),U_4940)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4939),U_4940))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4939)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4940))) ) )
      | ~ class_Rings_Olinordered__semidom(U_4938) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

cnf(f_1267_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4939),U_4940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4939)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4940)))
    | ~ class_Rings_Olinordered__semidom(U_4938) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

cnf(f_1267_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4938),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4939)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4938),U_4940)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4939),U_4940))
    | ~ class_Rings_Olinordered__semidom(U_4938) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

fof(f_1268_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_1268_2,plain,
    ! [U_4943,U_4942,U_4941] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4942),U_4943)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4941),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),U_4942)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),U_4943))
      | ~ class_Rings_Osemiring__1(U_4941) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

cnf(f_1268_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4942),U_4943)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4941),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),U_4942)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4941),U_4943))
    | ~ class_Rings_Osemiring__1(U_4941) ),
    inference(clausify,[status(thm)],[f_1268_2]) ).

fof(f_1269_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_1269_2,plain,
    ! [U_4946,U_4945,U_4944] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4945),U_4946)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4944),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),U_4945)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),U_4946))
      | ~ class_Rings_Osemiring__1(U_4944) ),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

cnf(f_1269_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4945),U_4946)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4944),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),U_4945)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4944),U_4946))
    | ~ class_Rings_Osemiring__1(U_4944) ),
    inference(clausify,[status(thm)],[f_1269_2]) ).

fof(f_1270_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_1270_2,plain,
    ! [U_4947] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4947),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4947)
      | ~ class_Rings_Osemiring__1(U_4947) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

cnf(f_1270_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4947),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4947)
    | ~ class_Rings_Osemiring__1(U_4947) ),
    inference(clausify,[status(thm)],[f_1270_2]) ).

fof(f_1271_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_1271_2,plain,
    ! [U_4949,U_4948] :
      ( hBOOL(hAPP(hAPP(c_member(U_4948),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4948),U_4949)),c_Int_Oring__1__class_OInts(U_4948)))
      | ~ class_Rings_Oring__1(U_4948) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

cnf(f_1271_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4948),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4948),U_4949)),c_Int_Oring__1__class_OInts(U_4948)))
    | ~ class_Rings_Oring__1(U_4948) ),
    inference(clausify,[status(thm)],[f_1271_2]) ).

fof(f_1272_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_1272_2,plain,
    ! [U_4951,U_4950] :
      ( c_Big__Operators_Olinorder__class_OMin(U_4950,hAPP(hAPP(c_Set_Oinsert(U_4950),U_4951),c_Orderings_Obot__class_Obot(tc_fun(U_4950,tc_HOL_Obool)))) = U_4951
      | ~ class_Orderings_Olinorder(U_4950) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

cnf(f_1272_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4950,hAPP(hAPP(c_Set_Oinsert(U_4950),U_4951),c_Orderings_Obot__class_Obot(tc_fun(U_4950,tc_HOL_Obool)))) = U_4951
    | ~ class_Orderings_Olinorder(U_4950) ),
    inference(clausify,[status(thm)],[f_1272_2]) ).

fof(f_1273_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_1273_2,plain,
    ! [U_4952] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4952))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4952)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4952))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4952)) ) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

fof(f_1273_3,plain,
    ( ! [U_4954] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4954))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4954)) )
    & ! [U_4953] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4953))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4953)) ) ),
    inference(miniscope,[status(thm)],[f_1273_2]) ).

cnf(f_1273_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4953))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4953)) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_5,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4954))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4954)) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

fof(f_1274_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_1274_2,plain,
    ! [U_4955] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4955),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4955)) ) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

fof(f_1274_3,plain,
    ( ! [U_4957] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4956),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4956)) ) ),
    inference(miniscope,[status(thm)],[f_1274_2]) ).

cnf(f_1274_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4956),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4956)) ),
    inference(clausify,[status(thm)],[f_1274_3]) ).

cnf(f_1274_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1274_3]) ).

fof(f_1275_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_1275_2,plain,
    ! [U_4958] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4958)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_4958 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_4958 = 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_4958)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

fof(f_1275_3,plain,
    ( ! [U_4960] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4960)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_4960 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4959] :
        ( U_4959 = 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_4959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1275_2]) ).

cnf(f_1275_4,plain,
    ( U_4959 = 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_4959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1275_3]) ).

cnf(f_1275_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_4960)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_4960 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1275_3]) ).

fof(f_1276_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_1276_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_1276_1]) ).

fof(f_1277_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_1277_2,plain,
    ! [U_4964,U_4963] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),U_4964))
        | ! [U_4962] : U_4964 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4963),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4962))) )
      & ( ? [U_4961] : U_4964 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4963),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4961)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),U_4964)) ) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

fof(f_1277_3,plain,
    ( ! [U_4968,U_4966] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),U_4968))
        | ! [U_4962] : U_4968 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4966),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4962))) )
    & ! [U_4967,U_4965] :
        ( ? [U_4961] : U_4967 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4965),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4961)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4965),U_4967)) ) ),
    inference(miniscope,[status(thm)],[f_1277_2]) ).

fof(f_1277_4,plain,
    ( ! [U_4968,U_4966] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),U_4968))
        | ! [U_4962] : U_4968 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4966),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4962))) )
    & ! [U_4967,U_4965] :
        ( U_4967 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4965),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK100(U_4967,U_4965))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4965),U_4967)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_4961,sK100(U_4967,U_4965))],[f_1277_3]) ).

cnf(f_1277_5,plain,
    ( U_4967 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4965),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK100(U_4967,U_4965))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4965),U_4967)) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

cnf(f_1277_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),U_4968))
    | U_4968 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4966),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4962))) ),
    inference(clausify,[status(thm)],[f_1277_4]) ).

fof(f_1278_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_1278_2,plain,
    ! [U_4969] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4969)) = 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_4969)),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

cnf(f_1278_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_4969)) = 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_4969)),
    inference(clausify,[status(thm)],[f_1278_2]) ).

fof(f_1279_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_1279_2,plain,
    ! [U_4971,U_4970] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4971)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4970)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4971),U_4970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4970),U_4971)) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

cnf(f_1279_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4971)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4970)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4971),U_4970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4970),U_4971)) ),
    inference(clausify,[status(thm)],[f_1279_2]) ).

fof(f_1280_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_1280_2,plain,
    ! [U_4973,U_4972] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4972),hAPP(c_Nat_OSuc,U_4973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4972),c_Groups_Oone__class_Oone(U_4972)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4972),U_4973))
      | ~ class_Rings_Osemiring__1(U_4972) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

cnf(f_1280_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4972),hAPP(c_Nat_OSuc,U_4973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4972),c_Groups_Oone__class_Oone(U_4972)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4972),U_4973))
    | ~ class_Rings_Osemiring__1(U_4972) ),
    inference(clausify,[status(thm)],[f_1280_2]) ).

fof(f_1281_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_1281_2,plain,
    ! [U_4976,U_4975,U_4974] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4976),U_4975)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4974),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),U_4976)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),U_4975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4975),U_4976))
      | ~ class_Rings_Oring__1(U_4974) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

cnf(f_1281_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4976),U_4975)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4974),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),U_4976)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4974),U_4975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4975),U_4976))
    | ~ class_Rings_Oring__1(U_4974) ),
    inference(clausify,[status(thm)],[f_1281_2]) ).

fof(f_1282_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_1282_2,plain,
    ! [U_4979,U_4978,U_4977] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4977),U_4979),c_Big__Operators_Olattice_OInf__fin(U_4977,c_Orderings_Oord__class_Omin(U_4977),U_4978)) = c_Big__Operators_Olattice_OInf__fin(U_4977,c_Orderings_Oord__class_Omin(U_4977),U_4978)
      | ~ hBOOL(hAPP(hAPP(c_member(U_4977),U_4979),U_4978))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4977),U_4978))
      | ~ class_Orderings_Olinorder(U_4977) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

cnf(f_1282_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4977),U_4979),c_Big__Operators_Olattice_OInf__fin(U_4977,c_Orderings_Oord__class_Omin(U_4977),U_4978)) = c_Big__Operators_Olattice_OInf__fin(U_4977,c_Orderings_Oord__class_Omin(U_4977),U_4978)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4977),U_4979),U_4978))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4977),U_4978))
    | ~ class_Orderings_Olinorder(U_4977) ),
    inference(clausify,[status(thm)],[f_1282_2]) ).

fof(f_1283_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_1283_2,plain,
    ! [U_4982,U_4981,U_4980] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4980),c_Big__Operators_Olinorder__class_OMin(U_4980,U_4981)),U_4982))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4980),U_4982),U_4981))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4980),U_4981))
      | ~ class_Orderings_Olinorder(U_4980) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

cnf(f_1283_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4980),c_Big__Operators_Olinorder__class_OMin(U_4980,U_4981)),U_4982))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4980),U_4982),U_4981))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4980),U_4981))
    | ~ class_Orderings_Olinorder(U_4980) ),
    inference(clausify,[status(thm)],[f_1283_2]) ).

fof(f_1284_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_1284_2,plain,
    ! [U_4984,U_4983] :
      ( c_Big__Operators_Olattice_OInf__fin(U_4983,c_Orderings_Oord__class_Omin(U_4983),hAPP(hAPP(c_Set_Oinsert(U_4983),U_4984),c_Orderings_Obot__class_Obot(tc_fun(U_4983,tc_HOL_Obool)))) = U_4984
      | ~ class_Orderings_Olinorder(U_4983) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

cnf(f_1284_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4983,c_Orderings_Oord__class_Omin(U_4983),hAPP(hAPP(c_Set_Oinsert(U_4983),U_4984),c_Orderings_Obot__class_Obot(tc_fun(U_4983,tc_HOL_Obool)))) = U_4984
    | ~ class_Orderings_Olinorder(U_4983) ),
    inference(clausify,[status(thm)],[f_1284_2]) ).

fof(f_1285_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_1285_2,plain,
    ! [U_4986,U_4985] :
      ( hBOOL(hAPP(hAPP(c_member(U_4985),c_Big__Operators_Olinorder__class_OMin(U_4985,U_4986)),U_4986))
      | U_4986 = c_Orderings_Obot__class_Obot(tc_fun(U_4985,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4985),U_4986))
      | ~ class_Orderings_Olinorder(U_4985) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

cnf(f_1285_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4985),c_Big__Operators_Olinorder__class_OMin(U_4985,U_4986)),U_4986))
    | U_4986 = c_Orderings_Obot__class_Obot(tc_fun(U_4985,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4985),U_4986))
    | ~ class_Orderings_Olinorder(U_4985) ),
    inference(clausify,[status(thm)],[f_1285_2]) ).

fof(f_1286_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_1286_2,plain,
    ! [U_4989,U_4988,U_4987] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4987),U_4989),c_Big__Operators_Olinorder__class_OMin(U_4987,U_4988)) = c_Big__Operators_Olinorder__class_OMin(U_4987,U_4988)
      | ~ hBOOL(hAPP(hAPP(c_member(U_4987),U_4989),U_4988))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4987),U_4988))
      | ~ class_Orderings_Olinorder(U_4987) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

cnf(f_1286_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4987),U_4989),c_Big__Operators_Olinorder__class_OMin(U_4987,U_4988)) = c_Big__Operators_Olinorder__class_OMin(U_4987,U_4988)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4987),U_4989),U_4988))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4987),U_4988))
    | ~ class_Orderings_Olinorder(U_4987) ),
    inference(clausify,[status(thm)],[f_1286_2]) ).

fof(f_1287_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_1287_2,plain,
    ! [U_4990] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4990) = 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_4990))) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

cnf(f_1287_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4990) = 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_4990))) ),
    inference(clausify,[status(thm)],[f_1287_2]) ).

fof(f_1288_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_1288_2,plain,
    ! [U_4992,U_4991] :
      ( c_Big__Operators_Olattice_OInf__fin(U_4991,c_Orderings_Oord__class_Omin(U_4991),U_4992) = hAPP(c_Finite__Set_Ofold1(U_4991,c_Orderings_Oord__class_Omin(U_4991)),U_4992)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4991),U_4992))
      | ~ class_Orderings_Olinorder(U_4991) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

cnf(f_1288_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4991,c_Orderings_Oord__class_Omin(U_4991),U_4992) = hAPP(c_Finite__Set_Ofold1(U_4991,c_Orderings_Oord__class_Omin(U_4991)),U_4992)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4991),U_4992))
    | ~ class_Orderings_Olinorder(U_4991) ),
    inference(clausify,[status(thm)],[f_1288_2]) ).

fof(f_1289_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_1289_2,plain,
    ! [U_4994,U_4993] :
      ( c_Big__Operators_Olinorder__class_OMin(U_4993,U_4994) = hAPP(c_Finite__Set_Ofold1(U_4993,c_Orderings_Oord__class_Omin(U_4993)),U_4994)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4993),U_4994))
      | ~ class_Orderings_Olinorder(U_4993) ),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

cnf(f_1289_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4993,U_4994) = hAPP(c_Finite__Set_Ofold1(U_4993,c_Orderings_Oord__class_Omin(U_4993)),U_4994)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4993),U_4994))
    | ~ class_Orderings_Olinorder(U_4993) ),
    inference(clausify,[status(thm)],[f_1289_2]) ).

fof(f_1290_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_1290_2,plain,
    ! [U_4995] :
      ( ( 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_4995)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4995)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4995))
        | ~ 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_4995))) ) ),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ( ! [U_4997] :
        ( 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_4997)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4997)) )
    & ! [U_4996] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4996))
        | ~ 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_4996))) ) ),
    inference(miniscope,[status(thm)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4996))
    | ~ 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_4996))) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

cnf(f_1290_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_4997)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4997)) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_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_1291_2,plain,
    ! [U_5000,U_4999,U_4998] :
      ( 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_5000)),U_4998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5000)),U_4999)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4998),U_4999)) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

cnf(f_1291_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_5000)),U_4998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5000)),U_4999)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4998),U_4999)) ),
    inference(clausify,[status(thm)],[f_1291_2]) ).

fof(f_1292_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_1292_2,plain,
    ! [U_5002,U_5001] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),c_Groups_Ozero__class_Ozero(U_5001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5001),U_5002)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5002)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5002))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),c_Groups_Ozero__class_Ozero(U_5001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5001),U_5002))) ) )
      | ~ class_Rings_Olinordered__semidom(U_5001) ),
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

cnf(f_1292_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5002))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),c_Groups_Ozero__class_Ozero(U_5001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5001),U_5002)))
    | ~ class_Rings_Olinordered__semidom(U_5001) ),
    inference(clausify,[status(thm)],[f_1292_2]) ).

cnf(f_1292_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5001),c_Groups_Ozero__class_Ozero(U_5001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5001),U_5002)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5002))
    | ~ class_Rings_Olinordered__semidom(U_5001) ),
    inference(clausify,[status(thm)],[f_1292_2]) ).

fof(f_1293_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_1293_2,plain,
    ! [U_5005,U_5004,U_5003] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5003,c_Orderings_Oord__class_Omin(U_5003),hAPP(hAPP(c_Set_Oinsert(U_5003),U_5005),U_5004)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5003),U_5005),c_Big__Operators_Olattice_OInf__fin(U_5003,c_Orderings_Oord__class_Omin(U_5003),U_5004))
      | U_5004 = c_Orderings_Obot__class_Obot(tc_fun(U_5003,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5003),U_5004))
      | ~ class_Orderings_Olinorder(U_5003) ),
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

cnf(f_1293_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5003,c_Orderings_Oord__class_Omin(U_5003),hAPP(hAPP(c_Set_Oinsert(U_5003),U_5005),U_5004)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5003),U_5005),c_Big__Operators_Olattice_OInf__fin(U_5003,c_Orderings_Oord__class_Omin(U_5003),U_5004))
    | U_5004 = c_Orderings_Obot__class_Obot(tc_fun(U_5003,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5003),U_5004))
    | ~ class_Orderings_Olinorder(U_5003) ),
    inference(clausify,[status(thm)],[f_1293_2]) ).

fof(f_1294_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_1294_2,plain,
    ! [U_5008,U_5007,U_5006] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5006),c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5008)),c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5007)) = c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5007)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5006,tc_HOL_Obool)),U_5008),U_5007))
      | U_5008 = c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5006),U_5007))
      | ~ class_Orderings_Olinorder(U_5006) ),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

cnf(f_1294_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5006),c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5008)),c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5007)) = c_Big__Operators_Olattice_OInf__fin(U_5006,c_Orderings_Oord__class_Omin(U_5006),U_5007)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5006,tc_HOL_Obool)),U_5008),U_5007))
    | U_5008 = c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5006),U_5007))
    | ~ class_Orderings_Olinorder(U_5006) ),
    inference(clausify,[status(thm)],[f_1294_2]) ).

fof(f_1295_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_1295_2,plain,
    ! [U_5011,U_5010,U_5009] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5009,tc_HOL_Obool)),U_5010),U_5011)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5009),c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),U_5010)),c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),U_5011))
      | U_5011 = c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5011))
      | U_5010 = c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5010))
      | ~ class_Orderings_Olinorder(U_5009) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

cnf(f_1295_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5009,tc_HOL_Obool)),U_5010),U_5011)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5009),c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),U_5010)),c_Big__Operators_Olattice_OInf__fin(U_5009,c_Orderings_Oord__class_Omin(U_5009),U_5011))
    | U_5011 = c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5011))
    | U_5010 = c_Orderings_Obot__class_Obot(tc_fun(U_5009,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5009),U_5010))
    | ~ class_Orderings_Olinorder(U_5009) ),
    inference(clausify,[status(thm)],[f_1295_2]) ).

fof(f_1296_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_1296_2,plain,
    ! [U_5014,U_5013,U_5012] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5012),c_Big__Operators_Olinorder__class_OMin(U_5012,U_5014)),c_Big__Operators_Olinorder__class_OMin(U_5012,U_5013)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5012),U_5014))
      | U_5013 = c_Orderings_Obot__class_Obot(tc_fun(U_5012,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5012,tc_HOL_Obool)),U_5013),U_5014))
      | ~ class_Orderings_Olinorder(U_5012) ),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

cnf(f_1296_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5012),c_Big__Operators_Olinorder__class_OMin(U_5012,U_5014)),c_Big__Operators_Olinorder__class_OMin(U_5012,U_5013)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5012),U_5014))
    | U_5013 = c_Orderings_Obot__class_Obot(tc_fun(U_5012,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5012,tc_HOL_Obool)),U_5013),U_5014))
    | ~ class_Orderings_Olinorder(U_5012) ),
    inference(clausify,[status(thm)],[f_1296_2]) ).

fof(f_1297_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_1297_2,plain,
    ! [U_5017,U_5016,U_5015] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5015,c_Orderings_Oord__class_Omin(U_5015),hAPP(hAPP(c_Set_Oinsert(U_5015),U_5017),U_5016)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5015,U_5015,c_Orderings_Oord__class_Omin(U_5015)),U_5017),U_5016)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5015),U_5016))
      | ~ class_Orderings_Olinorder(U_5015) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

cnf(f_1297_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5015,c_Orderings_Oord__class_Omin(U_5015),hAPP(hAPP(c_Set_Oinsert(U_5015),U_5017),U_5016)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5015,U_5015,c_Orderings_Oord__class_Omin(U_5015)),U_5017),U_5016)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5015),U_5016))
    | ~ class_Orderings_Olinorder(U_5015) ),
    inference(clausify,[status(thm)],[f_1297_2]) ).

fof(f_1298_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_1298_2,plain,
    ! [U_5020,U_5019,U_5018] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5018,hAPP(hAPP(c_Set_Oinsert(U_5018),U_5020),U_5019)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5018),U_5020),c_Big__Operators_Olinorder__class_OMin(U_5018,U_5019))
      | U_5019 = c_Orderings_Obot__class_Obot(tc_fun(U_5018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5018),U_5019))
      | ~ class_Orderings_Olinorder(U_5018) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

cnf(f_1298_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5018,hAPP(hAPP(c_Set_Oinsert(U_5018),U_5020),U_5019)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5018),U_5020),c_Big__Operators_Olinorder__class_OMin(U_5018,U_5019))
    | U_5019 = c_Orderings_Obot__class_Obot(tc_fun(U_5018,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5018),U_5019))
    | ~ class_Orderings_Olinorder(U_5018) ),
    inference(clausify,[status(thm)],[f_1298_2]) ).

fof(f_1299_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_1299_2,plain,
    ! [U_5023,U_5022,U_5021] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5021),c_Big__Operators_Olinorder__class_OMin(U_5021,U_5023)),c_Big__Operators_Olinorder__class_OMin(U_5021,U_5022)) = c_Big__Operators_Olinorder__class_OMin(U_5021,U_5022)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),U_5023),U_5022))
      | U_5023 = c_Orderings_Obot__class_Obot(tc_fun(U_5021,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5021),U_5022))
      | ~ class_Orderings_Olinorder(U_5021) ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

cnf(f_1299_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5021),c_Big__Operators_Olinorder__class_OMin(U_5021,U_5023)),c_Big__Operators_Olinorder__class_OMin(U_5021,U_5022)) = c_Big__Operators_Olinorder__class_OMin(U_5021,U_5022)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),U_5023),U_5022))
    | U_5023 = c_Orderings_Obot__class_Obot(tc_fun(U_5021,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5021),U_5022))
    | ~ class_Orderings_Olinorder(U_5021) ),
    inference(clausify,[status(thm)],[f_1299_2]) ).

fof(f_1300_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_1300_2,plain,
    ! [U_5026,U_5025,U_5024] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5024,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5024,tc_HOL_Obool)),U_5025),U_5026)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5024),c_Big__Operators_Olinorder__class_OMin(U_5024,U_5025)),c_Big__Operators_Olinorder__class_OMin(U_5024,U_5026))
      | U_5026 = c_Orderings_Obot__class_Obot(tc_fun(U_5024,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5024),U_5026))
      | U_5025 = c_Orderings_Obot__class_Obot(tc_fun(U_5024,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5024),U_5025))
      | ~ class_Orderings_Olinorder(U_5024) ),
    inference(variable_rename,[status(thm)],[f_1300_1]) ).

cnf(f_1300_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5024,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5024,tc_HOL_Obool)),U_5025),U_5026)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5024),c_Big__Operators_Olinorder__class_OMin(U_5024,U_5025)),c_Big__Operators_Olinorder__class_OMin(U_5024,U_5026))
    | U_5026 = c_Orderings_Obot__class_Obot(tc_fun(U_5024,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5024),U_5026))
    | U_5025 = c_Orderings_Obot__class_Obot(tc_fun(U_5024,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5024),U_5025))
    | ~ class_Orderings_Olinorder(U_5024) ),
    inference(clausify,[status(thm)],[f_1300_2]) ).

fof(f_1301_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_1301_2,plain,
    ! [U_5028,U_5027] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5027) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5028)
        | ( ( ( U_5027 != U_5028
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5028))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5027) != 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_5028))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5027))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5028)),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_5027))) ) )
      & ( ( ( ( ( U_5027 = U_5028
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5028))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5027) = 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_5028))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5027))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5028)),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_5027))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5027) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5028) ) ),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

fof(f_1301_3,plain,
    ( ! [U_5032,U_5030] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032)
        | ( ( ( U_5030 != U_5032
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030) != 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_5032))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)),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_5030))) ) )
    & ! [U_5031,U_5029] :
        ( ( ( ( ( U_5029 = U_5031
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5031))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5029) = 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_5031))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5029))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5031)),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_5029))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5029) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5031) ) ),
    inference(miniscope,[status(thm)],[f_1301_2]) ).

cnf(f_1301_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_5031)),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_5029)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5029) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5031) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5029) = 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_5031)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5029)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5029) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5031) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_6,plain,
    ( U_5029 = U_5031
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5031)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5029)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5029) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5031) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_7,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_8,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_9,plain,
    ( U_5030 != U_5032
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_10,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030) != 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_5030)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_11,plain,
    ( U_5030 != U_5032
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030) != 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_5030)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_12,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_14,plain,
    ( U_5030 != U_5032
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_15,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5032)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030) != 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_5032)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

cnf(f_1301_16,plain,
    ( U_5030 != U_5032
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5030) != 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_5032)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5032) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

fof(f_1302_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_1302_2,plain,
    ! [U_5035,U_5034,U_5033] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5034)),U_5035)) = 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_5033),U_5034))),U_5035)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5034))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5034)),U_5035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5033)),U_5035)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5034))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5033))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5034)),U_5035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5034)),U_5035)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5033))) ) ),
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

fof(f_1302_3,plain,
    ( ! [U_5041,U_5039,U_5037] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5039)),U_5041)) = 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_5037),U_5039))),U_5041)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5039))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5039)),U_5041)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),U_5041)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5039))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5037))) )
    & ! [U_5040,U_5038,U_5036] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5038)),U_5040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5038)),U_5040)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5036))) ) ),
    inference(miniscope,[status(thm)],[f_1302_2]) ).

cnf(f_1302_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5038)),U_5040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5038)),U_5040)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5036))) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

cnf(f_1302_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5039)),U_5041)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),U_5041)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5039)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5037))) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

cnf(f_1302_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5039)),U_5041)) = 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_5037),U_5039))),U_5041)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5039)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5037))) ),
    inference(clausify,[status(thm)],[f_1302_3]) ).

fof(f_1303_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_1303_2,plain,
    ! [U_5044,U_5043,U_5042] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5042,hAPP(hAPP(c_Set_Oinsert(U_5042),U_5044),U_5043)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5042,U_5042,c_Orderings_Oord__class_Omin(U_5042)),U_5044),U_5043)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5042),U_5043))
      | ~ class_Orderings_Olinorder(U_5042) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

cnf(f_1303_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5042,hAPP(hAPP(c_Set_Oinsert(U_5042),U_5044),U_5043)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5042,U_5042,c_Orderings_Oord__class_Omin(U_5042)),U_5044),U_5043)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5042),U_5043))
    | ~ class_Orderings_Olinorder(U_5042) ),
    inference(clausify,[status(thm)],[f_1303_2]) ).

fof(f_1304_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_1304_2,plain,
    ! [U_5046,U_5045] :
      ( 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_5045,U_5046)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5046))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5045)) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

cnf(f_1304_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_5045,U_5046)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5046))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5045)) ),
    inference(clausify,[status(thm)],[f_1304_2]) ).

fof(f_1305_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_1305_2,plain,
    ! [U_5048,U_5047] :
      ( c_Nat__Transfer_Otsub(U_5048,U_5047) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5048),U_5047)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5047),U_5048)) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

cnf(f_1305_3,plain,
    ( c_Nat__Transfer_Otsub(U_5048,U_5047) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5048),U_5047)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5047),U_5048)) ),
    inference(clausify,[status(thm)],[f_1305_2]) ).

fof(f_1306_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_1306_2,plain,
    ! [U_5051,U_5050,U_5049] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5049,c_Orderings_Oord__class_Omin(U_5049),hAPP(hAPP(c_Set_Oinsert(U_5049),U_5051),U_5050)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5049),U_5051),c_Big__Operators_Olattice_OInf__fin(U_5049,c_Orderings_Oord__class_Omin(U_5049),U_5050))
      | U_5050 = c_Orderings_Obot__class_Obot(tc_fun(U_5049,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_5049),U_5051),U_5050))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5049),U_5050))
      | ~ class_Orderings_Olinorder(U_5049) ),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

cnf(f_1306_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5049,c_Orderings_Oord__class_Omin(U_5049),hAPP(hAPP(c_Set_Oinsert(U_5049),U_5051),U_5050)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5049),U_5051),c_Big__Operators_Olattice_OInf__fin(U_5049,c_Orderings_Oord__class_Omin(U_5049),U_5050))
    | U_5050 = c_Orderings_Obot__class_Obot(tc_fun(U_5049,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_5049),U_5051),U_5050))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5049),U_5050))
    | ~ class_Orderings_Olinorder(U_5049) ),
    inference(clausify,[status(thm)],[f_1306_2]) ).

fof(f_1307_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_1307_2,plain,
    ! [U_5054,U_5053,U_5052] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),U_5053)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5052),U_5054),c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),U_5053)) = U_5054
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5052),U_5053))
      | ~ class_Orderings_Olinorder(U_5052) ),
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

cnf(f_1307_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),U_5053)) = U_5054
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5052),U_5053))
    | ~ class_Orderings_Olinorder(U_5052) ),
    inference(clausify,[status(thm)],[f_1307_2]) ).

cnf(f_1307_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),U_5053)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5052),U_5054),c_Big__Operators_Olattice_OInf__fin(U_5052,c_Orderings_Oord__class_Omin(U_5052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5052,tc_HOL_Obool)),U_5053),hAPP(hAPP(c_Set_Oinsert(U_5052),U_5054),c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5052,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5052),U_5053))
    | ~ class_Orderings_Olinorder(U_5052) ),
    inference(clausify,[status(thm)],[f_1307_2]) ).

fof(f_1308_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_1308_2,plain,
    ! [U_5057,U_5056,U_5055] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5055),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057))),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5055),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),U_5056)),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),U_5057))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057) = c_Orderings_Obot__class_Obot(tc_fun(U_5055,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5055),U_5057))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5055),U_5056))
      | ~ class_Orderings_Olinorder(U_5055) ),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

cnf(f_1308_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5055),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057))),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5055),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),U_5056)),c_Big__Operators_Olattice_OInf__fin(U_5055,c_Orderings_Oord__class_Omin(U_5055),U_5057))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5055,tc_HOL_Obool)),U_5056),U_5057) = c_Orderings_Obot__class_Obot(tc_fun(U_5055,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5055),U_5057))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5055),U_5056))
    | ~ class_Orderings_Olinorder(U_5055) ),
    inference(clausify,[status(thm)],[f_1308_2]) ).

fof(f_1309_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_1309_2,plain,
    ! [U_5060,U_5059,U_5058] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5058,tc_HOL_Obool)),U_5059),U_5060)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5058),c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),U_5059)),c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),U_5060))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5058,tc_HOL_Obool)),U_5059),U_5060) != c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
      | U_5060 = c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5058),U_5060))
      | U_5059 = c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5058),U_5059))
      | ~ class_Orderings_Olinorder(U_5058) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

cnf(f_1309_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5058,tc_HOL_Obool)),U_5059),U_5060)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5058),c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),U_5059)),c_Big__Operators_Olattice_OInf__fin(U_5058,c_Orderings_Oord__class_Omin(U_5058),U_5060))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5058,tc_HOL_Obool)),U_5059),U_5060) != c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
    | U_5060 = c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5058),U_5060))
    | U_5059 = c_Orderings_Obot__class_Obot(tc_fun(U_5058,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5058),U_5059))
    | ~ class_Orderings_Olinorder(U_5058) ),
    inference(clausify,[status(thm)],[f_1309_2]) ).

fof(f_1310_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_1310_2,plain,
    ! [U_5063,U_5062,U_5061] :
      ( c_Big__Operators_Olattice_OInf__fin(U_5061,c_Orderings_Oord__class_Omin(U_5061),hAPP(hAPP(c_Set_Oinsert(U_5061),U_5063),U_5062)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5061,U_5061,c_Orderings_Oord__class_Omin(U_5061)),U_5063),U_5062)
      | hBOOL(hAPP(hAPP(c_member(U_5061),U_5063),U_5062))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5061),U_5062))
      | ~ class_Orderings_Olinorder(U_5061) ),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

cnf(f_1310_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_5061,c_Orderings_Oord__class_Omin(U_5061),hAPP(hAPP(c_Set_Oinsert(U_5061),U_5063),U_5062)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5061,U_5061,c_Orderings_Oord__class_Omin(U_5061)),U_5063),U_5062)
    | hBOOL(hAPP(hAPP(c_member(U_5061),U_5063),U_5062))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5061),U_5062))
    | ~ class_Orderings_Olinorder(U_5061) ),
    inference(clausify,[status(thm)],[f_1310_2]) ).

fof(f_1311_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_1311_2,plain,
    ! [U_5066,U_5065,U_5064] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5064,hAPP(hAPP(c_Set_Oinsert(U_5064),U_5066),U_5065)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5064),U_5066),c_Big__Operators_Olinorder__class_OMin(U_5064,U_5065))
      | U_5065 = c_Orderings_Obot__class_Obot(tc_fun(U_5064,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_5064),U_5066),U_5065))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5064),U_5065))
      | ~ class_Orderings_Olinorder(U_5064) ),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

cnf(f_1311_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5064,hAPP(hAPP(c_Set_Oinsert(U_5064),U_5066),U_5065)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5064),U_5066),c_Big__Operators_Olinorder__class_OMin(U_5064,U_5065))
    | U_5065 = c_Orderings_Obot__class_Obot(tc_fun(U_5064,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_5064),U_5066),U_5065))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5064),U_5065))
    | ~ class_Orderings_Olinorder(U_5064) ),
    inference(clausify,[status(thm)],[f_1311_2]) ).

fof(f_1312_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_1312_2,plain,
    ! [U_5069,U_5068,U_5067] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),U_5068)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5067),U_5069),c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),U_5068)) = U_5069
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5067),U_5068))
      | ~ class_Orderings_Olinorder(U_5067) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

cnf(f_1312_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),U_5068)) = U_5069
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5067),U_5068))
    | ~ class_Orderings_Olinorder(U_5067) ),
    inference(clausify,[status(thm)],[f_1312_2]) ).

cnf(f_1312_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),U_5068)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5067),U_5069),c_Big__Operators_Olinorder__class_OMin(U_5067,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5067,tc_HOL_Obool)),U_5068),hAPP(hAPP(c_Set_Oinsert(U_5067),U_5069),c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5067,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5067),U_5068))
    | ~ class_Orderings_Olinorder(U_5067) ),
    inference(clausify,[status(thm)],[f_1312_2]) ).

fof(f_1313_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_1313_2,plain,
    ! [U_5072,U_5071,U_5070] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5070),c_Big__Operators_Olinorder__class_OMin(U_5070,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072))),c_Big__Operators_Olinorder__class_OMin(U_5070,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5070),c_Big__Operators_Olinorder__class_OMin(U_5070,U_5071)),c_Big__Operators_Olinorder__class_OMin(U_5070,U_5072))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072) = c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5070),U_5072))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5070),U_5071))
      | ~ class_Orderings_Olinorder(U_5070) ),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

cnf(f_1313_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5070),c_Big__Operators_Olinorder__class_OMin(U_5070,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072))),c_Big__Operators_Olinorder__class_OMin(U_5070,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5070),c_Big__Operators_Olinorder__class_OMin(U_5070,U_5071)),c_Big__Operators_Olinorder__class_OMin(U_5070,U_5072))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5070,tc_HOL_Obool)),U_5071),U_5072) = c_Orderings_Obot__class_Obot(tc_fun(U_5070,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5070),U_5072))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5070),U_5071))
    | ~ class_Orderings_Olinorder(U_5070) ),
    inference(clausify,[status(thm)],[f_1313_2]) ).

fof(f_1314_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_1314_2,plain,
    ! [U_5075,U_5074,U_5073] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5073,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5073,tc_HOL_Obool)),U_5074),U_5075)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5073),c_Big__Operators_Olinorder__class_OMin(U_5073,U_5074)),c_Big__Operators_Olinorder__class_OMin(U_5073,U_5075))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074),U_5075) != c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
      | U_5075 = c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5073),U_5075))
      | U_5074 = c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5073),U_5074))
      | ~ class_Orderings_Olinorder(U_5073) ),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_5073,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5073,tc_HOL_Obool)),U_5074),U_5075)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5073),c_Big__Operators_Olinorder__class_OMin(U_5073,U_5074)),c_Big__Operators_Olinorder__class_OMin(U_5073,U_5075))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074),U_5075) != c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
    | U_5075 = c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5073),U_5075))
    | U_5074 = c_Orderings_Obot__class_Obot(tc_fun(U_5073,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5073),U_5074))
    | ~ class_Orderings_Olinorder(U_5073) ),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_1,plain,
    ! [V_y_2,V_x_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_1315_2,plain,
    ! [U_5078,U_5077,U_5076] :
      ( ( hBOOL(hAPP(U_5076,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5077),U_5078))))
        | ( ~ hBOOL(hAPP(U_5076,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5077),U_5078)) )
        | ( ~ hBOOL(hAPP(U_5076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5077)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5078))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5078),U_5077)) ) )
      & ( ( ( hBOOL(hAPP(U_5076,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5077),U_5078)) )
          & ( hBOOL(hAPP(U_5076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5077)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5078))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5078),U_5077)) ) )
        | ~ hBOOL(hAPP(U_5076,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5077),U_5078)))) ) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

fof(f_1315_3,plain,
    ( ! [U_5084,U_5082,U_5080] :
        ( hBOOL(hAPP(U_5080,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5082),U_5084))))
        | ( ~ hBOOL(hAPP(U_5080,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5084)) )
        | ( ~ hBOOL(hAPP(U_5080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5082)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5084))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5084),U_5082)) ) )
    & ! [U_5083,U_5081,U_5079] :
        ( ( ( hBOOL(hAPP(U_5079,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5081),U_5083)) )
          & ( hBOOL(hAPP(U_5079,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5081)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5083))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5083),U_5081)) ) )
        | ~ hBOOL(hAPP(U_5079,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5081),U_5083)))) ) ),
    inference(miniscope,[status(thm)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( hBOOL(hAPP(U_5079,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5081)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5083))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5083),U_5081))
    | ~ hBOOL(hAPP(U_5079,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5081),U_5083)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_5,plain,
    ( hBOOL(hAPP(U_5079,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5081),U_5083))
    | ~ hBOOL(hAPP(U_5079,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5081),U_5083)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5084))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5084),U_5082))
    | hBOOL(hAPP(U_5080,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5082),U_5084)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_7,plain,
    ( ~ hBOOL(hAPP(U_5080,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5084),U_5082))
    | hBOOL(hAPP(U_5080,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5082),U_5084)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5082),U_5084))
    | ~ hBOOL(hAPP(U_5080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5082)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5084))))
    | hBOOL(hAPP(U_5080,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5082),U_5084)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

cnf(f_1315_9,plain,
    ( ~ hBOOL(hAPP(U_5080,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_5080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5082)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5084))))
    | hBOOL(hAPP(U_5080,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5082),U_5084)))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

fof(f_1316_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_1316_2,plain,
    ! [U_5088,U_5087] :
      ( hBOOL(hAPP(hAPP(c_member(U_5087),c_Big__Operators_Olattice_OInf__fin(U_5087,c_Orderings_Oord__class_Omin(U_5087),U_5088)),U_5088))
      | ? [U_5086,U_5085] : ~ hBOOL(hAPP(hAPP(c_member(U_5087),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5087),U_5086),U_5085)),hAPP(hAPP(c_Set_Oinsert(U_5087),U_5086),hAPP(hAPP(c_Set_Oinsert(U_5087),U_5085),c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))))))
      | U_5088 = c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5087),U_5088))
      | ~ class_Orderings_Olinorder(U_5087) ),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ! [U_5088,U_5087] :
      ( hBOOL(hAPP(hAPP(c_member(U_5087),c_Big__Operators_Olattice_OInf__fin(U_5087,c_Orderings_Oord__class_Omin(U_5087),U_5088)),U_5088))
      | ? [U_5085] : ~ hBOOL(hAPP(hAPP(c_member(U_5087),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5087),sK101(U_5088,U_5087)),U_5085)),hAPP(hAPP(c_Set_Oinsert(U_5087),sK101(U_5088,U_5087)),hAPP(hAPP(c_Set_Oinsert(U_5087),U_5085),c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))))))
      | U_5088 = c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5087),U_5088))
      | ~ class_Orderings_Olinorder(U_5087) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_5086,sK101(U_5088,U_5087))],[f_1316_2]) ).

fof(f_1316_4,plain,
    ! [U_5088,U_5087] :
      ( hBOOL(hAPP(hAPP(c_member(U_5087),c_Big__Operators_Olattice_OInf__fin(U_5087,c_Orderings_Oord__class_Omin(U_5087),U_5088)),U_5088))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5087),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5087),sK101(U_5088,U_5087)),sK102(U_5088,U_5087))),hAPP(hAPP(c_Set_Oinsert(U_5087),sK101(U_5088,U_5087)),hAPP(hAPP(c_Set_Oinsert(U_5087),sK102(U_5088,U_5087)),c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))))))
      | U_5088 = c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5087),U_5088))
      | ~ class_Orderings_Olinorder(U_5087) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_5085,sK102(U_5088,U_5087))],[f_1316_3]) ).

cnf(f_1316_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5087),c_Big__Operators_Olattice_OInf__fin(U_5087,c_Orderings_Oord__class_Omin(U_5087),U_5088)),U_5088))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5087),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5087),sK101(U_5088,U_5087)),sK102(U_5088,U_5087))),hAPP(hAPP(c_Set_Oinsert(U_5087),sK101(U_5088,U_5087)),hAPP(hAPP(c_Set_Oinsert(U_5087),sK102(U_5088,U_5087)),c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))))))
    | U_5088 = c_Orderings_Obot__class_Obot(tc_fun(U_5087,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5087),U_5088))
    | ~ class_Orderings_Olinorder(U_5087) ),
    inference(clausify,[status(thm)],[f_1316_4]) ).

fof(f_1317_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_1317_2,plain,
    ! [U_5092,U_5091] :
      ( hBOOL(hAPP(hAPP(c_member(U_5091),c_Big__Operators_Olinorder__class_OMin(U_5091,U_5092)),U_5092))
      | ? [U_5090,U_5089] : ~ hBOOL(hAPP(hAPP(c_member(U_5091),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5091),U_5090),U_5089)),hAPP(hAPP(c_Set_Oinsert(U_5091),U_5090),hAPP(hAPP(c_Set_Oinsert(U_5091),U_5089),c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))))))
      | U_5092 = c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5091),U_5092))
      | ~ class_Orderings_Olinorder(U_5091) ),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

fof(f_1317_3,plain,
    ! [U_5092,U_5091] :
      ( hBOOL(hAPP(hAPP(c_member(U_5091),c_Big__Operators_Olinorder__class_OMin(U_5091,U_5092)),U_5092))
      | ? [U_5089] : ~ hBOOL(hAPP(hAPP(c_member(U_5091),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5091),sK103(U_5092,U_5091)),U_5089)),hAPP(hAPP(c_Set_Oinsert(U_5091),sK103(U_5092,U_5091)),hAPP(hAPP(c_Set_Oinsert(U_5091),U_5089),c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))))))
      | U_5092 = c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5091),U_5092))
      | ~ class_Orderings_Olinorder(U_5091) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_5090,sK103(U_5092,U_5091))],[f_1317_2]) ).

fof(f_1317_4,plain,
    ! [U_5092,U_5091] :
      ( hBOOL(hAPP(hAPP(c_member(U_5091),c_Big__Operators_Olinorder__class_OMin(U_5091,U_5092)),U_5092))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5091),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5091),sK103(U_5092,U_5091)),sK104(U_5092,U_5091))),hAPP(hAPP(c_Set_Oinsert(U_5091),sK103(U_5092,U_5091)),hAPP(hAPP(c_Set_Oinsert(U_5091),sK104(U_5092,U_5091)),c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))))))
      | U_5092 = c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5091),U_5092))
      | ~ class_Orderings_Olinorder(U_5091) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_5089,sK104(U_5092,U_5091))],[f_1317_3]) ).

cnf(f_1317_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5091),c_Big__Operators_Olinorder__class_OMin(U_5091,U_5092)),U_5092))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5091),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5091),sK103(U_5092,U_5091)),sK104(U_5092,U_5091))),hAPP(hAPP(c_Set_Oinsert(U_5091),sK103(U_5092,U_5091)),hAPP(hAPP(c_Set_Oinsert(U_5091),sK104(U_5092,U_5091)),c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))))))
    | U_5092 = c_Orderings_Obot__class_Obot(tc_fun(U_5091,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5091),U_5092))
    | ~ class_Orderings_Olinorder(U_5091) ),
    inference(clausify,[status(thm)],[f_1317_4]) ).

fof(f_1318_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_1318_2,plain,
    ! [U_5098,U_5097,U_5096,U_5095,U_5094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5095,U_5094),U_5097),U_5096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5094),hAPP(c_Finite__Set_Ocard(U_5095),U_5096))),U_5098)))
      | ? [U_5093] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(U_5097,U_5093)),U_5098))
          & hBOOL(hAPP(hAPP(c_member(U_5095),U_5093),U_5096)) )
      | ~ class_Rings_Osemiring__1(U_5094)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5094) ),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

fof(f_1318_3,plain,
    ! [U_5098,U_5097,U_5096,U_5095,U_5094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5095,U_5094),U_5097),U_5096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5094),hAPP(c_Finite__Set_Ocard(U_5095),U_5096))),U_5098)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(U_5097,sK105(U_5098,U_5097,U_5096,U_5095,U_5094))),U_5098))
        & hBOOL(hAPP(hAPP(c_member(U_5095),sK105(U_5098,U_5097,U_5096,U_5095,U_5094)),U_5096)) )
      | ~ class_Rings_Osemiring__1(U_5094)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5094) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_5093,sK105(U_5098,U_5097,U_5096,U_5095,U_5094))],[f_1318_2]) ).

cnf(f_1318_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5095),sK105(U_5098,U_5097,U_5096,U_5095,U_5094)),U_5096))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5095,U_5094),U_5097),U_5096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5094),hAPP(c_Finite__Set_Ocard(U_5095),U_5096))),U_5098)))
    | ~ class_Rings_Osemiring__1(U_5094)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5094) ),
    inference(clausify,[status(thm)],[f_1318_3]) ).

cnf(f_1318_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(U_5097,sK105(U_5098,U_5097,U_5096,U_5095,U_5094))),U_5098))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5095,U_5094),U_5097),U_5096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5094),hAPP(c_Finite__Set_Ocard(U_5095),U_5096))),U_5098)))
    | ~ class_Rings_Osemiring__1(U_5094)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5094) ),
    inference(clausify,[status(thm)],[f_1318_3]) ).

fof(f_1319_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_1319_2,plain,
    ! [U_5099] :
      ( ( 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_5099)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5099))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5099),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_5099)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5099),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

fof(f_1319_3,plain,
    ( ! [U_5101] :
        ( 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_5101)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5101))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5101),c_Int_OPls)) )
    & ! [U_5100] :
        ( 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_5100)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5100),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1319_2]) ).

cnf(f_1319_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_5100)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5100),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1319_3]) ).

cnf(f_1319_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_5101)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5101),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1319_3]) ).

fof(f_1320_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_1320_2,plain,
    ! [U_5102] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5102)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5102))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5102),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5102)),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_5102),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

fof(f_1320_3,plain,
    ( ! [U_5104] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5104)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5104),c_Int_OPls)) )
    & ! [U_5103] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5103)),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_5103),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1320_2]) ).

cnf(f_1320_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5103)),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_5103),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

cnf(f_1320_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5104)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5104))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5104),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

fof(f_1321_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_1321_2,plain,
    ! [U_5105] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5105))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5105) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5105) = 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_5105)))) ) ),
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ( ! [U_5107] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5107))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5107) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5106] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106) = 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_5106)))) ) ),
    inference(miniscope,[status(thm)],[f_1321_2]) ).

cnf(f_1321_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106) = 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_5106)))) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

cnf(f_1321_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5107))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5107) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

fof(f_1322_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_1322_2,plain,
    ! [U_5109,U_5108] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5108) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5109)
        | U_5108 != U_5109 )
      & ( U_5108 = U_5109
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5108) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5109) ) ),
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ( ! [U_5113,U_5111] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5111) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5113)
        | U_5111 != U_5113 )
    & ! [U_5112,U_5110] :
        ( U_5110 = U_5112
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5110) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5112) ) ),
    inference(miniscope,[status(thm)],[f_1322_2]) ).

cnf(f_1322_4,plain,
    ( U_5110 = U_5112
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5110) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5112) ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

cnf(f_1322_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5111) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5113)
    | U_5111 != U_5113 ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

fof(f_1323_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_1323_2,plain,
    ! [U_5115,U_5114] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5114) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5115)
        | U_5114 != U_5115 )
      & ( U_5114 = U_5115
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5114) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5115) ) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

fof(f_1323_3,plain,
    ( ! [U_5119,U_5117] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5117) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5119)
        | U_5117 != U_5119 )
    & ! [U_5118,U_5116] :
        ( U_5116 = U_5118
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5116) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5118) ) ),
    inference(miniscope,[status(thm)],[f_1323_2]) ).

cnf(f_1323_4,plain,
    ( U_5116 = U_5118
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5116) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5118) ),
    inference(clausify,[status(thm)],[f_1323_3]) ).

cnf(f_1323_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5117) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5119)
    | U_5117 != U_5119 ),
    inference(clausify,[status(thm)],[f_1323_3]) ).

fof(f_1324_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

cnf(f_1324_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1324_1]) ).

fof(f_1325_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_1325_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_1325_1]) ).

fof(f_1326_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_1326_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1326_1]) ).

fof(f_1327_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_1327_2,plain,
    ! [U_5120] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5120),c_Int_OPls) = U_5120,
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

cnf(f_1327_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5120),c_Int_OPls) = U_5120,
    inference(clausify,[status(thm)],[f_1327_2]) ).

fof(f_1328_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_1328_2,plain,
    ! [U_5121] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_5121) = U_5121,
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

cnf(f_1328_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_5121) = U_5121,
    inference(clausify,[status(thm)],[f_1328_2]) ).

fof(f_1329_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_1329_2,plain,
    ! [U_5122] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_5122) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

cnf(f_1329_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_5122) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1329_2]) ).

fof(f_1330_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_1330_2,plain,
    ! [U_5123] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5123),c_Int_OPls) = U_5123,
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

cnf(f_1330_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5123),c_Int_OPls) = U_5123,
    inference(clausify,[status(thm)],[f_1330_2]) ).

fof(f_1331_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_1331_2,plain,
    ! [U_5124] : c_Int_Osucc(c_Int_Opred(U_5124)) = U_5124,
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

cnf(f_1331_3,plain,
    c_Int_Osucc(c_Int_Opred(U_5124)) = U_5124,
    inference(clausify,[status(thm)],[f_1331_2]) ).

fof(f_1332_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_1332_2,plain,
    ! [U_5125] :
      ( c_Groups_Ozero__class_Ozero(U_5125) = hAPP(c_Int_Onumber__class_Onumber__of(U_5125),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_5125) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

cnf(f_1332_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_5125) = hAPP(c_Int_Onumber__class_Onumber__of(U_5125),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_5125) ),
    inference(clausify,[status(thm)],[f_1332_2]) ).

fof(f_1333_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_1333_2,plain,
    ! [U_5126] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5126),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_5126)
      | ~ class_Int_Onumber__ring(U_5126) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

cnf(f_1333_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5126),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_5126)
    | ~ class_Int_Onumber__ring(U_5126) ),
    inference(clausify,[status(thm)],[f_1333_2]) ).

fof(f_1334_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_1334_2,plain,
    ! [U_5128,U_5127] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5127),hAPP(c_Int_Onumber__class_Onumber__of(U_5127),c_Int_OPls)),U_5128) = U_5128
      | ~ class_Int_Onumber__ring(U_5127) ),
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

cnf(f_1334_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5127),hAPP(c_Int_Onumber__class_Onumber__of(U_5127),c_Int_OPls)),U_5128) = U_5128
    | ~ class_Int_Onumber__ring(U_5127) ),
    inference(clausify,[status(thm)],[f_1334_2]) ).

fof(f_1335_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_1335_2,plain,
    ! [U_5130,U_5129] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5129),U_5130),hAPP(c_Int_Onumber__class_Onumber__of(U_5129),c_Int_OPls)) = U_5130
      | ~ class_Int_Onumber__ring(U_5129) ),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

cnf(f_1335_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5129),U_5130),hAPP(c_Int_Onumber__class_Onumber__of(U_5129),c_Int_OPls)) = U_5130
    | ~ class_Int_Onumber__ring(U_5129) ),
    inference(clausify,[status(thm)],[f_1335_2]) ).

fof(f_1336_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_1336_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_1336_1]) ).

fof(f_1337_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_1337_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_1337_1]) ).

fof(f_1338_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_1338_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_1338_1]) ).

fof(f_1339_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_1339_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_1339_1]) ).

fof(f_1340_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_1340_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_1340_1]) ).

fof(f_1341_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_1341_2,plain,
    ! [U_5132,U_5131] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5131)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5132),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5131)) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

cnf(f_1341_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5131)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5132),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5131)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5131)) ),
    inference(clausify,[status(thm)],[f_1341_2]) ).

fof(f_1342_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_1342_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_1342_1]) ).

fof(f_1343_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_1343_2,plain,
    ! [U_5134,U_5133] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5133),U_5134))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5133)),U_5134)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5133)),U_5134))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5133),U_5134)) ) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

fof(f_1343_3,plain,
    ( ! [U_5138,U_5136] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5136),U_5138))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5136)),U_5138)) )
    & ! [U_5137,U_5135] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5135)),U_5137))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5135),U_5137)) ) ),
    inference(miniscope,[status(thm)],[f_1343_2]) ).

cnf(f_1343_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5135)),U_5137))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5135),U_5137)) ),
    inference(clausify,[status(thm)],[f_1343_3]) ).

cnf(f_1343_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5136),U_5138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5136)),U_5138)) ),
    inference(clausify,[status(thm)],[f_1343_3]) ).

fof(f_1344_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_1344_2,plain,
    ! [U_5139] : c_Int_Opred(U_5139) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5139),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

cnf(f_1344_3,plain,
    c_Int_Opred(U_5139) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5139),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1344_2]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_5140] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5140)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5140))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5140),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5140)),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_5140),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

fof(f_1345_3,plain,
    ( ! [U_5142] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5142)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5142))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5142),c_Int_OPls)) )
    & ! [U_5141] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5141)),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_5141),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1345_2]) ).

cnf(f_1345_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5141)),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_5141),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_3]) ).

cnf(f_1345_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5142)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5142))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5142),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_3]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_5144,U_5143] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5143),U_5144),hAPP(c_Int_Onumber__class_Onumber__of(U_5143),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5143)
      | ~ class_Int_Onumber__ring(U_5143)
      | ~ class_Fields_Ofield__inverse__zero(U_5143) ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

cnf(f_1346_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5143),U_5144),hAPP(c_Int_Onumber__class_Onumber__of(U_5143),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5143)
    | ~ class_Int_Onumber__ring(U_5143)
    | ~ class_Fields_Ofield__inverse__zero(U_5143) ),
    inference(clausify,[status(thm)],[f_1346_2]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_5145] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5145) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ( ! [U_5147] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5147) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5147),c_Int_OPls)) )
    & ! [U_5146] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5146),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5146) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5146),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5146) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

cnf(f_1347_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5147) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5147),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_5148] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5148)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5148),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5148),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5148) ) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ( ! [U_5150] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5150)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5150),c_Int_OPls)) )
    & ! [U_5149] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5149),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5149) ) ),
    inference(miniscope,[status(thm)],[f_1348_2]) ).

cnf(f_1348_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5149),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5149) ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

cnf(f_1348_5,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5150)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5150),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

fof(f_1349_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_1349_2,plain,
    ! [U_5152,U_5151] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5151)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5152)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5152))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5152))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5152)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5152))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5152))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5152)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5151)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5152))) ) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

fof(f_1349_3,plain,
    ( ! [U_5156,U_5154] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5154)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5156)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5156))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5156))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5156)) ) )
    & ! [U_5155,U_5153] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),U_5155))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5155))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),U_5155)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5153)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5155))) ) ),
    inference(miniscope,[status(thm)],[f_1349_2]) ).

cnf(f_1349_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),U_5155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5153)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5155))) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

cnf(f_1349_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),U_5155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5153)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5155))) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

cnf(f_1349_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5156))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5154)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5156))) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

cnf(f_1349_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5156))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5154)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5156))) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

fof(f_1350_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_1350_2,plain,
    ! [U_5158,U_5157] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5157)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5158)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5157),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5157),U_5158)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5157),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5157),U_5158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5157)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5158))) ) ),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

fof(f_1350_3,plain,
    ( ! [U_5162,U_5160] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5162)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5160),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5160),U_5162)) ) )
    & ! [U_5161,U_5159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5159),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5159),U_5161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5159)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5161))) ) ),
    inference(miniscope,[status(thm)],[f_1350_2]) ).

cnf(f_1350_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5159),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5159),U_5161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5159)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5161))) ),
    inference(clausify,[status(thm)],[f_1350_3]) ).

cnf(f_1350_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5160),U_5162))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5162))) ),
    inference(clausify,[status(thm)],[f_1350_3]) ).

cnf(f_1350_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5160),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_5160)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5162))) ),
    inference(clausify,[status(thm)],[f_1350_3]) ).

fof(f_1351_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_1351_2,plain,
    ! [U_5164,U_5163] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5163),hAPP(c_Int_Onumber__class_Onumber__of(U_5163),U_5164)),c_Groups_Ozero__class_Ozero(U_5163)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5164),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5164),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5163),hAPP(c_Int_Onumber__class_Onumber__of(U_5163),U_5164)),c_Groups_Ozero__class_Ozero(U_5163))) ) )
      | ~ class_Rings_Olinordered__idom(U_5163)
      | ~ class_Int_Onumber__ring(U_5163) ),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

cnf(f_1351_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5164),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5163),hAPP(c_Int_Onumber__class_Onumber__of(U_5163),U_5164)),c_Groups_Ozero__class_Ozero(U_5163)))
    | ~ class_Rings_Olinordered__idom(U_5163)
    | ~ class_Int_Onumber__ring(U_5163) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5163),hAPP(c_Int_Onumber__class_Onumber__of(U_5163),U_5164)),c_Groups_Ozero__class_Ozero(U_5163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5164),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_5163)
    | ~ class_Int_Onumber__ring(U_5163) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

fof(f_1352_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_1352_2,plain,
    ! [U_5166,U_5165] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),hAPP(c_Int_Onumber__class_Onumber__of(U_5165),U_5166)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5166)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5166))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),hAPP(c_Int_Onumber__class_Onumber__of(U_5165),U_5166))) ) )
      | ~ class_Rings_Olinordered__idom(U_5165)
      | ~ class_Int_Onumber__ring(U_5165) ),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

cnf(f_1352_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5166))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),hAPP(c_Int_Onumber__class_Onumber__of(U_5165),U_5166)))
    | ~ class_Rings_Olinordered__idom(U_5165)
    | ~ class_Int_Onumber__ring(U_5165) ),
    inference(clausify,[status(thm)],[f_1352_2]) ).

cnf(f_1352_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),c_Groups_Ozero__class_Ozero(U_5165)),hAPP(c_Int_Onumber__class_Onumber__of(U_5165),U_5166)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5166))
    | ~ class_Rings_Olinordered__idom(U_5165)
    | ~ class_Int_Onumber__ring(U_5165) ),
    inference(clausify,[status(thm)],[f_1352_2]) ).

fof(f_1353_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_1353_2,plain,
    ! [U_5168,U_5167] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5167),c_Groups_Ozero__class_Ozero(U_5167)),hAPP(c_Int_Onumber__class_Onumber__of(U_5167),U_5168)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5168)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5168))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5167),c_Groups_Ozero__class_Ozero(U_5167)),hAPP(c_Int_Onumber__class_Onumber__of(U_5167),U_5168))) ) )
      | ~ class_Rings_Olinordered__idom(U_5167)
      | ~ class_Int_Onumber__ring(U_5167) ),
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

cnf(f_1353_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5168))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5167),c_Groups_Ozero__class_Ozero(U_5167)),hAPP(c_Int_Onumber__class_Onumber__of(U_5167),U_5168)))
    | ~ class_Rings_Olinordered__idom(U_5167)
    | ~ class_Int_Onumber__ring(U_5167) ),
    inference(clausify,[status(thm)],[f_1353_2]) ).

cnf(f_1353_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5167),c_Groups_Ozero__class_Ozero(U_5167)),hAPP(c_Int_Onumber__class_Onumber__of(U_5167),U_5168)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5168))
    | ~ class_Rings_Olinordered__idom(U_5167)
    | ~ class_Int_Onumber__ring(U_5167) ),
    inference(clausify,[status(thm)],[f_1353_2]) ).

fof(f_1354_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_1354_2,plain,
    ! [U_5170,U_5169] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(c_Int_Onumber__class_Onumber__of(U_5169),U_5170)),c_Groups_Ozero__class_Ozero(U_5169)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5170),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5170),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(c_Int_Onumber__class_Onumber__of(U_5169),U_5170)),c_Groups_Ozero__class_Ozero(U_5169))) ) )
      | ~ class_Rings_Olinordered__idom(U_5169)
      | ~ class_Int_Onumber__ring(U_5169) ),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

cnf(f_1354_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5170),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(c_Int_Onumber__class_Onumber__of(U_5169),U_5170)),c_Groups_Ozero__class_Ozero(U_5169)))
    | ~ class_Rings_Olinordered__idom(U_5169)
    | ~ class_Int_Onumber__ring(U_5169) ),
    inference(clausify,[status(thm)],[f_1354_2]) ).

cnf(f_1354_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),hAPP(c_Int_Onumber__class_Onumber__of(U_5169),U_5170)),c_Groups_Ozero__class_Ozero(U_5169)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5170),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_5169)
    | ~ class_Int_Onumber__ring(U_5169) ),
    inference(clausify,[status(thm)],[f_1354_2]) ).

fof(f_1355_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_1355_2,plain,
    ! [U_5171] :
      ( ( 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_5171)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5171)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5171))
        | ~ 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_5171))) ) ),
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

fof(f_1355_3,plain,
    ( ! [U_5173] :
        ( 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_5173)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5173)) )
    & ! [U_5172] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5172))
        | ~ 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_5172))) ) ),
    inference(miniscope,[status(thm)],[f_1355_2]) ).

cnf(f_1355_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5172))
    | ~ 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_5172))) ),
    inference(clausify,[status(thm)],[f_1355_3]) ).

cnf(f_1355_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_5173)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5173)) ),
    inference(clausify,[status(thm)],[f_1355_3]) ).

fof(f_1356_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_1356_2,plain,
    ! [U_5175,U_5174] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5175)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5174),U_5175))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5175),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5175)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5174)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5175),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5174),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5175)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5175)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5174),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ( ! [U_5179,U_5177] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5179)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5177),U_5179))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5179),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5179)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5179),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5177),c_Int_OPls)) )
    & ! [U_5178,U_5176] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5176)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5178)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5178)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5176),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5176)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5178)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5178)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5176),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

cnf(f_1356_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5179)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5179),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5177),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

cnf(f_1356_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5177)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5179)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5177),U_5179))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5179),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5177),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_5182,U_5181,U_5180] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5181)),U_5182)) = 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_5180),U_5181))),U_5182)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5180),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5181)),U_5182)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5180),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

fof(f_1357_3,plain,
    ( ! [U_5188,U_5186,U_5184] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5184)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5186)),U_5188)) = 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_5184),U_5186))),U_5188)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5184),c_Int_OPls)) )
    & ! [U_5187,U_5185,U_5183] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5185)),U_5187)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5183),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1357_2]) ).

cnf(f_1357_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5183)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5185)),U_5187)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5183),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1357_3]) ).

cnf(f_1357_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5184)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5186)),U_5188)) = 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_5184),U_5186))),U_5188)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5184),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1357_3]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_5190,U_5189] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5189)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5190)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5189),U_5190))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5189),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5189)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5190)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5189),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

fof(f_1358_3,plain,
    ( ! [U_5194,U_5192] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5192)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5194)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5192),U_5194))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5192),c_Int_OPls)) )
    & ! [U_5193,U_5191] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5191)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5193)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5191),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1358_2]) ).

cnf(f_1358_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5191)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5193)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5191),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1358_3]) ).

cnf(f_1358_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5192)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5194)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5192),U_5194))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5192),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1358_3]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_5196,U_5195] :
      ( hBOOL(hAPP(hAPP(c_member(U_5195),hAPP(c_Int_Onumber__class_Onumber__of(U_5195),U_5196)),c_Nat_Osemiring__1__class_ONats(U_5195)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5196))
      | ~ class_Int_Onumber__ring(U_5195) ),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

cnf(f_1359_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5195),hAPP(c_Int_Onumber__class_Onumber__of(U_5195),U_5196)),c_Nat_Osemiring__1__class_ONats(U_5195)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5196))
    | ~ class_Int_Onumber__ring(U_5195) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

fof(f_1360_1,plain,
    ! [V_k_2,V_Pa_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_Pa_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_1360_2,plain,
    ! [U_5201,U_5200,U_5199] :
      ( ! [U_5198] :
          ( hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5201),U_5199))))
          | ~ hBOOL(hAPP(U_5200,U_5198)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5201))
      | ? [U_5197] :
          ( ~ hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5197),U_5199)))
          & hBOOL(hAPP(U_5200,U_5197)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5199)) ),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

fof(f_1360_3,plain,
    ! [U_5201,U_5200,U_5199] :
      ( ! [U_5198] :
          ( hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5201),U_5199))))
          | ~ hBOOL(hAPP(U_5200,U_5198)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5201))
      | ( ~ hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_5201,U_5200,U_5199)),U_5199)))
        & hBOOL(hAPP(U_5200,sK106(U_5201,U_5200,U_5199))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5199)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_5197,sK106(U_5201,U_5200,U_5199))],[f_1360_2]) ).

cnf(f_1360_4,plain,
    ( hBOOL(hAPP(U_5200,sK106(U_5201,U_5200,U_5199)))
    | hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5201),U_5199))))
    | ~ hBOOL(hAPP(U_5200,U_5198))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5201))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5199)) ),
    inference(clausify,[status(thm)],[f_1360_3]) ).

cnf(f_1360_5,plain,
    ( ~ hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_5201,U_5200,U_5199)),U_5199)))
    | hBOOL(hAPP(U_5200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5201),U_5199))))
    | ~ hBOOL(hAPP(U_5200,U_5198))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5201))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5199)) ),
    inference(clausify,[status(thm)],[f_1360_3]) ).

fof(f_1361_1,plain,
    ! [V_k_2,V_Pa_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_Pa_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_1361_2,plain,
    ! [U_5206,U_5205,U_5204] :
      ( ! [U_5203] :
          ( hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5206),U_5204))))
          | ~ hBOOL(hAPP(U_5205,U_5203)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5206))
      | ? [U_5202] :
          ( ~ hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5202),U_5204)))
          & hBOOL(hAPP(U_5205,U_5202)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5204)) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

fof(f_1361_3,plain,
    ! [U_5206,U_5205,U_5204] :
      ( ! [U_5203] :
          ( hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5206),U_5204))))
          | ~ hBOOL(hAPP(U_5205,U_5203)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5206))
      | ( ~ hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK107(U_5206,U_5205,U_5204)),U_5204)))
        & hBOOL(hAPP(U_5205,sK107(U_5206,U_5205,U_5204))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5204)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_5202,sK107(U_5206,U_5205,U_5204))],[f_1361_2]) ).

cnf(f_1361_4,plain,
    ( hBOOL(hAPP(U_5205,sK107(U_5206,U_5205,U_5204)))
    | hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5206),U_5204))))
    | ~ hBOOL(hAPP(U_5205,U_5203))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5206))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5204)) ),
    inference(clausify,[status(thm)],[f_1361_3]) ).

cnf(f_1361_5,plain,
    ( ~ hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK107(U_5206,U_5205,U_5204)),U_5204)))
    | hBOOL(hAPP(U_5205,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5206),U_5204))))
    | ~ hBOOL(hAPP(U_5205,U_5203))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5206))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5204)) ),
    inference(clausify,[status(thm)],[f_1361_3]) ).

fof(f_1362_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_1362_2,plain,
    ! [U_5208] :
      ( ? [U_5207] :
          ( U_5208 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5207)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5207)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5208)) ),
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

fof(f_1362_3,plain,
    ! [U_5208] :
      ( ( U_5208 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK108(U_5208))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK108(U_5208))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5208)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_5207,sK108(U_5208))],[f_1362_2]) ).

cnf(f_1362_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK108(U_5208)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5208)) ),
    inference(clausify,[status(thm)],[f_1362_3]) ).

cnf(f_1362_5,plain,
    ( U_5208 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK108(U_5208))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5208)) ),
    inference(clausify,[status(thm)],[f_1362_3]) ).

fof(f_1363_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_1363_2,plain,
    ! [U_5211,U_5210,U_5209] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5210),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_5210),U_5211))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5209))),U_5211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5209)) ),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

cnf(f_1363_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5210),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_5210),U_5211))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5209))),U_5211))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5209)) ),
    inference(clausify,[status(thm)],[f_1363_2]) ).

fof(f_1364_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_1364_2,plain,
    ! [U_5214,U_5213,U_5212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5214),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_5214),U_5213))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5212))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5212)) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

cnf(f_1364_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5214),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_5214),U_5213))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5212))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5212)) ),
    inference(clausify,[status(thm)],[f_1364_2]) ).

fof(f_1365_1,plain,
    ! [V_ca_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_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_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_1365_2,plain,
    ! [U_5219,U_5218,U_5217,U_5216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5216),U_5218),U_5219)),hAPP(hAPP(c_Finite__Set_Ofold(U_5216,U_5216,c_Orderings_Oord__class_Omin(U_5216)),U_5219),U_5217)))
      | ? [U_5215] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),U_5218),U_5215))
          & hBOOL(hAPP(hAPP(c_member(U_5216),U_5215),U_5217)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5216),U_5217))
      | ~ class_Orderings_Olinorder(U_5216) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ! [U_5219,U_5218,U_5217,U_5216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5216),U_5218),U_5219)),hAPP(hAPP(c_Finite__Set_Ofold(U_5216,U_5216,c_Orderings_Oord__class_Omin(U_5216)),U_5219),U_5217)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),U_5218),sK109(U_5219,U_5218,U_5217,U_5216)))
        & hBOOL(hAPP(hAPP(c_member(U_5216),sK109(U_5219,U_5218,U_5217,U_5216)),U_5217)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5216),U_5217))
      | ~ class_Orderings_Olinorder(U_5216) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_5215,sK109(U_5219,U_5218,U_5217,U_5216))],[f_1365_2]) ).

cnf(f_1365_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5216),sK109(U_5219,U_5218,U_5217,U_5216)),U_5217))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5216),U_5218),U_5219)),hAPP(hAPP(c_Finite__Set_Ofold(U_5216,U_5216,c_Orderings_Oord__class_Omin(U_5216)),U_5219),U_5217)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5216),U_5217))
    | ~ class_Orderings_Olinorder(U_5216) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

cnf(f_1365_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),U_5218),sK109(U_5219,U_5218,U_5217,U_5216)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5216),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5216),U_5218),U_5219)),hAPP(hAPP(c_Finite__Set_Ofold(U_5216,U_5216,c_Orderings_Oord__class_Omin(U_5216)),U_5219),U_5217)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5216),U_5217))
    | ~ class_Orderings_Olinorder(U_5216) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

fof(f_1366_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_1366_2,plain,
    ! [U_5221,U_5220] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5220),hAPP(c_Groups_Oabs__class_Oabs(U_5220),U_5221)) = hAPP(c_Groups_Oabs__class_Oabs(U_5220),U_5221)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5220) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

cnf(f_1366_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5220),hAPP(c_Groups_Oabs__class_Oabs(U_5220),U_5221)) = hAPP(c_Groups_Oabs__class_Oabs(U_5220),U_5221)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5220) ),
    inference(clausify,[status(thm)],[f_1366_2]) ).

fof(f_1367_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_1367_2,plain,
    ! [U_5224,U_5223,U_5222] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),U_5223),U_5224))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Oabs__class_Oabs(U_5222),U_5223)),U_5224))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5222) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

cnf(f_1367_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),U_5223),U_5224))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Oabs__class_Oabs(U_5222),U_5223)),U_5224))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5222) ),
    inference(clausify,[status(thm)],[f_1367_2]) ).

fof(f_1368_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_1368_2,plain,
    ! [U_5226,U_5225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5225),U_5226),hAPP(c_Groups_Oabs__class_Oabs(U_5225),U_5226)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5225) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

cnf(f_1368_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5225),U_5226),hAPP(c_Groups_Oabs__class_Oabs(U_5225),U_5226)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5225) ),
    inference(clausify,[status(thm)],[f_1368_2]) ).

fof(f_1369_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_1369_2,plain,
    ! [U_5227] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5227),c_Groups_Ozero__class_Ozero(U_5227)) = c_Groups_Ozero__class_Ozero(U_5227)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5227) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

cnf(f_1369_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5227),c_Groups_Ozero__class_Ozero(U_5227)) = c_Groups_Ozero__class_Ozero(U_5227)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5227) ),
    inference(clausify,[status(thm)],[f_1369_2]) ).

fof(f_1370_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_1370_2,plain,
    ! [U_5229,U_5228] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_5228),U_5229) = c_Groups_Ozero__class_Ozero(U_5228)
          | U_5229 != c_Groups_Ozero__class_Ozero(U_5228) )
        & ( U_5229 = c_Groups_Ozero__class_Ozero(U_5228)
          | hAPP(c_Groups_Oabs__class_Oabs(U_5228),U_5229) != c_Groups_Ozero__class_Ozero(U_5228) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5228) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

cnf(f_1370_3,plain,
    ( U_5229 = c_Groups_Ozero__class_Ozero(U_5228)
    | hAPP(c_Groups_Oabs__class_Oabs(U_5228),U_5229) != c_Groups_Ozero__class_Ozero(U_5228)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5228) ),
    inference(clausify,[status(thm)],[f_1370_2]) ).

cnf(f_1370_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5228),U_5229) = c_Groups_Ozero__class_Ozero(U_5228)
    | U_5229 != c_Groups_Ozero__class_Ozero(U_5228)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5228) ),
    inference(clausify,[status(thm)],[f_1370_2]) ).

fof(f_1371_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_1371_2,plain,
    ! [U_5232,U_5231,U_5230] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5230),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5231)),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5230),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5231)),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5232))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5230) ),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

cnf(f_1371_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5230),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5231)),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5230),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5231)),hAPP(c_Groups_Oabs__class_Oabs(U_5230),U_5232))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5230) ),
    inference(clausify,[status(thm)],[f_1371_2]) ).

fof(f_1372_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_1372_2,plain,
    ! [U_5234,U_5233] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5233),hAPP(c_Groups_Oabs__class_Oabs(U_5233),U_5234)),hAPP(c_Groups_Oabs__class_Oabs(U_5233),U_5234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5233),U_5234),U_5234)
      | ~ class_Rings_Olinordered__idom(U_5233) ),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

cnf(f_1372_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5233),hAPP(c_Groups_Oabs__class_Oabs(U_5233),U_5234)),hAPP(c_Groups_Oabs__class_Oabs(U_5233),U_5234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5233),U_5234),U_5234)
    | ~ class_Rings_Olinordered__idom(U_5233) ),
    inference(clausify,[status(thm)],[f_1372_2]) ).

fof(f_1373_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_1373_2,plain,
    ! [U_5237,U_5236,U_5235] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5235),U_5236),U_5237)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5235),hAPP(c_Groups_Oabs__class_Oabs(U_5235),U_5236)),hAPP(c_Groups_Oabs__class_Oabs(U_5235),U_5237))
      | ~ class_Rings_Olinordered__idom(U_5235) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

cnf(f_1373_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5235),U_5236),U_5237)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5235),hAPP(c_Groups_Oabs__class_Oabs(U_5235),U_5236)),hAPP(c_Groups_Oabs__class_Oabs(U_5235),U_5237))
    | ~ class_Rings_Olinordered__idom(U_5235) ),
    inference(clausify,[status(thm)],[f_1373_2]) ).

fof(f_1374_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_1374_2,plain,
    ! [U_5240,U_5239,U_5238] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5238),U_5239),U_5240)) = hAPP(c_Groups_Oabs__class_Oabs(U_5238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5238),U_5240),U_5239))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5238) ),
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

cnf(f_1374_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5238),U_5239),U_5240)) = hAPP(c_Groups_Oabs__class_Oabs(U_5238),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5238),U_5240),U_5239))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5238) ),
    inference(clausify,[status(thm)],[f_1374_2]) ).

fof(f_1375_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_1375_2,plain,
    ! [U_5241] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5241),c_Groups_Oone__class_Oone(U_5241)) = c_Groups_Oone__class_Oone(U_5241)
      | ~ class_Rings_Olinordered__idom(U_5241) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

cnf(f_1375_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5241),c_Groups_Oone__class_Oone(U_5241)) = c_Groups_Oone__class_Oone(U_5241)
    | ~ class_Rings_Olinordered__idom(U_5241) ),
    inference(clausify,[status(thm)],[f_1375_2]) ).

fof(f_1376_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_1376_2,plain,
    ! [U_5243,U_5242] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5242),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5242),U_5243)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5242),U_5243)
      | ~ class_Rings_Olinordered__idom(U_5242) ),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

cnf(f_1376_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5242),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5242),U_5243)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5242),U_5243)
    | ~ class_Rings_Olinordered__idom(U_5242) ),
    inference(clausify,[status(thm)],[f_1376_2]) ).

fof(f_1377_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_1377_2,plain,
    ! [U_5246,U_5245,U_5244] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),U_5245),U_5246)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),hAPP(c_Groups_Oabs__class_Oabs(U_5244),U_5245)),hAPP(c_Groups_Oabs__class_Oabs(U_5244),U_5246))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5244) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

cnf(f_1377_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),U_5245),U_5246)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5244),hAPP(c_Groups_Oabs__class_Oabs(U_5244),U_5245)),hAPP(c_Groups_Oabs__class_Oabs(U_5244),U_5246))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5244) ),
    inference(clausify,[status(thm)],[f_1377_2]) ).

fof(f_1378_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_1378_2,plain,
    ! [U_5247] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5247)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5247),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

cnf(f_1378_3,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5247)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5247),
    inference(clausify,[status(thm)],[f_1378_2]) ).

fof(f_1379_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_1379_2,plain,
    ! [U_5249,U_5248] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5248),U_5249) = U_5249
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5248),c_Groups_Ozero__class_Ozero(U_5248)),U_5249))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5248) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

cnf(f_1379_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5248),U_5249) = U_5249
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5248),c_Groups_Ozero__class_Ozero(U_5248)),U_5249))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5248) ),
    inference(clausify,[status(thm)],[f_1379_2]) ).

fof(f_1380_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_1380_2,plain,
    ! [U_5251,U_5250] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5250),hAPP(c_Groups_Oabs__class_Oabs(U_5250),U_5251)),c_Groups_Ozero__class_Ozero(U_5250)))
          | U_5251 != c_Groups_Ozero__class_Ozero(U_5250) )
        & ( U_5251 = c_Groups_Ozero__class_Ozero(U_5250)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5250),hAPP(c_Groups_Oabs__class_Oabs(U_5250),U_5251)),c_Groups_Ozero__class_Ozero(U_5250))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5250) ),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

cnf(f_1380_3,plain,
    ( U_5251 = c_Groups_Ozero__class_Ozero(U_5250)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5250),hAPP(c_Groups_Oabs__class_Oabs(U_5250),U_5251)),c_Groups_Ozero__class_Ozero(U_5250)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5250) ),
    inference(clausify,[status(thm)],[f_1380_2]) ).

cnf(f_1380_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5250),hAPP(c_Groups_Oabs__class_Oabs(U_5250),U_5251)),c_Groups_Ozero__class_Ozero(U_5250)))
    | U_5251 != c_Groups_Ozero__class_Ozero(U_5250)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5250) ),
    inference(clausify,[status(thm)],[f_1380_2]) ).

fof(f_1381_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_1381_2,plain,
    ! [U_5253,U_5252] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5252),c_Groups_Ozero__class_Ozero(U_5252)),hAPP(c_Groups_Oabs__class_Oabs(U_5252),U_5253)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5252) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

cnf(f_1381_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5252),c_Groups_Ozero__class_Ozero(U_5252)),hAPP(c_Groups_Oabs__class_Oabs(U_5252),U_5253)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5252) ),
    inference(clausify,[status(thm)],[f_1381_2]) ).

fof(f_1382_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_1382_2,plain,
    ! [U_5255,U_5254] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5254),U_5255) = U_5255
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5254),c_Groups_Ozero__class_Ozero(U_5254)),U_5255))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5254) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

cnf(f_1382_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5254),U_5255) = U_5255
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5254),c_Groups_Ozero__class_Ozero(U_5254)),U_5255))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5254) ),
    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(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_1383_2,plain,
    ! [U_5257,U_5256] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5256),c_Groups_Ozero__class_Ozero(U_5256)),hAPP(c_Groups_Oabs__class_Oabs(U_5256),U_5257)))
          | U_5257 = c_Groups_Ozero__class_Ozero(U_5256) )
        & ( U_5257 != c_Groups_Ozero__class_Ozero(U_5256)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5256),c_Groups_Ozero__class_Ozero(U_5256)),hAPP(c_Groups_Oabs__class_Oabs(U_5256),U_5257))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5256) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

cnf(f_1383_3,plain,
    ( U_5257 != c_Groups_Ozero__class_Ozero(U_5256)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5256),c_Groups_Ozero__class_Ozero(U_5256)),hAPP(c_Groups_Oabs__class_Oabs(U_5256),U_5257)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5256) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5256),c_Groups_Ozero__class_Ozero(U_5256)),hAPP(c_Groups_Oabs__class_Oabs(U_5256),U_5257)))
    | U_5257 = c_Groups_Ozero__class_Ozero(U_5256)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5256) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

fof(f_1384_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_1384_2,plain,
    ! [U_5259,U_5258] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5258),hAPP(c_Groups_Oabs__class_Oabs(U_5258),U_5259)),c_Groups_Ozero__class_Ozero(U_5258)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5258) ),
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5258),hAPP(c_Groups_Oabs__class_Oabs(U_5258),U_5259)),c_Groups_Ozero__class_Ozero(U_5258)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5258) ),
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_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_1385_2,plain,
    ! [U_5262,U_5261,U_5260] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),hAPP(c_Groups_Oabs__class_Oabs(U_5260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5260),U_5261),U_5262))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5260),hAPP(c_Groups_Oabs__class_Oabs(U_5260),U_5261)),hAPP(c_Groups_Oabs__class_Oabs(U_5260),U_5262))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5260) ),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

cnf(f_1385_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),hAPP(c_Groups_Oabs__class_Oabs(U_5260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5260),U_5261),U_5262))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5260),hAPP(c_Groups_Oabs__class_Oabs(U_5260),U_5261)),hAPP(c_Groups_Oabs__class_Oabs(U_5260),U_5262))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5260) ),
    inference(clausify,[status(thm)],[f_1385_2]) ).

fof(f_1386_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_1386_2,plain,
    ! [U_5267,U_5266,U_5265,U_5264,U_5263] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5264)),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5266))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5267)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5266)),U_5267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5264)),U_5265))
      | ~ class_Rings_Olinordered__idom(U_5263) ),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

cnf(f_1386_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5264)),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5266))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5263),U_5265),U_5267)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5266)),U_5267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5263),hAPP(c_Groups_Oabs__class_Oabs(U_5263),U_5264)),U_5265))
    | ~ class_Rings_Olinordered__idom(U_5263) ),
    inference(clausify,[status(thm)],[f_1386_2]) ).

fof(f_1387_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_1387_2,plain,
    ! [U_5270,U_5269,U_5268] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5268),hAPP(c_Groups_Oabs__class_Oabs(U_5268),U_5269)),hAPP(c_Groups_Oabs__class_Oabs(U_5268),U_5270))),hAPP(c_Groups_Oabs__class_Oabs(U_5268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5268),U_5270),U_5269))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5268) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

cnf(f_1387_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5268),hAPP(c_Groups_Oabs__class_Oabs(U_5268),U_5269)),hAPP(c_Groups_Oabs__class_Oabs(U_5268),U_5270))),hAPP(c_Groups_Oabs__class_Oabs(U_5268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5268),U_5270),U_5269))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5268) ),
    inference(clausify,[status(thm)],[f_1387_2]) ).

fof(f_1388_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_1388_2,plain,
    ! [U_5273,U_5272,U_5271] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5271),hAPP(c_Groups_Oabs__class_Oabs(U_5271),U_5272)),hAPP(c_Groups_Oabs__class_Oabs(U_5271),U_5273))),hAPP(c_Groups_Oabs__class_Oabs(U_5271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5271),U_5272),U_5273))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5271) ),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

cnf(f_1388_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5271),hAPP(c_Groups_Oabs__class_Oabs(U_5271),U_5272)),hAPP(c_Groups_Oabs__class_Oabs(U_5271),U_5273))),hAPP(c_Groups_Oabs__class_Oabs(U_5271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5271),U_5272),U_5273))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5271) ),
    inference(clausify,[status(thm)],[f_1388_2]) ).

fof(f_1389_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_1389_2,plain,
    ! [U_5276,U_5275,U_5274] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5274),hAPP(c_Groups_Oabs__class_Oabs(U_5274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5274),hAPP(c_Groups_Oabs__class_Oabs(U_5274),U_5275)),hAPP(c_Groups_Oabs__class_Oabs(U_5274),U_5276)))),hAPP(c_Groups_Oabs__class_Oabs(U_5274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5274),U_5275),U_5276))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5274) ),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

cnf(f_1389_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5274),hAPP(c_Groups_Oabs__class_Oabs(U_5274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5274),hAPP(c_Groups_Oabs__class_Oabs(U_5274),U_5275)),hAPP(c_Groups_Oabs__class_Oabs(U_5274),U_5276)))),hAPP(c_Groups_Oabs__class_Oabs(U_5274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5274),U_5275),U_5276))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5274) ),
    inference(clausify,[status(thm)],[f_1389_2]) ).

fof(f_1390_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_1390_2,plain,
    ! [U_5279,U_5278,U_5277] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5277),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5277),U_5279),U_5278)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5277),hAPP(c_Groups_Oabs__class_Oabs(U_5277),U_5279)),hAPP(c_Groups_Oabs__class_Oabs(U_5277),U_5278))
      | U_5278 = c_Groups_Ozero__class_Ozero(U_5277)
      | ~ class_Fields_Olinordered__field(U_5277) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

cnf(f_1390_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5277),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5277),U_5279),U_5278)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5277),hAPP(c_Groups_Oabs__class_Oabs(U_5277),U_5279)),hAPP(c_Groups_Oabs__class_Oabs(U_5277),U_5278))
    | U_5278 = c_Groups_Ozero__class_Ozero(U_5277)
    | ~ class_Fields_Olinordered__field(U_5277) ),
    inference(clausify,[status(thm)],[f_1390_2]) ).

fof(f_1391_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_1391_2,plain,
    ! [U_5281,U_5280] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5280) = 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_5280),U_5281)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

cnf(f_1391_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5280) = 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_5280),U_5281)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1391_2]) ).

fof(f_1392_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_1392_2,plain,
    ! [U_5284,U_5283,U_5282] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5282),hAPP(c_Groups_Oabs__class_Oabs(U_5282),U_5284)),U_5283) = hAPP(c_Groups_Oabs__class_Oabs(U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5282),U_5284),U_5283))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5282),c_Groups_Ozero__class_Ozero(U_5282)),U_5283))
      | ~ class_Rings_Olinordered__idom(U_5282) ),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

cnf(f_1392_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5282),hAPP(c_Groups_Oabs__class_Oabs(U_5282),U_5284)),U_5283) = hAPP(c_Groups_Oabs__class_Oabs(U_5282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5282),U_5284),U_5283))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5282),c_Groups_Ozero__class_Ozero(U_5282)),U_5283))
    | ~ class_Rings_Olinordered__idom(U_5282) ),
    inference(clausify,[status(thm)],[f_1392_2]) ).

fof(f_1393_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_1393_2,plain,
    ! [U_5287,U_5286,U_5285] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),U_5286),U_5287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5286)),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5287))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5287),c_Groups_Ozero__class_Ozero(U_5285)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5287)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5286),c_Groups_Ozero__class_Ozero(U_5285)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5286)) )
      | ~ class_Rings_Oordered__ring__abs(U_5285) ),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

cnf(f_1393_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5287))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5286))
    | hAPP(c_Groups_Oabs__class_Oabs(U_5285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),U_5286),U_5287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5286)),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5287))
    | ~ class_Rings_Oordered__ring__abs(U_5285) ),
    inference(clausify,[status(thm)],[f_1393_2]) ).

cnf(f_1393_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5287),c_Groups_Ozero__class_Ozero(U_5285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5286))
    | hAPP(c_Groups_Oabs__class_Oabs(U_5285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),U_5286),U_5287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5286)),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5287))
    | ~ class_Rings_Oordered__ring__abs(U_5285) ),
    inference(clausify,[status(thm)],[f_1393_2]) ).

cnf(f_1393_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),c_Groups_Ozero__class_Ozero(U_5285)),U_5287))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5286),c_Groups_Ozero__class_Ozero(U_5285)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_5285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),U_5286),U_5287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5286)),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5287))
    | ~ class_Rings_Oordered__ring__abs(U_5285) ),
    inference(clausify,[status(thm)],[f_1393_2]) ).

cnf(f_1393_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5287),c_Groups_Ozero__class_Ozero(U_5285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5285),U_5286),c_Groups_Ozero__class_Ozero(U_5285)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_5285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),U_5286),U_5287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5285),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5286)),hAPP(c_Groups_Oabs__class_Oabs(U_5285),U_5287))
    | ~ class_Rings_Oordered__ring__abs(U_5285) ),
    inference(clausify,[status(thm)],[f_1393_2]) ).

fof(f_1394_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_1394_2,plain,
    ! [U_5292,U_5291,U_5290,U_5289,U_5288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),U_5289),U_5290)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),U_5291),U_5292)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),U_5289),U_5291))),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),U_5290),U_5292)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5288) ),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

cnf(f_1394_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),U_5289),U_5290)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),U_5291),U_5292)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5288),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),U_5289),U_5291))),hAPP(c_Groups_Oabs__class_Oabs(U_5288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5288),U_5290),U_5292)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5288) ),
    inference(clausify,[status(thm)],[f_1394_2]) ).

fof(f_1395_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_1395_2,plain,
    ! [U_5295,U_5294,U_5293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5293),hAPP(c_Groups_Oabs__class_Oabs(U_5293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5293),U_5294),U_5295))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5293),hAPP(c_Groups_Oabs__class_Oabs(U_5293),U_5294)),hAPP(c_Groups_Oabs__class_Oabs(U_5293),U_5295))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5293) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

cnf(f_1395_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5293),hAPP(c_Groups_Oabs__class_Oabs(U_5293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5293),U_5294),U_5295))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5293),hAPP(c_Groups_Oabs__class_Oabs(U_5293),U_5294)),hAPP(c_Groups_Oabs__class_Oabs(U_5293),U_5295))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5293) ),
    inference(clausify,[status(thm)],[f_1395_2]) ).

fof(f_1396_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_1396_2,plain,
    ! [U_5298,U_5297,U_5296] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5296),hAPP(c_Groups_Oabs__class_Oabs(U_5296),U_5298)),U_5297) = hAPP(c_Groups_Oabs__class_Oabs(U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5296),U_5298),U_5297))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5296),c_Groups_Ozero__class_Ozero(U_5296)),U_5297))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5296) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

cnf(f_1396_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5296),hAPP(c_Groups_Oabs__class_Oabs(U_5296),U_5298)),U_5297) = hAPP(c_Groups_Oabs__class_Oabs(U_5296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5296),U_5298),U_5297))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5296),c_Groups_Ozero__class_Ozero(U_5296)),U_5297))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5296) ),
    inference(clausify,[status(thm)],[f_1396_2]) ).

fof(f_1397_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_1397_2,plain,
    ! [U_5299] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5299)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_5299 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_5299 = 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_5299)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ( ! [U_5301] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5301)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_5301 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_5300] :
        ( U_5300 = 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_5300)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1397_2]) ).

cnf(f_1397_4,plain,
    ( U_5300 = 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_5300)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5301)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_5301 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

fof(f_1398_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_1398_2,plain,
    ! [U_5302] :
      ( hBOOL(hAPP(hAPP(c_member(U_5302),c_Groups_Ozero__class_Ozero(U_5302)),c_Nat_Osemiring__1__class_ONats(U_5302)))
      | ~ class_Rings_Osemiring__1(U_5302) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

cnf(f_1398_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5302),c_Groups_Ozero__class_Ozero(U_5302)),c_Nat_Osemiring__1__class_ONats(U_5302)))
    | ~ class_Rings_Osemiring__1(U_5302) ),
    inference(clausify,[status(thm)],[f_1398_2]) ).

fof(f_1399_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_1399_2,plain,
    ! [U_5305,U_5304,U_5303] :
      ( hBOOL(hAPP(hAPP(c_member(U_5303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5303),U_5304),U_5305)),c_Nat_Osemiring__1__class_ONats(U_5303)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5303),U_5305),c_Nat_Osemiring__1__class_ONats(U_5303)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5303),U_5304),c_Nat_Osemiring__1__class_ONats(U_5303)))
      | ~ class_Rings_Osemiring__1(U_5303) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

cnf(f_1399_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5303),U_5304),U_5305)),c_Nat_Osemiring__1__class_ONats(U_5303)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5303),U_5305),c_Nat_Osemiring__1__class_ONats(U_5303)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5303),U_5304),c_Nat_Osemiring__1__class_ONats(U_5303)))
    | ~ class_Rings_Osemiring__1(U_5303) ),
    inference(clausify,[status(thm)],[f_1399_2]) ).

fof(f_1400_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_1400_2,plain,
    ! [U_5308,U_5307,U_5306] :
      ( hBOOL(hAPP(hAPP(c_member(U_5306),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5306),U_5307),U_5308)),c_Nat_Osemiring__1__class_ONats(U_5306)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5306),U_5308),c_Nat_Osemiring__1__class_ONats(U_5306)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5306),U_5307),c_Nat_Osemiring__1__class_ONats(U_5306)))
      | ~ class_Rings_Osemiring__1(U_5306) ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

cnf(f_1400_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5306),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5306),U_5307),U_5308)),c_Nat_Osemiring__1__class_ONats(U_5306)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5306),U_5308),c_Nat_Osemiring__1__class_ONats(U_5306)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5306),U_5307),c_Nat_Osemiring__1__class_ONats(U_5306)))
    | ~ class_Rings_Osemiring__1(U_5306) ),
    inference(clausify,[status(thm)],[f_1400_2]) ).

fof(f_1401_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_1401_2,plain,
    ! [U_5309] :
      ( hBOOL(hAPP(hAPP(c_member(U_5309),c_Groups_Oone__class_Oone(U_5309)),c_Nat_Osemiring__1__class_ONats(U_5309)))
      | ~ class_Rings_Osemiring__1(U_5309) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

cnf(f_1401_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5309),c_Groups_Oone__class_Oone(U_5309)),c_Nat_Osemiring__1__class_ONats(U_5309)))
    | ~ class_Rings_Osemiring__1(U_5309) ),
    inference(clausify,[status(thm)],[f_1401_2]) ).

fof(f_1402_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_1402_2,plain,
    ! [U_5311,U_5310] :
      ( hBOOL(hAPP(hAPP(c_member(U_5310),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5310),U_5311)),c_Nat_Osemiring__1__class_ONats(U_5310)))
      | ~ class_Rings_Osemiring__1(U_5310) ),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

cnf(f_1402_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5310),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5310),U_5311)),c_Nat_Osemiring__1__class_ONats(U_5310)))
    | ~ class_Rings_Osemiring__1(U_5310) ),
    inference(clausify,[status(thm)],[f_1402_2]) ).

fof(f_1403_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_1403_2,plain,
    ! [U_5316,U_5315,U_5314] :
      ( ? [U_5313] :
          ( hAPP(U_5315,U_5313) = U_5316
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5313),U_5314)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
      | ? [U_5312] :
          ( ~ 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_5315,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5312),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5315,U_5312)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5312),U_5314)) ) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ! [U_5316,U_5315,U_5314] :
      ( ? [U_5313] :
          ( hAPP(U_5315,U_5313) = U_5316
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5313),U_5314)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
      | ( ~ 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_5315,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5315,sK110(U_5316,U_5315,U_5314))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),U_5314)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_5312,sK110(U_5316,U_5315,U_5314))],[f_1403_2]) ).

fof(f_1403_4,plain,
    ! [U_5316,U_5315,U_5314] :
      ( ( hAPP(U_5315,sK111(U_5316,U_5315,U_5314)) = U_5316
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5316,U_5315,U_5314)),U_5314)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
      | ( ~ 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_5315,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5315,sK110(U_5316,U_5315,U_5314))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),U_5314)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_5313,sK111(U_5316,U_5315,U_5314))],[f_1403_3]) ).

cnf(f_1403_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5316,U_5315,U_5314)),U_5314))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),U_5314)) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

cnf(f_1403_6,plain,
    ( hAPP(U_5315,sK111(U_5316,U_5315,U_5314)) = U_5316
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),U_5314)) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

cnf(f_1403_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5316,U_5315,U_5314)),U_5314))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
    | ~ 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_5315,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5315,sK110(U_5316,U_5315,U_5314))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

cnf(f_1403_8,plain,
    ( hAPP(U_5315,sK111(U_5316,U_5315,U_5314)) = U_5316
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5316),hAPP(U_5315,U_5314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5315,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5316))
    | ~ 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_5315,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK110(U_5316,U_5315,U_5314)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5315,sK110(U_5316,U_5315,U_5314))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

fof(f_1404_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_1404_2,plain,
    ! [U_5321,U_5320,U_5319] :
      ( ? [U_5318] :
          ( hAPP(U_5320,U_5318) = U_5321
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5318),U_5319)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
      | ? [U_5317] :
          ( ~ 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_5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5317),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5320,U_5317)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5317),U_5319)) ) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ! [U_5321,U_5320,U_5319] :
      ( ? [U_5318] :
          ( hAPP(U_5320,U_5318) = U_5321
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5318),U_5319)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
      | ( ~ 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_5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5320,sK112(U_5321,U_5320,U_5319))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),U_5319)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_5317,sK112(U_5321,U_5320,U_5319))],[f_1404_2]) ).

fof(f_1404_4,plain,
    ! [U_5321,U_5320,U_5319] :
      ( ( hAPP(U_5320,sK113(U_5321,U_5320,U_5319)) = U_5321
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK113(U_5321,U_5320,U_5319)),U_5319)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
      | ( ~ 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_5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5320,sK112(U_5321,U_5320,U_5319))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),U_5319)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_5318,sK113(U_5321,U_5320,U_5319))],[f_1404_3]) ).

cnf(f_1404_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK113(U_5321,U_5320,U_5319)),U_5319))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),U_5319)) ),
    inference(clausify,[status(thm)],[f_1404_4]) ).

cnf(f_1404_6,plain,
    ( hAPP(U_5320,sK113(U_5321,U_5320,U_5319)) = U_5321
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),U_5319)) ),
    inference(clausify,[status(thm)],[f_1404_4]) ).

cnf(f_1404_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK113(U_5321,U_5320,U_5319)),U_5319))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
    | ~ 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_5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5320,sK112(U_5321,U_5320,U_5319))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1404_4]) ).

cnf(f_1404_8,plain,
    ( hAPP(U_5320,sK113(U_5321,U_5320,U_5319)) = U_5321
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5321),hAPP(U_5320,U_5319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5320,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5321))
    | ~ 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_5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK112(U_5321,U_5320,U_5319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5320,sK112(U_5321,U_5320,U_5319))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1404_4]) ).

fof(f_1405_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_1405_2,plain,
    ! [U_5325,U_5324,U_5323] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5323,U_5324) = U_5325
      | ~ hBOOL(hAPP(hAPP(c_member(U_5323),U_5325),U_5324))
      | ? [U_5322] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),U_5322))
          & hBOOL(hAPP(hAPP(c_member(U_5323),U_5322),U_5324)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5323),U_5324))
      | ~ class_Orderings_Olinorder(U_5323) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ! [U_5325,U_5324,U_5323] :
      ( c_Big__Operators_Olinorder__class_OMin(U_5323,U_5324) = U_5325
      | ~ hBOOL(hAPP(hAPP(c_member(U_5323),U_5325),U_5324))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),sK114(U_5325,U_5324,U_5323)))
        & hBOOL(hAPP(hAPP(c_member(U_5323),sK114(U_5325,U_5324,U_5323)),U_5324)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5323),U_5324))
      | ~ class_Orderings_Olinorder(U_5323) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_5322,sK114(U_5325,U_5324,U_5323))],[f_1405_2]) ).

cnf(f_1405_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5323),sK114(U_5325,U_5324,U_5323)),U_5324))
    | c_Big__Operators_Olinorder__class_OMin(U_5323,U_5324) = U_5325
    | ~ hBOOL(hAPP(hAPP(c_member(U_5323),U_5325),U_5324))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5323),U_5324))
    | ~ class_Orderings_Olinorder(U_5323) ),
    inference(clausify,[status(thm)],[f_1405_3]) ).

cnf(f_1405_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),sK114(U_5325,U_5324,U_5323)))
    | c_Big__Operators_Olinorder__class_OMin(U_5323,U_5324) = U_5325
    | ~ hBOOL(hAPP(hAPP(c_member(U_5323),U_5325),U_5324))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5323),U_5324))
    | ~ class_Orderings_Olinorder(U_5323) ),
    inference(clausify,[status(thm)],[f_1405_3]) ).

fof(f_1406_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_1406_2,plain,
    ! [U_5331,U_5330,U_5329,U_5328] :
      ( ? [U_5327] :
          ( hAPP(U_5330,U_5327) = U_5331
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5327),U_5329))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),U_5327)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
      | ? [U_5326] :
          ( ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5326),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,U_5326)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5326),U_5329))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),U_5326)) ) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ! [U_5331,U_5330,U_5329,U_5328] :
      ( ? [U_5327] :
          ( hAPP(U_5330,U_5327) = U_5331
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5327),U_5329))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),U_5327)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
      | ( ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,sK115(U_5331,U_5330,U_5329,U_5328))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),U_5329))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK115(U_5331,U_5330,U_5329,U_5328))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_5326,sK115(U_5331,U_5330,U_5329,U_5328))],[f_1406_2]) ).

fof(f_1406_4,plain,
    ! [U_5331,U_5330,U_5329,U_5328] :
      ( ( hAPP(U_5330,sK116(U_5331,U_5330,U_5329,U_5328)) = U_5331
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK116(U_5331,U_5330,U_5329,U_5328)),U_5329))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK116(U_5331,U_5330,U_5329,U_5328))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
      | ( ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,sK115(U_5331,U_5330,U_5329,U_5328))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),U_5329))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK115(U_5331,U_5330,U_5329,U_5328))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_5327,sK116(U_5331,U_5330,U_5329,U_5328))],[f_1406_3]) ).

cnf(f_1406_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK116(U_5331,U_5330,U_5329,U_5328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK115(U_5331,U_5330,U_5329,U_5328))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK116(U_5331,U_5330,U_5329,U_5328)),U_5329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK115(U_5331,U_5330,U_5329,U_5328))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_7,plain,
    ( hAPP(U_5330,sK116(U_5331,U_5330,U_5329,U_5328)) = U_5331
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK115(U_5331,U_5330,U_5329,U_5328))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK116(U_5331,U_5330,U_5329,U_5328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),U_5329)) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK116(U_5331,U_5330,U_5329,U_5328)),U_5329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),U_5329)) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_10,plain,
    ( hAPP(U_5330,sK116(U_5331,U_5330,U_5329,U_5328)) = U_5331
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),U_5329)) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5328),sK116(U_5331,U_5330,U_5329,U_5328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,sK115(U_5331,U_5330,U_5329,U_5328))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK116(U_5331,U_5330,U_5329,U_5328)),U_5329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,sK115(U_5331,U_5330,U_5329,U_5328))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_13,plain,
    ( hAPP(U_5330,sK116(U_5331,U_5330,U_5329,U_5328)) = U_5331
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5331),hAPP(U_5330,U_5329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5330,U_5328)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5329))
    | ~ 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_5330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK115(U_5331,U_5330,U_5329,U_5328)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5330,sK115(U_5331,U_5330,U_5329,U_5328))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

fof(f_1407_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_1407_2,plain,
    ! [U_5333,U_5332] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5333)),U_5332) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5332),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_5332)) ),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

cnf(f_1407_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5333)),U_5332) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5332),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_5332)) ),
    inference(clausify,[status(thm)],[f_1407_2]) ).

fof(f_1408_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_Pa_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_1408_2,plain,
    ! [U_5344,U_5343,U_5342] :
      ( ( hBOOL(hAPP(U_5342,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5343,U_5344)))
        | ( ? [U_5341,U_5340] :
              ( ~ hBOOL(hAPP(U_5342,U_5340))
              & U_5343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5344),U_5341)),U_5340)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5344),U_5340)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_5339,U_5338] :
              ( ~ hBOOL(hAPP(U_5342,U_5338))
              & U_5343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5344),U_5339)),U_5338)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5338),U_5344))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5338)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5344)) )
        | ( ~ hBOOL(hAPP(U_5342,U_5343))
          & U_5344 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5342,U_5336))
                | U_5343 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5344),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5344),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5342,U_5334))
                | U_5343 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5344),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5344))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5344)) )
          & ( hBOOL(hAPP(U_5342,U_5343))
            | U_5344 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5342,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5343,U_5344))) ) ),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ( ! [U_5350,U_5348,U_5346] :
        ( hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350)))
        | ( ? [U_5341,U_5340] :
              ( ~ hBOOL(hAPP(U_5346,U_5340))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),U_5341)),U_5340)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),U_5340)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_5339,U_5338] :
              ( ~ hBOOL(hAPP(U_5346,U_5338))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),U_5339)),U_5338)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5338),U_5350))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5338)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350)) )
        | ( ~ hBOOL(hAPP(U_5346,U_5348))
          & U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_5349,U_5347,U_5345] :
        ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5345,U_5336))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5345,U_5334))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349)) )
          & ( hBOOL(hAPP(U_5345,U_5347))
            | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ) ),
    inference(miniscope,[status(thm)],[f_1408_2]) ).

fof(f_1408_4,plain,
    ( ! [U_5350,U_5348,U_5346] :
        ( hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350)))
        | ( ? [U_5341,U_5340] :
              ( ~ hBOOL(hAPP(U_5346,U_5340))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),U_5341)),U_5340)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),U_5340)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_5338] :
              ( ~ hBOOL(hAPP(U_5346,U_5338))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),U_5338)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5338),U_5350))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5338)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350)) )
        | ( ~ hBOOL(hAPP(U_5346,U_5348))
          & U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_5349,U_5347,U_5345] :
        ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5345,U_5336))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5345,U_5334))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349)) )
          & ( hBOOL(hAPP(U_5345,U_5347))
            | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_5339,sK117(U_5350,U_5348,U_5346))],[f_1408_3]) ).

fof(f_1408_5,plain,
    ( ! [U_5350,U_5348,U_5346] :
        ( hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350)))
        | ( ? [U_5341,U_5340] :
              ( ~ hBOOL(hAPP(U_5346,U_5340))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),U_5341)),U_5340)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),U_5340)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
          & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350)) )
        | ( ~ hBOOL(hAPP(U_5346,U_5348))
          & U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_5349,U_5347,U_5345] :
        ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5345,U_5336))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5345,U_5334))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349)) )
          & ( hBOOL(hAPP(U_5345,U_5347))
            | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_5338,sK118(U_5350,U_5348,U_5346))],[f_1408_4]) ).

fof(f_1408_6,plain,
    ( ! [U_5350,U_5348,U_5346] :
        ( hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350)))
        | ( ? [U_5340] :
              ( ~ hBOOL(hAPP(U_5346,U_5340))
              & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),U_5340)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5340),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),U_5340)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
          & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350)) )
        | ( ~ hBOOL(hAPP(U_5346,U_5348))
          & U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_5349,U_5347,U_5345] :
        ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5345,U_5336))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5345,U_5334))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349)) )
          & ( hBOOL(hAPP(U_5345,U_5347))
            | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_5341,sK119(U_5350,U_5348,U_5346))],[f_1408_5]) ).

fof(f_1408_7,plain,
    ( ! [U_5350,U_5348,U_5346] :
        ( hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350)))
        | ( ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
          & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
          & U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350)) )
        | ( ~ hBOOL(hAPP(U_5346,U_5348))
          & U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_5349,U_5347,U_5345] :
        ( ( ( ! [U_5337,U_5336] :
                ( hBOOL(hAPP(U_5345,U_5336))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_5335,U_5334] :
                ( hBOOL(hAPP(U_5345,U_5334))
                | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349)) )
          & ( hBOOL(hAPP(U_5345,U_5347))
            | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_5340,sK120(U_5350,U_5348,U_5346))],[f_1408_6]) ).

cnf(f_1408_8,plain,
    ( hBOOL(hAPP(U_5345,U_5347))
    | U_5349 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_9,plain,
    ( hBOOL(hAPP(U_5345,U_5334))
    | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5335)),U_5334)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5334),U_5349))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5349))
    | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_10,plain,
    ( hBOOL(hAPP(U_5345,U_5336))
    | U_5347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5349),U_5337)),U_5336)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5336),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),U_5336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5349),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_5345,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5347,U_5349))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_14,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_15,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_19,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_20,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_24,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_25,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_29,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_30,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_34,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_35,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_39,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_40,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | U_5350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_44,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_45,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5350),sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_49,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_50,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK120(U_5350,U_5348,U_5346)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_54,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_55,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK119(U_5350,U_5348,U_5346))),sK120(U_5350,U_5348,U_5346))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK118(U_5350,U_5348,U_5346)),U_5350))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_59,plain,
    ( U_5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5350),sK117(U_5350,U_5348,U_5346))),sK118(U_5350,U_5348,U_5346))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

cnf(f_1408_60,plain,
    ( ~ hBOOL(hAPP(U_5346,sK118(U_5350,U_5348,U_5346)))
    | ~ hBOOL(hAPP(U_5346,U_5348))
    | ~ hBOOL(hAPP(U_5346,sK120(U_5350,U_5348,U_5346)))
    | hBOOL(hAPP(U_5346,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5348,U_5350))) ),
    inference(clausify,[status(thm)],[f_1408_7]) ).

fof(f_1409_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_1409_2,plain,
    ! [U_5353,U_5352,U_5351] :
      ( c_Divides_Odiv__class_Omod(U_5351,c_Divides_Odiv__class_Omod(U_5351,U_5352,U_5353),U_5353) = c_Divides_Odiv__class_Omod(U_5351,U_5352,U_5353)
      | ~ class_Divides_Osemiring__div(U_5351) ),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

cnf(f_1409_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5351,c_Divides_Odiv__class_Omod(U_5351,U_5352,U_5353),U_5353) = c_Divides_Odiv__class_Omod(U_5351,U_5352,U_5353)
    | ~ class_Divides_Osemiring__div(U_5351) ),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_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_1410_2,plain,
    ! [U_5355,U_5354] :
      ( ( c_Int_OBit1(U_5354) = c_Int_OBit1(U_5355)
        | U_5354 != U_5355 )
      & ( U_5354 = U_5355
        | c_Int_OBit1(U_5354) != c_Int_OBit1(U_5355) ) ),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

fof(f_1410_3,plain,
    ( ! [U_5359,U_5357] :
        ( c_Int_OBit1(U_5357) = c_Int_OBit1(U_5359)
        | U_5357 != U_5359 )
    & ! [U_5358,U_5356] :
        ( U_5356 = U_5358
        | c_Int_OBit1(U_5356) != c_Int_OBit1(U_5358) ) ),
    inference(miniscope,[status(thm)],[f_1410_2]) ).

cnf(f_1410_4,plain,
    ( U_5356 = U_5358
    | c_Int_OBit1(U_5356) != c_Int_OBit1(U_5358) ),
    inference(clausify,[status(thm)],[f_1410_3]) ).

cnf(f_1410_5,plain,
    ( c_Int_OBit1(U_5357) = c_Int_OBit1(U_5359)
    | U_5357 != U_5359 ),
    inference(clausify,[status(thm)],[f_1410_3]) ).

fof(f_1411_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_1411_2,plain,
    ! [U_5361,U_5360] :
      ( c_Divides_Odiv__class_Omod(U_5360,c_Groups_Ozero__class_Ozero(U_5360),U_5361) = c_Groups_Ozero__class_Ozero(U_5360)
      | ~ class_Divides_Osemiring__div(U_5360) ),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

cnf(f_1411_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5360,c_Groups_Ozero__class_Ozero(U_5360),U_5361) = c_Groups_Ozero__class_Ozero(U_5360)
    | ~ class_Divides_Osemiring__div(U_5360) ),
    inference(clausify,[status(thm)],[f_1411_2]) ).

fof(f_1412_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_1412_2,plain,
    ! [U_5363,U_5362] :
      ( c_Divides_Odiv__class_Omod(U_5362,U_5363,c_Groups_Ozero__class_Ozero(U_5362)) = U_5363
      | ~ class_Divides_Osemiring__div(U_5362) ),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

cnf(f_1412_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5362,U_5363,c_Groups_Ozero__class_Ozero(U_5362)) = U_5363
    | ~ class_Divides_Osemiring__div(U_5362) ),
    inference(clausify,[status(thm)],[f_1412_2]) ).

fof(f_1413_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_1413_2,plain,
    ! [U_5365,U_5364] :
      ( c_Divides_Odiv__class_Omod(U_5364,U_5365,U_5365) = c_Groups_Ozero__class_Ozero(U_5364)
      | ~ class_Divides_Osemiring__div(U_5364) ),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

cnf(f_1413_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5364,U_5365,U_5365) = c_Groups_Ozero__class_Ozero(U_5364)
    | ~ class_Divides_Osemiring__div(U_5364) ),
    inference(clausify,[status(thm)],[f_1413_2]) ).

fof(f_1414_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_1414_2,plain,
    ! [U_5368,U_5367,U_5366] :
      ( c_Divides_Odiv__class_Omod(U_5366,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),U_5367),U_5368),U_5368) = c_Divides_Odiv__class_Omod(U_5366,U_5367,U_5368)
      | ~ class_Divides_Osemiring__div(U_5366) ),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

cnf(f_1414_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5366,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),U_5367),U_5368),U_5368) = c_Divides_Odiv__class_Omod(U_5366,U_5367,U_5368)
    | ~ class_Divides_Osemiring__div(U_5366) ),
    inference(clausify,[status(thm)],[f_1414_2]) ).

fof(f_1415_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_1415_2,plain,
    ! [U_5371,U_5370,U_5369] :
      ( c_Divides_Odiv__class_Omod(U_5369,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5369),U_5370),U_5371),U_5370) = c_Divides_Odiv__class_Omod(U_5369,U_5371,U_5370)
      | ~ class_Divides_Osemiring__div(U_5369) ),
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

cnf(f_1415_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5369,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5369),U_5370),U_5371),U_5370) = c_Divides_Odiv__class_Omod(U_5369,U_5371,U_5370)
    | ~ class_Divides_Osemiring__div(U_5369) ),
    inference(clausify,[status(thm)],[f_1415_2]) ).

fof(f_1416_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_1416_2,plain,
    ! [U_5375,U_5374,U_5373,U_5372] :
      ( c_Divides_Odiv__class_Omod(U_5372,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5372),U_5373),U_5374),U_5375) = c_Divides_Odiv__class_Omod(U_5372,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5372),U_5373),c_Divides_Odiv__class_Omod(U_5372,U_5374,U_5375)),U_5375)
      | ~ class_Divides_Osemiring__div(U_5372) ),
    inference(variable_rename,[status(thm)],[f_1416_1]) ).

cnf(f_1416_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5372,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5372),U_5373),U_5374),U_5375) = c_Divides_Odiv__class_Omod(U_5372,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5372),U_5373),c_Divides_Odiv__class_Omod(U_5372,U_5374,U_5375)),U_5375)
    | ~ class_Divides_Osemiring__div(U_5372) ),
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_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_1417_2,plain,
    ! [U_5379,U_5378,U_5377,U_5376] :
      ( c_Divides_Odiv__class_Omod(U_5376,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5376),U_5377),U_5378),U_5379) = c_Divides_Odiv__class_Omod(U_5376,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5376),c_Divides_Odiv__class_Omod(U_5376,U_5377,U_5379)),U_5378),U_5379)
      | ~ class_Divides_Osemiring__div(U_5376) ),
    inference(variable_rename,[status(thm)],[f_1417_1]) ).

cnf(f_1417_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5376,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5376),U_5377),U_5378),U_5379) = c_Divides_Odiv__class_Omod(U_5376,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5376),c_Divides_Odiv__class_Omod(U_5376,U_5377,U_5379)),U_5378),U_5379)
    | ~ class_Divides_Osemiring__div(U_5376) ),
    inference(clausify,[status(thm)],[f_1417_2]) ).

fof(f_1418_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_1418_2,plain,
    ! [U_5383,U_5382,U_5381,U_5380] :
      ( c_Divides_Odiv__class_Omod(U_5380,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5380),U_5381),U_5382),U_5383) = c_Divides_Odiv__class_Omod(U_5380,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5380),c_Divides_Odiv__class_Omod(U_5380,U_5381,U_5383)),c_Divides_Odiv__class_Omod(U_5380,U_5382,U_5383)),U_5383)
      | ~ class_Divides_Osemiring__div(U_5380) ),
    inference(variable_rename,[status(thm)],[f_1418_1]) ).

cnf(f_1418_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5380,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5380),U_5381),U_5382),U_5383) = c_Divides_Odiv__class_Omod(U_5380,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5380),c_Divides_Odiv__class_Omod(U_5380,U_5381,U_5383)),c_Divides_Odiv__class_Omod(U_5380,U_5382,U_5383)),U_5383)
    | ~ class_Divides_Osemiring__div(U_5380) ),
    inference(clausify,[status(thm)],[f_1418_2]) ).

fof(f_1419_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_1419_2,plain,
    ! [U_5387,U_5386,U_5385,U_5384] :
      ( c_Divides_Odiv__class_Omod(U_5384,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5384),U_5385),c_Divides_Odiv__class_Omod(U_5384,U_5386,U_5387)),U_5387) = c_Divides_Odiv__class_Omod(U_5384,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5384),U_5385),U_5386),U_5387)
      | ~ class_Divides_Osemiring__div(U_5384) ),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

cnf(f_1419_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5384,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5384),U_5385),c_Divides_Odiv__class_Omod(U_5384,U_5386,U_5387)),U_5387) = c_Divides_Odiv__class_Omod(U_5384,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5384),U_5385),U_5386),U_5387)
    | ~ class_Divides_Osemiring__div(U_5384) ),
    inference(clausify,[status(thm)],[f_1419_2]) ).

fof(f_1420_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_1420_2,plain,
    ! [U_5391,U_5390,U_5389,U_5388] :
      ( c_Divides_Odiv__class_Omod(U_5388,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5388),c_Divides_Odiv__class_Omod(U_5388,U_5389,U_5390)),U_5391),U_5390) = c_Divides_Odiv__class_Omod(U_5388,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5388),U_5389),U_5391),U_5390)
      | ~ class_Divides_Osemiring__div(U_5388) ),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

cnf(f_1420_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5388,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5388),c_Divides_Odiv__class_Omod(U_5388,U_5389,U_5390)),U_5391),U_5390) = c_Divides_Odiv__class_Omod(U_5388,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5388),U_5389),U_5391),U_5390)
    | ~ class_Divides_Osemiring__div(U_5388) ),
    inference(clausify,[status(thm)],[f_1420_2]) ).

fof(f_1421_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_1421_2,plain,
    ! [U_5397,U_5396,U_5395,U_5394,U_5393,U_5392] :
      ( c_Divides_Odiv__class_Omod(U_5392,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5392),U_5393),U_5396),U_5394) = c_Divides_Odiv__class_Omod(U_5392,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5392),U_5395),U_5397),U_5394)
      | c_Divides_Odiv__class_Omod(U_5392,U_5396,U_5394) != c_Divides_Odiv__class_Omod(U_5392,U_5397,U_5394)
      | c_Divides_Odiv__class_Omod(U_5392,U_5393,U_5394) != c_Divides_Odiv__class_Omod(U_5392,U_5395,U_5394)
      | ~ class_Divides_Osemiring__div(U_5392) ),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

cnf(f_1421_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5392,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5392),U_5393),U_5396),U_5394) = c_Divides_Odiv__class_Omod(U_5392,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5392),U_5395),U_5397),U_5394)
    | c_Divides_Odiv__class_Omod(U_5392,U_5396,U_5394) != c_Divides_Odiv__class_Omod(U_5392,U_5397,U_5394)
    | c_Divides_Odiv__class_Omod(U_5392,U_5393,U_5394) != c_Divides_Odiv__class_Omod(U_5392,U_5395,U_5394)
    | ~ class_Divides_Osemiring__div(U_5392) ),
    inference(clausify,[status(thm)],[f_1421_2]) ).

fof(f_1422_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_1422_2,plain,
    ! [U_5403,U_5402,U_5401,U_5400,U_5399,U_5398] :
      ( c_Divides_Odiv__class_Omod(U_5398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5398),U_5399),U_5402),U_5400) = c_Divides_Odiv__class_Omod(U_5398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5398),U_5401),U_5403),U_5400)
      | c_Divides_Odiv__class_Omod(U_5398,U_5402,U_5400) != c_Divides_Odiv__class_Omod(U_5398,U_5403,U_5400)
      | c_Divides_Odiv__class_Omod(U_5398,U_5399,U_5400) != c_Divides_Odiv__class_Omod(U_5398,U_5401,U_5400)
      | ~ class_Divides_Osemiring__div(U_5398) ),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

cnf(f_1422_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5398),U_5399),U_5402),U_5400) = c_Divides_Odiv__class_Omod(U_5398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5398),U_5401),U_5403),U_5400)
    | c_Divides_Odiv__class_Omod(U_5398,U_5402,U_5400) != c_Divides_Odiv__class_Omod(U_5398,U_5403,U_5400)
    | c_Divides_Odiv__class_Omod(U_5398,U_5399,U_5400) != c_Divides_Odiv__class_Omod(U_5398,U_5401,U_5400)
    | ~ class_Divides_Osemiring__div(U_5398) ),
    inference(clausify,[status(thm)],[f_1422_2]) ).

fof(f_1423_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_1423_2,plain,
    ! [U_5407,U_5406,U_5405,U_5404] :
      ( c_Divides_Odiv__class_Omod(U_5404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5404),c_Divides_Odiv__class_Omod(U_5404,U_5405,U_5406)),U_5407),U_5406) = c_Divides_Odiv__class_Omod(U_5404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5404),U_5405),U_5407),U_5406)
      | ~ class_Divides_Osemiring__div(U_5404) ),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

cnf(f_1423_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5404),c_Divides_Odiv__class_Omod(U_5404,U_5405,U_5406)),U_5407),U_5406) = c_Divides_Odiv__class_Omod(U_5404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5404),U_5405),U_5407),U_5406)
    | ~ class_Divides_Osemiring__div(U_5404) ),
    inference(clausify,[status(thm)],[f_1423_2]) ).

fof(f_1424_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_1424_2,plain,
    ! [U_5411,U_5410,U_5409,U_5408] :
      ( c_Divides_Odiv__class_Omod(U_5408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),U_5409),U_5410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),U_5411),U_5410)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),c_Divides_Odiv__class_Omod(U_5408,U_5409,U_5411)),U_5410)
      | ~ class_Divides_Osemiring__div(U_5408) ),
    inference(variable_rename,[status(thm)],[f_1424_1]) ).

cnf(f_1424_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),U_5409),U_5410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),U_5411),U_5410)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5408),c_Divides_Odiv__class_Omod(U_5408,U_5409,U_5411)),U_5410)
    | ~ class_Divides_Osemiring__div(U_5408) ),
    inference(clausify,[status(thm)],[f_1424_2]) ).

fof(f_1425_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_1425_2,plain,
    ! [U_5415,U_5414,U_5413,U_5412] :
      ( c_Divides_Odiv__class_Omod(U_5412,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),U_5415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),c_Divides_Odiv__class_Omod(U_5412,U_5414,U_5415))
      | ~ class_Divides_Osemiring__div(U_5412) ),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

cnf(f_1425_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5412,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),U_5415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5412),U_5413),c_Divides_Odiv__class_Omod(U_5412,U_5414,U_5415))
    | ~ class_Divides_Osemiring__div(U_5412) ),
    inference(clausify,[status(thm)],[f_1425_2]) ).

fof(f_1426_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_1426_2,plain,
    ! [U_5419,U_5418,U_5417,U_5416] :
      ( c_Divides_Odiv__class_Omod(U_5416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5416),U_5417),U_5418),U_5419) = c_Divides_Odiv__class_Omod(U_5416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5416),c_Divides_Odiv__class_Omod(U_5416,U_5417,U_5419)),c_Divides_Odiv__class_Omod(U_5416,U_5418,U_5419)),U_5419)
      | ~ class_Divides_Osemiring__div(U_5416) ),
    inference(variable_rename,[status(thm)],[f_1426_1]) ).

cnf(f_1426_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5416),U_5417),U_5418),U_5419) = c_Divides_Odiv__class_Omod(U_5416,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5416),c_Divides_Odiv__class_Omod(U_5416,U_5417,U_5419)),c_Divides_Odiv__class_Omod(U_5416,U_5418,U_5419)),U_5419)
    | ~ class_Divides_Osemiring__div(U_5416) ),
    inference(clausify,[status(thm)],[f_1426_2]) ).

fof(f_1427_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_1427_2,plain,
    ! [U_5423,U_5422,U_5421,U_5420] :
      ( c_Divides_Odiv__class_Omod(U_5420,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5420),U_5421),U_5422),U_5423) = c_Divides_Odiv__class_Omod(U_5420,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5420),c_Divides_Odiv__class_Omod(U_5420,U_5421,U_5423)),U_5422),U_5423)
      | ~ class_Divides_Osemiring__div(U_5420) ),
    inference(variable_rename,[status(thm)],[f_1427_1]) ).

cnf(f_1427_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5420,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5420),U_5421),U_5422),U_5423) = c_Divides_Odiv__class_Omod(U_5420,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5420),c_Divides_Odiv__class_Omod(U_5420,U_5421,U_5423)),U_5422),U_5423)
    | ~ class_Divides_Osemiring__div(U_5420) ),
    inference(clausify,[status(thm)],[f_1427_2]) ).

fof(f_1428_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_1428_2,plain,
    ! [U_5427,U_5426,U_5425,U_5424] :
      ( c_Divides_Odiv__class_Omod(U_5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5424),U_5425),U_5426),U_5427) = c_Divides_Odiv__class_Omod(U_5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5424),U_5425),c_Divides_Odiv__class_Omod(U_5424,U_5426,U_5427)),U_5427)
      | ~ class_Divides_Osemiring__div(U_5424) ),
    inference(variable_rename,[status(thm)],[f_1428_1]) ).

cnf(f_1428_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5424),U_5425),U_5426),U_5427) = c_Divides_Odiv__class_Omod(U_5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5424),U_5425),c_Divides_Odiv__class_Omod(U_5424,U_5426,U_5427)),U_5427)
    | ~ class_Divides_Osemiring__div(U_5424) ),
    inference(clausify,[status(thm)],[f_1428_2]) ).

fof(f_1429_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_1429_2,plain,
    ! [U_5431,U_5430,U_5429,U_5428] :
      ( c_Divides_Odiv__class_Omod(U_5428,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5428),U_5429),U_5430),U_5431) = c_Divides_Odiv__class_Omod(U_5428,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5428),U_5429),c_Divides_Odiv__class_Omod(U_5428,U_5430,U_5431)),U_5431)
      | ~ class_Divides_Oring__div(U_5428) ),
    inference(variable_rename,[status(thm)],[f_1429_1]) ).

cnf(f_1429_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5428,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5428),U_5429),U_5430),U_5431) = c_Divides_Odiv__class_Omod(U_5428,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5428),U_5429),c_Divides_Odiv__class_Omod(U_5428,U_5430,U_5431)),U_5431)
    | ~ class_Divides_Oring__div(U_5428) ),
    inference(clausify,[status(thm)],[f_1429_2]) ).

fof(f_1430_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_1430_2,plain,
    ! [U_5435,U_5434,U_5433,U_5432] :
      ( c_Divides_Odiv__class_Omod(U_5432,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5432),U_5433),U_5434),U_5435) = c_Divides_Odiv__class_Omod(U_5432,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5432),c_Divides_Odiv__class_Omod(U_5432,U_5433,U_5435)),U_5434),U_5435)
      | ~ class_Divides_Oring__div(U_5432) ),
    inference(variable_rename,[status(thm)],[f_1430_1]) ).

cnf(f_1430_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5432,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5432),U_5433),U_5434),U_5435) = c_Divides_Odiv__class_Omod(U_5432,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5432),c_Divides_Odiv__class_Omod(U_5432,U_5433,U_5435)),U_5434),U_5435)
    | ~ class_Divides_Oring__div(U_5432) ),
    inference(clausify,[status(thm)],[f_1430_2]) ).

fof(f_1431_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_1431_2,plain,
    ! [U_5439,U_5438,U_5437,U_5436] :
      ( c_Divides_Odiv__class_Omod(U_5436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5436),U_5437),U_5438),U_5439) = c_Divides_Odiv__class_Omod(U_5436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5436),c_Divides_Odiv__class_Omod(U_5436,U_5437,U_5439)),c_Divides_Odiv__class_Omod(U_5436,U_5438,U_5439)),U_5439)
      | ~ class_Divides_Oring__div(U_5436) ),
    inference(variable_rename,[status(thm)],[f_1431_1]) ).

cnf(f_1431_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5436),U_5437),U_5438),U_5439) = c_Divides_Odiv__class_Omod(U_5436,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5436),c_Divides_Odiv__class_Omod(U_5436,U_5437,U_5439)),c_Divides_Odiv__class_Omod(U_5436,U_5438,U_5439)),U_5439)
    | ~ class_Divides_Oring__div(U_5436) ),
    inference(clausify,[status(thm)],[f_1431_2]) ).

fof(f_1432_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_1432_2,plain,
    ! [U_5445,U_5444,U_5443,U_5442,U_5441,U_5440] :
      ( c_Divides_Odiv__class_Omod(U_5440,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5440),U_5441),U_5444),U_5442) = c_Divides_Odiv__class_Omod(U_5440,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5440),U_5443),U_5445),U_5442)
      | c_Divides_Odiv__class_Omod(U_5440,U_5444,U_5442) != c_Divides_Odiv__class_Omod(U_5440,U_5445,U_5442)
      | c_Divides_Odiv__class_Omod(U_5440,U_5441,U_5442) != c_Divides_Odiv__class_Omod(U_5440,U_5443,U_5442)
      | ~ class_Divides_Oring__div(U_5440) ),
    inference(variable_rename,[status(thm)],[f_1432_1]) ).

cnf(f_1432_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5440,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5440),U_5441),U_5444),U_5442) = c_Divides_Odiv__class_Omod(U_5440,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5440),U_5443),U_5445),U_5442)
    | c_Divides_Odiv__class_Omod(U_5440,U_5444,U_5442) != c_Divides_Odiv__class_Omod(U_5440,U_5445,U_5442)
    | c_Divides_Odiv__class_Omod(U_5440,U_5441,U_5442) != c_Divides_Odiv__class_Omod(U_5440,U_5443,U_5442)
    | ~ class_Divides_Oring__div(U_5440) ),
    inference(clausify,[status(thm)],[f_1432_2]) ).

fof(f_1433_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_1433_2,plain,
    ! [U_5446] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5446) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1433_1]) ).

cnf(f_1433_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5446) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1433_2]) ).

fof(f_1434_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_1434_2,plain,
    ! [U_5447] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5447,U_5447) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1434_1]) ).

cnf(f_1434_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5447,U_5447) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1434_2]) ).

fof(f_1435_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_1435_2,plain,
    ! [U_5449,U_5448] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5448)),c_Int_OBit1(U_5449)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5448),U_5449)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5448),U_5449))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5448)),c_Int_OBit1(U_5449))) ) ),
    inference(variable_rename,[status(thm)],[f_1435_1]) ).

fof(f_1435_3,plain,
    ( ! [U_5453,U_5451] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5451)),c_Int_OBit1(U_5453)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5451),U_5453)) )
    & ! [U_5452,U_5450] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5450),U_5452))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5450)),c_Int_OBit1(U_5452))) ) ),
    inference(miniscope,[status(thm)],[f_1435_2]) ).

cnf(f_1435_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5450),U_5452))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5450)),c_Int_OBit1(U_5452))) ),
    inference(clausify,[status(thm)],[f_1435_3]) ).

cnf(f_1435_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5451)),c_Int_OBit1(U_5453)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5451),U_5453)) ),
    inference(clausify,[status(thm)],[f_1435_3]) ).

fof(f_1436_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_1436_2,plain,
    ! [U_5455,U_5454] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5454)),c_Int_OBit1(U_5455)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5454),U_5455)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5454),U_5455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5454)),c_Int_OBit1(U_5455))) ) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

fof(f_1436_3,plain,
    ( ! [U_5459,U_5457] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5457)),c_Int_OBit1(U_5459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5457),U_5459)) )
    & ! [U_5458,U_5456] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5456),U_5458))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5456)),c_Int_OBit1(U_5458))) ) ),
    inference(miniscope,[status(thm)],[f_1436_2]) ).

cnf(f_1436_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5456),U_5458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5456)),c_Int_OBit1(U_5458))) ),
    inference(clausify,[status(thm)],[f_1436_3]) ).

cnf(f_1436_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5457)),c_Int_OBit1(U_5459)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5457),U_5459)) ),
    inference(clausify,[status(thm)],[f_1436_3]) ).

fof(f_1437_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_1437_2,plain,
    ! [U_5461,U_5460] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5460)),c_Int_OBit1(U_5461)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5460),U_5461)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5460),U_5461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5460)),c_Int_OBit1(U_5461))) ) ),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

fof(f_1437_3,plain,
    ( ! [U_5465,U_5463] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5463)),c_Int_OBit1(U_5465)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5463),U_5465)) )
    & ! [U_5464,U_5462] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5462),U_5464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5462)),c_Int_OBit1(U_5464))) ) ),
    inference(miniscope,[status(thm)],[f_1437_2]) ).

cnf(f_1437_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5462),U_5464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5462)),c_Int_OBit1(U_5464))) ),
    inference(clausify,[status(thm)],[f_1437_3]) ).

cnf(f_1437_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5463)),c_Int_OBit1(U_5465)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5463),U_5465)) ),
    inference(clausify,[status(thm)],[f_1437_3]) ).

fof(f_1438_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_1438_2,plain,
    ! [U_5467,U_5466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5466)),c_Int_OBit1(U_5467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5466),U_5467)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5466),U_5467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5466)),c_Int_OBit1(U_5467))) ) ),
    inference(variable_rename,[status(thm)],[f_1438_1]) ).

fof(f_1438_3,plain,
    ( ! [U_5471,U_5469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5469)),c_Int_OBit1(U_5471)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),U_5471)) )
    & ! [U_5470,U_5468] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5468),U_5470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5468)),c_Int_OBit1(U_5470))) ) ),
    inference(miniscope,[status(thm)],[f_1438_2]) ).

cnf(f_1438_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5468),U_5470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5468)),c_Int_OBit1(U_5470))) ),
    inference(clausify,[status(thm)],[f_1438_3]) ).

cnf(f_1438_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5469)),c_Int_OBit1(U_5471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),U_5471)) ),
    inference(clausify,[status(thm)],[f_1438_3]) ).

fof(f_1439_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_1439_2,plain,
    ! [U_5472] : c_Int_OBit1(U_5472) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1439_1]) ).

cnf(f_1439_3,plain,
    c_Int_OBit1(U_5472) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1439_2]) ).

fof(f_1440_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_1440_2,plain,
    ! [U_5473] : c_Int_OPls != c_Int_OBit1(U_5473),
    inference(variable_rename,[status(thm)],[f_1440_1]) ).

cnf(f_1440_3,plain,
    c_Int_OPls != c_Int_OBit1(U_5473),
    inference(clausify,[status(thm)],[f_1440_2]) ).

fof(f_1441_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_1441_2,plain,
    ! [U_5476,U_5475,U_5474] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5474),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5475,U_5476)),U_5476) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5474),U_5475),U_5476),
    inference(variable_rename,[status(thm)],[f_1441_1]) ).

cnf(f_1441_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5474),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5475,U_5476)),U_5476) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5474),U_5475),U_5476),
    inference(clausify,[status(thm)],[f_1441_2]) ).

fof(f_1442_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_1442_2,plain,
    ! [U_5479,U_5478,U_5477] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5477),U_5478),U_5479) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5477),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5478,U_5479)),U_5479),
    inference(variable_rename,[status(thm)],[f_1442_1]) ).

cnf(f_1442_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5477),U_5478),U_5479) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5477),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5478,U_5479)),U_5479),
    inference(clausify,[status(thm)],[f_1442_2]) ).

fof(f_1443_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_1443_2,plain,
    ! [U_5482,U_5481,U_5480] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5480),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5481,U_5482)),U_5482) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5480),U_5481),U_5482),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

cnf(f_1443_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5480),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5481,U_5482)),U_5482) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5480),U_5481),U_5482),
    inference(clausify,[status(thm)],[f_1443_2]) ).

fof(f_1444_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_1444_2,plain,
    ! [U_5485,U_5484,U_5483] : 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_5483,U_5484)),U_5485),U_5484) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5483),U_5485),U_5484),
    inference(variable_rename,[status(thm)],[f_1444_1]) ).

cnf(f_1444_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_5483,U_5484)),U_5485),U_5484) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5483),U_5485),U_5484),
    inference(clausify,[status(thm)],[f_1444_2]) ).

fof(f_1445_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_1445_2,plain,
    ! [U_5488,U_5487,U_5486] :
      ( c_Divides_Odiv__class_Omod(U_5486,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5486),U_5487),U_5488),U_5488) = c_Groups_Ozero__class_Ozero(U_5486)
      | ~ class_Divides_Osemiring__div(U_5486) ),
    inference(variable_rename,[status(thm)],[f_1445_1]) ).

cnf(f_1445_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5486,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5486),U_5487),U_5488),U_5488) = c_Groups_Ozero__class_Ozero(U_5486)
    | ~ class_Divides_Osemiring__div(U_5486) ),
    inference(clausify,[status(thm)],[f_1445_2]) ).

fof(f_1446_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_1446_2,plain,
    ! [U_5491,U_5490,U_5489] :
      ( c_Divides_Odiv__class_Omod(U_5489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5489),U_5490),U_5491),U_5490) = c_Groups_Ozero__class_Ozero(U_5489)
      | ~ class_Divides_Osemiring__div(U_5489) ),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

cnf(f_1446_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5489),U_5490),U_5491),U_5490) = c_Groups_Ozero__class_Ozero(U_5489)
    | ~ class_Divides_Osemiring__div(U_5489) ),
    inference(clausify,[status(thm)],[f_1446_2]) ).

fof(f_1447_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_1447_2,plain,
    ! [U_5495,U_5494,U_5493,U_5492] :
      ( c_Divides_Odiv__class_Omod(U_5492,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5492),U_5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5492),U_5494),U_5495)),U_5495) = c_Divides_Odiv__class_Omod(U_5492,U_5493,U_5495)
      | ~ class_Divides_Osemiring__div(U_5492) ),
    inference(variable_rename,[status(thm)],[f_1447_1]) ).

cnf(f_1447_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5492,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5492),U_5493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5492),U_5494),U_5495)),U_5495) = c_Divides_Odiv__class_Omod(U_5492,U_5493,U_5495)
    | ~ class_Divides_Osemiring__div(U_5492) ),
    inference(clausify,[status(thm)],[f_1447_2]) ).

fof(f_1448_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_1448_2,plain,
    ! [U_5499,U_5498,U_5497,U_5496] :
      ( c_Divides_Odiv__class_Omod(U_5496,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5496),U_5497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5496),U_5498),U_5499)),U_5498) = c_Divides_Odiv__class_Omod(U_5496,U_5497,U_5498)
      | ~ class_Divides_Osemiring__div(U_5496) ),
    inference(variable_rename,[status(thm)],[f_1448_1]) ).

cnf(f_1448_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5496,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5496),U_5497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5496),U_5498),U_5499)),U_5498) = c_Divides_Odiv__class_Omod(U_5496,U_5497,U_5498)
    | ~ class_Divides_Osemiring__div(U_5496) ),
    inference(clausify,[status(thm)],[f_1448_2]) ).

fof(f_1449_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_1449_2,plain,
    ! [U_5501,U_5500] :
      ( c_Divides_Odiv__class_Omod(U_5500,U_5501,c_Groups_Oone__class_Oone(U_5500)) = c_Groups_Ozero__class_Ozero(U_5500)
      | ~ class_Divides_Osemiring__div(U_5500) ),
    inference(variable_rename,[status(thm)],[f_1449_1]) ).

cnf(f_1449_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5500,U_5501,c_Groups_Oone__class_Oone(U_5500)) = c_Groups_Ozero__class_Ozero(U_5500)
    | ~ class_Divides_Osemiring__div(U_5500) ),
    inference(clausify,[status(thm)],[f_1449_2]) ).

fof(f_1450_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_1450_2,plain,
    ! [U_5503,U_5502] :
      ( 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_5502,U_5503)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5502)) ),
    inference(variable_rename,[status(thm)],[f_1450_1]) ).

cnf(f_1450_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_5502,U_5503)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5503))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5502)) ),
    inference(clausify,[status(thm)],[f_1450_2]) ).

fof(f_1451_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_1451_2,plain,
    ! [U_5505,U_5504] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5504,U_5505)),U_5504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5504)) ),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

cnf(f_1451_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5504,U_5505)),U_5504))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5504)) ),
    inference(clausify,[status(thm)],[f_1451_2]) ).

fof(f_1452_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_1452_2,plain,
    ! [U_5507,U_5506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5507,U_5506)),U_5506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506)) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

cnf(f_1452_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5507,U_5506)),U_5506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5506)) ),
    inference(clausify,[status(thm)],[f_1452_2]) ).

fof(f_1453_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_1453_2,plain,
    ! [U_5509,U_5508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5508),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5509,U_5508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5508),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

cnf(f_1453_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5508),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5509,U_5508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5508),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1453_2]) ).

fof(f_1454_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_1454_2,plain,
    ! [U_5510] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5510)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5510),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5510),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5510)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

fof(f_1454_3,plain,
    ( ! [U_5512] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5512)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5512),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5511] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5511)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1454_2]) ).

cnf(f_1454_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5511)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1454_3]) ).

cnf(f_1454_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5512)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5512),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1454_3]) ).

fof(f_1455_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_1455_2,plain,
    ! [U_5516,U_5515] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5515,U_5516) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_5514] : U_5515 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5516),U_5514) )
      & ( ? [U_5513] : U_5515 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5516),U_5513)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5515,U_5516) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

fof(f_1455_3,plain,
    ( ! [U_5520,U_5518] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5518,U_5520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_5514] : U_5518 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5520),U_5514) )
    & ! [U_5519,U_5517] :
        ( ? [U_5513] : U_5517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5519),U_5513)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5517,U_5519) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1455_2]) ).

fof(f_1455_4,plain,
    ( ! [U_5520,U_5518] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5518,U_5520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_5514] : U_5518 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5520),U_5514) )
    & ! [U_5519,U_5517] :
        ( U_5517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5519),sK121(U_5519,U_5517))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5517,U_5519) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_5513,sK121(U_5519,U_5517))],[f_1455_3]) ).

cnf(f_1455_5,plain,
    ( U_5517 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5519),sK121(U_5519,U_5517))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5517,U_5519) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1455_4]) ).

cnf(f_1455_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5518,U_5520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5518 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5520),U_5514) ),
    inference(clausify,[status(thm)],[f_1455_4]) ).

fof(f_1456_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_1456_2,plain,
    ! [U_5521] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5521)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5521)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5521))) ) ),
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

fof(f_1456_3,plain,
    ( ! [U_5523] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5523)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5523)) )
    & ! [U_5522] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5522))) ) ),
    inference(miniscope,[status(thm)],[f_1456_2]) ).

cnf(f_1456_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5522))) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

cnf(f_1456_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5523)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5523)) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

fof(f_1457_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_1457_2,plain,
    ! [U_5524] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5524)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5524),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5524),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5524)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

fof(f_1457_3,plain,
    ( ! [U_5526] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5526)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5526),c_Int_OPls)) )
    & ! [U_5525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5525),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5525)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1457_2]) ).

cnf(f_1457_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5525),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5525)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

cnf(f_1457_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5526)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5526),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

fof(f_1458_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_1458_2,plain,
    ! [U_5527] : c_Int_OBit1(U_5527) = 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_5527)),U_5527),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

cnf(f_1458_3,plain,
    c_Int_OBit1(U_5527) = 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_5527)),U_5527),
    inference(clausify,[status(thm)],[f_1458_2]) ).

fof(f_1459_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_1459_2,plain,
    ! [U_5528] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5528))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5528))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5528)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5528)))) ) ),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

fof(f_1459_3,plain,
    ( ! [U_5530] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5530))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5530))) )
    & ! [U_5529] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5529)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5529)))) ) ),
    inference(miniscope,[status(thm)],[f_1459_2]) ).

cnf(f_1459_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5529)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5529)))) ),
    inference(clausify,[status(thm)],[f_1459_3]) ).

cnf(f_1459_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5530))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5530))) ),
    inference(clausify,[status(thm)],[f_1459_3]) ).

fof(f_1460_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

cnf(f_1460_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_1460_1]) ).

fof(f_1461_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_1461_2,plain,
    ! [U_5532,U_5531] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5531),c_Int_OBit1(U_5532)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5531),c_Groups_Oone__class_Oone(U_5531)),hAPP(c_Int_Onumber__class_Onumber__of(U_5531),U_5532))),hAPP(c_Int_Onumber__class_Onumber__of(U_5531),U_5532))
      | ~ class_Int_Onumber__ring(U_5531) ),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

cnf(f_1461_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5531),c_Int_OBit1(U_5532)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5531),c_Groups_Oone__class_Oone(U_5531)),hAPP(c_Int_Onumber__class_Onumber__of(U_5531),U_5532))),hAPP(c_Int_Onumber__class_Onumber__of(U_5531),U_5532))
    | ~ class_Int_Onumber__ring(U_5531) ),
    inference(clausify,[status(thm)],[f_1461_2]) ).

fof(f_1462_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_1462_2,plain,
    ! [U_5534,U_5533] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5533),hAPP(c_Int_Onumber__class_Onumber__of(U_5533),c_Int_OBit1(c_Int_OPls))),U_5534) = U_5534
      | ~ class_Int_Onumber__ring(U_5533) ),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

cnf(f_1462_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5533),hAPP(c_Int_Onumber__class_Onumber__of(U_5533),c_Int_OBit1(c_Int_OPls))),U_5534) = U_5534
    | ~ class_Int_Onumber__ring(U_5533) ),
    inference(clausify,[status(thm)],[f_1462_2]) ).

fof(f_1463_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_1463_2,plain,
    ! [U_5536,U_5535] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5535),U_5536),hAPP(c_Int_Onumber__class_Onumber__of(U_5535),c_Int_OBit1(c_Int_OPls))) = U_5536
      | ~ class_Int_Onumber__ring(U_5535) ),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

cnf(f_1463_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5535),U_5536),hAPP(c_Int_Onumber__class_Onumber__of(U_5535),c_Int_OBit1(c_Int_OPls))) = U_5536
    | ~ class_Int_Onumber__ring(U_5535) ),
    inference(clausify,[status(thm)],[f_1463_2]) ).

fof(f_1464_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_1464_2,plain,
    ! [U_5538,U_5537] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5537,U_5538) = U_5537
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5538),U_5537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5537),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

cnf(f_1464_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5537,U_5538) = U_5537
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5538),U_5537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5537),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1464_2]) ).

fof(f_1465_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_1465_2,plain,
    ! [U_5540,U_5539] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5539),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5539)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5539)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5539),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

cnf(f_1465_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5539)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5539),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1465_2]) ).

cnf(f_1465_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5539),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5540,U_5539)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5539),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1465_2]) ).

fof(f_1466_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_1466_2,plain,
    ! [U_5542,U_5541] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5542,U_5541)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5541),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

cnf(f_1466_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5542,U_5541)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5541),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1466_2]) ).

fof(f_1467_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_1467_2,plain,
    ! [U_5544,U_5543] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5543,U_5544) = U_5543
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5543),U_5544))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5543)) ),
    inference(variable_rename,[status(thm)],[f_1467_1]) ).

cnf(f_1467_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5543,U_5544) = U_5543
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5543),U_5544))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5543)) ),
    inference(clausify,[status(thm)],[f_1467_2]) ).

fof(f_1468_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_1468_2,plain,
    ! [U_5546,U_5545] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5546,U_5545)),U_5545))
        & 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_5546,U_5545))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5545)) ),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

cnf(f_1468_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_5546,U_5545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5545)) ),
    inference(clausify,[status(thm)],[f_1468_2]) ).

cnf(f_1468_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5546,U_5545)),U_5545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5545)) ),
    inference(clausify,[status(thm)],[f_1468_2]) ).

fof(f_1469_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_1469_2,plain,
    ! [U_5548,U_5547] :
      ( 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_5548,U_5547)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5547)) ),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

cnf(f_1469_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_5548,U_5547)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5547)) ),
    inference(clausify,[status(thm)],[f_1469_2]) ).

fof(f_1470_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_1470_2,plain,
    ! [U_5549] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5549),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5549)
      | ~ class_Int_Onumber__ring(U_5549) ),
    inference(variable_rename,[status(thm)],[f_1470_1]) ).

cnf(f_1470_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5549),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5549)
    | ~ class_Int_Onumber__ring(U_5549) ),
    inference(clausify,[status(thm)],[f_1470_2]) ).

fof(f_1471_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_1471_2,plain,
    ! [U_5550] :
      ( c_Groups_Oone__class_Oone(U_5550) = hAPP(c_Int_Onumber__class_Onumber__of(U_5550),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_5550) ),
    inference(variable_rename,[status(thm)],[f_1471_1]) ).

cnf(f_1471_3,plain,
    ( c_Groups_Oone__class_Oone(U_5550) = hAPP(c_Int_Onumber__class_Onumber__of(U_5550),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_5550) ),
    inference(clausify,[status(thm)],[f_1471_2]) ).

fof(f_1472_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_1472_2,plain,
    ! [U_5551] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5551)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5551)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5551))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5551))) ) ),
    inference(variable_rename,[status(thm)],[f_1472_1]) ).

fof(f_1472_3,plain,
    ( ! [U_5553] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5553)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5553)) )
    & ! [U_5552] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5552))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5552))) ) ),
    inference(miniscope,[status(thm)],[f_1472_2]) ).

cnf(f_1472_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5552))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5552))) ),
    inference(clausify,[status(thm)],[f_1472_3]) ).

cnf(f_1472_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5553)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5553)) ),
    inference(clausify,[status(thm)],[f_1472_3]) ).

fof(f_1473_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_1473_2,plain,
    ! [U_5554] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5554)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5554),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5554),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5554)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

fof(f_1473_3,plain,
    ( ! [U_5556] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5556)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5556),c_Int_OPls)) )
    & ! [U_5555] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5555),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5555)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1473_2]) ).

cnf(f_1473_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5555),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5555)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

cnf(f_1473_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5556)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5556),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1473_3]) ).

fof(f_1474_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_1474_2,plain,
    ! [U_5558,U_5557] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5558),hAPP(c_Int_Onumber__class_Onumber__of(U_5557),c_Int_OBit1(c_Int_OPls))) = U_5558
      | ~ class_Int_Onumber__ring(U_5557)
      | ~ class_Fields_Ofield(U_5557) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

cnf(f_1474_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5558),hAPP(c_Int_Onumber__class_Onumber__of(U_5557),c_Int_OBit1(c_Int_OPls))) = U_5558
    | ~ class_Int_Onumber__ring(U_5557)
    | ~ class_Fields_Ofield(U_5557) ),
    inference(clausify,[status(thm)],[f_1474_2]) ).

fof(f_1475_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_1475_2,plain,
    ! [U_5560,U_5559] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5559),U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5559),c_Int_OBit1(c_Int_OPls))) = U_5560
      | ~ class_Int_Onumber__ring(U_5559)
      | ~ class_Fields_Ofield(U_5559) ),
    inference(variable_rename,[status(thm)],[f_1475_1]) ).

cnf(f_1475_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5559),U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5559),c_Int_OBit1(c_Int_OPls))) = U_5560
    | ~ class_Int_Onumber__ring(U_5559)
    | ~ class_Fields_Ofield(U_5559) ),
    inference(clausify,[status(thm)],[f_1475_2]) ).

fof(f_1476_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_1476_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_1476_1]) ).

fof(f_1477_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_1477_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_1477_1]) ).

fof(f_1478_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_1478_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_1478_1]) ).

fof(f_1479_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_1479_2,plain,
    ! [U_5562,U_5561] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5561,U_5562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5561),U_5562)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5561),U_5562)),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_5561)) ),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

cnf(f_1479_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5561,U_5562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5561),U_5562)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5561),U_5562)),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_5561)) ),
    inference(clausify,[status(thm)],[f_1479_2]) ).

fof(f_1480_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_1480_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_1480_1]) ).

fof(f_1481_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_1481_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_1481_1]) ).

fof(f_1482_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_1482_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_1482_1]) ).

fof(f_1483_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_1483_2,plain,
    ! [U_5563] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5563))) = 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_5563),
    inference(variable_rename,[status(thm)],[f_1483_1]) ).

cnf(f_1483_3,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5563))) = 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_5563),
    inference(clausify,[status(thm)],[f_1483_2]) ).

fof(f_1484_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_1484_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_1484_1]) ).

fof(f_1485_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_1485_2,plain,
    ! [U_5565,U_5564] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),c_Groups_Oone__class_Oone(U_5564)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5565),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5565),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),c_Groups_Oone__class_Oone(U_5564))) ) )
      | ~ class_Rings_Olinordered__idom(U_5564)
      | ~ class_Int_Onumber__ring(U_5564) ),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

cnf(f_1485_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5565),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),c_Groups_Oone__class_Oone(U_5564)))
    | ~ class_Rings_Olinordered__idom(U_5564)
    | ~ class_Int_Onumber__ring(U_5564) ),
    inference(clausify,[status(thm)],[f_1485_2]) ).

cnf(f_1485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),c_Groups_Oone__class_Oone(U_5564)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5565),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_5564)
    | ~ class_Int_Onumber__ring(U_5564) ),
    inference(clausify,[status(thm)],[f_1485_2]) ).

fof(f_1486_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_1486_2,plain,
    ! [U_5567,U_5566] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5566),c_Groups_Oone__class_Oone(U_5566)),hAPP(c_Int_Onumber__class_Onumber__of(U_5566),U_5567)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5567)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5567))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5566),c_Groups_Oone__class_Oone(U_5566)),hAPP(c_Int_Onumber__class_Onumber__of(U_5566),U_5567))) ) )
      | ~ class_Rings_Olinordered__idom(U_5566)
      | ~ class_Int_Onumber__ring(U_5566) ),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

cnf(f_1486_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5567))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5566),c_Groups_Oone__class_Oone(U_5566)),hAPP(c_Int_Onumber__class_Onumber__of(U_5566),U_5567)))
    | ~ class_Rings_Olinordered__idom(U_5566)
    | ~ class_Int_Onumber__ring(U_5566) ),
    inference(clausify,[status(thm)],[f_1486_2]) ).

cnf(f_1486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5566),c_Groups_Oone__class_Oone(U_5566)),hAPP(c_Int_Onumber__class_Onumber__of(U_5566),U_5567)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5567))
    | ~ class_Rings_Olinordered__idom(U_5566)
    | ~ class_Int_Onumber__ring(U_5566) ),
    inference(clausify,[status(thm)],[f_1486_2]) ).

fof(f_1487_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_1487_2,plain,
    ! [U_5569,U_5568] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5568),c_Groups_Oone__class_Oone(U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5568),U_5569)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5569)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5569))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5568),c_Groups_Oone__class_Oone(U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5568),U_5569))) ) )
      | ~ class_Rings_Olinordered__idom(U_5568)
      | ~ class_Int_Onumber__ring(U_5568) ),
    inference(variable_rename,[status(thm)],[f_1487_1]) ).

cnf(f_1487_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5568),c_Groups_Oone__class_Oone(U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5568),U_5569)))
    | ~ class_Rings_Olinordered__idom(U_5568)
    | ~ class_Int_Onumber__ring(U_5568) ),
    inference(clausify,[status(thm)],[f_1487_2]) ).

cnf(f_1487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5568),c_Groups_Oone__class_Oone(U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5568),U_5569)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5569))
    | ~ class_Rings_Olinordered__idom(U_5568)
    | ~ class_Int_Onumber__ring(U_5568) ),
    inference(clausify,[status(thm)],[f_1487_2]) ).

fof(f_1488_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_1488_2,plain,
    ! [U_5571,U_5570] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5570),hAPP(c_Int_Onumber__class_Onumber__of(U_5570),U_5571)),c_Groups_Oone__class_Oone(U_5570)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5571),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5571),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5570),hAPP(c_Int_Onumber__class_Onumber__of(U_5570),U_5571)),c_Groups_Oone__class_Oone(U_5570))) ) )
      | ~ class_Rings_Olinordered__idom(U_5570)
      | ~ class_Int_Onumber__ring(U_5570) ),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

cnf(f_1488_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5571),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5570),hAPP(c_Int_Onumber__class_Onumber__of(U_5570),U_5571)),c_Groups_Oone__class_Oone(U_5570)))
    | ~ class_Rings_Olinordered__idom(U_5570)
    | ~ class_Int_Onumber__ring(U_5570) ),
    inference(clausify,[status(thm)],[f_1488_2]) ).

cnf(f_1488_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5570),hAPP(c_Int_Onumber__class_Onumber__of(U_5570),U_5571)),c_Groups_Oone__class_Oone(U_5570)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5571),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_5570)
    | ~ class_Int_Onumber__ring(U_5570) ),
    inference(clausify,[status(thm)],[f_1488_2]) ).

fof(f_1489_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_1489_2,plain,
    ! [U_5573,U_5572] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5572),hAPP(c_Int_Onumber__class_Onumber__of(U_5572),U_5573)),c_Groups_Oone__class_Oone(U_5572)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5572),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5573),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5572) ),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

cnf(f_1489_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5572),hAPP(c_Int_Onumber__class_Onumber__of(U_5572),U_5573)),c_Groups_Oone__class_Oone(U_5572)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5572),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5573),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5572) ),
    inference(clausify,[status(thm)],[f_1489_2]) ).

fof(f_1490_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_1490_2,plain,
    ! [U_5575,U_5574] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5574),c_Groups_Oone__class_Oone(U_5574)),hAPP(c_Int_Onumber__class_Onumber__of(U_5574),U_5575)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5575))
      | ~ class_Int_Onumber__ring(U_5574) ),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

cnf(f_1490_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5574),c_Groups_Oone__class_Oone(U_5574)),hAPP(c_Int_Onumber__class_Onumber__of(U_5574),U_5575)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5575))
    | ~ class_Int_Onumber__ring(U_5574) ),
    inference(clausify,[status(thm)],[f_1490_2]) ).

fof(f_1491_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_1491_2,plain,
    ! [U_5579,U_5578,U_5577,U_5576] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5576,U_5577) = U_5579
      | U_5577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5579),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5577),U_5579)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5579),U_5577))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5579)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577)) )
      | U_5576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5577),U_5578)),U_5579) ),
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

cnf(f_1491_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5576,U_5577) = U_5579
    | U_5577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5577),U_5578)),U_5579) ),
    inference(clausify,[status(thm)],[f_1491_2]) ).

cnf(f_1491_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5579),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5577),U_5579))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5576,U_5577) = U_5579
    | U_5577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5577),U_5578)),U_5579) ),
    inference(clausify,[status(thm)],[f_1491_2]) ).

cnf(f_1491_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5579),U_5577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5579))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5576,U_5577) = U_5579
    | U_5577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5577),U_5578)),U_5579) ),
    inference(clausify,[status(thm)],[f_1491_2]) ).

cnf(f_1491_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5579),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5577),U_5579))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5579),U_5577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5579))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5576,U_5577) = U_5579
    | U_5577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5576 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5577),U_5578)),U_5579) ),
    inference(clausify,[status(thm)],[f_1491_2]) ).

fof(f_1492_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_1492_2,plain,
    ! [U_5583,U_5582,U_5581,U_5580] :
      ( 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_5581),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5583,U_5580))),U_5582)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5582),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5581),U_5582))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5580)) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

cnf(f_1492_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_5581),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5583,U_5580))),U_5582)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5582),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5581),U_5582))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5580)) ),
    inference(clausify,[status(thm)],[f_1492_2]) ).

fof(f_1493_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_1493_2,plain,
    ! [U_5587,U_5586,U_5585,U_5584] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5585),U_5584)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5585),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5587,U_5584))),U_5586)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5586),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5585),U_5586))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5584)) ),
    inference(variable_rename,[status(thm)],[f_1493_1]) ).

cnf(f_1493_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5585),U_5584)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5585),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5587,U_5584))),U_5586)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5586),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5585),U_5586))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5584)) ),
    inference(clausify,[status(thm)],[f_1493_2]) ).

fof(f_1494_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_1494_2,plain,
    ! [U_5591,U_5590,U_5589,U_5588] :
      ( 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_5590),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5591,U_5588))),U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5590),U_5588)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5589),U_5590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5589))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5588)) ),
    inference(variable_rename,[status(thm)],[f_1494_1]) ).

cnf(f_1494_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_5590),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5591,U_5588))),U_5589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5590),U_5588)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5589),U_5590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5589))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5588)) ),
    inference(clausify,[status(thm)],[f_1494_2]) ).

fof(f_1495_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_1495_2,plain,
    ! [U_5595,U_5594,U_5593,U_5592] :
      ( 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_5594),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5595,U_5592))),U_5593)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5593),U_5594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5593))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5592)) ),
    inference(variable_rename,[status(thm)],[f_1495_1]) ).

cnf(f_1495_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_5594),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5595,U_5592))),U_5593)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5593),U_5594))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5593))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5592)) ),
    inference(clausify,[status(thm)],[f_1495_2]) ).

fof(f_1496_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_1496_2,plain,
    ! [U_5597,U_5596] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5597)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5596))) = 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_5597)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5596)))),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_5596))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5597)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5596))) = 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_5597),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5596)))),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_5596))) ) ),
    inference(variable_rename,[status(thm)],[f_1496_1]) ).

fof(f_1496_3,plain,
    ( ! [U_5601,U_5599] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5599))) = 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_5601)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5599)))),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_5599))) )
    & ! [U_5600,U_5598] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5600)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5598))) = 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_5600),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5598)))),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_5598))) ) ),
    inference(miniscope,[status(thm)],[f_1496_2]) ).

cnf(f_1496_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5600)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5598))) = 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_5600),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5598)))),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_5598))) ),
    inference(clausify,[status(thm)],[f_1496_3]) ).

cnf(f_1496_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5599))) = 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_5601)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5599)))),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_5599))) ),
    inference(clausify,[status(thm)],[f_1496_3]) ).

fof(f_1497_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_1497_2,plain,
    ! [U_5603,U_5602] :
      ( 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_5603)),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_5602)) = 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_5603),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5602))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5602),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1497_1]) ).

cnf(f_1497_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_5603)),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_5602)) = 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_5603),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5602))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5602),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1497_2]) ).

fof(f_1498_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_1498_2,plain,
    ! [U_5605,U_5604] :
      ( 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_5605)),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_5604)) = 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_5605,U_5604)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5604)) ),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

cnf(f_1498_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_5605)),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_5604)) = 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_5605,U_5604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5604)) ),
    inference(clausify,[status(thm)],[f_1498_2]) ).

fof(f_1499_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_1499_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_1499_1]) ).

fof(f_1500_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_1500_2,plain,
    ! [U_5606] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5606) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5606),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_5606)) ),
    inference(variable_rename,[status(thm)],[f_1500_1]) ).

cnf(f_1500_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5606) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5606),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_5606)) ),
    inference(clausify,[status(thm)],[f_1500_2]) ).

fof(f_1501_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_1501_2,plain,
    ! [U_5608,U_5607] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5608)),c_Groups_Oone__class_Oone(U_5607)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5608),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_5607) ),
    inference(variable_rename,[status(thm)],[f_1501_1]) ).

cnf(f_1501_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5608)),c_Groups_Oone__class_Oone(U_5607)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5608),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_5607) ),
    inference(clausify,[status(thm)],[f_1501_2]) ).

fof(f_1502_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_1502_2,plain,
    ! [U_5610,U_5609] : 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_5609))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5610))),
    inference(variable_rename,[status(thm)],[f_1502_1]) ).

cnf(f_1502_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_5609))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5610))),
    inference(clausify,[status(thm)],[f_1502_2]) ).

fof(f_1503_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_1503_2,plain,
    ! [U_5612,U_5611] : 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_5611)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5612))),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

cnf(f_1503_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_5611)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5612))),
    inference(clausify,[status(thm)],[f_1503_2]) ).

fof(f_1504_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_1504_2,plain,
    ! [U_5614,U_5613] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),hAPP(c_Int_Onumber__class_Onumber__of(U_5613),c_Int_OMin)),U_5614) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5613),U_5614)
      | ~ class_Int_Onumber__ring(U_5613) ),
    inference(variable_rename,[status(thm)],[f_1504_1]) ).

cnf(f_1504_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),hAPP(c_Int_Onumber__class_Onumber__of(U_5613),c_Int_OMin)),U_5614) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5613),U_5614)
    | ~ class_Int_Onumber__ring(U_5613) ),
    inference(clausify,[status(thm)],[f_1504_2]) ).

fof(f_1505_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_1505_2,plain,
    ! [U_5616,U_5615] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5615),U_5616),hAPP(c_Int_Onumber__class_Onumber__of(U_5615),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5615),U_5616)
      | ~ class_Int_Onumber__ring(U_5615) ),
    inference(variable_rename,[status(thm)],[f_1505_1]) ).

cnf(f_1505_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5615),U_5616),hAPP(c_Int_Onumber__class_Onumber__of(U_5615),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5615),U_5616)
    | ~ class_Int_Onumber__ring(U_5615) ),
    inference(clausify,[status(thm)],[f_1505_2]) ).

fof(f_1506_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_1506_2,plain,
    ! [U_5619,U_5618,U_5617] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5617),hAPP(c_Groups_Ouminus__class_Ouminus(U_5617),hAPP(c_Int_Onumber__class_Onumber__of(U_5617),U_5618))),U_5619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5617),hAPP(c_Int_Onumber__class_Onumber__of(U_5617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5618))),U_5619)
      | ~ class_Int_Onumber__ring(U_5617) ),
    inference(variable_rename,[status(thm)],[f_1506_1]) ).

cnf(f_1506_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5617),hAPP(c_Groups_Ouminus__class_Ouminus(U_5617),hAPP(c_Int_Onumber__class_Onumber__of(U_5617),U_5618))),U_5619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5617),hAPP(c_Int_Onumber__class_Onumber__of(U_5617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5618))),U_5619)
    | ~ class_Int_Onumber__ring(U_5617) ),
    inference(clausify,[status(thm)],[f_1506_2]) ).

fof(f_1507_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

cnf(f_1507_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_1507_1]) ).

fof(f_1508_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_1508_2,plain,
    ! [U_5620] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5620)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5620),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5620),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5620)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

fof(f_1508_3,plain,
    ( ! [U_5622] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5622)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5622),c_Int_OMin)) )
    & ! [U_5621] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5621),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5621)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1508_2]) ).

cnf(f_1508_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5621),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5621)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5622)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5622),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

fof(f_1509_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_1509_2,plain,
    ! [U_5623] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5623)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5623)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5623))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5623))) ) ),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

fof(f_1509_3,plain,
    ( ! [U_5625] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5625)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5625)) )
    & ! [U_5624] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5624))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5624))) ) ),
    inference(miniscope,[status(thm)],[f_1509_2]) ).

cnf(f_1509_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5624))) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

cnf(f_1509_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5625)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5625)) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

fof(f_1510_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_1510_2,plain,
    ! [U_5626] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_5626) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5626),
    inference(variable_rename,[status(thm)],[f_1510_1]) ).

cnf(f_1510_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_5626) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5626),
    inference(clausify,[status(thm)],[f_1510_2]) ).

fof(f_1511_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_1511_2,plain,
    ! [U_5628,U_5627] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5627),hAPP(c_Groups_Ouminus__class_Ouminus(U_5627),U_5628)) = U_5628
      | ~ class_Lattices_Oboolean__algebra(U_5627) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

cnf(f_1511_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5627),hAPP(c_Groups_Ouminus__class_Ouminus(U_5627),U_5628)) = U_5628
    | ~ class_Lattices_Oboolean__algebra(U_5627) ),
    inference(clausify,[status(thm)],[f_1511_2]) ).

fof(f_1512_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_1512_2,plain,
    ! [U_5632,U_5631,U_5630,U_5629] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5630,U_5629)),U_5631),U_5632) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5629),hAPP(U_5631,U_5632))
      | ~ class_Groups_Ouminus(U_5629) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

cnf(f_1512_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5630,U_5629)),U_5631),U_5632) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5629),hAPP(U_5631,U_5632))
    | ~ class_Groups_Ouminus(U_5629) ),
    inference(clausify,[status(thm)],[f_1512_2]) ).

fof(f_1513_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_1513_2,plain,
    ! [U_5635,U_5634,U_5633] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5635)
          | U_5634 != U_5635 )
        & ( U_5634 = U_5635
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5635) ) )
      | ~ class_Lattices_Oboolean__algebra(U_5633) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

cnf(f_1513_3,plain,
    ( U_5634 = U_5635
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5635)
    | ~ class_Lattices_Oboolean__algebra(U_5633) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

cnf(f_1513_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5635)
    | U_5634 != U_5635
    | ~ class_Lattices_Oboolean__algebra(U_5633) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

fof(f_1514_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_1514_2,plain,
    ! [U_5637,U_5636] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),U_5637)) = U_5637
      | ~ class_Groups_Ogroup__add(U_5636) ),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

cnf(f_1514_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),hAPP(c_Groups_Ouminus__class_Ouminus(U_5636),U_5637)) = U_5637
    | ~ class_Groups_Ogroup__add(U_5636) ),
    inference(clausify,[status(thm)],[f_1514_2]) ).

fof(f_1515_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_1515_2,plain,
    ! [U_5640,U_5639,U_5638] :
      ( ( ( U_5639 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5640)
          | U_5640 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5639) )
        & ( U_5640 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5639)
          | U_5639 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5640) ) )
      | ~ class_Groups_Ogroup__add(U_5638) ),
    inference(variable_rename,[status(thm)],[f_1515_1]) ).

cnf(f_1515_3,plain,
    ( U_5640 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5639)
    | U_5639 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5640)
    | ~ class_Groups_Ogroup__add(U_5638) ),
    inference(clausify,[status(thm)],[f_1515_2]) ).

cnf(f_1515_4,plain,
    ( U_5639 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5640)
    | U_5640 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5638),U_5639)
    | ~ class_Groups_Ogroup__add(U_5638) ),
    inference(clausify,[status(thm)],[f_1515_2]) ).

fof(f_1516_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_1516_2,plain,
    ! [U_5643,U_5642,U_5641] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642) = U_5643
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5643) != U_5642 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5643) = U_5642
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642) != U_5643 ) )
      | ~ class_Groups_Ogroup__add(U_5641) ),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

cnf(f_1516_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5643) = U_5642
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642) != U_5643
    | ~ class_Groups_Ogroup__add(U_5641) ),
    inference(clausify,[status(thm)],[f_1516_2]) ).

cnf(f_1516_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642) = U_5643
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5643) != U_5642
    | ~ class_Groups_Ogroup__add(U_5641) ),
    inference(clausify,[status(thm)],[f_1516_2]) ).

fof(f_1517_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_1517_2,plain,
    ! [U_5646,U_5645,U_5644] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5645) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5646)
          | U_5645 != U_5646 )
        & ( U_5645 = U_5646
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5645) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5646) ) )
      | ~ class_Groups_Ogroup__add(U_5644) ),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

cnf(f_1517_3,plain,
    ( U_5645 = U_5646
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5645) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5646)
    | ~ class_Groups_Ogroup__add(U_5644) ),
    inference(clausify,[status(thm)],[f_1517_2]) ).

cnf(f_1517_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5645) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5644),U_5646)
    | U_5645 != U_5646
    | ~ class_Groups_Ogroup__add(U_5644) ),
    inference(clausify,[status(thm)],[f_1517_2]) ).

fof(f_1518_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_1518_2,plain,
    ! [U_5647] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5647)) = U_5647,
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

cnf(f_1518_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5647)) = U_5647,
    inference(clausify,[status(thm)],[f_1518_2]) ).

fof(f_1519_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_1519_2,plain,
    ! [U_5648] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5648)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5648)),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

cnf(f_1519_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5648)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5648)),
    inference(clausify,[status(thm)],[f_1519_2]) ).

fof(f_1520_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_1520_2,plain,
    ! [U_5649] : c_Int_OMin != c_Int_OBit0(U_5649),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

cnf(f_1520_3,plain,
    c_Int_OMin != c_Int_OBit0(U_5649),
    inference(clausify,[status(thm)],[f_1520_2]) ).

fof(f_1521_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_1521_2,plain,
    ! [U_5650] : c_Int_OBit0(U_5650) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

cnf(f_1521_3,plain,
    c_Int_OBit0(U_5650) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1521_2]) ).

fof(f_1522_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_1522_2,plain,
    ! [U_5652,U_5651] :
      ( ( c_Int_OBit0(U_5651) = c_Int_OBit0(U_5652)
        | U_5651 != U_5652 )
      & ( U_5651 = U_5652
        | c_Int_OBit0(U_5651) != c_Int_OBit0(U_5652) ) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

fof(f_1522_3,plain,
    ( ! [U_5656,U_5654] :
        ( c_Int_OBit0(U_5654) = c_Int_OBit0(U_5656)
        | U_5654 != U_5656 )
    & ! [U_5655,U_5653] :
        ( U_5653 = U_5655
        | c_Int_OBit0(U_5653) != c_Int_OBit0(U_5655) ) ),
    inference(miniscope,[status(thm)],[f_1522_2]) ).

cnf(f_1522_4,plain,
    ( U_5653 = U_5655
    | c_Int_OBit0(U_5653) != c_Int_OBit0(U_5655) ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

cnf(f_1522_5,plain,
    ( c_Int_OBit0(U_5654) = c_Int_OBit0(U_5656)
    | U_5654 != U_5656 ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

fof(f_1523_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_1523_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_1523_1]) ).

fof(f_1524_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_1524_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_1524_1]) ).

fof(f_1525_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_1525_2,plain,
    ! [U_5658,U_5657] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5657),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5658)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5657),hAPP(c_Int_Onumber__class_Onumber__of(U_5657),U_5658))
      | ~ class_Int_Onumber__ring(U_5657) ),
    inference(variable_rename,[status(thm)],[f_1525_1]) ).

cnf(f_1525_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5657),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5658)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5657),hAPP(c_Int_Onumber__class_Onumber__of(U_5657),U_5658))
    | ~ class_Int_Onumber__ring(U_5657) ),
    inference(clausify,[status(thm)],[f_1525_2]) ).

fof(f_1526_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_1526_2,plain,
    ! [U_5660,U_5659] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5659),hAPP(c_Int_Onumber__class_Onumber__of(U_5659),U_5660)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5659),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5660))
      | ~ class_Int_Onumber__ring(U_5659) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

cnf(f_1526_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5659),hAPP(c_Int_Onumber__class_Onumber__of(U_5659),U_5660)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5659),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5660))
    | ~ class_Int_Onumber__ring(U_5659) ),
    inference(clausify,[status(thm)],[f_1526_2]) ).

fof(f_1527_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_1527_2,plain,
    ! [U_5661] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5661),c_Groups_Oone__class_Oone(U_5661)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5661),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_5661) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

cnf(f_1527_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5661),c_Groups_Oone__class_Oone(U_5661)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5661),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_5661) ),
    inference(clausify,[status(thm)],[f_1527_2]) ).

fof(f_1528_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_1528_2,plain,
    ! [U_5662] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5662),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5662),c_Groups_Oone__class_Oone(U_5662))
      | ~ class_Int_Onumber__ring(U_5662) ),
    inference(variable_rename,[status(thm)],[f_1528_1]) ).

cnf(f_1528_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5662),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5662),c_Groups_Oone__class_Oone(U_5662))
    | ~ class_Int_Onumber__ring(U_5662) ),
    inference(clausify,[status(thm)],[f_1528_2]) ).

fof(f_1529_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_1529_2,plain,
    ! [U_5663] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5663)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5663),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5663),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5663)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1529_1]) ).

fof(f_1529_3,plain,
    ( ! [U_5665] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5665)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5665),c_Int_OMin)) )
    & ! [U_5664] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5664),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5664)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1529_2]) ).

cnf(f_1529_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5664),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5664)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1529_3]) ).

cnf(f_1529_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5665)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5665),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1529_3]) ).

fof(f_1530_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_1530_2,plain,
    ! [U_5666] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5666)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5666)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5666))) ) ),
    inference(variable_rename,[status(thm)],[f_1530_1]) ).

fof(f_1530_3,plain,
    ( ! [U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5668)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5668)) )
    & ! [U_5667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5667))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5667))) ) ),
    inference(miniscope,[status(thm)],[f_1530_2]) ).

cnf(f_1530_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5667))) ),
    inference(clausify,[status(thm)],[f_1530_3]) ).

cnf(f_1530_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5668)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5668)) ),
    inference(clausify,[status(thm)],[f_1530_3]) ).

fof(f_1531_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_1531_2,plain,
    ! [U_5670,U_5669] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5669),U_5670)
      | ~ class_Int_Onumber__ring(U_5669)
      | ~ class_Fields_Ofield__inverse__zero(U_5669) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

cnf(f_1531_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5669),U_5670)
    | ~ class_Int_Onumber__ring(U_5669)
    | ~ class_Fields_Ofield__inverse__zero(U_5669) ),
    inference(clausify,[status(thm)],[f_1531_2]) ).

fof(f_1532_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_1532_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_1532_1]) ).

fof(f_1533_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_1533_2,plain,
    ! [U_5671] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5671)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5671)),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

cnf(f_1533_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5671)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5671)),
    inference(clausify,[status(thm)],[f_1533_2]) ).

fof(f_1534_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_1534_2,plain,
    ! [U_5672] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5672)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5672)),
    inference(variable_rename,[status(thm)],[f_1534_1]) ).

cnf(f_1534_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5672)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5672)),
    inference(clausify,[status(thm)],[f_1534_2]) ).

fof(f_1535_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_1535_2,plain,
    ! [U_5675,U_5674,U_5673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5673),hAPP(c_Groups_Ouminus__class_Ouminus(U_5673),U_5675)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5673),U_5674)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5673),U_5674),U_5675))
      | ~ class_Groups_Oordered__ab__group__add(U_5673) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

cnf(f_1535_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5673),hAPP(c_Groups_Ouminus__class_Ouminus(U_5673),U_5675)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5673),U_5674)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5673),U_5674),U_5675))
    | ~ class_Groups_Oordered__ab__group__add(U_5673) ),
    inference(clausify,[status(thm)],[f_1535_2]) ).

fof(f_1536_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_1536_2,plain,
    ! [U_5678,U_5677,U_5676] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5678)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),U_5678),U_5677)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),U_5678),U_5677))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5678))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5676) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

cnf(f_1536_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),U_5678),U_5677))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5678)))
    | ~ class_Groups_Oordered__ab__group__add(U_5676) ),
    inference(clausify,[status(thm)],[f_1536_2]) ).

cnf(f_1536_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5677)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5676),U_5678)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5676),U_5678),U_5677))
    | ~ class_Groups_Oordered__ab__group__add(U_5676) ),
    inference(clausify,[status(thm)],[f_1536_2]) ).

fof(f_1537_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_1537_2,plain,
    ! [U_5681,U_5680,U_5679] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5680)),U_5681))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5681)),U_5680)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5681)),U_5680))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5680)),U_5681)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5679) ),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

cnf(f_1537_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5681)),U_5680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5680)),U_5681))
    | ~ class_Groups_Oordered__ab__group__add(U_5679) ),
    inference(clausify,[status(thm)],[f_1537_2]) ).

cnf(f_1537_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5680)),U_5681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(c_Groups_Ouminus__class_Ouminus(U_5679),U_5681)),U_5680))
    | ~ class_Groups_Oordered__ab__group__add(U_5679) ),
    inference(clausify,[status(thm)],[f_1537_2]) ).

fof(f_1538_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_1538_2,plain,
    ! [U_5684,U_5683,U_5682] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5683),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5684)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5684),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5683))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5684),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5683)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5683),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5684))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5682) ),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

cnf(f_1538_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5684),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5683)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5683),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5684)))
    | ~ class_Groups_Oordered__ab__group__add(U_5682) ),
    inference(clausify,[status(thm)],[f_1538_2]) ).

cnf(f_1538_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5683),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5682),U_5684),hAPP(c_Groups_Ouminus__class_Ouminus(U_5682),U_5683)))
    | ~ class_Groups_Oordered__ab__group__add(U_5682) ),
    inference(clausify,[status(thm)],[f_1538_2]) ).

fof(f_1539_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_1539_2,plain,
    ! [U_5687,U_5686,U_5685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5685),hAPP(c_Groups_Ouminus__class_Ouminus(U_5685),U_5687)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5685),U_5686)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5685),U_5686),U_5687))
      | ~ class_Lattices_Oboolean__algebra(U_5685) ),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

cnf(f_1539_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5685),hAPP(c_Groups_Ouminus__class_Ouminus(U_5685),U_5687)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5685),U_5686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5685),U_5686),U_5687))
    | ~ class_Lattices_Oboolean__algebra(U_5685) ),
    inference(clausify,[status(thm)],[f_1539_2]) ).

fof(f_1540_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_1540_2,plain,
    ! [U_5690,U_5689,U_5688] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5690)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),U_5690),U_5689)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),U_5690),U_5689))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5690))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_5688) ),
    inference(variable_rename,[status(thm)],[f_1540_1]) ).

cnf(f_1540_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),U_5690),U_5689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5690)))
    | ~ class_Lattices_Oboolean__algebra(U_5688) ),
    inference(clausify,[status(thm)],[f_1540_2]) ).

cnf(f_1540_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5689)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5688),U_5690)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5688),U_5690),U_5689))
    | ~ class_Lattices_Oboolean__algebra(U_5688) ),
    inference(clausify,[status(thm)],[f_1540_2]) ).

fof(f_1541_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_1541_2,plain,
    ! [U_5691] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5691),c_Groups_Ozero__class_Ozero(U_5691)) = c_Groups_Ozero__class_Ozero(U_5691)
      | ~ class_Groups_Ogroup__add(U_5691) ),
    inference(variable_rename,[status(thm)],[f_1541_1]) ).

cnf(f_1541_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5691),c_Groups_Ozero__class_Ozero(U_5691)) = c_Groups_Ozero__class_Ozero(U_5691)
    | ~ class_Groups_Ogroup__add(U_5691) ),
    inference(clausify,[status(thm)],[f_1541_2]) ).

fof(f_1542_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_1542_2,plain,
    ! [U_5693,U_5692] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_5692) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5692),U_5693)
          | c_Groups_Ozero__class_Ozero(U_5692) != U_5693 )
        & ( c_Groups_Ozero__class_Ozero(U_5692) = U_5693
          | c_Groups_Ozero__class_Ozero(U_5692) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5692),U_5693) ) )
      | ~ class_Groups_Ogroup__add(U_5692) ),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

cnf(f_1542_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_5692) = U_5693
    | c_Groups_Ozero__class_Ozero(U_5692) != hAPP(c_Groups_Ouminus__class_Ouminus(U_5692),U_5693)
    | ~ class_Groups_Ogroup__add(U_5692) ),
    inference(clausify,[status(thm)],[f_1542_2]) ).

cnf(f_1542_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_5692) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5692),U_5693)
    | c_Groups_Ozero__class_Ozero(U_5692) != U_5693
    | ~ class_Groups_Ogroup__add(U_5692) ),
    inference(clausify,[status(thm)],[f_1542_2]) ).

fof(f_1543_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_1543_2,plain,
    ! [U_5695,U_5694] :
      ( ( ( U_5695 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5694),U_5695)
          | U_5695 != c_Groups_Ozero__class_Ozero(U_5694) )
        & ( U_5695 = c_Groups_Ozero__class_Ozero(U_5694)
          | U_5695 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5694),U_5695) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5694) ),
    inference(variable_rename,[status(thm)],[f_1543_1]) ).

cnf(f_1543_3,plain,
    ( U_5695 = c_Groups_Ozero__class_Ozero(U_5694)
    | U_5695 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5694),U_5695)
    | ~ class_Groups_Olinordered__ab__group__add(U_5694) ),
    inference(clausify,[status(thm)],[f_1543_2]) ).

cnf(f_1543_4,plain,
    ( U_5695 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5694),U_5695)
    | U_5695 != c_Groups_Ozero__class_Ozero(U_5694)
    | ~ class_Groups_Olinordered__ab__group__add(U_5694) ),
    inference(clausify,[status(thm)],[f_1543_2]) ).

fof(f_1544_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_1544_2,plain,
    ! [U_5697,U_5696] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5696),U_5697) = c_Groups_Ozero__class_Ozero(U_5696)
          | U_5697 != c_Groups_Ozero__class_Ozero(U_5696) )
        & ( U_5697 = c_Groups_Ozero__class_Ozero(U_5696)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5696),U_5697) != c_Groups_Ozero__class_Ozero(U_5696) ) )
      | ~ class_Groups_Ogroup__add(U_5696) ),
    inference(variable_rename,[status(thm)],[f_1544_1]) ).

cnf(f_1544_3,plain,
    ( U_5697 = c_Groups_Ozero__class_Ozero(U_5696)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5696),U_5697) != c_Groups_Ozero__class_Ozero(U_5696)
    | ~ class_Groups_Ogroup__add(U_5696) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5696),U_5697) = c_Groups_Ozero__class_Ozero(U_5696)
    | U_5697 != c_Groups_Ozero__class_Ozero(U_5696)
    | ~ class_Groups_Ogroup__add(U_5696) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

fof(f_1545_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_1545_2,plain,
    ! [U_5699,U_5698] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5698),U_5699) = U_5699
          | U_5699 != c_Groups_Ozero__class_Ozero(U_5698) )
        & ( U_5699 = c_Groups_Ozero__class_Ozero(U_5698)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_5698),U_5699) != U_5699 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5698) ),
    inference(variable_rename,[status(thm)],[f_1545_1]) ).

cnf(f_1545_3,plain,
    ( U_5699 = c_Groups_Ozero__class_Ozero(U_5698)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_5698),U_5699) != U_5699
    | ~ class_Groups_Olinordered__ab__group__add(U_5698) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5698),U_5699) = U_5699
    | U_5699 != c_Groups_Ozero__class_Ozero(U_5698)
    | ~ class_Groups_Olinordered__ab__group__add(U_5698) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

fof(f_1546_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_1546_2,plain,
    ! [U_5702,U_5701,U_5700] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5701)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5702)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5702),U_5701)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5702),U_5701))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5701)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5702))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5700) ),
    inference(variable_rename,[status(thm)],[f_1546_1]) ).

cnf(f_1546_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5702),U_5701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5701)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5702)))
    | ~ class_Groups_Oordered__ab__group__add(U_5700) ),
    inference(clausify,[status(thm)],[f_1546_2]) ).

cnf(f_1546_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5701)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5700),U_5702)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5702),U_5701))
    | ~ class_Groups_Oordered__ab__group__add(U_5700) ),
    inference(clausify,[status(thm)],[f_1546_2]) ).

fof(f_1547_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_1547_2,plain,
    ! [U_5705,U_5704,U_5703] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5704)),U_5705))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5705)),U_5704)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5705)),U_5704))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5704)),U_5705)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5703) ),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

cnf(f_1547_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5705)),U_5704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5704)),U_5705))
    | ~ class_Groups_Oordered__ab__group__add(U_5703) ),
    inference(clausify,[status(thm)],[f_1547_2]) ).

cnf(f_1547_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5704)),U_5705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5703),hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),U_5705)),U_5704))
    | ~ class_Groups_Oordered__ab__group__add(U_5703) ),
    inference(clausify,[status(thm)],[f_1547_2]) ).

fof(f_1548_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_1548_2,plain,
    ! [U_5708,U_5707,U_5706] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5708),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5707))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5708),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5707)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5706) ),
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

cnf(f_1548_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5708),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5707)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708)))
    | ~ class_Groups_Oordered__ab__group__add(U_5706) ),
    inference(clausify,[status(thm)],[f_1548_2]) ).

cnf(f_1548_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5706),U_5708),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5707)))
    | ~ class_Groups_Oordered__ab__group__add(U_5706) ),
    inference(clausify,[status(thm)],[f_1548_2]) ).

fof(f_1549_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_1549_2,plain,
    ! [U_5711,U_5710,U_5709] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5709),U_5710),U_5711)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5709),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5710)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5711))
      | ~ class_Groups_Oab__group__add(U_5709) ),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

cnf(f_1549_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5709),U_5710),U_5711)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5709),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5710)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5711))
    | ~ class_Groups_Oab__group__add(U_5709) ),
    inference(clausify,[status(thm)],[f_1549_2]) ).

fof(f_1550_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_1550_2,plain,
    ! [U_5714,U_5713,U_5712] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5712),U_5713),U_5714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5712),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5714)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5713))
      | ~ class_Groups_Ogroup__add(U_5712) ),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

cnf(f_1550_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5712),U_5713),U_5714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5712),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5714)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5713))
    | ~ class_Groups_Ogroup__add(U_5712) ),
    inference(clausify,[status(thm)],[f_1550_2]) ).

fof(f_1551_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_1551_2,plain,
    ! [U_5717,U_5716,U_5715] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5715),U_5716),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5715),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5716)),U_5717)) = U_5717
      | ~ class_Groups_Ogroup__add(U_5715) ),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

cnf(f_1551_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5715),U_5716),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5715),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5716)),U_5717)) = U_5717
    | ~ class_Groups_Ogroup__add(U_5715) ),
    inference(clausify,[status(thm)],[f_1551_2]) ).

fof(f_1552_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_1552_2,plain,
    ! [U_5720,U_5719,U_5718] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5718),hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5718),U_5719),U_5720)) = U_5720
      | ~ class_Groups_Ogroup__add(U_5718) ),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

cnf(f_1552_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5718),hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5718),U_5719),U_5720)) = U_5720
    | ~ class_Groups_Ogroup__add(U_5718) ),
    inference(clausify,[status(thm)],[f_1552_2]) ).

fof(f_1553_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_1553_2,plain,
    ! [U_5723,U_5722,U_5721] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5722),U_5722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5723),U_5723)
          | ( U_5722 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5721),U_5723)
            & U_5722 != U_5723 ) )
        & ( U_5722 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5721),U_5723)
          | U_5722 = U_5723
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5722),U_5722) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5723),U_5723) ) )
      | ~ class_Rings_Oidom(U_5721) ),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

cnf(f_1553_3,plain,
    ( U_5722 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5721),U_5723)
    | U_5722 = U_5723
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5722),U_5722) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5723),U_5723)
    | ~ class_Rings_Oidom(U_5721) ),
    inference(clausify,[status(thm)],[f_1553_2]) ).

cnf(f_1553_4,plain,
    ( U_5722 != U_5723
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5722),U_5722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5723),U_5723)
    | ~ class_Rings_Oidom(U_5721) ),
    inference(clausify,[status(thm)],[f_1553_2]) ).

cnf(f_1553_5,plain,
    ( U_5722 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5721),U_5723)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5722),U_5722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5721),U_5723),U_5723)
    | ~ class_Rings_Oidom(U_5721) ),
    inference(clausify,[status(thm)],[f_1553_2]) ).

fof(f_1554_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_1554_2,plain,
    ! [U_5726,U_5725,U_5724] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5724),hAPP(c_Groups_Ouminus__class_Ouminus(U_5724),U_5725)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5724),U_5726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5724),U_5725),U_5726)
      | ~ class_Rings_Oring(U_5724) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

cnf(f_1554_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5724),hAPP(c_Groups_Ouminus__class_Ouminus(U_5724),U_5725)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5724),U_5726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5724),U_5725),U_5726)
    | ~ class_Rings_Oring(U_5724) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

fof(f_1555_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_1555_2,plain,
    ! [U_5729,U_5728,U_5727] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5727),hAPP(c_Groups_Ouminus__class_Ouminus(U_5727),U_5728)),U_5729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5727),U_5728),hAPP(c_Groups_Ouminus__class_Ouminus(U_5727),U_5729))
      | ~ class_Rings_Oring(U_5727) ),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

cnf(f_1555_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5727),hAPP(c_Groups_Ouminus__class_Ouminus(U_5727),U_5728)),U_5729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5727),U_5728),hAPP(c_Groups_Ouminus__class_Ouminus(U_5727),U_5729))
    | ~ class_Rings_Oring(U_5727) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

fof(f_1556_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_1556_2,plain,
    ! [U_5732,U_5731,U_5730] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5731),U_5732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),hAPP(c_Groups_Ouminus__class_Ouminus(U_5730),U_5731)),U_5732)
      | ~ class_Rings_Oring(U_5730) ),
    inference(variable_rename,[status(thm)],[f_1556_1]) ).

cnf(f_1556_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5731),U_5732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),hAPP(c_Groups_Ouminus__class_Ouminus(U_5730),U_5731)),U_5732)
    | ~ class_Rings_Oring(U_5730) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

fof(f_1557_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_1557_2,plain,
    ! [U_5735,U_5734,U_5733] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5733),U_5734),U_5735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5733),U_5734),hAPP(c_Groups_Ouminus__class_Ouminus(U_5733),U_5735))
      | ~ class_Rings_Oring(U_5733) ),
    inference(variable_rename,[status(thm)],[f_1557_1]) ).

cnf(f_1557_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5733),U_5734),U_5735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5733),U_5734),hAPP(c_Groups_Ouminus__class_Ouminus(U_5733),U_5735))
    | ~ class_Rings_Oring(U_5733) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

fof(f_1558_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_1558_2,plain,
    ! [U_5738,U_5737,U_5736] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5736),U_5737),U_5738)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5736),U_5738),U_5737)
      | ~ class_Groups_Oab__group__add(U_5736) ),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

cnf(f_1558_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5736),U_5737),U_5738)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5736),U_5738),U_5737)
    | ~ class_Groups_Oab__group__add(U_5736) ),
    inference(clausify,[status(thm)],[f_1558_2]) ).

fof(f_1559_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_1559_2,plain,
    ! [U_5740,U_5739] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5739),U_5740) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5739,U_5740)),U_5740),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

cnf(f_1559_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5739),U_5740) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5739,U_5740)),U_5740),
    inference(clausify,[status(thm)],[f_1559_2]) ).

fof(f_1560_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_1560_2,plain,
    ! [U_5742,U_5741] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5741,U_5742) = U_5741
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5741),U_5742)) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

cnf(f_1560_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5741,U_5742) = U_5741
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5741),U_5742)) ),
    inference(clausify,[status(thm)],[f_1560_2]) ).

fof(f_1561_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_1561_2,plain,
    ! [U_5745,U_5744,U_5743] :
      ( c_Divides_Odiv__class_Omod(U_5743,hAPP(c_Groups_Ouminus__class_Ouminus(U_5743),U_5744),U_5745) = c_Divides_Odiv__class_Omod(U_5743,hAPP(c_Groups_Ouminus__class_Ouminus(U_5743),c_Divides_Odiv__class_Omod(U_5743,U_5744,U_5745)),U_5745)
      | ~ class_Divides_Oring__div(U_5743) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

cnf(f_1561_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5743,hAPP(c_Groups_Ouminus__class_Ouminus(U_5743),U_5744),U_5745) = c_Divides_Odiv__class_Omod(U_5743,hAPP(c_Groups_Ouminus__class_Ouminus(U_5743),c_Divides_Odiv__class_Omod(U_5743,U_5744,U_5745)),U_5745)
    | ~ class_Divides_Oring__div(U_5743) ),
    inference(clausify,[status(thm)],[f_1561_2]) ).

fof(f_1562_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_1562_2,plain,
    ! [U_5749,U_5748,U_5747,U_5746] :
      ( c_Divides_Odiv__class_Omod(U_5746,hAPP(c_Groups_Ouminus__class_Ouminus(U_5746),U_5747),U_5748) = c_Divides_Odiv__class_Omod(U_5746,hAPP(c_Groups_Ouminus__class_Ouminus(U_5746),U_5749),U_5748)
      | c_Divides_Odiv__class_Omod(U_5746,U_5747,U_5748) != c_Divides_Odiv__class_Omod(U_5746,U_5749,U_5748)
      | ~ class_Divides_Oring__div(U_5746) ),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

cnf(f_1562_3,plain,
    ( c_Divides_Odiv__class_Omod(U_5746,hAPP(c_Groups_Ouminus__class_Ouminus(U_5746),U_5747),U_5748) = c_Divides_Odiv__class_Omod(U_5746,hAPP(c_Groups_Ouminus__class_Ouminus(U_5746),U_5749),U_5748)
    | c_Divides_Odiv__class_Omod(U_5746,U_5747,U_5748) != c_Divides_Odiv__class_Omod(U_5746,U_5749,U_5748)
    | ~ class_Divides_Oring__div(U_5746) ),
    inference(clausify,[status(thm)],[f_1562_2]) ).

fof(f_1563_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_1563_2,plain,
    ! [U_5751,U_5750] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5750,U_5751)),U_5750)),
    inference(variable_rename,[status(thm)],[f_1563_1]) ).

cnf(f_1563_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5750,U_5751)),U_5750)),
    inference(clausify,[status(thm)],[f_1563_2]) ).

fof(f_1564_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_1564_2,plain,
    ! [U_5753,U_5752] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5752)),c_Int_OBit0(U_5753)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5752),U_5753)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5752),U_5753))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5752)),c_Int_OBit0(U_5753))) ) ),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

fof(f_1564_3,plain,
    ( ! [U_5757,U_5755] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5755)),c_Int_OBit0(U_5757)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5755),U_5757)) )
    & ! [U_5756,U_5754] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5754),U_5756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5754)),c_Int_OBit0(U_5756))) ) ),
    inference(miniscope,[status(thm)],[f_1564_2]) ).

cnf(f_1564_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5754),U_5756))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5754)),c_Int_OBit0(U_5756))) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

cnf(f_1564_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5755)),c_Int_OBit0(U_5757)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5755),U_5757)) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

fof(f_1565_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_1565_2,plain,
    ! [U_5759,U_5758] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5758)),c_Int_OBit0(U_5759)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5758),U_5759)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5758),U_5759))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5758)),c_Int_OBit0(U_5759))) ) ),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

fof(f_1565_3,plain,
    ( ! [U_5763,U_5761] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5761)),c_Int_OBit0(U_5763)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5761),U_5763)) )
    & ! [U_5762,U_5760] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5760),U_5762))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5760)),c_Int_OBit0(U_5762))) ) ),
    inference(miniscope,[status(thm)],[f_1565_2]) ).

cnf(f_1565_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5760),U_5762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5760)),c_Int_OBit0(U_5762))) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

cnf(f_1565_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5761)),c_Int_OBit0(U_5763)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5761),U_5763)) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

fof(f_1566_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_1566_2,plain,
    ! [U_5765,U_5764] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5764)),c_Int_OBit0(U_5765)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5764),U_5765)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5764),U_5765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5764)),c_Int_OBit0(U_5765))) ) ),
    inference(variable_rename,[status(thm)],[f_1566_1]) ).

fof(f_1566_3,plain,
    ( ! [U_5769,U_5767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5767)),c_Int_OBit0(U_5769)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5767),U_5769)) )
    & ! [U_5768,U_5766] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5766),U_5768))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5766)),c_Int_OBit0(U_5768))) ) ),
    inference(miniscope,[status(thm)],[f_1566_2]) ).

cnf(f_1566_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5766),U_5768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5766)),c_Int_OBit0(U_5768))) ),
    inference(clausify,[status(thm)],[f_1566_3]) ).

cnf(f_1566_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5767)),c_Int_OBit0(U_5769)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5767),U_5769)) ),
    inference(clausify,[status(thm)],[f_1566_3]) ).

fof(f_1567_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_1567_2,plain,
    ! [U_5771,U_5770] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5770)),c_Int_OBit0(U_5771)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5770),U_5771)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5770),U_5771))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5770)),c_Int_OBit0(U_5771))) ) ),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

fof(f_1567_3,plain,
    ( ! [U_5775,U_5773] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5773)),c_Int_OBit0(U_5775)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5773),U_5775)) )
    & ! [U_5774,U_5772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5772),U_5774))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5772)),c_Int_OBit0(U_5774))) ) ),
    inference(miniscope,[status(thm)],[f_1567_2]) ).

cnf(f_1567_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5772),U_5774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5772)),c_Int_OBit0(U_5774))) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

cnf(f_1567_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5773)),c_Int_OBit0(U_5775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5773),U_5775)) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

fof(f_1568_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_1568_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_1568_1]) ).

fof(f_1569_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

cnf(f_1569_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1569_1]) ).

fof(f_1570_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_1570_2,plain,
    ! [U_5776] :
      ( ( c_Int_OPls = c_Int_OBit0(U_5776)
        | c_Int_OPls != U_5776 )
      & ( c_Int_OPls = U_5776
        | c_Int_OPls != c_Int_OBit0(U_5776) ) ),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

fof(f_1570_3,plain,
    ( ! [U_5778] :
        ( c_Int_OPls = c_Int_OBit0(U_5778)
        | c_Int_OPls != U_5778 )
    & ! [U_5777] :
        ( c_Int_OPls = U_5777
        | c_Int_OPls != c_Int_OBit0(U_5777) ) ),
    inference(miniscope,[status(thm)],[f_1570_2]) ).

cnf(f_1570_4,plain,
    ( c_Int_OPls = U_5777
    | c_Int_OPls != c_Int_OBit0(U_5777) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

cnf(f_1570_5,plain,
    ( c_Int_OPls = c_Int_OBit0(U_5778)
    | c_Int_OPls != U_5778 ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

fof(f_1571_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_1571_2,plain,
    ! [U_5779] :
      ( ( c_Int_OBit0(U_5779) = c_Int_OPls
        | U_5779 != c_Int_OPls )
      & ( U_5779 = c_Int_OPls
        | c_Int_OBit0(U_5779) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

fof(f_1571_3,plain,
    ( ! [U_5781] :
        ( c_Int_OBit0(U_5781) = c_Int_OPls
        | U_5781 != c_Int_OPls )
    & ! [U_5780] :
        ( U_5780 = c_Int_OPls
        | c_Int_OBit0(U_5780) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_1571_2]) ).

cnf(f_1571_4,plain,
    ( U_5780 = c_Int_OPls
    | c_Int_OBit0(U_5780) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

cnf(f_1571_5,plain,
    ( c_Int_OBit0(U_5781) = c_Int_OPls
    | U_5781 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1571_3]) ).

fof(f_1572_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_1572_2,plain,
    ! [U_5783,U_5782] : c_Int_OBit0(U_5782) != c_Int_OBit1(U_5783),
    inference(variable_rename,[status(thm)],[f_1572_1]) ).

cnf(f_1572_3,plain,
    c_Int_OBit0(U_5782) != c_Int_OBit1(U_5783),
    inference(clausify,[status(thm)],[f_1572_2]) ).

fof(f_1573_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_1573_2,plain,
    ! [U_5785,U_5784] : c_Int_OBit1(U_5784) != c_Int_OBit0(U_5785),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

cnf(f_1573_3,plain,
    c_Int_OBit1(U_5784) != c_Int_OBit0(U_5785),
    inference(clausify,[status(thm)],[f_1573_2]) ).

fof(f_1574_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_1574_2,plain,
    ! [U_5788,U_5787,U_5786] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5787,U_5788)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),U_5787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),U_5788)),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

cnf(f_1574_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5787,U_5788)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),U_5787),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5786),U_5788)),
    inference(clausify,[status(thm)],[f_1574_2]) ).

fof(f_1575_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_1575_2,plain,
    ! [U_5791,U_5790,U_5789] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5789,U_5790)),U_5791) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5789),U_5791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5790),U_5791)),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

cnf(f_1575_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5789,U_5790)),U_5791) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5789),U_5791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5790),U_5791)),
    inference(clausify,[status(thm)],[f_1575_2]) ).

fof(f_1576_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_1576_2,plain,
    ! [U_5792] : c_Int_OBit0(U_5792) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5792),U_5792),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

cnf(f_1576_3,plain,
    c_Int_OBit0(U_5792) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5792),U_5792),
    inference(clausify,[status(thm)],[f_1576_2]) ).

fof(f_1577_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_1577_2,plain,
    ! [U_5794,U_5793] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5793)),c_Int_OBit0(U_5794)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5793),U_5794)),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

cnf(f_1577_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5793)),c_Int_OBit0(U_5794)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5793),U_5794)),
    inference(clausify,[status(thm)],[f_1577_2]) ).

fof(f_1578_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_1578_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_1578_1]) ).

fof(f_1579_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_1579_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1579_1]) ).

fof(f_1580_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_1580_2,plain,
    ! [U_5797,U_5796,U_5795] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5796),U_5797)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5796),hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),U_5797))
      | ~ class_Fields_Ofield__inverse__zero(U_5795) ),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

cnf(f_1580_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5796),U_5797)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5796),hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),U_5797))
    | ~ class_Fields_Ofield__inverse__zero(U_5795) ),
    inference(clausify,[status(thm)],[f_1580_2]) ).

fof(f_1581_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_1581_2,plain,
    ! [U_5800,U_5799,U_5798] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5798),hAPP(c_Groups_Ouminus__class_Ouminus(U_5798),U_5799)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5798),U_5800)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5798),U_5799),U_5800)
      | ~ class_Fields_Ofield__inverse__zero(U_5798) ),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

cnf(f_1581_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5798),hAPP(c_Groups_Ouminus__class_Ouminus(U_5798),U_5799)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5798),U_5800)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5798),U_5799),U_5800)
    | ~ class_Fields_Ofield__inverse__zero(U_5798) ),
    inference(clausify,[status(thm)],[f_1581_2]) ).

fof(f_1582_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_1582_2,plain,
    ! [U_5803,U_5802,U_5801] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5801),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5801),U_5802),U_5803)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5801),hAPP(c_Groups_Ouminus__class_Ouminus(U_5801),U_5802)),U_5803)
      | ~ class_Rings_Odivision__ring(U_5801) ),
    inference(variable_rename,[status(thm)],[f_1582_1]) ).

cnf(f_1582_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5801),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5801),U_5802),U_5803)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5801),hAPP(c_Groups_Ouminus__class_Ouminus(U_5801),U_5802)),U_5803)
    | ~ class_Rings_Odivision__ring(U_5801) ),
    inference(clausify,[status(thm)],[f_1582_2]) ).

fof(f_1583_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_1583_2,plain,
    ! [U_5805,U_5804] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5804)),U_5805) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5804),U_5805)),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

cnf(f_1583_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5804)),U_5805) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5804),U_5805)),
    inference(clausify,[status(thm)],[f_1583_2]) ).

fof(f_1584_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_1584_2,plain,
    ! [U_5807,U_5806] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5806),hAPP(c_Groups_Ouminus__class_Ouminus(U_5806),U_5807)) = hAPP(c_Groups_Oabs__class_Oabs(U_5806),U_5807)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5806) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

cnf(f_1584_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5806),hAPP(c_Groups_Ouminus__class_Ouminus(U_5806),U_5807)) = hAPP(c_Groups_Oabs__class_Oabs(U_5806),U_5807)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5806) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

fof(f_1585_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

cnf(f_1585_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1585_1]) ).

fof(f_1586_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

cnf(f_1586_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1586_1]) ).

fof(f_1587_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

cnf(f_1587_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1587_1]) ).

fof(f_1588_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_1588_2,plain,
    ! [U_5808] :
      ( ( c_Int_OMin = c_Int_OBit1(U_5808)
        | c_Int_OMin != U_5808 )
      & ( c_Int_OMin = U_5808
        | c_Int_OMin != c_Int_OBit1(U_5808) ) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

fof(f_1588_3,plain,
    ( ! [U_5810] :
        ( c_Int_OMin = c_Int_OBit1(U_5810)
        | c_Int_OMin != U_5810 )
    & ! [U_5809] :
        ( c_Int_OMin = U_5809
        | c_Int_OMin != c_Int_OBit1(U_5809) ) ),
    inference(miniscope,[status(thm)],[f_1588_2]) ).

cnf(f_1588_4,plain,
    ( c_Int_OMin = U_5809
    | c_Int_OMin != c_Int_OBit1(U_5809) ),
    inference(clausify,[status(thm)],[f_1588_3]) ).

cnf(f_1588_5,plain,
    ( c_Int_OMin = c_Int_OBit1(U_5810)
    | c_Int_OMin != U_5810 ),
    inference(clausify,[status(thm)],[f_1588_3]) ).

fof(f_1589_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_1589_2,plain,
    ! [U_5811] :
      ( ( c_Int_OBit1(U_5811) = c_Int_OMin
        | U_5811 != c_Int_OMin )
      & ( U_5811 = c_Int_OMin
        | c_Int_OBit1(U_5811) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_1589_1]) ).

fof(f_1589_3,plain,
    ( ! [U_5813] :
        ( c_Int_OBit1(U_5813) = c_Int_OMin
        | U_5813 != c_Int_OMin )
    & ! [U_5812] :
        ( U_5812 = c_Int_OMin
        | c_Int_OBit1(U_5812) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_1589_2]) ).

cnf(f_1589_4,plain,
    ( U_5812 = c_Int_OMin
    | c_Int_OBit1(U_5812) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1589_3]) ).

cnf(f_1589_5,plain,
    ( c_Int_OBit1(U_5813) = c_Int_OMin
    | U_5813 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1589_3]) ).

fof(f_1590_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_1590_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1590_1]) ).

fof(f_1591_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_1591_2,plain,
    ! [U_5815,U_5814] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5814),U_5815)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5814)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5815)),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

cnf(f_1591_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5814),U_5815)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5814)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5815)),
    inference(clausify,[status(thm)],[f_1591_2]) ).

fof(f_1592_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_1592_2,plain,
    ! [U_5816] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5816)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5816)),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

cnf(f_1592_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5816)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5816)),
    inference(clausify,[status(thm)],[f_1592_2]) ).

fof(f_1593_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_1593_2,plain,
    ! [U_5818,U_5817] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5817)),c_Int_OBit0(U_5818)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5817),U_5818)),
    inference(variable_rename,[status(thm)],[f_1593_1]) ).

cnf(f_1593_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5817)),c_Int_OBit0(U_5818)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5817),U_5818)),
    inference(clausify,[status(thm)],[f_1593_2]) ).

fof(f_1594_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_1594_2,plain,
    ! [U_5820,U_5819] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5819)),U_5820) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5819),U_5820)),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

cnf(f_1594_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5819)),U_5820) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5819),U_5820)),
    inference(clausify,[status(thm)],[f_1594_2]) ).

fof(f_1595_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_1595_2,plain,
    ! [U_5822,U_5821] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5821,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5822)) = 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_5821),U_5822)),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

cnf(f_1595_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5821,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5822)) = 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_5821),U_5822)),
    inference(clausify,[status(thm)],[f_1595_2]) ).

fof(f_1596_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_1596_2,plain,
    ! [U_5824,U_5823] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5823),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5824)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5823,U_5824)),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

cnf(f_1596_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5823),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5824)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5823,U_5824)),
    inference(clausify,[status(thm)],[f_1596_2]) ).

fof(f_1597_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_1597_2,plain,
    ! [U_5826,U_5825] : 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_5825,U_5826)),U_5826) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5825),U_5826),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

cnf(f_1597_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_5825,U_5826)),U_5826) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5825),U_5826),
    inference(clausify,[status(thm)],[f_1597_2]) ).

fof(f_1598_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_1598_2,plain,
    ! [U_5828,U_5827] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5827),hAPP(c_Int_Onumber__class_Onumber__of(U_5827),c_Int_OMin)),U_5828) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5827),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5827),c_Groups_Oone__class_Oone(U_5827)),U_5828))
      | ~ class_Int_Onumber__ring(U_5827)
      | ~ class_Fields_Ofield__inverse__zero(U_5827) ),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

cnf(f_1598_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5827),hAPP(c_Int_Onumber__class_Onumber__of(U_5827),c_Int_OMin)),U_5828) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5827),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5827),c_Groups_Oone__class_Oone(U_5827)),U_5828))
    | ~ class_Int_Onumber__ring(U_5827)
    | ~ class_Fields_Ofield__inverse__zero(U_5827) ),
    inference(clausify,[status(thm)],[f_1598_2]) ).

fof(f_1599_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_1599_2,plain,
    ! [U_5829] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5829)),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_5829,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_1599_1]) ).

cnf(f_1599_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5829)),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_5829,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1599_2]) ).

fof(f_1600_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_1600_2,plain,
    ! [U_5831,U_5830] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(c_Groups_Ouminus__class_Ouminus(U_5830),U_5831)),U_5831))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(c_Groups_Ouminus__class_Ouminus(U_5830),U_5831)),U_5831)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5830) ),
    inference(variable_rename,[status(thm)],[f_1600_1]) ).

cnf(f_1600_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(c_Groups_Ouminus__class_Ouminus(U_5830),U_5831)),U_5831))
    | ~ class_Groups_Olinordered__ab__group__add(U_5830) ),
    inference(clausify,[status(thm)],[f_1600_2]) ).

cnf(f_1600_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(c_Groups_Ouminus__class_Ouminus(U_5830),U_5831)),U_5831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831))
    | ~ class_Groups_Olinordered__ab__group__add(U_5830) ),
    inference(clausify,[status(thm)],[f_1600_2]) ).

fof(f_1601_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_1601_2,plain,
    ! [U_5833,U_5832] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),hAPP(c_Groups_Ouminus__class_Ouminus(U_5832),U_5833)),c_Groups_Ozero__class_Ozero(U_5832)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),hAPP(c_Groups_Ouminus__class_Ouminus(U_5832),U_5833)),c_Groups_Ozero__class_Ozero(U_5832))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5832) ),
    inference(variable_rename,[status(thm)],[f_1601_1]) ).

cnf(f_1601_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),hAPP(c_Groups_Ouminus__class_Ouminus(U_5832),U_5833)),c_Groups_Ozero__class_Ozero(U_5832)))
    | ~ class_Groups_Oordered__ab__group__add(U_5832) ),
    inference(clausify,[status(thm)],[f_1601_2]) ).

cnf(f_1601_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),hAPP(c_Groups_Ouminus__class_Ouminus(U_5832),U_5833)),c_Groups_Ozero__class_Ozero(U_5832)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
    | ~ class_Groups_Oordered__ab__group__add(U_5832) ),
    inference(clausify,[status(thm)],[f_1601_2]) ).

fof(f_1602_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_1602_2,plain,
    ! [U_5835,U_5834] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),hAPP(c_Groups_Ouminus__class_Ouminus(U_5834),U_5835)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),c_Groups_Ozero__class_Ozero(U_5834))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),c_Groups_Ozero__class_Ozero(U_5834)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),hAPP(c_Groups_Ouminus__class_Ouminus(U_5834),U_5835))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5834) ),
    inference(variable_rename,[status(thm)],[f_1602_1]) ).

cnf(f_1602_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),c_Groups_Ozero__class_Ozero(U_5834)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),hAPP(c_Groups_Ouminus__class_Ouminus(U_5834),U_5835)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5834) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

cnf(f_1602_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),hAPP(c_Groups_Ouminus__class_Ouminus(U_5834),U_5835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5834),U_5835),c_Groups_Ozero__class_Ozero(U_5834)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5834) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

fof(f_1603_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_1603_2,plain,
    ! [U_5837,U_5836] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5836),U_5837)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),c_Groups_Ozero__class_Ozero(U_5836))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),c_Groups_Ozero__class_Ozero(U_5836)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5836),U_5837))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5836) ),
    inference(variable_rename,[status(thm)],[f_1603_1]) ).

cnf(f_1603_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),c_Groups_Ozero__class_Ozero(U_5836)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5836),U_5837)))
    | ~ class_Groups_Oordered__ab__group__add(U_5836) ),
    inference(clausify,[status(thm)],[f_1603_2]) ).

cnf(f_1603_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5836),U_5837)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),c_Groups_Ozero__class_Ozero(U_5836)))
    | ~ class_Groups_Oordered__ab__group__add(U_5836) ),
    inference(clausify,[status(thm)],[f_1603_2]) ).

fof(f_1604_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_1604_2,plain,
    ! [U_5839,U_5838] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),hAPP(c_Groups_Ouminus__class_Ouminus(U_5838),U_5839)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),c_Groups_Ozero__class_Ozero(U_5838))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),c_Groups_Ozero__class_Ozero(U_5838)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),hAPP(c_Groups_Ouminus__class_Ouminus(U_5838),U_5839))) ) )
      | ~ class_Rings_Olinordered__idom(U_5838) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

cnf(f_1604_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),c_Groups_Ozero__class_Ozero(U_5838)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),hAPP(c_Groups_Ouminus__class_Ouminus(U_5838),U_5839)))
    | ~ class_Rings_Olinordered__idom(U_5838) ),
    inference(clausify,[status(thm)],[f_1604_2]) ).

cnf(f_1604_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),hAPP(c_Groups_Ouminus__class_Ouminus(U_5838),U_5839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5839),c_Groups_Ozero__class_Ozero(U_5838)))
    | ~ class_Rings_Olinordered__idom(U_5838) ),
    inference(clausify,[status(thm)],[f_1604_2]) ).

fof(f_1605_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_1605_2,plain,
    ! [U_5841,U_5840] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),hAPP(c_Groups_Ouminus__class_Ouminus(U_5840),U_5841)),U_5841))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),hAPP(c_Groups_Ouminus__class_Ouminus(U_5840),U_5841)),U_5841)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5840) ),
    inference(variable_rename,[status(thm)],[f_1605_1]) ).

cnf(f_1605_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),hAPP(c_Groups_Ouminus__class_Ouminus(U_5840),U_5841)),U_5841))
    | ~ class_Groups_Olinordered__ab__group__add(U_5840) ),
    inference(clausify,[status(thm)],[f_1605_2]) ).

cnf(f_1605_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),hAPP(c_Groups_Ouminus__class_Ouminus(U_5840),U_5841)),U_5841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5840),c_Groups_Ozero__class_Ozero(U_5840)),U_5841))
    | ~ class_Groups_Olinordered__ab__group__add(U_5840) ),
    inference(clausify,[status(thm)],[f_1605_2]) ).

fof(f_1606_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_1606_2,plain,
    ! [U_5843,U_5842] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),hAPP(c_Groups_Ouminus__class_Ouminus(U_5842),U_5843)),c_Groups_Ozero__class_Ozero(U_5842)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),c_Groups_Ozero__class_Ozero(U_5842)),U_5843)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),c_Groups_Ozero__class_Ozero(U_5842)),U_5843))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),hAPP(c_Groups_Ouminus__class_Ouminus(U_5842),U_5843)),c_Groups_Ozero__class_Ozero(U_5842))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5842) ),
    inference(variable_rename,[status(thm)],[f_1606_1]) ).

cnf(f_1606_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),c_Groups_Ozero__class_Ozero(U_5842)),U_5843))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),hAPP(c_Groups_Ouminus__class_Ouminus(U_5842),U_5843)),c_Groups_Ozero__class_Ozero(U_5842)))
    | ~ class_Groups_Oordered__ab__group__add(U_5842) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),hAPP(c_Groups_Ouminus__class_Ouminus(U_5842),U_5843)),c_Groups_Ozero__class_Ozero(U_5842)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5842),c_Groups_Ozero__class_Ozero(U_5842)),U_5843))
    | ~ class_Groups_Oordered__ab__group__add(U_5842) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

fof(f_1607_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_1607_2,plain,
    ! [U_5845,U_5844] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),c_Groups_Ozero__class_Ozero(U_5844)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5844),U_5845)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),U_5845),c_Groups_Ozero__class_Ozero(U_5844))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),U_5845),c_Groups_Ozero__class_Ozero(U_5844)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),c_Groups_Ozero__class_Ozero(U_5844)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5844),U_5845))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5844) ),
    inference(variable_rename,[status(thm)],[f_1607_1]) ).

cnf(f_1607_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),U_5845),c_Groups_Ozero__class_Ozero(U_5844)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),c_Groups_Ozero__class_Ozero(U_5844)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5844),U_5845)))
    | ~ class_Groups_Oordered__ab__group__add(U_5844) ),
    inference(clausify,[status(thm)],[f_1607_2]) ).

cnf(f_1607_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),c_Groups_Ozero__class_Ozero(U_5844)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5844),U_5845)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5844),U_5845),c_Groups_Ozero__class_Ozero(U_5844)))
    | ~ class_Groups_Oordered__ab__group__add(U_5844) ),
    inference(clausify,[status(thm)],[f_1607_2]) ).

fof(f_1608_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_1608_2,plain,
    ! [U_5847,U_5846] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),U_5847),hAPP(c_Groups_Ouminus__class_Ouminus(U_5846),U_5847)) = c_Groups_Ozero__class_Ozero(U_5846)
      | ~ class_Groups_Ogroup__add(U_5846) ),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

cnf(f_1608_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5846),U_5847),hAPP(c_Groups_Ouminus__class_Ouminus(U_5846),U_5847)) = c_Groups_Ozero__class_Ozero(U_5846)
    | ~ class_Groups_Ogroup__add(U_5846) ),
    inference(clausify,[status(thm)],[f_1608_2]) ).

fof(f_1609_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_1609_2,plain,
    ! [U_5850,U_5849,U_5848] :
      ( ( ( U_5849 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5848),U_5850)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5848),U_5849),U_5850) != c_Groups_Ozero__class_Ozero(U_5848) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5848),U_5849),U_5850) = c_Groups_Ozero__class_Ozero(U_5848)
          | U_5849 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5848),U_5850) ) )
      | ~ class_Groups_Ogroup__add(U_5848) ),
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

cnf(f_1609_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5848),U_5849),U_5850) = c_Groups_Ozero__class_Ozero(U_5848)
    | U_5849 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5848),U_5850)
    | ~ class_Groups_Ogroup__add(U_5848) ),
    inference(clausify,[status(thm)],[f_1609_2]) ).

cnf(f_1609_4,plain,
    ( U_5849 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5848),U_5850)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5848),U_5849),U_5850) != c_Groups_Ozero__class_Ozero(U_5848)
    | ~ class_Groups_Ogroup__add(U_5848) ),
    inference(clausify,[status(thm)],[f_1609_2]) ).

fof(f_1610_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_1610_2,plain,
    ! [U_5852,U_5851] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5851),hAPP(c_Groups_Ouminus__class_Ouminus(U_5851),U_5852)),U_5852) = c_Groups_Ozero__class_Ozero(U_5851)
      | ~ class_Groups_Ogroup__add(U_5851) ),
    inference(variable_rename,[status(thm)],[f_1610_1]) ).

cnf(f_1610_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5851),hAPP(c_Groups_Ouminus__class_Ouminus(U_5851),U_5852)),U_5852) = c_Groups_Ozero__class_Ozero(U_5851)
    | ~ class_Groups_Ogroup__add(U_5851) ),
    inference(clausify,[status(thm)],[f_1610_2]) ).

fof(f_1611_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_1611_2,plain,
    ! [U_5854,U_5853] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5853),hAPP(c_Groups_Ouminus__class_Ouminus(U_5853),U_5854)),U_5854) = c_Groups_Ozero__class_Ozero(U_5853)
      | ~ class_Groups_Oab__group__add(U_5853) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

cnf(f_1611_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5853),hAPP(c_Groups_Ouminus__class_Ouminus(U_5853),U_5854)),U_5854) = c_Groups_Ozero__class_Ozero(U_5853)
    | ~ class_Groups_Oab__group__add(U_5853) ),
    inference(clausify,[status(thm)],[f_1611_2]) ).

fof(f_1612_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_1612_2,plain,
    ! [U_5857,U_5856,U_5855] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5855),U_5856) = U_5857
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5855),U_5856),U_5857) != c_Groups_Ozero__class_Ozero(U_5855)
      | ~ class_Groups_Ogroup__add(U_5855) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

cnf(f_1612_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5855),U_5856) = U_5857
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5855),U_5856),U_5857) != c_Groups_Ozero__class_Ozero(U_5855)
    | ~ class_Groups_Ogroup__add(U_5855) ),
    inference(clausify,[status(thm)],[f_1612_2]) ).

fof(f_1613_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_1613_2,plain,
    ! [U_5859,U_5858] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5859) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5858),U_5859)
      | ~ class_Groups_Ogroup__add(U_5858) ),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

cnf(f_1613_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5859) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5858),U_5859)
    | ~ class_Groups_Ogroup__add(U_5858) ),
    inference(clausify,[status(thm)],[f_1613_2]) ).

fof(f_1614_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_1614_2,plain,
    ! [U_5862,U_5861,U_5860] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5860),U_5861),U_5862) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5860),U_5861),hAPP(c_Groups_Ouminus__class_Ouminus(U_5860),U_5862))
      | ~ class_Rings_Ocomm__ring__1(U_5860) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

cnf(f_1614_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5860),U_5861),U_5862) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5860),U_5861),hAPP(c_Groups_Ouminus__class_Ouminus(U_5860),U_5862))
    | ~ class_Rings_Ocomm__ring__1(U_5860) ),
    inference(clausify,[status(thm)],[f_1614_2]) ).

fof(f_1615_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_1615_2,plain,
    ! [U_5865,U_5864,U_5863] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5863),U_5864),U_5865) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5863),U_5864),hAPP(c_Groups_Ouminus__class_Ouminus(U_5863),U_5865))
      | ~ class_Groups_Ogroup__add(U_5863) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

cnf(f_1615_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5863),U_5864),U_5865) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5863),U_5864),hAPP(c_Groups_Ouminus__class_Ouminus(U_5863),U_5865))
    | ~ class_Groups_Ogroup__add(U_5863) ),
    inference(clausify,[status(thm)],[f_1615_2]) ).

fof(f_1616_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_1616_2,plain,
    ! [U_5868,U_5867,U_5866] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5866),U_5867),U_5868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5866),U_5867),hAPP(c_Groups_Ouminus__class_Ouminus(U_5866),U_5868))
      | ~ class_Groups_Oab__group__add(U_5866) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

cnf(f_1616_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5866),U_5867),U_5868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5866),U_5867),hAPP(c_Groups_Ouminus__class_Ouminus(U_5866),U_5868))
    | ~ class_Groups_Oab__group__add(U_5866) ),
    inference(clausify,[status(thm)],[f_1616_2]) ).

fof(f_1617_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_1617_2,plain,
    ! [U_5871,U_5870,U_5869] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5869),U_5870),hAPP(c_Groups_Ouminus__class_Ouminus(U_5869),U_5871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5869),U_5870),U_5871)
      | ~ class_Groups_Ogroup__add(U_5869) ),
    inference(variable_rename,[status(thm)],[f_1617_1]) ).

cnf(f_1617_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5869),U_5870),hAPP(c_Groups_Ouminus__class_Ouminus(U_5869),U_5871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5869),U_5870),U_5871)
    | ~ class_Groups_Ogroup__add(U_5869) ),
    inference(clausify,[status(thm)],[f_1617_2]) ).

fof(f_1618_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_1618_2,plain,
    ! [U_5873,U_5872] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5872),U_5873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5872),hAPP(c_Groups_Ouminus__class_Ouminus(U_5872),c_Groups_Oone__class_Oone(U_5872))),U_5873)
      | ~ class_Rings_Ocomm__ring__1(U_5872) ),
    inference(variable_rename,[status(thm)],[f_1618_1]) ).

cnf(f_1618_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5872),U_5873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5872),hAPP(c_Groups_Ouminus__class_Ouminus(U_5872),c_Groups_Oone__class_Oone(U_5872))),U_5873)
    | ~ class_Rings_Ocomm__ring__1(U_5872) ),
    inference(clausify,[status(thm)],[f_1618_2]) ).

fof(f_1619_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_1619_2,plain,
    ! [U_5875,U_5874] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5875),U_5875) = c_Groups_Oone__class_Oone(U_5874)
          | ( U_5875 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5874),c_Groups_Oone__class_Oone(U_5874))
            & U_5875 != c_Groups_Oone__class_Oone(U_5874) ) )
        & ( U_5875 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5874),c_Groups_Oone__class_Oone(U_5874))
          | U_5875 = c_Groups_Oone__class_Oone(U_5874)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5875),U_5875) != c_Groups_Oone__class_Oone(U_5874) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_5874) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

cnf(f_1619_3,plain,
    ( U_5875 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5874),c_Groups_Oone__class_Oone(U_5874))
    | U_5875 = c_Groups_Oone__class_Oone(U_5874)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5875),U_5875) != c_Groups_Oone__class_Oone(U_5874)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5874) ),
    inference(clausify,[status(thm)],[f_1619_2]) ).

cnf(f_1619_4,plain,
    ( U_5875 != c_Groups_Oone__class_Oone(U_5874)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5875),U_5875) = c_Groups_Oone__class_Oone(U_5874)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5874) ),
    inference(clausify,[status(thm)],[f_1619_2]) ).

cnf(f_1619_5,plain,
    ( U_5875 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5874),c_Groups_Oone__class_Oone(U_5874))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5875),U_5875) = c_Groups_Oone__class_Oone(U_5874)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5874) ),
    inference(clausify,[status(thm)],[f_1619_2]) ).

fof(f_1620_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_1620_2,plain,
    ! [U_5877,U_5876] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5876),hAPP(c_Groups_Ouminus__class_Ouminus(U_5876),U_5877)),U_5877) = c_Orderings_Obot__class_Obot(U_5876)
      | ~ class_Lattices_Oboolean__algebra(U_5876) ),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

cnf(f_1620_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5876),hAPP(c_Groups_Ouminus__class_Ouminus(U_5876),U_5877)),U_5877) = c_Orderings_Obot__class_Obot(U_5876)
    | ~ class_Lattices_Oboolean__algebra(U_5876) ),
    inference(clausify,[status(thm)],[f_1620_2]) ).

fof(f_1621_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_1621_2,plain,
    ! [U_5879,U_5878] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5878),U_5879),hAPP(c_Groups_Ouminus__class_Ouminus(U_5878),U_5879)) = c_Orderings_Obot__class_Obot(U_5878)
      | ~ class_Lattices_Oboolean__algebra(U_5878) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

cnf(f_1621_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5878),U_5879),hAPP(c_Groups_Ouminus__class_Ouminus(U_5878),U_5879)) = c_Orderings_Obot__class_Obot(U_5878)
    | ~ class_Lattices_Oboolean__algebra(U_5878) ),
    inference(clausify,[status(thm)],[f_1621_2]) ).

fof(f_1622_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_1622_2,plain,
    ! [U_5882,U_5881,U_5880] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5880),U_5881),U_5882) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5880),U_5881),hAPP(c_Groups_Ouminus__class_Ouminus(U_5880),U_5882))
      | ~ class_Lattices_Oboolean__algebra(U_5880) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

cnf(f_1622_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5880),U_5881),U_5882) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5880),U_5881),hAPP(c_Groups_Ouminus__class_Ouminus(U_5880),U_5882))
    | ~ class_Lattices_Oboolean__algebra(U_5880) ),
    inference(clausify,[status(thm)],[f_1622_2]) ).

fof(f_1623_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_1623_2,plain,
    ! [U_5884,U_5883] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5883),U_5884) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5883,U_5884))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5883,U_5884)) = U_5884 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5883),U_5884) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5883,U_5884)) != U_5884 ) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

fof(f_1623_3,plain,
    ( ! [U_5888,U_5886] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5886),U_5888) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5886,U_5888))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5886,U_5888)) = U_5888 )
    & ! [U_5887,U_5885] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5885),U_5887) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5885,U_5887)) != U_5887 ) ),
    inference(miniscope,[status(thm)],[f_1623_2]) ).

cnf(f_1623_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5885),U_5887) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5885,U_5887)) != U_5887 ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5886),U_5888) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5886,U_5888))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5886,U_5888)) = U_5888 ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

fof(f_1624_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_1624_2,plain,
    ! [U_5889] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5889,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_1624_1]) ).

cnf(f_1624_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5889,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_1624_2]) ).

fof(f_1625_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_1625_2,plain,
    ! [U_5891,U_5890] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5891,U_5890)),U_5890))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5890)) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

cnf(f_1625_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5891,U_5890)),U_5890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5890)) ),
    inference(clausify,[status(thm)],[f_1625_2]) ).

fof(f_1626_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_1626_2,plain,
    ! [U_5894,U_5893,U_5892] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5892),U_5893),U_5894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5892),hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),U_5893)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),U_5894))
      | ~ class_Lattices_Oboolean__algebra(U_5892) ),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

cnf(f_1626_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5892),U_5893),U_5894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5892),hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),U_5893)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5892),U_5894))
    | ~ class_Lattices_Oboolean__algebra(U_5892) ),
    inference(clausify,[status(thm)],[f_1626_2]) ).

fof(f_1627_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_1627_2,plain,
    ! [U_5897,U_5896,U_5895] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5895),U_5896),U_5897)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5895),hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),U_5896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),U_5897))
      | ~ class_Lattices_Oboolean__algebra(U_5895) ),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

cnf(f_1627_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5895),U_5896),U_5897)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5895),hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),U_5896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5895),U_5897))
    | ~ class_Lattices_Oboolean__algebra(U_5895) ),
    inference(clausify,[status(thm)],[f_1627_2]) ).

fof(f_1628_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_1628_2,plain,
    ! [U_5900,U_5899,U_5898] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5898),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5898),U_5900),U_5899)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5898),U_5900),hAPP(c_Groups_Ouminus__class_Ouminus(U_5898),U_5899))
      | U_5899 = c_Groups_Ozero__class_Ozero(U_5898)
      | ~ class_Rings_Odivision__ring(U_5898) ),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

cnf(f_1628_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5898),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5898),U_5900),U_5899)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5898),U_5900),hAPP(c_Groups_Ouminus__class_Ouminus(U_5898),U_5899))
    | U_5899 = c_Groups_Ozero__class_Ozero(U_5898)
    | ~ class_Rings_Odivision__ring(U_5898) ),
    inference(clausify,[status(thm)],[f_1628_2]) ).

fof(f_1629_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_1629_2,plain,
    ! [U_5903,U_5902,U_5901] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5901),hAPP(c_Groups_Ouminus__class_Ouminus(U_5901),U_5903)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5901),U_5902)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5901),U_5903),U_5902)
      | U_5902 = c_Groups_Ozero__class_Ozero(U_5901)
      | ~ class_Rings_Odivision__ring(U_5901) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

cnf(f_1629_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5901),hAPP(c_Groups_Ouminus__class_Ouminus(U_5901),U_5903)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5901),U_5902)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5901),U_5903),U_5902)
    | U_5902 = c_Groups_Ozero__class_Ozero(U_5901)
    | ~ class_Rings_Odivision__ring(U_5901) ),
    inference(clausify,[status(thm)],[f_1629_2]) ).

fof(f_1630_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_1630_2,plain,
    ! [U_5905,U_5904] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5904),hAPP(c_Groups_Ouminus__class_Ouminus(U_5904),U_5905)),hAPP(c_Groups_Oabs__class_Oabs(U_5904),U_5905)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5904) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

cnf(f_1630_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5904),hAPP(c_Groups_Ouminus__class_Ouminus(U_5904),U_5905)),hAPP(c_Groups_Oabs__class_Oabs(U_5904),U_5905)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5904) ),
    inference(clausify,[status(thm)],[f_1630_2]) ).

fof(f_1631_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_1631_2,plain,
    ! [U_5908,U_5907,U_5906] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Oabs__class_Oabs(U_5906),U_5907)),U_5908))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Ouminus__class_Ouminus(U_5906),U_5907)),U_5908))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),U_5907),U_5908)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Ouminus__class_Ouminus(U_5906),U_5907)),U_5908))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),U_5907),U_5908)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Oabs__class_Oabs(U_5906),U_5907)),U_5908)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5906) ),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

cnf(f_1631_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),U_5907),U_5908))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Oabs__class_Oabs(U_5906),U_5907)),U_5908))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5906) ),
    inference(clausify,[status(thm)],[f_1631_2]) ).

cnf(f_1631_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Ouminus__class_Ouminus(U_5906),U_5907)),U_5908))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Oabs__class_Oabs(U_5906),U_5907)),U_5908))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5906) ),
    inference(clausify,[status(thm)],[f_1631_2]) ).

cnf(f_1631_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Oabs__class_Oabs(U_5906),U_5907)),U_5908))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(c_Groups_Ouminus__class_Ouminus(U_5906),U_5907)),U_5908))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),U_5907),U_5908))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5906) ),
    inference(clausify,[status(thm)],[f_1631_2]) ).

fof(f_1632_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_1632_2,plain,
    ! [U_5911,U_5910,U_5909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),hAPP(c_Groups_Oabs__class_Oabs(U_5909),U_5910)),U_5911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),hAPP(c_Groups_Ouminus__class_Ouminus(U_5909),U_5910)),U_5911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),U_5910),U_5911))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5909) ),
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

cnf(f_1632_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),hAPP(c_Groups_Oabs__class_Oabs(U_5909),U_5910)),U_5911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),hAPP(c_Groups_Ouminus__class_Ouminus(U_5909),U_5910)),U_5911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5909),U_5910),U_5911))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5909) ),
    inference(clausify,[status(thm)],[f_1632_2]) ).

fof(f_1633_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_1633_2,plain,
    ! [U_5914,U_5913,U_5912] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5912),hAPP(c_Groups_Ouminus__class_Ouminus(U_5912),U_5913)),U_5914))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5912),hAPP(c_Groups_Oabs__class_Oabs(U_5912),U_5913)),U_5914))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_5912) ),
    inference(variable_rename,[status(thm)],[f_1633_1]) ).

cnf(f_1633_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5912),hAPP(c_Groups_Ouminus__class_Ouminus(U_5912),U_5913)),U_5914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5912),hAPP(c_Groups_Oabs__class_Oabs(U_5912),U_5913)),U_5914))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_5912) ),
    inference(clausify,[status(thm)],[f_1633_2]) ).

fof(f_1634_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_1634_2,plain,
    ! [U_5917,U_5916,U_5915] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Oabs__class_Oabs(U_5915),U_5916)),U_5917))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Ouminus__class_Ouminus(U_5915),U_5916)),U_5917))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),U_5916),U_5917)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Ouminus__class_Ouminus(U_5915),U_5916)),U_5917))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),U_5916),U_5917)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Oabs__class_Oabs(U_5915),U_5916)),U_5917)) ) )
      | ~ class_Rings_Olinordered__idom(U_5915) ),
    inference(variable_rename,[status(thm)],[f_1634_1]) ).

cnf(f_1634_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),U_5916),U_5917))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Oabs__class_Oabs(U_5915),U_5916)),U_5917))
    | ~ class_Rings_Olinordered__idom(U_5915) ),
    inference(clausify,[status(thm)],[f_1634_2]) ).

cnf(f_1634_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Ouminus__class_Ouminus(U_5915),U_5916)),U_5917))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Oabs__class_Oabs(U_5915),U_5916)),U_5917))
    | ~ class_Rings_Olinordered__idom(U_5915) ),
    inference(clausify,[status(thm)],[f_1634_2]) ).

cnf(f_1634_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Oabs__class_Oabs(U_5915),U_5916)),U_5917))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),hAPP(c_Groups_Ouminus__class_Ouminus(U_5915),U_5916)),U_5917))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),U_5916),U_5917))
    | ~ class_Rings_Olinordered__idom(U_5915) ),
    inference(clausify,[status(thm)],[f_1634_2]) ).

fof(f_1635_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_1635_2,plain,
    ! [U_5921,U_5920] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5920,U_5921) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_5919] : U_5920 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5921),U_5919) )
      & ( ? [U_5918] : U_5920 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5921),U_5918)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5920,U_5921) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1635_1]) ).

fof(f_1635_3,plain,
    ( ! [U_5925,U_5923] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5923,U_5925) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_5919] : U_5923 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5925),U_5919) )
    & ! [U_5924,U_5922] :
        ( ? [U_5918] : U_5922 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5924),U_5918)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5922,U_5924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1635_2]) ).

fof(f_1635_4,plain,
    ( ! [U_5925,U_5923] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5923,U_5925) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_5919] : U_5923 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5925),U_5919) )
    & ! [U_5924,U_5922] :
        ( U_5922 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5924),sK122(U_5924,U_5922))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5922,U_5924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_5918,sK122(U_5924,U_5922))],[f_1635_3]) ).

cnf(f_1635_5,plain,
    ( U_5922 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5924),sK122(U_5924,U_5922))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5922,U_5924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1635_4]) ).

cnf(f_1635_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5923,U_5925) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5923 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5925),U_5919) ),
    inference(clausify,[status(thm)],[f_1635_4]) ).

fof(f_1636_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_1636_2,plain,
    ! [U_5926] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5926)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5926),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5926),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5926)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

fof(f_1636_3,plain,
    ( ! [U_5928] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5928)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5928),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5927] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5927),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5927)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1636_2]) ).

cnf(f_1636_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5927),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5927)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

cnf(f_1636_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5928)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5928),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

fof(f_1637_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_1637_2,plain,
    ! [U_5930,U_5929] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5929,U_5930) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5929),U_5930),U_5930)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5929),U_5930)) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

cnf(f_1637_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5929,U_5930) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5929),U_5930),U_5930)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5929),U_5930)) ),
    inference(clausify,[status(thm)],[f_1637_2]) ).

fof(f_1638_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_1638_2,plain,
    ! [U_5932,U_5931] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5931,U_5932) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5931),U_5932),U_5932)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5931),U_5932)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5931,U_5932) = U_5931
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5931),U_5932)) ) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

fof(f_1638_3,plain,
    ( ! [U_5936,U_5934] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5934,U_5936) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5934),U_5936),U_5936)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5934),U_5936)) )
    & ! [U_5935,U_5933] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5933,U_5935) = U_5933
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5933),U_5935)) ) ),
    inference(miniscope,[status(thm)],[f_1638_2]) ).

cnf(f_1638_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5933,U_5935) = U_5933
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5933),U_5935)) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

cnf(f_1638_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5934,U_5936) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5934),U_5936),U_5936)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5934),U_5936)) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

fof(f_1639_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_1639_2,plain,
    ! [U_5939,U_5938,U_5937] : 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_5937),U_5938)),U_5939),U_5938) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5939,U_5938),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

cnf(f_1639_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_5937),U_5938)),U_5939),U_5938) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5939,U_5938),
    inference(clausify,[status(thm)],[f_1639_2]) ).

fof(f_1640_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_1640_2,plain,
    ! [U_5940] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5940)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5940),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5940),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5940)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

fof(f_1640_3,plain,
    ( ! [U_5942] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5942)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5942),c_Int_OPls)) )
    & ! [U_5941] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5941),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5941)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1640_2]) ).

cnf(f_1640_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5941),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5941)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1640_3]) ).

cnf(f_1640_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5942)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5942),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1640_3]) ).

fof(f_1641_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_1641_2,plain,
    ! [U_5943] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5943)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5943)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5943))) ) ),
    inference(variable_rename,[status(thm)],[f_1641_1]) ).

fof(f_1641_3,plain,
    ( ! [U_5945] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5945)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5945)) )
    & ! [U_5944] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5944))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5944))) ) ),
    inference(miniscope,[status(thm)],[f_1641_2]) ).

cnf(f_1641_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5944))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5944))) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

cnf(f_1641_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5945)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5945)) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

fof(f_1642_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_1642_2,plain,
    ! [U_5947,U_5946] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5946)),c_Int_OBit1(U_5947)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5946),U_5947)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5946),U_5947))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5946)),c_Int_OBit1(U_5947))) ) ),
    inference(variable_rename,[status(thm)],[f_1642_1]) ).

fof(f_1642_3,plain,
    ( ! [U_5951,U_5949] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5949)),c_Int_OBit1(U_5951)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5949),U_5951)) )
    & ! [U_5950,U_5948] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5948),U_5950))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5948)),c_Int_OBit1(U_5950))) ) ),
    inference(miniscope,[status(thm)],[f_1642_2]) ).

cnf(f_1642_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5948),U_5950))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5948)),c_Int_OBit1(U_5950))) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

cnf(f_1642_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5949)),c_Int_OBit1(U_5951)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5949),U_5951)) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

fof(f_1643_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_1643_2,plain,
    ! [U_5953,U_5952] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5952)),c_Int_OBit1(U_5953)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5952),U_5953)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5952),U_5953))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5952)),c_Int_OBit1(U_5953))) ) ),
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

fof(f_1643_3,plain,
    ( ! [U_5957,U_5955] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5955)),c_Int_OBit1(U_5957)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5955),U_5957)) )
    & ! [U_5956,U_5954] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5954),U_5956))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5954)),c_Int_OBit1(U_5956))) ) ),
    inference(miniscope,[status(thm)],[f_1643_2]) ).

cnf(f_1643_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5954),U_5956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5954)),c_Int_OBit1(U_5956))) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

cnf(f_1643_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5955)),c_Int_OBit1(U_5957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5955),U_5957)) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

fof(f_1644_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_1644_2,plain,
    ! [U_5959,U_5958] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5959,U_5958) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5959),U_5958),U_5958)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5958),U_5959)) ),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

cnf(f_1644_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5959,U_5958) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5959),U_5958),U_5958)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5958),U_5959)) ),
    inference(clausify,[status(thm)],[f_1644_2]) ).

fof(f_1645_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_1645_2,plain,
    ! [U_5960] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5960)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5960)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5960))) ) ),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

fof(f_1645_3,plain,
    ( ! [U_5962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5962)) )
    & ! [U_5961] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5961))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5961))) ) ),
    inference(miniscope,[status(thm)],[f_1645_2]) ).

cnf(f_1645_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5961))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5961))) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

cnf(f_1645_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5962)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5962)) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

fof(f_1646_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_1646_2,plain,
    ! [U_5963] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5963)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5963),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5963),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5963)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

fof(f_1646_3,plain,
    ( ! [U_5965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5965)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5965),c_Int_OPls)) )
    & ! [U_5964] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5964),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5964)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1646_2]) ).

cnf(f_1646_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5964),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5964)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

cnf(f_1646_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5965)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5965),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

fof(f_1647_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_1647_2,plain,
    ! [U_5967,U_5966] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5966)),c_Int_OBit0(U_5967)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5966),U_5967)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5966),U_5967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5966)),c_Int_OBit0(U_5967))) ) ),
    inference(variable_rename,[status(thm)],[f_1647_1]) ).

fof(f_1647_3,plain,
    ( ! [U_5971,U_5969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5969)),c_Int_OBit0(U_5971)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5969),U_5971)) )
    & ! [U_5970,U_5968] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5968),U_5970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5968)),c_Int_OBit0(U_5970))) ) ),
    inference(miniscope,[status(thm)],[f_1647_2]) ).

cnf(f_1647_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5968),U_5970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5968)),c_Int_OBit0(U_5970))) ),
    inference(clausify,[status(thm)],[f_1647_3]) ).

cnf(f_1647_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5969)),c_Int_OBit0(U_5971)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5969),U_5971)) ),
    inference(clausify,[status(thm)],[f_1647_3]) ).

fof(f_1648_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_1648_2,plain,
    ! [U_5973,U_5972] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5972)),c_Int_OBit0(U_5973)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5972),U_5973)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5972),U_5973))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5972)),c_Int_OBit0(U_5973))) ) ),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

fof(f_1648_3,plain,
    ( ! [U_5977,U_5975] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5975)),c_Int_OBit0(U_5977)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5975),U_5977)) )
    & ! [U_5976,U_5974] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5974),U_5976))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5974)),c_Int_OBit0(U_5976))) ) ),
    inference(miniscope,[status(thm)],[f_1648_2]) ).

cnf(f_1648_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5974),U_5976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5974)),c_Int_OBit0(U_5976))) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

cnf(f_1648_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5975)),c_Int_OBit0(U_5977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5975),U_5977)) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

fof(f_1649_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_1649_2,plain,
    ! [U_5979,U_5978] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5978)),c_Int_OBit0(U_5979)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5978),U_5979)),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

cnf(f_1649_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5978)),c_Int_OBit0(U_5979)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5978),U_5979)),
    inference(clausify,[status(thm)],[f_1649_2]) ).

fof(f_1650_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_1650_2,plain,
    ! [U_5981,U_5980] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5980)),c_Int_OBit1(U_5981)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5980),U_5981)),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

cnf(f_1650_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5980)),c_Int_OBit1(U_5981)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5980),U_5981)),
    inference(clausify,[status(thm)],[f_1650_2]) ).

fof(f_1651_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_1651_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_1651_1]) ).

fof(f_1652_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_1652_2,plain,
    ! [U_5982] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5982)),U_5982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

cnf(f_1652_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5982)),U_5982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1652_2]) ).

fof(f_1653_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_1653_2,plain,
    ! [U_5984,U_5983] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5983)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5984)
        | U_5984 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5983 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_5984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5983 = 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_5983)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5984) ) ),
    inference(variable_rename,[status(thm)],[f_1653_1]) ).

fof(f_1653_3,plain,
    ( ! [U_5988,U_5986] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5986)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5988)
        | U_5988 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5986 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5987,U_5985] :
        ( ( U_5987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5985 = 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_5985)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5987) ) ),
    inference(miniscope,[status(thm)],[f_1653_2]) ).

cnf(f_1653_4,plain,
    ( U_5985 = 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_5985)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5987) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_5,plain,
    ( U_5987 = 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_5985)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5987) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5986)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5988)
    | U_5988 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5986 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

fof(f_1654_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_1654_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_1654_1]) ).

fof(f_1655_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_1655_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_1655_1]) ).

fof(f_1656_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_1656_2,plain,
    ! [U_5989] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5989)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5989),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5989),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5989)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

fof(f_1656_3,plain,
    ( ! [U_5991] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5991)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5991),c_Int_OMin)) )
    & ! [U_5990] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5990),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5990)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1656_2]) ).

cnf(f_1656_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5990),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5990)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

cnf(f_1656_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5991)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5991),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

fof(f_1657_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_1657_2,plain,
    ! [U_5992] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5992)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5992)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5992))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5992))) ) ),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

fof(f_1657_3,plain,
    ( ! [U_5994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5994)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5994)) )
    & ! [U_5993] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5993))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5993))) ) ),
    inference(miniscope,[status(thm)],[f_1657_2]) ).

cnf(f_1657_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5993))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5993))) ),
    inference(clausify,[status(thm)],[f_1657_3]) ).

cnf(f_1657_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5994)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5994)) ),
    inference(clausify,[status(thm)],[f_1657_3]) ).

fof(f_1658_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_1658_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1658_1]) ).

fof(f_1659_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_1659_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1659_1]) ).

fof(f_1660_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_1660_2,plain,
    ! [U_5995] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5995)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5995)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5995))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5995))) ) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

fof(f_1660_3,plain,
    ( ! [U_5997] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5997)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5997)) )
    & ! [U_5996] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5996))) ) ),
    inference(miniscope,[status(thm)],[f_1660_2]) ).

cnf(f_1660_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5996))) ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

cnf(f_1660_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5997)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5997)) ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

fof(f_1661_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_1661_2,plain,
    ! [U_5998] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5998)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5998),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5998),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5998)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

fof(f_1661_3,plain,
    ( ! [U_6000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6000)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6000),c_Int_OMin)) )
    & ! [U_5999] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5999),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5999)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1661_2]) ).

cnf(f_1661_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5999),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5999)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1661_3]) ).

cnf(f_1661_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6000)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6000),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1661_3]) ).

fof(f_1662_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_1662_2,plain,
    ! [U_6001] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_6001)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_6001)),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

cnf(f_1662_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_6001)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_6001)),
    inference(clausify,[status(thm)],[f_1662_2]) ).

fof(f_1663_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_1663_2,plain,
    ! [U_6003,U_6002] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_6002)),c_Int_OBit0(U_6003)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6002),U_6003)),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

cnf(f_1663_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_6002)),c_Int_OBit0(U_6003)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6002),U_6003)),
    inference(clausify,[status(thm)],[f_1663_2]) ).

fof(f_1664_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_1664_2,plain,
    ! [U_6005,U_6004] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_6004)),c_Int_OBit1(U_6005)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6004),U_6005)),
    inference(variable_rename,[status(thm)],[f_1664_1]) ).

cnf(f_1664_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_6004)),c_Int_OBit1(U_6005)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6004),U_6005)),
    inference(clausify,[status(thm)],[f_1664_2]) ).

fof(f_1665_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_1665_2,plain,
    ! [U_6007,U_6006] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6006,U_6007)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6006),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6007)),
    inference(variable_rename,[status(thm)],[f_1665_1]) ).

cnf(f_1665_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6006,U_6007)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6006),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6007)),
    inference(clausify,[status(thm)],[f_1665_2]) ).

fof(f_1666_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_1666_2,plain,
    ! [U_6009,U_6008] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6008),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6009)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6008,U_6009)),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

cnf(f_1666_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6008),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6009)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6008,U_6009)),
    inference(clausify,[status(thm)],[f_1666_2]) ).

fof(f_1667_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_1667_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_1667_1]) ).

fof(f_1668_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_1668_2,plain,
    ! [U_6011,U_6010] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6010)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6011)))),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

cnf(f_1668_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_6010)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6011)))),
    inference(clausify,[status(thm)],[f_1668_2]) ).

fof(f_1669_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_1669_2,plain,
    ! [U_6013,U_6012] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6012,U_6013) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6012,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6013)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

cnf(f_1669_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6012,U_6013) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6012,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6013)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1669_2]) ).

fof(f_1670_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_1670_2,plain,
    ! [U_6015,U_6014] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6014,U_6015) != 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_6014),U_6015) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

cnf(f_1670_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6014,U_6015) != 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_6014),U_6015) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1670_2]) ).

fof(f_1671_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_1671_2,plain,
    ! [U_6017,U_6016] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6016),U_6017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6016),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6017)),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

cnf(f_1671_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6016),U_6017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6016),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6017)),
    inference(clausify,[status(thm)],[f_1671_2]) ).

fof(f_1672_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_1672_2,plain,
    ! [U_6019,U_6018] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6018),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6018),U_6019),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

cnf(f_1672_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6018),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6018),U_6019),
    inference(clausify,[status(thm)],[f_1672_2]) ).

fof(f_1673_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_1673_2,plain,
    ! [U_6021,U_6020] :
      ( hBOOL(hAPP(hAPP(c_member(U_6020),hAPP(c_Groups_Ouminus__class_Ouminus(U_6020),U_6021)),c_Int_Oring__1__class_OInts(U_6020)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6021),c_Int_Oring__1__class_OInts(U_6020)))
      | ~ class_Rings_Oring__1(U_6020) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

cnf(f_1673_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6020),hAPP(c_Groups_Ouminus__class_Ouminus(U_6020),U_6021)),c_Int_Oring__1__class_OInts(U_6020)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6021),c_Int_Oring__1__class_OInts(U_6020)))
    | ~ class_Rings_Oring__1(U_6020) ),
    inference(clausify,[status(thm)],[f_1673_2]) ).

fof(f_1674_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_1674_2,plain,
    ! [U_6022] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6022))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6022))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6022)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6022)))) ) ),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

fof(f_1674_3,plain,
    ( ! [U_6024] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6024))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6024))) )
    & ! [U_6023] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6023)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6023)))) ) ),
    inference(miniscope,[status(thm)],[f_1674_2]) ).

cnf(f_1674_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6023)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6023)))) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

cnf(f_1674_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6024))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6024))) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

fof(f_1675_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_1675_2,plain,
    ! [U_6025] : c_Int_Opred(c_Int_OBit0(U_6025)) = c_Int_OBit1(c_Int_Opred(U_6025)),
    inference(variable_rename,[status(thm)],[f_1675_1]) ).

cnf(f_1675_3,plain,
    c_Int_Opred(c_Int_OBit0(U_6025)) = c_Int_OBit1(c_Int_Opred(U_6025)),
    inference(clausify,[status(thm)],[f_1675_2]) ).

fof(f_1676_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_1676_2,plain,
    ! [U_6026] : c_Int_Opred(c_Int_OBit1(U_6026)) = c_Int_OBit0(U_6026),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

cnf(f_1676_3,plain,
    c_Int_Opred(c_Int_OBit1(U_6026)) = c_Int_OBit0(U_6026),
    inference(clausify,[status(thm)],[f_1676_2]) ).

fof(f_1677_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_1677_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_1677_1]) ).

fof(f_1678_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

cnf(f_1678_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1678_1]) ).

fof(f_1679_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_1679_2,plain,
    ! [U_6027] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_6027)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6027))),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

cnf(f_1679_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_6027)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6027))),
    inference(clausify,[status(thm)],[f_1679_2]) ).

fof(f_1680_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_1680_2,plain,
    ! [U_6028] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6028),c_Int_OMin) = c_Int_Opred(U_6028),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

cnf(f_1680_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6028),c_Int_OMin) = c_Int_Opred(U_6028),
    inference(clausify,[status(thm)],[f_1680_2]) ).

fof(f_1681_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_1681_2,plain,
    ! [U_6029] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_6029) = c_Int_Opred(U_6029),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

cnf(f_1681_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_6029) = c_Int_Opred(U_6029),
    inference(clausify,[status(thm)],[f_1681_2]) ).

fof(f_1682_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_1682_2,plain,
    ! [U_6030] : c_Int_Osucc(c_Int_OBit1(U_6030)) = c_Int_OBit0(c_Int_Osucc(U_6030)),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

cnf(f_1682_3,plain,
    c_Int_Osucc(c_Int_OBit1(U_6030)) = c_Int_OBit0(c_Int_Osucc(U_6030)),
    inference(clausify,[status(thm)],[f_1682_2]) ).

fof(f_1683_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_1683_2,plain,
    ! [U_6031] : c_Int_Osucc(c_Int_OBit0(U_6031)) = c_Int_OBit1(U_6031),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

cnf(f_1683_3,plain,
    c_Int_Osucc(c_Int_OBit0(U_6031)) = c_Int_OBit1(U_6031),
    inference(clausify,[status(thm)],[f_1683_2]) ).

fof(f_1684_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

cnf(f_1684_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1684_1]) ).

fof(f_1685_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_1685_2,plain,
    ! [U_6032] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6032),c_Int_OMin) = c_Int_Osucc(U_6032),
    inference(variable_rename,[status(thm)],[f_1685_1]) ).

cnf(f_1685_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6032),c_Int_OMin) = c_Int_Osucc(U_6032),
    inference(clausify,[status(thm)],[f_1685_2]) ).

fof(f_1686_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_1686_2,plain,
    ! [U_6033] :
      ( ( 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_6033,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_6033,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_6033,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_6033,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_1686_1]) ).

fof(f_1686_3,plain,
    ( ! [U_6035] :
        ( 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_6035,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_6035,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_6034] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6034,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_6034,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_1686_2]) ).

cnf(f_1686_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6034,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_6034,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_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_6035,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_6035,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_1686_3]) ).

fof(f_1687_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_1687_2,plain,
    ! [U_6037,U_6036] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6036),c_Int_OBit0(U_6037)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6036),c_Groups_Ozero__class_Ozero(U_6036)),hAPP(c_Int_Onumber__class_Onumber__of(U_6036),U_6037))),hAPP(c_Int_Onumber__class_Onumber__of(U_6036),U_6037))
      | ~ class_Int_Onumber__ring(U_6036) ),
    inference(variable_rename,[status(thm)],[f_1687_1]) ).

cnf(f_1687_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6036),c_Int_OBit0(U_6037)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6036),c_Groups_Ozero__class_Ozero(U_6036)),hAPP(c_Int_Onumber__class_Onumber__of(U_6036),U_6037))),hAPP(c_Int_Onumber__class_Onumber__of(U_6036),U_6037))
    | ~ class_Int_Onumber__ring(U_6036) ),
    inference(clausify,[status(thm)],[f_1687_2]) ).

fof(f_1688_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_1688_2,plain,
    ! [U_6039,U_6038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6038),hAPP(c_Groups_Ouminus__class_Ouminus(U_6038),hAPP(c_Groups_Oabs__class_Oabs(U_6038),U_6039))),c_Groups_Ozero__class_Ozero(U_6038)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_6038) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

cnf(f_1688_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6038),hAPP(c_Groups_Ouminus__class_Ouminus(U_6038),hAPP(c_Groups_Oabs__class_Oabs(U_6038),U_6039))),c_Groups_Ozero__class_Ozero(U_6038)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_6038) ),
    inference(clausify,[status(thm)],[f_1688_2]) ).

fof(f_1689_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_1689_2,plain,
    ! [U_6041,U_6040] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6040),U_6041) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6040),U_6041)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6040),U_6041),c_Groups_Ozero__class_Ozero(U_6040)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_6040) ),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

cnf(f_1689_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6040),U_6041) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6040),U_6041)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6040),U_6041),c_Groups_Ozero__class_Ozero(U_6040)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_6040) ),
    inference(clausify,[status(thm)],[f_1689_2]) ).

fof(f_1690_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_1690_2,plain,
    ! [U_6043,U_6042] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6042),U_6043) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6042),U_6043)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6042),U_6043),c_Groups_Ozero__class_Ozero(U_6042)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_6042) ),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

cnf(f_1690_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6042),U_6043) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6042),U_6043)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6042),U_6043),c_Groups_Ozero__class_Ozero(U_6042)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_6042) ),
    inference(clausify,[status(thm)],[f_1690_2]) ).

fof(f_1691_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_1691_2,plain,
    ! [U_6045,U_6044] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_6044),U_6045) = U_6045
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Ozero__class_Ozero(U_6044))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_6044),U_6045) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6044),U_6045)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Ozero__class_Ozero(U_6044))) ) )
      | ~ class_Groups_Oabs__if(U_6044) ),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

cnf(f_1691_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6044),U_6045) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6044),U_6045)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Ozero__class_Ozero(U_6044)))
    | ~ class_Groups_Oabs__if(U_6044) ),
    inference(clausify,[status(thm)],[f_1691_2]) ).

cnf(f_1691_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6044),U_6045) = U_6045
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6044),U_6045),c_Groups_Ozero__class_Ozero(U_6044)))
    | ~ class_Groups_Oabs__if(U_6044) ),
    inference(clausify,[status(thm)],[f_1691_2]) ).

fof(f_1692_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_1692_2,plain,
    ! [U_6047,U_6046] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6047,U_6046)),U_6046))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6046)) ),
    inference(variable_rename,[status(thm)],[f_1692_1]) ).

cnf(f_1692_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6047,U_6046)),U_6046))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6046)) ),
    inference(clausify,[status(thm)],[f_1692_2]) ).

fof(f_1693_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_1693_2,plain,
    ! [U_6050,U_6049,U_6048] : 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_6048),U_6049)),U_6050)),U_6049) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6050),U_6049),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

cnf(f_1693_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_6048),U_6049)),U_6050)),U_6049) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6050),U_6049),
    inference(clausify,[status(thm)],[f_1693_2]) ).

fof(f_1694_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_1694_2,plain,
    ! [U_6052,U_6051] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6051)),c_Int_OBit0(U_6052)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6051),U_6052)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6051),U_6052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6051)),c_Int_OBit0(U_6052))) ) ),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

fof(f_1694_3,plain,
    ( ! [U_6056,U_6054] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6054)),c_Int_OBit0(U_6056)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6054),U_6056)) )
    & ! [U_6055,U_6053] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053),U_6055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6053)),c_Int_OBit0(U_6055))) ) ),
    inference(miniscope,[status(thm)],[f_1694_2]) ).

cnf(f_1694_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053),U_6055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6053)),c_Int_OBit0(U_6055))) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6054)),c_Int_OBit0(U_6056)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6054),U_6056)) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

fof(f_1695_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_1695_2,plain,
    ! [U_6058,U_6057] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6057)),c_Int_OBit0(U_6058)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6057),U_6058)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6057),U_6058))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6057)),c_Int_OBit0(U_6058))) ) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

fof(f_1695_3,plain,
    ( ! [U_6062,U_6060] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6060)),c_Int_OBit0(U_6062)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6060),U_6062)) )
    & ! [U_6061,U_6059] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),U_6061))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6059)),c_Int_OBit0(U_6061))) ) ),
    inference(miniscope,[status(thm)],[f_1695_2]) ).

cnf(f_1695_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),U_6061))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6059)),c_Int_OBit0(U_6061))) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6060)),c_Int_OBit0(U_6062)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6060),U_6062)) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

fof(f_1696_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_1696_2,plain,
    ! [U_6064,U_6063] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6063)),c_Int_OBit1(U_6064)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6063),U_6064)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6063),U_6064))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6063)),c_Int_OBit1(U_6064))) ) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

fof(f_1696_3,plain,
    ( ! [U_6068,U_6066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6066)),c_Int_OBit1(U_6068)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6066),U_6068)) )
    & ! [U_6067,U_6065] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6065),U_6067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6065)),c_Int_OBit1(U_6067))) ) ),
    inference(miniscope,[status(thm)],[f_1696_2]) ).

cnf(f_1696_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6065),U_6067))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6065)),c_Int_OBit1(U_6067))) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6066)),c_Int_OBit1(U_6068)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6066),U_6068)) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

fof(f_1697_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_1697_2,plain,
    ! [U_6070,U_6069] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6069)),c_Int_OBit1(U_6070)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6069),U_6070)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6069),U_6070))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6069)),c_Int_OBit1(U_6070))) ) ),
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

fof(f_1697_3,plain,
    ( ! [U_6074,U_6072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6072)),c_Int_OBit1(U_6074)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6072),U_6074)) )
    & ! [U_6073,U_6071] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6071),U_6073))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6071)),c_Int_OBit1(U_6073))) ) ),
    inference(miniscope,[status(thm)],[f_1697_2]) ).

cnf(f_1697_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6071),U_6073))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6071)),c_Int_OBit1(U_6073))) ),
    inference(clausify,[status(thm)],[f_1697_3]) ).

cnf(f_1697_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_6072)),c_Int_OBit1(U_6074)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6072),U_6074)) ),
    inference(clausify,[status(thm)],[f_1697_3]) ).

fof(f_1698_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_1698_2,plain,
    ! [U_6077,U_6076,U_6075] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6075),hAPP(c_Int_Onumber__class_Onumber__of(U_6075),U_6076)),hAPP(c_Int_Onumber__class_Onumber__of(U_6075),U_6077)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6077)))
      | ~ class_Int_Onumber__ring(U_6075) ),
    inference(variable_rename,[status(thm)],[f_1698_1]) ).

cnf(f_1698_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6075),hAPP(c_Int_Onumber__class_Onumber__of(U_6075),U_6076)),hAPP(c_Int_Onumber__class_Onumber__of(U_6075),U_6077)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6076),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6077)))
    | ~ class_Int_Onumber__ring(U_6075) ),
    inference(clausify,[status(thm)],[f_1698_2]) ).

fof(f_1699_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_1699_2,plain,
    ! [U_6079,U_6078] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_6078)),U_6079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6078),U_6079))),U_6079),
    inference(variable_rename,[status(thm)],[f_1699_1]) ).

cnf(f_1699_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_6078)),U_6079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6078),U_6079))),U_6079),
    inference(clausify,[status(thm)],[f_1699_2]) ).

fof(f_1700_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_1700_2,plain,
    ! [U_6080] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6080),hAPP(c_Int_Onumber__class_Onumber__of(U_6080),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_6080)
      | ~ class_Rings_Olinordered__idom(U_6080)
      | ~ class_Int_Onumber__ring(U_6080) ),
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

cnf(f_1700_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6080),hAPP(c_Int_Onumber__class_Onumber__of(U_6080),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_6080)
    | ~ class_Rings_Olinordered__idom(U_6080)
    | ~ class_Int_Onumber__ring(U_6080) ),
    inference(clausify,[status(thm)],[f_1700_2]) ).

fof(f_1701_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_1701_2,plain,
    ! [U_6082,U_6081] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6081)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6082))))
        | U_6082 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6081 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_6082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6081 = 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_6081)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6082)))) ) ),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

fof(f_1701_3,plain,
    ( ! [U_6086,U_6084] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6084)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6086))))
        | U_6086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6084 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6085,U_6083] :
        ( ( U_6085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6083 = 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_6083)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6085)))) ) ),
    inference(miniscope,[status(thm)],[f_1701_2]) ).

cnf(f_1701_4,plain,
    ( U_6083 = 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_6083)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6085)))) ),
    inference(clausify,[status(thm)],[f_1701_3]) ).

cnf(f_1701_5,plain,
    ( U_6085 = 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_6083)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6085)))) ),
    inference(clausify,[status(thm)],[f_1701_3]) ).

cnf(f_1701_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_6084)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6086))))
    | U_6086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6084 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1701_3]) ).

fof(f_1702_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_1702_2,plain,
    ! [U_6087] : 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_6087))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

cnf(f_1702_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_6087))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1702_2]) ).

fof(f_1703_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_1703_2,plain,
    ! [U_6088] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6088,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_1703_1]) ).

cnf(f_1703_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6088,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_1703_2]) ).

fof(f_1704_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_1704_2,plain,
    ! [U_6089] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_6089)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_6089)),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

cnf(f_1704_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_6089)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_6089)),
    inference(clausify,[status(thm)],[f_1704_2]) ).

fof(f_1705_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_1705_2,plain,
    ! [U_6091,U_6090] :
      ( U_6090 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_6090 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6090),U_6091) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

cnf(f_1705_3,plain,
    ( U_6090 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6090 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6090),U_6091) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1705_2]) ).

fof(f_1706_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_1706_2,plain,
    ! [U_6093,U_6092] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6092),U_6093) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_6093 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_6092 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_6093 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_6092 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_6093 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_6092 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_6093 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_6092 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6092),U_6093) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

fof(f_1706_3,plain,
    ( ! [U_6097,U_6095] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6095),U_6097) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_6097 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_6095 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_6097 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_6095 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_6096,U_6094] :
        ( ( U_6096 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_6094 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_6096 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_6094 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6094),U_6096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1706_2]) ).

cnf(f_1706_4,plain,
    ( U_6094 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6094 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6094),U_6096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

cnf(f_1706_5,plain,
    ( U_6096 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6094 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6094),U_6096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

cnf(f_1706_6,plain,
    ( U_6094 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6096 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6094),U_6096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

cnf(f_1706_7,plain,
    ( U_6096 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6096 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6094),U_6096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

cnf(f_1706_8,plain,
    ( U_6097 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6095 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6095),U_6097) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

cnf(f_1706_9,plain,
    ( U_6097 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_6095 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6095),U_6097) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1706_3]) ).

fof(f_1707_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_1707_2,plain,
    ! [U_6099,U_6098] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6098)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6099)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6098),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6099))),
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

cnf(f_1707_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6098)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6099)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6098),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6099))),
    inference(clausify,[status(thm)],[f_1707_2]) ).

fof(f_1708_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_1708_2,plain,
    ! [U_6101,U_6100] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6100),U_6101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6101),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6100,U_6101))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6100,U_6101) = 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_6100),U_6101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6100,U_6101) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1708_1]) ).

fof(f_1708_3,plain,
    ( ! [U_6105,U_6103] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6103),U_6105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6105),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6103,U_6105))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6103,U_6105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6104,U_6102] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6102),U_6104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6102,U_6104) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1708_2]) ).

cnf(f_1708_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6102),U_6104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6102,U_6104) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1708_3]) ).

cnf(f_1708_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6103),U_6105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6105),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6103,U_6105))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6103,U_6105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1708_3]) ).

fof(f_1709_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_1709_2,plain,
    ! [U_6107,U_6106] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6106,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6107)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6106,U_6107)),U_6107)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6106,U_6107) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6106,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6107)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6106,U_6107) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1709_1]) ).

fof(f_1709_3,plain,
    ( ! [U_6111,U_6109] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,U_6111)),U_6111)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,U_6111) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6110,U_6108] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6108,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6110)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6108,U_6110) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1709_2]) ).

cnf(f_1709_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6108,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6110)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6108,U_6110) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1709_3]) ).

cnf(f_1709_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,U_6111)),U_6111)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6109,U_6111) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1709_3]) ).

fof(f_1710_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_1710_2,plain,
    ! [U_6112] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6112) = U_6112
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6112) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6112)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ( ! [U_6114] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6114) = U_6114
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6114),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6113] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6113) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6113)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6113),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1710_2]) ).

cnf(f_1710_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6113) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6113)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6113),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6114) = U_6114
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6114),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

fof(f_1711_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_1711_2,plain,
    ! [U_6115] : 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_6115))))),
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

cnf(f_1711_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_6115))))),
    inference(clausify,[status(thm)],[f_1711_2]) ).

fof(f_1712_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_1712_2,plain,
    ! [U_6117,U_6116] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_6116)),c_Int_OBit1(U_6117)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_6116)),U_6117)),
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

cnf(f_1712_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_6116)),c_Int_OBit1(U_6117)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_6116)),U_6117)),
    inference(clausify,[status(thm)],[f_1712_2]) ).

fof(f_1713_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_1713_2,plain,
    ! [U_6119,U_6118] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_6118)),c_Int_OBit1(U_6119)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6118),c_Int_Osucc(U_6119))),
    inference(variable_rename,[status(thm)],[f_1713_1]) ).

cnf(f_1713_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_6118)),c_Int_OBit1(U_6119)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6118),c_Int_Osucc(U_6119))),
    inference(clausify,[status(thm)],[f_1713_2]) ).

fof(f_1714_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_1714_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_1714_1]) ).

fof(f_1715_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_1715_2,plain,
    ! [U_6121,U_6120] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6120),c_Groups_Oone__class_Oone(U_6120)),c_Groups_Oone__class_Oone(U_6120))),hAPP(c_Int_Onumber__class_Onumber__of(U_6120),U_6121)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6120),c_Int_OBit0(U_6121))
      | ~ class_Int_Onumber__ring(U_6120) ),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

cnf(f_1715_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6120),c_Groups_Oone__class_Oone(U_6120)),c_Groups_Oone__class_Oone(U_6120))),hAPP(c_Int_Onumber__class_Onumber__of(U_6120),U_6121)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6120),c_Int_OBit0(U_6121))
    | ~ class_Int_Onumber__ring(U_6120) ),
    inference(clausify,[status(thm)],[f_1715_2]) ).

fof(f_1716_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_1716_2,plain,
    ! [U_6123,U_6122] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)),c_Groups_Ozero__class_Ozero(U_6122))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)),c_Groups_Ozero__class_Ozero(U_6122))) ) )
      | ~ class_Rings_Olinordered__idom(U_6122)
      | ~ class_Int_Onumber__ring(U_6122) ),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

cnf(f_1716_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)),c_Groups_Ozero__class_Ozero(U_6122)))
    | ~ class_Rings_Olinordered__idom(U_6122)
    | ~ class_Int_Onumber__ring(U_6122) ),
    inference(clausify,[status(thm)],[f_1716_2]) ).

cnf(f_1716_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6122),hAPP(c_Int_Onumber__class_Onumber__of(U_6122),U_6123)),c_Groups_Ozero__class_Ozero(U_6122)))
    | ~ class_Rings_Olinordered__idom(U_6122)
    | ~ class_Int_Onumber__ring(U_6122) ),
    inference(clausify,[status(thm)],[f_1716_2]) ).

fof(f_1717_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_Pa_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_Pa_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_Pa_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_1717_2,plain,
    ! [U_6130,U_6129,U_6128] :
      ( ( hBOOL(hAPP(U_6128,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6129,U_6130)))
        | ( ? [U_6127,U_6126] :
              ( ~ hBOOL(hAPP(U_6128,U_6126))
              & U_6129 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6130),U_6127)),U_6126)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6126),U_6130)) )
          & U_6130 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6128,U_6129))
          & U_6130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_6125,U_6124] :
                ( hBOOL(hAPP(U_6128,U_6124))
                | U_6129 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6130),U_6125)),U_6124)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6124),U_6130)) )
            | U_6130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6128,U_6129))
            | U_6130 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6128,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6129,U_6130))) ) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

fof(f_1717_3,plain,
    ( ! [U_6136,U_6134,U_6132] :
        ( hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136)))
        | ( ? [U_6127,U_6126] :
              ( ~ hBOOL(hAPP(U_6132,U_6126))
              & U_6134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6136),U_6127)),U_6126)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6126),U_6136)) )
          & U_6136 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6132,U_6134))
          & U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6135,U_6133,U_6131] :
        ( ( ( ! [U_6125,U_6124] :
                ( hBOOL(hAPP(U_6131,U_6124))
                | U_6133 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6135),U_6125)),U_6124)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6124),U_6135)) )
            | U_6135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6131,U_6133))
            | U_6135 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6131,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6133,U_6135))) ) ),
    inference(miniscope,[status(thm)],[f_1717_2]) ).

fof(f_1717_4,plain,
    ( ! [U_6136,U_6134,U_6132] :
        ( hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136)))
        | ( ? [U_6126] :
              ( ~ hBOOL(hAPP(U_6132,U_6126))
              & U_6134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6136),sK123(U_6136,U_6134,U_6132))),U_6126)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6126),U_6136)) )
          & U_6136 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6132,U_6134))
          & U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6135,U_6133,U_6131] :
        ( ( ( ! [U_6125,U_6124] :
                ( hBOOL(hAPP(U_6131,U_6124))
                | U_6133 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6135),U_6125)),U_6124)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6124),U_6135)) )
            | U_6135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6131,U_6133))
            | U_6135 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6131,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6133,U_6135))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_6127,sK123(U_6136,U_6134,U_6132))],[f_1717_3]) ).

fof(f_1717_5,plain,
    ( ! [U_6136,U_6134,U_6132] :
        ( hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136)))
        | ( ~ hBOOL(hAPP(U_6132,sK124(U_6136,U_6134,U_6132)))
          & U_6134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6136),sK123(U_6136,U_6134,U_6132))),sK124(U_6136,U_6134,U_6132))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK124(U_6136,U_6134,U_6132)),U_6136))
          & U_6136 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6132,U_6134))
          & U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6135,U_6133,U_6131] :
        ( ( ( ! [U_6125,U_6124] :
                ( hBOOL(hAPP(U_6131,U_6124))
                | U_6133 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6135),U_6125)),U_6124)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6124),U_6135)) )
            | U_6135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6131,U_6133))
            | U_6135 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6131,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6133,U_6135))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_6126,sK124(U_6136,U_6134,U_6132))],[f_1717_4]) ).

cnf(f_1717_6,plain,
    ( hBOOL(hAPP(U_6131,U_6133))
    | U_6135 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6131,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6133,U_6135))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_7,plain,
    ( hBOOL(hAPP(U_6131,U_6124))
    | U_6133 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6135),U_6125)),U_6124)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6124),U_6135))
    | U_6135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6131,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6133,U_6135))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_8,plain,
    ( U_6136 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK124(U_6136,U_6134,U_6132)),U_6136))
    | U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_10,plain,
    ( U_6134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6136),sK123(U_6136,U_6134,U_6132))),sK124(U_6136,U_6134,U_6132))
    | U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_11,plain,
    ( ~ hBOOL(hAPP(U_6132,sK124(U_6136,U_6134,U_6132)))
    | U_6136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_12,plain,
    ( U_6136 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6132,U_6134))
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK124(U_6136,U_6134,U_6132)),U_6136))
    | ~ hBOOL(hAPP(U_6132,U_6134))
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_14,plain,
    ( U_6134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6136),sK123(U_6136,U_6134,U_6132))),sK124(U_6136,U_6134,U_6132))
    | ~ hBOOL(hAPP(U_6132,U_6134))
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

cnf(f_1717_15,plain,
    ( ~ hBOOL(hAPP(U_6132,sK124(U_6136,U_6134,U_6132)))
    | ~ hBOOL(hAPP(U_6132,U_6134))
    | hBOOL(hAPP(U_6132,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6134,U_6136))) ),
    inference(clausify,[status(thm)],[f_1717_5]) ).

fof(f_1718_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_1718_2,plain,
    ! [U_6140,U_6139,U_6138,U_6137] :
      ( 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_6139),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6140,U_6137))),U_6138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6139),U_6137)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6138),U_6139))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6137)) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

cnf(f_1718_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_6139),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6140,U_6137))),U_6138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6139),U_6137)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6138),U_6139))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6137)) ),
    inference(clausify,[status(thm)],[f_1718_2]) ).

fof(f_1719_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_1719_2,plain,
    ! [U_6144,U_6143,U_6142,U_6141] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6141),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),U_6142)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6141),U_6143),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),U_6144))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6141),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6142),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6144)))),U_6143)
      | ~ class_Int_Onumber__ring(U_6141) ),
    inference(variable_rename,[status(thm)],[f_1719_1]) ).

cnf(f_1719_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6141),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),U_6142)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6141),U_6143),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),U_6144))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6141),hAPP(c_Int_Onumber__class_Onumber__of(U_6141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6142),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6144)))),U_6143)
    | ~ class_Int_Onumber__ring(U_6141) ),
    inference(clausify,[status(thm)],[f_1719_2]) ).

fof(f_1720_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_1720_2,plain,
    ! [U_6145] :
      ( ( 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_6145))))
        & 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_6145)))) )
      | ~ 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_6145))) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

cnf(f_1720_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_6145))))
    | ~ 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_6145))) ),
    inference(clausify,[status(thm)],[f_1720_2]) ).

cnf(f_1720_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_6145))))
    | ~ 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_6145))) ),
    inference(clausify,[status(thm)],[f_1720_2]) ).

fof(f_1721_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_1721_2,plain,
    ! [U_6147,U_6146] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6146),U_6147)),U_6146) = 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_6146)) ),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

cnf(f_1721_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_6146),U_6147)),U_6146) = 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_6146)) ),
    inference(clausify,[status(thm)],[f_1721_2]) ).

fof(f_1722_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_1722_2,plain,
    ! [U_6149,U_6148] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6148),c_Int_Opred(U_6149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6148),hAPP(c_Groups_Ouminus__class_Ouminus(U_6148),c_Groups_Oone__class_Oone(U_6148))),hAPP(c_Int_Onumber__class_Onumber__of(U_6148),U_6149))
      | ~ class_Int_Onumber__ring(U_6148) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

cnf(f_1722_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6148),c_Int_Opred(U_6149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6148),hAPP(c_Groups_Ouminus__class_Ouminus(U_6148),c_Groups_Oone__class_Oone(U_6148))),hAPP(c_Int_Onumber__class_Onumber__of(U_6148),U_6149))
    | ~ class_Int_Onumber__ring(U_6148) ),
    inference(clausify,[status(thm)],[f_1722_2]) ).

fof(f_1723_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_1723_2,plain,
    ! [U_6150] : ~ 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_6150))))),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

cnf(f_1723_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_6150))))),
    inference(clausify,[status(thm)],[f_1723_2]) ).

fof(f_1724_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_1724_2,plain,
    ! [U_6151] : 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_6151)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

cnf(f_1724_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_6151)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1724_2]) ).

fof(f_1725_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_1725_2,plain,
    ! [U_6153,U_6152] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),hAPP(c_Int_Onumber__class_Onumber__of(U_6152),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),U_6153),U_6153)
      | ~ class_Int_Onumber__ring(U_6152) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

cnf(f_1725_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),hAPP(c_Int_Onumber__class_Onumber__of(U_6152),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),U_6153),U_6153)
    | ~ class_Int_Onumber__ring(U_6152) ),
    inference(clausify,[status(thm)],[f_1725_2]) ).

fof(f_1726_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_1726_2,plain,
    ! [U_6155,U_6154] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6154),hAPP(c_Int_Onumber__class_Onumber__of(U_6154),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6154),U_6155),U_6155)
      | ~ class_Int_Onumber__ring(U_6154) ),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

cnf(f_1726_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6154),hAPP(c_Int_Onumber__class_Onumber__of(U_6154),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6154),U_6155),U_6155)
    | ~ class_Int_Onumber__ring(U_6154) ),
    inference(clausify,[status(thm)],[f_1726_2]) ).

fof(f_1727_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_1727_2,plain,
    ! [U_6156] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6156),c_Groups_Oone__class_Oone(U_6156)),c_Groups_Oone__class_Oone(U_6156)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6156),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_6156) ),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

cnf(f_1727_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6156),c_Groups_Oone__class_Oone(U_6156)),c_Groups_Oone__class_Oone(U_6156)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6156),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_6156) ),
    inference(clausify,[status(thm)],[f_1727_2]) ).

fof(f_1728_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_1728_2,plain,
    ! [U_6158,U_6157] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6157,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6158)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6157,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_6158)),
    inference(variable_rename,[status(thm)],[f_1728_1]) ).

cnf(f_1728_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6157,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6158)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6157,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_6158)),
    inference(clausify,[status(thm)],[f_1728_2]) ).

fof(f_1729_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_1729_2,plain,
    ! [U_6160,U_6159] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6159))),U_6160) = 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_6159),U_6160),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

cnf(f_1729_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6159))),U_6160) = 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_6159),U_6160),
    inference(clausify,[status(thm)],[f_1729_2]) ).

fof(f_1730_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_1730_2,plain,
    ! [U_6162,U_6161] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6161))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6162)) = 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_6161),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6162)),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

cnf(f_1730_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6161))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6162)) = 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_6161),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6162)),
    inference(clausify,[status(thm)],[f_1730_2]) ).

fof(f_1731_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_1731_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_1731_1]) ).

fof(f_1732_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_1732_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_1732_1]) ).

fof(f_1733_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_1733_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_1733_1]) ).

fof(f_1734_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_1734_2,plain,
    ! [U_6163] : 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_6163) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6163)),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

cnf(f_1734_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_6163) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6163)),
    inference(clausify,[status(thm)],[f_1734_2]) ).

fof(f_1735_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_1735_2,plain,
    ! [U_6164] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6164),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_6164)),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

cnf(f_1735_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6164),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_6164)),
    inference(clausify,[status(thm)],[f_1735_2]) ).

fof(f_1736_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_1736_2,plain,
    ! [U_6165] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),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_6165),U_6165),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

cnf(f_1736_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),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_6165),U_6165),
    inference(clausify,[status(thm)],[f_1736_2]) ).

fof(f_1737_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_1737_2,plain,
    ! [U_6166] : 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_6166) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6166),U_6166),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

cnf(f_1737_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_6166) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6166),U_6166),
    inference(clausify,[status(thm)],[f_1737_2]) ).

fof(f_1738_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_1738_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_1738_1]) ).

fof(f_1739_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_1739_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_1739_1]) ).

fof(f_1740_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_1740_2,plain,
    ! [U_6168,U_6167] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6167)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6168))) = 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_6167),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6168))),
    inference(variable_rename,[status(thm)],[f_1740_1]) ).

cnf(f_1740_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6167)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6168))) = 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_6167),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6168))),
    inference(clausify,[status(thm)],[f_1740_2]) ).

fof(f_1741_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_1741_2,plain,
    ! [U_6170,U_6169] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6169),c_Groups_Ozero__class_Ozero(U_6169)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6169),U_6170),hAPP(c_Int_Onumber__class_Onumber__of(U_6169),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6169),c_Groups_Ozero__class_Ozero(U_6169)),U_6170))
      | ~ class_Int_Onumber__ring(U_6169)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6169) ),
    inference(variable_rename,[status(thm)],[f_1741_1]) ).

cnf(f_1741_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6169),c_Groups_Ozero__class_Ozero(U_6169)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6169),U_6170),hAPP(c_Int_Onumber__class_Onumber__of(U_6169),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6169),c_Groups_Ozero__class_Ozero(U_6169)),U_6170))
    | ~ class_Int_Onumber__ring(U_6169)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6169) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

fof(f_1742_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_1742_2,plain,
    ! [U_6172,U_6171] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6171),U_6172),hAPP(c_Int_Onumber__class_Onumber__of(U_6171),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),U_6172)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),U_6172))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6171),U_6172),hAPP(c_Int_Onumber__class_Onumber__of(U_6171),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_6171)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6171) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

cnf(f_1742_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),U_6172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6171),U_6172),hAPP(c_Int_Onumber__class_Onumber__of(U_6171),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Int_Onumber__ring(U_6171)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6171) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6171),U_6172),hAPP(c_Int_Onumber__class_Onumber__of(U_6171),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6171),c_Groups_Ozero__class_Ozero(U_6171)),U_6172))
    | ~ class_Int_Onumber__ring(U_6171)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6171) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

fof(f_1743_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_1743_2,plain,
    ! [U_6173] :
      ( U_6173 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_6173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6173),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_1743_1]) ).

cnf(f_1743_3,plain,
    ( U_6173 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_6173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

fof(f_1744_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_1744_2,plain,
    ! [U_6175,U_6174] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6174),c_Groups_Oone__class_Oone(U_6174)),hAPP(c_Int_Onumber__class_Onumber__of(U_6174),U_6175)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6174),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_6175)))
      | ~ class_Int_Onumber__ring(U_6174) ),
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

cnf(f_1744_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6174),c_Groups_Oone__class_Oone(U_6174)),hAPP(c_Int_Onumber__class_Onumber__of(U_6174),U_6175)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6174),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_6175)))
    | ~ class_Int_Onumber__ring(U_6174) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

fof(f_1745_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_1745_2,plain,
    ! [U_6177,U_6176] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6176),U_6177) = c_Groups_Oone__class_Oone(U_6176)
          | ~ c_Int_Oiszero(U_6176,hAPP(c_Int_Onumber__class_Onumber__of(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6177),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_6176,hAPP(c_Int_Onumber__class_Onumber__of(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6177),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6176),U_6177) != c_Groups_Oone__class_Oone(U_6176) ) )
      | ~ class_Int_Onumber__ring(U_6176) ),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

cnf(f_1745_3,plain,
    ( c_Int_Oiszero(U_6176,hAPP(c_Int_Onumber__class_Onumber__of(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6177),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6176),U_6177) != c_Groups_Oone__class_Oone(U_6176)
    | ~ class_Int_Onumber__ring(U_6176) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6176),U_6177) = c_Groups_Oone__class_Oone(U_6176)
    | ~ c_Int_Oiszero(U_6176,hAPP(c_Int_Onumber__class_Onumber__of(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6177),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Int_Onumber__ring(U_6176) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

fof(f_1746_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_1746_2,plain,
    ! [U_6179,U_6178] :
      ( ( ( c_Groups_Oone__class_Oone(U_6178) = hAPP(c_Int_Onumber__class_Onumber__of(U_6178),U_6179)
          | ~ c_Int_Oiszero(U_6178,hAPP(c_Int_Onumber__class_Onumber__of(U_6178),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_6179)))) )
        & ( c_Int_Oiszero(U_6178,hAPP(c_Int_Onumber__class_Onumber__of(U_6178),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_6179))))
          | c_Groups_Oone__class_Oone(U_6178) != hAPP(c_Int_Onumber__class_Onumber__of(U_6178),U_6179) ) )
      | ~ class_Int_Onumber__ring(U_6178) ),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

cnf(f_1746_3,plain,
    ( c_Int_Oiszero(U_6178,hAPP(c_Int_Onumber__class_Onumber__of(U_6178),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_6179))))
    | c_Groups_Oone__class_Oone(U_6178) != hAPP(c_Int_Onumber__class_Onumber__of(U_6178),U_6179)
    | ~ class_Int_Onumber__ring(U_6178) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_4,plain,
    ( c_Groups_Oone__class_Oone(U_6178) = hAPP(c_Int_Onumber__class_Onumber__of(U_6178),U_6179)
    | ~ c_Int_Oiszero(U_6178,hAPP(c_Int_Onumber__class_Onumber__of(U_6178),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_6179))))
    | ~ class_Int_Onumber__ring(U_6178) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

fof(f_1747_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_1747_2,plain,
    ! [U_6181,U_6180] :
      ( ( c_SMT_Oz3mod(U_6181,U_6180) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6180))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) )
      & ( c_SMT_Oz3mod(U_6181,U_6180) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6181,U_6180)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6180)) ) ),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

fof(f_1747_3,plain,
    ( ! [U_6185,U_6183] :
        ( c_SMT_Oz3mod(U_6185,U_6183) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6185,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6183))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6183)) )
    & ! [U_6184,U_6182] :
        ( c_SMT_Oz3mod(U_6184,U_6182) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6184,U_6182)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6182)) ) ),
    inference(miniscope,[status(thm)],[f_1747_2]) ).

cnf(f_1747_4,plain,
    ( c_SMT_Oz3mod(U_6184,U_6182) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6184,U_6182)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6182)) ),
    inference(clausify,[status(thm)],[f_1747_3]) ).

cnf(f_1747_5,plain,
    ( c_SMT_Oz3mod(U_6185,U_6183) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6185,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6183))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6183)) ),
    inference(clausify,[status(thm)],[f_1747_3]) ).

fof(f_1748_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_1748_2,plain,
    ! [U_6187,U_6186] :
      ( 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_6187))),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_6186)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6187),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6186)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6186),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

cnf(f_1748_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_6187))),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_6186)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6187),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6186)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6186),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1748_2]) ).

fof(f_1749_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_1749_2,plain,
    ! [U_6189,U_6188] :
      ( 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_6189))),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_6188)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6189),U_6188)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6188)) ),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

cnf(f_1749_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_6189))),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_6188)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6189),U_6188)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6188)) ),
    inference(clausify,[status(thm)],[f_1749_2]) ).

fof(f_1750_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_1750_2,plain,
    ! [U_6191,U_6190] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),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_6191))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),hAPP(c_Int_Onat,U_6191))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),hAPP(c_Int_Onat,U_6191)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6191))
      | ~ class_Rings_Osemiring__1(U_6190) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

cnf(f_1750_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),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_6191))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),hAPP(c_Int_Onat,U_6191))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6190),hAPP(c_Int_Onat,U_6191)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6191))
    | ~ class_Rings_Osemiring__1(U_6190) ),
    inference(clausify,[status(thm)],[f_1750_2]) ).

fof(f_1751_1,plain,
    ! [V_A_2,V_ca_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ComplI]) ).

fof(f_1751_2,plain,
    ! [U_6194,U_6193,U_6192] :
      ( hBOOL(hAPP(hAPP(c_member(U_6192),U_6193),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6192,tc_HOL_Obool)),U_6194)))
      | hBOOL(hAPP(hAPP(c_member(U_6192),U_6193),U_6194)) ),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

cnf(f_1751_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6192),U_6193),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6192,tc_HOL_Obool)),U_6194)))
    | hBOOL(hAPP(hAPP(c_member(U_6192),U_6193),U_6194)) ),
    inference(clausify,[status(thm)],[f_1751_2]) ).

fof(f_1752_1,plain,
    ! [V_A_2,V_ca_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_1752_2,plain,
    ! [U_6197,U_6196,U_6195] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_6195),U_6196),U_6197))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6195),U_6196),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6195,tc_HOL_Obool)),U_6197))) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

cnf(f_1752_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6195),U_6196),U_6197))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6195),U_6196),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6195,tc_HOL_Obool)),U_6197))) ),
    inference(clausify,[status(thm)],[f_1752_2]) ).

fof(f_1753_1,plain,
    ! [V_A_2,V_ca_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_1753_2,plain,
    ! [U_6200,U_6199,U_6198] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_6198),U_6199),U_6200))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6198),U_6199),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6198,tc_HOL_Obool)),U_6200))) ),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

cnf(f_1753_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6198),U_6199),U_6200))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6198),U_6199),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6198,tc_HOL_Obool)),U_6200))) ),
    inference(clausify,[status(thm)],[f_1753_2]) ).

fof(f_1754_1,plain,
    ! [V_A_2,V_ca_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_ca_2),V_A_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_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_1754_2,plain,
    ! [U_6203,U_6202,U_6201] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6201),U_6202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6201,tc_HOL_Obool)),U_6203)))
        | hBOOL(hAPP(hAPP(c_member(U_6201),U_6202),U_6203)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_6201),U_6202),U_6203))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6201),U_6202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6201,tc_HOL_Obool)),U_6203))) ) ),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ( ! [U_6209,U_6207,U_6205] :
        ( hBOOL(hAPP(hAPP(c_member(U_6205),U_6207),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6205,tc_HOL_Obool)),U_6209)))
        | hBOOL(hAPP(hAPP(c_member(U_6205),U_6207),U_6209)) )
    & ! [U_6208,U_6206,U_6204] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6204),U_6206),U_6208))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6204),U_6206),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6204,tc_HOL_Obool)),U_6208))) ) ),
    inference(miniscope,[status(thm)],[f_1754_2]) ).

cnf(f_1754_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6204),U_6206),U_6208))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6204),U_6206),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6204,tc_HOL_Obool)),U_6208))) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

cnf(f_1754_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6205),U_6207),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6205,tc_HOL_Obool)),U_6209)))
    | hBOOL(hAPP(hAPP(c_member(U_6205),U_6207),U_6209)) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

fof(f_1755_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_1755_2,plain,
    ! [U_6210] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

cnf(f_1755_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6210) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1755_2]) ).

fof(f_1756_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_1756_2,plain,
    ! [U_6213,U_6212,U_6211] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6211,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6211,tc_HOL_Obool)),U_6213)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6211,tc_HOL_Obool)),U_6212)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6211,tc_HOL_Obool)),U_6212),U_6213)) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

cnf(f_1756_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6211,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6211,tc_HOL_Obool)),U_6213)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6211,tc_HOL_Obool)),U_6212)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6211,tc_HOL_Obool)),U_6212),U_6213)) ),
    inference(clausify,[status(thm)],[f_1756_2]) ).

fof(f_1757_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_1757_2,plain,
    ! [U_6216,U_6215,U_6214] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6214,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6214,tc_HOL_Obool)),U_6215)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6214,tc_HOL_Obool)),U_6216)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6214,tc_HOL_Obool)),U_6216),U_6215)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6214,tc_HOL_Obool)),U_6216),U_6215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6214,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6214,tc_HOL_Obool)),U_6215)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6214,tc_HOL_Obool)),U_6216))) ) ),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

fof(f_1757_3,plain,
    ( ! [U_6222,U_6220,U_6218] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6218,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6218,tc_HOL_Obool)),U_6220)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6218,tc_HOL_Obool)),U_6222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6218,tc_HOL_Obool)),U_6222),U_6220)) )
    & ! [U_6221,U_6219,U_6217] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6217,tc_HOL_Obool)),U_6221),U_6219))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6217,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6217,tc_HOL_Obool)),U_6219)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6217,tc_HOL_Obool)),U_6221))) ) ),
    inference(miniscope,[status(thm)],[f_1757_2]) ).

cnf(f_1757_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6217,tc_HOL_Obool)),U_6221),U_6219))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6217,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6217,tc_HOL_Obool)),U_6219)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6217,tc_HOL_Obool)),U_6221))) ),
    inference(clausify,[status(thm)],[f_1757_3]) ).

cnf(f_1757_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6218,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6218,tc_HOL_Obool)),U_6220)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6218,tc_HOL_Obool)),U_6222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6218,tc_HOL_Obool)),U_6222),U_6220)) ),
    inference(clausify,[status(thm)],[f_1757_3]) ).

fof(f_1758_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_1758_2,plain,
    ! [U_6223] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6223)) = U_6223,
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

cnf(f_1758_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6223)) = U_6223,
    inference(clausify,[status(thm)],[f_1758_2]) ).

fof(f_1759_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_1759_2,plain,
    ! [U_6225,U_6224] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6224)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6225)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6224),U_6225),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

cnf(f_1759_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6224)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6225)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6224),U_6225),
    inference(clausify,[status(thm)],[f_1759_2]) ).

fof(f_1760_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_1760_2,plain,
    ! [U_6227,U_6226] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6227)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6226)),U_6227),
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

cnf(f_1760_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6227)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6226)),U_6227),
    inference(clausify,[status(thm)],[f_1760_2]) ).

fof(f_1761_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_1761_2,plain,
    ! [U_6229,U_6228] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),U_6229) = c_Groups_Ozero__class_Ozero(U_6228)
      | ~ class_Divides_Osemiring__div(U_6228) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

cnf(f_1761_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),U_6229) = c_Groups_Ozero__class_Ozero(U_6228)
    | ~ class_Divides_Osemiring__div(U_6228) ),
    inference(clausify,[status(thm)],[f_1761_2]) ).

fof(f_1762_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_1762_2,plain,
    ! [U_6231,U_6230] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6230),U_6231),c_Groups_Ozero__class_Ozero(U_6230)) = c_Groups_Ozero__class_Ozero(U_6230)
      | ~ class_Divides_Osemiring__div(U_6230) ),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

cnf(f_1762_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6230),U_6231),c_Groups_Ozero__class_Ozero(U_6230)) = c_Groups_Ozero__class_Ozero(U_6230)
    | ~ class_Divides_Osemiring__div(U_6230) ),
    inference(clausify,[status(thm)],[f_1762_2]) ).

fof(f_1763_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_1763_2,plain,
    ! [U_6233,U_6232] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6232),U_6233),c_Groups_Oone__class_Oone(U_6232)) = U_6233
      | ~ class_Divides_Osemiring__div(U_6232) ),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

cnf(f_1763_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6232),U_6233),c_Groups_Oone__class_Oone(U_6232)) = U_6233
    | ~ class_Divides_Osemiring__div(U_6232) ),
    inference(clausify,[status(thm)],[f_1763_2]) ).

fof(f_1764_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_1764_2,plain,
    ! [U_6234] :
      ( c_Int_Oiszero(U_6234,c_Groups_Ozero__class_Ozero(U_6234))
      | ~ class_Rings_Osemiring__1(U_6234) ),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

cnf(f_1764_3,plain,
    ( c_Int_Oiszero(U_6234,c_Groups_Ozero__class_Ozero(U_6234))
    | ~ class_Rings_Osemiring__1(U_6234) ),
    inference(clausify,[status(thm)],[f_1764_2]) ).

fof(f_1765_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_1765_2,plain,
    ! [U_6236,U_6235] :
      ( ( ( c_Int_Oiszero(U_6235,U_6236)
          | U_6236 != c_Groups_Ozero__class_Ozero(U_6235) )
        & ( U_6236 = c_Groups_Ozero__class_Ozero(U_6235)
          | ~ c_Int_Oiszero(U_6235,U_6236) ) )
      | ~ class_Rings_Osemiring__1(U_6235) ),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

cnf(f_1765_3,plain,
    ( U_6236 = c_Groups_Ozero__class_Ozero(U_6235)
    | ~ c_Int_Oiszero(U_6235,U_6236)
    | ~ class_Rings_Osemiring__1(U_6235) ),
    inference(clausify,[status(thm)],[f_1765_2]) ).

cnf(f_1765_4,plain,
    ( c_Int_Oiszero(U_6235,U_6236)
    | U_6236 != c_Groups_Ozero__class_Ozero(U_6235)
    | ~ class_Rings_Osemiring__1(U_6235) ),
    inference(clausify,[status(thm)],[f_1765_2]) ).

fof(f_1766_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_1766_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_1766_1]) ).

fof(f_1767_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_1767_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_1767_1]) ).

fof(f_1768_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_1768_2,plain,
    ! [U_6238,U_6237] :
      ( 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_6237),U_6238)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6238))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6237)) ),
    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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6237),U_6238)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6238))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6237)) ),
    inference(clausify,[status(thm)],[f_1768_2]) ).

fof(f_1769_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_1769_2,plain,
    ! [U_6239] :
      ( ~ c_Int_Oiszero(U_6239,c_Groups_Oone__class_Oone(U_6239))
      | ~ class_Rings_Osemiring__1(U_6239) ),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

cnf(f_1769_3,plain,
    ( ~ c_Int_Oiszero(U_6239,c_Groups_Oone__class_Oone(U_6239))
    | ~ class_Rings_Osemiring__1(U_6239) ),
    inference(clausify,[status(thm)],[f_1769_2]) ).

fof(f_1770_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_1770_2,plain,
    ! [U_6241,U_6240] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6241),U_6240)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6241),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6241),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_6241),U_6240)),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_6240)) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

cnf(f_1770_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6241),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_6241),U_6240)),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_6240)) ),
    inference(clausify,[status(thm)],[f_1770_2]) ).

cnf(f_1770_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6241),U_6240)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6241),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_6240)) ),
    inference(clausify,[status(thm)],[f_1770_2]) ).

fof(f_1771_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_1771_2,plain,
    ! [U_6243,U_6242] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6242)),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_6243)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6243))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6242)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6242),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

cnf(f_1771_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6242)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6242),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1771_2]) ).

cnf(f_1771_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6243),U_6242)),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_6243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6242),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1771_2]) ).

fof(f_1772_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_1772_2,plain,
    ! [U_6245,U_6244] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6244),U_6245)),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_6245))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6244),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

cnf(f_1772_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6244),U_6245)),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_6245))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6244),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1772_2]) ).

fof(f_1773_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_1773_2,plain,
    ! [U_6247,U_6246] :
      ( ( ( hAPP(c_Int_Onat,U_6246) = hAPP(c_Int_Onat,U_6247)
          | U_6246 != U_6247 )
        & ( U_6246 = U_6247
          | hAPP(c_Int_Onat,U_6246) != hAPP(c_Int_Onat,U_6247) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6246)) ),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

cnf(f_1773_3,plain,
    ( U_6246 = U_6247
    | hAPP(c_Int_Onat,U_6246) != hAPP(c_Int_Onat,U_6247)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6246)) ),
    inference(clausify,[status(thm)],[f_1773_2]) ).

cnf(f_1773_4,plain,
    ( hAPP(c_Int_Onat,U_6246) = hAPP(c_Int_Onat,U_6247)
    | U_6246 != U_6247
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6246)) ),
    inference(clausify,[status(thm)],[f_1773_2]) ).

fof(f_1774_1,plain,
    ! [V_Pa_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat]) ).

fof(f_1774_2,plain,
    ! [U_6252] :
      ( ( ! [U_6251] : hBOOL(hAPP(U_6252,U_6251))
        | ? [U_6250] :
            ( ~ hBOOL(hAPP(U_6252,hAPP(c_Int_Onat,U_6250)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6250)) ) )
      & ( ! [U_6249] :
            ( hBOOL(hAPP(U_6252,hAPP(c_Int_Onat,U_6249)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6249)) )
        | ? [U_6248] : ~ hBOOL(hAPP(U_6252,U_6248)) ) ),
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

fof(f_1774_3,plain,
    ( ! [U_6254] :
        ( ! [U_6251] : hBOOL(hAPP(U_6254,U_6251))
        | ? [U_6250] :
            ( ~ hBOOL(hAPP(U_6254,hAPP(c_Int_Onat,U_6250)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6250)) ) )
    & ! [U_6253] :
        ( ! [U_6249] :
            ( hBOOL(hAPP(U_6253,hAPP(c_Int_Onat,U_6249)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6249)) )
        | ? [U_6248] : ~ hBOOL(hAPP(U_6253,U_6248)) ) ),
    inference(miniscope,[status(thm)],[f_1774_2]) ).

fof(f_1774_4,plain,
    ( ! [U_6254] :
        ( ! [U_6251] : hBOOL(hAPP(U_6254,U_6251))
        | ? [U_6250] :
            ( ~ hBOOL(hAPP(U_6254,hAPP(c_Int_Onat,U_6250)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6250)) ) )
    & ! [U_6253] :
        ( ! [U_6249] :
            ( hBOOL(hAPP(U_6253,hAPP(c_Int_Onat,U_6249)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6249)) )
        | ~ hBOOL(hAPP(U_6253,sK125(U_6253))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_6248,sK125(U_6253))],[f_1774_3]) ).

fof(f_1774_5,plain,
    ( ! [U_6254] :
        ( ! [U_6251] : hBOOL(hAPP(U_6254,U_6251))
        | ( ~ hBOOL(hAPP(U_6254,hAPP(c_Int_Onat,sK126(U_6254))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_6254))) ) )
    & ! [U_6253] :
        ( ! [U_6249] :
            ( hBOOL(hAPP(U_6253,hAPP(c_Int_Onat,U_6249)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6249)) )
        | ~ hBOOL(hAPP(U_6253,sK125(U_6253))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_6250,sK126(U_6254))],[f_1774_4]) ).

cnf(f_1774_6,plain,
    ( hBOOL(hAPP(U_6253,hAPP(c_Int_Onat,U_6249)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6249))
    | ~ hBOOL(hAPP(U_6253,sK125(U_6253))) ),
    inference(clausify,[status(thm)],[f_1774_5]) ).

cnf(f_1774_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_6254)))
    | hBOOL(hAPP(U_6254,U_6251)) ),
    inference(clausify,[status(thm)],[f_1774_5]) ).

cnf(f_1774_8,plain,
    ( ~ hBOOL(hAPP(U_6254,hAPP(c_Int_Onat,sK126(U_6254))))
    | hBOOL(hAPP(U_6254,U_6251)) ),
    inference(clausify,[status(thm)],[f_1774_5]) ).

fof(f_1775_1,plain,
    ! [V_Pa_2] :
      ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).

fof(f_1775_2,plain,
    ! [U_6259] :
      ( ( ? [U_6258] : hBOOL(hAPP(U_6259,U_6258))
        | ! [U_6257] :
            ( ~ hBOOL(hAPP(U_6259,hAPP(c_Int_Onat,U_6257)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6257)) ) )
      & ( ? [U_6256] :
            ( hBOOL(hAPP(U_6259,hAPP(c_Int_Onat,U_6256)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6256)) )
        | ! [U_6255] : ~ hBOOL(hAPP(U_6259,U_6255)) ) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

fof(f_1775_3,plain,
    ( ! [U_6261] :
        ( ? [U_6258] : hBOOL(hAPP(U_6261,U_6258))
        | ! [U_6257] :
            ( ~ hBOOL(hAPP(U_6261,hAPP(c_Int_Onat,U_6257)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6257)) ) )
    & ! [U_6260] :
        ( ? [U_6256] :
            ( hBOOL(hAPP(U_6260,hAPP(c_Int_Onat,U_6256)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6256)) )
        | ! [U_6255] : ~ hBOOL(hAPP(U_6260,U_6255)) ) ),
    inference(miniscope,[status(thm)],[f_1775_2]) ).

fof(f_1775_4,plain,
    ( ! [U_6261] :
        ( ? [U_6258] : hBOOL(hAPP(U_6261,U_6258))
        | ! [U_6257] :
            ( ~ hBOOL(hAPP(U_6261,hAPP(c_Int_Onat,U_6257)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6257)) ) )
    & ! [U_6260] :
        ( ( hBOOL(hAPP(U_6260,hAPP(c_Int_Onat,sK127(U_6260))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6260))) )
        | ! [U_6255] : ~ hBOOL(hAPP(U_6260,U_6255)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_6256,sK127(U_6260))],[f_1775_3]) ).

fof(f_1775_5,plain,
    ( ! [U_6261] :
        ( hBOOL(hAPP(U_6261,sK128(U_6261)))
        | ! [U_6257] :
            ( ~ hBOOL(hAPP(U_6261,hAPP(c_Int_Onat,U_6257)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6257)) ) )
    & ! [U_6260] :
        ( ( hBOOL(hAPP(U_6260,hAPP(c_Int_Onat,sK127(U_6260))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6260))) )
        | ! [U_6255] : ~ hBOOL(hAPP(U_6260,U_6255)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_6258,sK128(U_6261))],[f_1775_4]) ).

cnf(f_1775_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6260)))
    | ~ hBOOL(hAPP(U_6260,U_6255)) ),
    inference(clausify,[status(thm)],[f_1775_5]) ).

cnf(f_1775_7,plain,
    ( hBOOL(hAPP(U_6260,hAPP(c_Int_Onat,sK127(U_6260))))
    | ~ hBOOL(hAPP(U_6260,U_6255)) ),
    inference(clausify,[status(thm)],[f_1775_5]) ).

cnf(f_1775_8,plain,
    ( hBOOL(hAPP(U_6261,sK128(U_6261)))
    | ~ hBOOL(hAPP(U_6261,hAPP(c_Int_Onat,U_6257)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6257)) ),
    inference(clausify,[status(thm)],[f_1775_5]) ).

fof(f_1776_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_1776_2,plain,
    ! [U_6263,U_6262] :
      ( ( ( hAPP(c_Int_Onat,U_6262) = hAPP(c_Int_Onat,U_6263)
          | U_6262 != U_6263 )
        & ( U_6262 = U_6263
          | hAPP(c_Int_Onat,U_6262) != hAPP(c_Int_Onat,U_6263) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6263))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6262)) ),
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

cnf(f_1776_3,plain,
    ( U_6262 = U_6263
    | hAPP(c_Int_Onat,U_6262) != hAPP(c_Int_Onat,U_6263)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6262)) ),
    inference(clausify,[status(thm)],[f_1776_2]) ).

cnf(f_1776_4,plain,
    ( hAPP(c_Int_Onat,U_6262) = hAPP(c_Int_Onat,U_6263)
    | U_6262 != U_6263
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6262)) ),
    inference(clausify,[status(thm)],[f_1776_2]) ).

fof(f_1777_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_1777_2,plain,
    ! [U_6264] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6264),U_6264) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_6264 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

cnf(f_1777_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6264),U_6264) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6264 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1777_2]) ).

fof(f_1778_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_1778_2,plain,
    ! [U_6266,U_6265] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6265,tc_HOL_Obool)),U_6266),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6265,tc_HOL_Obool)),U_6266)))
        | U_6266 != c_Orderings_Obot__class_Obot(tc_fun(U_6265,tc_HOL_Obool)) )
      & ( U_6266 = c_Orderings_Obot__class_Obot(tc_fun(U_6265,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6265,tc_HOL_Obool)),U_6266),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6265,tc_HOL_Obool)),U_6266))) ) ),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

fof(f_1778_3,plain,
    ( ! [U_6270,U_6268] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6268,tc_HOL_Obool)),U_6270),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6268,tc_HOL_Obool)),U_6270)))
        | U_6270 != c_Orderings_Obot__class_Obot(tc_fun(U_6268,tc_HOL_Obool)) )
    & ! [U_6269,U_6267] :
        ( U_6269 = c_Orderings_Obot__class_Obot(tc_fun(U_6267,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6267,tc_HOL_Obool)),U_6269),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6267,tc_HOL_Obool)),U_6269))) ) ),
    inference(miniscope,[status(thm)],[f_1778_2]) ).

cnf(f_1778_4,plain,
    ( U_6269 = c_Orderings_Obot__class_Obot(tc_fun(U_6267,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6267,tc_HOL_Obool)),U_6269),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6267,tc_HOL_Obool)),U_6269))) ),
    inference(clausify,[status(thm)],[f_1778_3]) ).

cnf(f_1778_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6268,tc_HOL_Obool)),U_6270),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6268,tc_HOL_Obool)),U_6270)))
    | U_6270 != c_Orderings_Obot__class_Obot(tc_fun(U_6268,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1778_3]) ).

fof(f_1779_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_1779_2,plain,
    ! [U_6272,U_6271] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6271,tc_HOL_Obool)),U_6272),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6271,tc_HOL_Obool)),U_6272)) = c_Orderings_Obot__class_Obot(tc_fun(U_6271,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

cnf(f_1779_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6271,tc_HOL_Obool)),U_6272),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6271,tc_HOL_Obool)),U_6272)) = c_Orderings_Obot__class_Obot(tc_fun(U_6271,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1779_2]) ).

fof(f_1780_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_1780_2,plain,
    ! [U_6274,U_6273] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6273,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6273,tc_HOL_Obool)),U_6274)),U_6274) = c_Orderings_Obot__class_Obot(tc_fun(U_6273,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

cnf(f_1780_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6273,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6273,tc_HOL_Obool)),U_6274)),U_6274) = c_Orderings_Obot__class_Obot(tc_fun(U_6273,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1780_2]) ).

fof(f_1781_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_1781_2,plain,
    ! [U_6276,U_6275] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6275))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6276))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6276)),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

cnf(f_1781_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_6275))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6276))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6276)),
    inference(clausify,[status(thm)],[f_1781_2]) ).

fof(f_1782_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_1782_2,plain,
    ! [U_6278,U_6277] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6277,U_6278)),U_6278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

cnf(f_1782_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6277,U_6278)),U_6278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1782_2]) ).

fof(f_1783_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_1783_2,plain,
    ! [U_6279] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6279,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6279
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6279),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

fof(f_1783_3,plain,
    ( ! [U_6281] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6281,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6281
    & ! [U_6280] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6280),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_1783_2]) ).

cnf(f_1783_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6280),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1783_3]) ).

cnf(f_1783_5,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6281,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6281,
    inference(clausify,[status(thm)],[f_1783_3]) ).

fof(f_1784_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_1784_2,plain,
    ! [U_6282] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6282) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6282)),
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

cnf(f_1784_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6282) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6282)),
    inference(clausify,[status(thm)],[f_1784_2]) ).

fof(f_1785_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_1785_2,plain,
    ! [U_6283] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6283)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6283),
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

cnf(f_1785_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6283)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6283),
    inference(clausify,[status(thm)],[f_1785_2]) ).

fof(f_1786_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_1786_2,plain,
    ! [U_6286,U_6285,U_6284] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6284,tc_HOL_Obool)),U_6285),U_6286)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6284,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),U_6285)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),U_6286)),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

cnf(f_1786_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6284,tc_HOL_Obool)),U_6285),U_6286)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6284,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),U_6285)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6284,tc_HOL_Obool)),U_6286)),
    inference(clausify,[status(thm)],[f_1786_2]) ).

fof(f_1787_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_1787_2,plain,
    ! [U_6289,U_6288,U_6287] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6287,tc_HOL_Obool)),U_6288),U_6289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6287,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),U_6288)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),U_6289)),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

cnf(f_1787_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6287,tc_HOL_Obool)),U_6288),U_6289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6287,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),U_6288)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6287,tc_HOL_Obool)),U_6289)),
    inference(clausify,[status(thm)],[f_1787_2]) ).

fof(f_1788_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_1788_2,plain,
    ! [U_6292,U_6291,U_6290] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6290),U_6291)),U_6292) = 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_6290),U_6292)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6291),U_6292))),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_6290,U_6292)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6291,U_6292))),U_6292)),
    inference(variable_rename,[status(thm)],[f_1788_1]) ).

cnf(f_1788_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6290),U_6291)),U_6292) = 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_6290),U_6292)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6291),U_6292))),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_6290,U_6292)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6291,U_6292))),U_6292)),
    inference(clausify,[status(thm)],[f_1788_2]) ).

fof(f_1789_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_1789_2,plain,
    ! [U_6295,U_6294,U_6293] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6293,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6293,tc_HOL_Obool)),U_6294),U_6295)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6293,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6293,tc_HOL_Obool)),U_6294)),U_6295),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

cnf(f_1789_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6293,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6293,tc_HOL_Obool)),U_6294),U_6295)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6293,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6293,tc_HOL_Obool)),U_6294)),U_6295),
    inference(clausify,[status(thm)],[f_1789_2]) ).

fof(f_1790_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_1790_2,plain,
    ! [U_6298,U_6297,U_6296] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6296,tc_HOL_Obool)),U_6297),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6296,tc_HOL_Obool)),U_6298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6296,tc_HOL_Obool)),U_6297),U_6298),
    inference(variable_rename,[status(thm)],[f_1790_1]) ).

cnf(f_1790_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6296,tc_HOL_Obool)),U_6297),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6296,tc_HOL_Obool)),U_6298)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6296,tc_HOL_Obool)),U_6297),U_6298),
    inference(clausify,[status(thm)],[f_1790_2]) ).

fof(f_1791_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_1791_2,plain,
    ! [U_6301,U_6300,U_6299] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6299,tc_HOL_Obool)),U_6300),U_6301) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6299,tc_HOL_Obool)),U_6300),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6299,tc_HOL_Obool)),U_6301)),
    inference(variable_rename,[status(thm)],[f_1791_1]) ).

cnf(f_1791_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6299,tc_HOL_Obool)),U_6300),U_6301) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6299,tc_HOL_Obool)),U_6300),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6299,tc_HOL_Obool)),U_6301)),
    inference(clausify,[status(thm)],[f_1791_2]) ).

fof(f_1792_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_1792_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_1792_1]) ).

fof(f_1793_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_1793_2,plain,
    ! [U_6302] :
      ( hAPP(c_Int_Onat,U_6302) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6302)) ),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

cnf(f_1793_3,plain,
    ( hAPP(c_Int_Onat,U_6302) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6302)) ),
    inference(clausify,[status(thm)],[f_1793_2]) ).

fof(f_1794_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_1794_2,plain,
    ! [U_6303] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6303)) = U_6303
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6303)) ),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

cnf(f_1794_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6303)) = U_6303
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6303)) ),
    inference(clausify,[status(thm)],[f_1794_2]) ).

fof(f_1795_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_1795_2,plain,
    ! [U_6307,U_6306,U_6305,U_6304] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6307)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),U_6306),U_6307)
          | U_6305 = c_Groups_Ozero__class_Ozero(U_6304) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6307)) = c_Groups_Ozero__class_Ozero(U_6304)
          | U_6305 != c_Groups_Ozero__class_Ozero(U_6304) ) )
      | ~ class_Divides_Osemiring__div(U_6304) ),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

cnf(f_1795_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6307)) = c_Groups_Ozero__class_Ozero(U_6304)
    | U_6305 != c_Groups_Ozero__class_Ozero(U_6304)
    | ~ class_Divides_Osemiring__div(U_6304) ),
    inference(clausify,[status(thm)],[f_1795_2]) ).

cnf(f_1795_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6304),U_6305),U_6307)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6304),U_6306),U_6307)
    | U_6305 = c_Groups_Ozero__class_Ozero(U_6304)
    | ~ class_Divides_Osemiring__div(U_6304) ),
    inference(clausify,[status(thm)],[f_1795_2]) ).

fof(f_1796_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_1796_2,plain,
    ! [U_6310,U_6309,U_6308] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6310),U_6309)),U_6309) = U_6310
      | U_6309 = c_Groups_Ozero__class_Ozero(U_6308)
      | ~ class_Divides_Osemiring__div(U_6308) ),
    inference(variable_rename,[status(thm)],[f_1796_1]) ).

cnf(f_1796_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6310),U_6309)),U_6309) = U_6310
    | U_6309 = c_Groups_Ozero__class_Ozero(U_6308)
    | ~ class_Divides_Osemiring__div(U_6308) ),
    inference(clausify,[status(thm)],[f_1796_2]) ).

fof(f_1797_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_1797_2,plain,
    ! [U_6313,U_6312,U_6311] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6311),U_6312),U_6313)),U_6312) = U_6313
      | U_6312 = c_Groups_Ozero__class_Ozero(U_6311)
      | ~ class_Divides_Osemiring__div(U_6311) ),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

cnf(f_1797_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6311),U_6312),U_6313)),U_6312) = U_6313
    | U_6312 = c_Groups_Ozero__class_Ozero(U_6311)
    | ~ class_Divides_Osemiring__div(U_6311) ),
    inference(clausify,[status(thm)],[f_1797_2]) ).

fof(f_1798_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_1798_2,plain,
    ! [U_6317,U_6316,U_6315,U_6314] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6314),U_6316),U_6315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6314),U_6317),U_6315)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6314),U_6316),U_6317)
      | U_6315 = c_Groups_Ozero__class_Ozero(U_6314)
      | ~ class_Divides_Osemiring__div(U_6314) ),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

cnf(f_1798_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6314),U_6316),U_6315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6314),U_6317),U_6315)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6314),U_6316),U_6317)
    | U_6315 = c_Groups_Ozero__class_Ozero(U_6314)
    | ~ class_Divides_Osemiring__div(U_6314) ),
    inference(clausify,[status(thm)],[f_1798_2]) ).

fof(f_1799_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_1799_2,plain,
    ! [U_6321,U_6320,U_6319,U_6318] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6318),U_6319),U_6320)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6318),U_6319),U_6321)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6318),U_6320),U_6321)
      | U_6319 = c_Groups_Ozero__class_Ozero(U_6318)
      | ~ class_Divides_Osemiring__div(U_6318) ),
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

cnf(f_1799_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6318),U_6319),U_6320)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6318),U_6319),U_6321)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6318),U_6320),U_6321)
    | U_6319 = c_Groups_Ozero__class_Ozero(U_6318)
    | ~ class_Divides_Osemiring__div(U_6318) ),
    inference(clausify,[status(thm)],[f_1799_2]) ).

fof(f_1800_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_1800_2,plain,
    ! [U_6323,U_6322] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6322),U_6323),U_6323) = c_Groups_Oone__class_Oone(U_6322)
      | U_6323 = c_Groups_Ozero__class_Ozero(U_6322)
      | ~ class_Divides_Osemiring__div(U_6322) ),
    inference(variable_rename,[status(thm)],[f_1800_1]) ).

cnf(f_1800_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6322),U_6323),U_6323) = c_Groups_Oone__class_Oone(U_6322)
    | U_6323 = c_Groups_Ozero__class_Ozero(U_6322)
    | ~ class_Divides_Osemiring__div(U_6322) ),
    inference(clausify,[status(thm)],[f_1800_2]) ).

fof(f_1801_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_1801_2,plain,
    ! [U_6326,U_6325,U_6324] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6324),c_Divides_Odiv__class_Omod(U_6324,U_6325,U_6326)),U_6326) = c_Groups_Ozero__class_Ozero(U_6324)
      | ~ class_Divides_Osemiring__div(U_6324) ),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

cnf(f_1801_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6324),c_Divides_Odiv__class_Omod(U_6324,U_6325,U_6326)),U_6326) = c_Groups_Ozero__class_Ozero(U_6324)
    | ~ class_Divides_Osemiring__div(U_6324) ),
    inference(clausify,[status(thm)],[f_1801_2]) ).

fof(f_1802_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_1802_2,plain,
    ! [U_6327] :
      ( hAPP(c_Int_Onat,U_6327) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6327),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

cnf(f_1802_3,plain,
    ( hAPP(c_Int_Onat,U_6327) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6327),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1802_2]) ).

fof(f_1803_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_1803_2,plain,
    ! [U_6328] :
      ( ( hAPP(c_Int_Onat,U_6328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6328),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6328),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_6328) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1803_1]) ).

fof(f_1803_3,plain,
    ( ! [U_6330] :
        ( hAPP(c_Int_Onat,U_6330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6329] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_6329) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1803_2]) ).

cnf(f_1803_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_6329) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1803_3]) ).

cnf(f_1803_5,plain,
    ( hAPP(c_Int_Onat,U_6330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6330),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1803_3]) ).

fof(f_1804_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_1804_2,plain,
    ! [U_6333,U_6332,U_6331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6332),U_6333)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6331),U_6333)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6333),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6332)) ),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

cnf(f_1804_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_6332),U_6333)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6331),U_6333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6333),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6331),U_6332)) ),
    inference(clausify,[status(thm)],[f_1804_2]) ).

fof(f_1805_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_1805_2,plain,
    ! [U_6336,U_6335,U_6334] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6334),U_6336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6335),U_6336)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6336))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6334),U_6335)) ),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

cnf(f_1805_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_6334),U_6336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6335),U_6336)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6334),U_6335)) ),
    inference(clausify,[status(thm)],[f_1805_2]) ).

fof(f_1806_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_1806_2,plain,
    ! [U_6338,U_6337] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6337),U_6338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6338),U_6337))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6337),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

cnf(f_1806_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6337),U_6338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6338),U_6337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6337),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1806_2]) ).

fof(f_1807_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_1807_2,plain,
    ! [U_6341,U_6340,U_6339] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6339),U_6340)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6339),U_6341)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6340),U_6341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6340))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6339),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6339),U_6340)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6339),U_6341)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6340),U_6341))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6339),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1807_2]) ).

fof(f_1808_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_1808_2,plain,
    ! [U_6343,U_6342] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6342),U_6343)),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_6343))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6342),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6342),U_6343)),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_6343))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6342),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1808_2]) ).

fof(f_1809_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_1809_2,plain,
    ! [U_6345,U_6344] :
      ( ( ( 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_6345),U_6344)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6345),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6345),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_6345),U_6344))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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_6345),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_6345),U_6344)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1809_2]) ).

cnf(f_1809_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_6345),U_6344)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6345),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6344),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1809_2]) ).

fof(f_1810_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_1810_2,plain,
    ! [U_6347,U_6346] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6346),U_6347) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6346),U_6347))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6346)) ),
    inference(variable_rename,[status(thm)],[f_1810_1]) ).

cnf(f_1810_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6346),U_6347) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6346),U_6347))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6346)) ),
    inference(clausify,[status(thm)],[f_1810_2]) ).

fof(f_1811_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_1811_2,plain,
    ! [U_6349,U_6348] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6348),U_6349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6349),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_6348)) ),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

cnf(f_1811_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_6348),U_6349)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6349),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_6348)) ),
    inference(clausify,[status(thm)],[f_1811_2]) ).

fof(f_1812_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_1812_2,plain,
    ! [U_6352,U_6351,U_6350] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6350),U_6352)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6350),U_6351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6351),U_6352))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6351))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6350)) ),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

cnf(f_1812_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_6350),U_6352)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6350),U_6351)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6351),U_6352))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6351))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6350)) ),
    inference(clausify,[status(thm)],[f_1812_2]) ).

fof(f_1813_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_1813_2,plain,
    ! [U_6354,U_6353] :
      ( ( ( 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_6353),U_6354)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6354))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6354),U_6353)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6354))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6354),U_6353)) )
          | ~ 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_6353),U_6354))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6353)) ),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

cnf(f_1813_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6354),U_6353))
    | ~ 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_6353),U_6354)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6353)) ),
    inference(clausify,[status(thm)],[f_1813_2]) ).

cnf(f_1813_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6354))
    | ~ 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_6353),U_6354)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6353)) ),
    inference(clausify,[status(thm)],[f_1813_2]) ).

cnf(f_1813_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_6353),U_6354)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6354))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6354),U_6353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6353)) ),
    inference(clausify,[status(thm)],[f_1813_2]) ).

fof(f_1814_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_1814_2,plain,
    ! [U_6356,U_6355] :
      ( ( ( 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_6356),U_6355)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6355),U_6356)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6355),U_6356))
          | ~ 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_6356),U_6355))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6355)) ),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

cnf(f_1814_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6355),U_6356))
    | ~ 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_6356),U_6355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6355)) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

cnf(f_1814_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_6356),U_6355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6355),U_6356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6355)) ),
    inference(clausify,[status(thm)],[f_1814_2]) ).

fof(f_1815_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_1815_2,plain,
    ! [U_6358,U_6357] :
      ( ( ( 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_6358),U_6357)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6358)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6358))
          | ~ 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_6358),U_6357))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357)) ),
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

cnf(f_1815_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6358))
    | ~ 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_6358),U_6357)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357)) ),
    inference(clausify,[status(thm)],[f_1815_2]) ).

cnf(f_1815_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_6358),U_6357)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357)) ),
    inference(clausify,[status(thm)],[f_1815_2]) ).

fof(f_1816_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_1816_2,plain,
    ! [U_6360,U_6359] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6359),U_6360) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6360),U_6359))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6359),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6359),U_6360))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6359)) )
          & U_6360 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6360),U_6359))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6359),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6359),U_6360))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6359)) )
        | U_6360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6359),U_6360) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1816_1]) ).

fof(f_1816_3,plain,
    ( ! [U_6364,U_6362] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6362),U_6364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6362))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6362),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6362),U_6364))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6362)) )
          & U_6364 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6363,U_6361] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6363),U_6361))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6361),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6361),U_6363))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6361)) )
        | U_6363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6361),U_6363) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1816_2]) ).

cnf(f_1816_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6361),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_6361))
    | U_6363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6361),U_6363) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6363),U_6361))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6361))
    | U_6363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6361),U_6363) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6361),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6361),U_6363))
    | U_6363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6361),U_6363) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6363),U_6361))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6361),U_6363))
    | U_6363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6361),U_6363) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_8,plain,
    ( U_6364 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6362),U_6364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6362),U_6364))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6362))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6362),U_6364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

cnf(f_1816_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6362),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6362),U_6364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

fof(f_1817_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_1817_2,plain,
    ! [U_6366,U_6365] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6365)),hAPP(c_Int_Onat,U_6366)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6365),U_6366))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6366)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6365),U_6366))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6366)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6365)),hAPP(c_Int_Onat,U_6366))) ) ),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

fof(f_1817_3,plain,
    ( ! [U_6370,U_6368] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6368)),hAPP(c_Int_Onat,U_6370)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6368),U_6370))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6370)) )
    & ! [U_6369,U_6367] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6367),U_6369))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6369)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6367)),hAPP(c_Int_Onat,U_6369))) ) ),
    inference(miniscope,[status(thm)],[f_1817_2]) ).

cnf(f_1817_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6367)),hAPP(c_Int_Onat,U_6369))) ),
    inference(clausify,[status(thm)],[f_1817_3]) ).

cnf(f_1817_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6367),U_6369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6367)),hAPP(c_Int_Onat,U_6369))) ),
    inference(clausify,[status(thm)],[f_1817_3]) ).

cnf(f_1817_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6368)),hAPP(c_Int_Onat,U_6370)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6368),U_6370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6370)) ),
    inference(clausify,[status(thm)],[f_1817_3]) ).

fof(f_1818_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_1818_2,plain,
    ! [U_6372,U_6371] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6372)),hAPP(c_Int_Onat,U_6371)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6372),U_6371)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6372),U_6371))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6372)),hAPP(c_Int_Onat,U_6371))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6371)) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

cnf(f_1818_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6372),U_6371))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6372)),hAPP(c_Int_Onat,U_6371)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6371)) ),
    inference(clausify,[status(thm)],[f_1818_2]) ).

cnf(f_1818_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6372)),hAPP(c_Int_Onat,U_6371)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6372),U_6371))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6371)) ),
    inference(clausify,[status(thm)],[f_1818_2]) ).

fof(f_1819_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_1819_2,plain,
    ! [U_6374,U_6373] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6373)),hAPP(c_Int_Onat,U_6374)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6373),U_6374)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6373),U_6374))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6373)),hAPP(c_Int_Onat,U_6374))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6374))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6373)) ),
    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_6373),U_6374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6373)),hAPP(c_Int_Onat,U_6374)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6373)) ),
    inference(clausify,[status(thm)],[f_1819_2]) ).

cnf(f_1819_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6373)),hAPP(c_Int_Onat,U_6374)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6373),U_6374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6373)) ),
    inference(clausify,[status(thm)],[f_1819_2]) ).

fof(f_1820_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_1820_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_1820_1]) ).

fof(f_1821_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_1821_2,plain,
    ! [U_6376,U_6375] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6375),U_6376)),U_6375))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6376))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6375)) ),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

cnf(f_1821_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6375),U_6376)),U_6375))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6376))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6375)) ),
    inference(clausify,[status(thm)],[f_1821_2]) ).

fof(f_1822_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_1822_2,plain,
    ! [U_6379,U_6378,U_6377] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6379),U_6377)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6378),U_6379)),U_6377)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6377)) ),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

cnf(f_1822_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6379),U_6377)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6378),U_6379)),U_6377)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6377)) ),
    inference(clausify,[status(thm)],[f_1822_2]) ).

fof(f_1823_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_1823_2,plain,
    ! [U_6380] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6380)) = U_6380
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6380)) ),
    inference(variable_rename,[status(thm)],[f_1823_1]) ).

cnf(f_1823_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6380)) = U_6380
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6380)) ),
    inference(clausify,[status(thm)],[f_1823_2]) ).

fof(f_1824_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_1824_2,plain,
    ! [U_6382,U_6381] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6381) = U_6382
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6382))
        | U_6381 != hAPP(c_Int_Onat,U_6382) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6382))
          & U_6381 = hAPP(c_Int_Onat,U_6382) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6381) != U_6382 ) ),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

fof(f_1824_3,plain,
    ( ! [U_6386,U_6384] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6384) = U_6386
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6386))
        | U_6384 != hAPP(c_Int_Onat,U_6386) )
    & ! [U_6385,U_6383] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6385))
          & U_6383 = hAPP(c_Int_Onat,U_6385) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6383) != U_6385 ) ),
    inference(miniscope,[status(thm)],[f_1824_2]) ).

cnf(f_1824_4,plain,
    ( U_6383 = hAPP(c_Int_Onat,U_6385)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6383) != U_6385 ),
    inference(clausify,[status(thm)],[f_1824_3]) ).

cnf(f_1824_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6385))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6383) != U_6385 ),
    inference(clausify,[status(thm)],[f_1824_3]) ).

cnf(f_1824_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6384) = U_6386
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6386))
    | U_6384 != hAPP(c_Int_Onat,U_6386) ),
    inference(clausify,[status(thm)],[f_1824_3]) ).

fof(f_1825_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_1825_2,plain,
    ! [U_6387] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6387)) = 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_6387)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6387)) = U_6387
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6387)) ) ),
    inference(variable_rename,[status(thm)],[f_1825_1]) ).

fof(f_1825_3,plain,
    ( ! [U_6389] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6389)) = 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_6389)) )
    & ! [U_6388] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6388)) = U_6388
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6388)) ) ),
    inference(miniscope,[status(thm)],[f_1825_2]) ).

cnf(f_1825_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6388)) = U_6388
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6388)) ),
    inference(clausify,[status(thm)],[f_1825_3]) ).

cnf(f_1825_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6389)) = 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_6389)) ),
    inference(clausify,[status(thm)],[f_1825_3]) ).

fof(f_1826_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_1826_2,plain,
    ! [U_6391,U_6390] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6390),hAPP(c_Int_Onat,U_6391)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6390)),U_6391)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6390)),U_6391))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6390),hAPP(c_Int_Onat,U_6391))) ) ),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

fof(f_1826_3,plain,
    ( ! [U_6395,U_6393] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6393),hAPP(c_Int_Onat,U_6395)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6393)),U_6395)) )
    & ! [U_6394,U_6392] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6392)),U_6394))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6392),hAPP(c_Int_Onat,U_6394))) ) ),
    inference(miniscope,[status(thm)],[f_1826_2]) ).

cnf(f_1826_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_6392)),U_6394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6392),hAPP(c_Int_Onat,U_6394))) ),
    inference(clausify,[status(thm)],[f_1826_3]) ).

cnf(f_1826_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6393),hAPP(c_Int_Onat,U_6395)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6393)),U_6395)) ),
    inference(clausify,[status(thm)],[f_1826_3]) ).

fof(f_1827_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_1827_2,plain,
    ! [U_6398,U_6397,U_6396] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6396,tc_HOL_Obool)),U_6397),U_6398) = c_Orderings_Obot__class_Obot(tc_fun(U_6396,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6396,tc_HOL_Obool)),U_6397),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6396,tc_HOL_Obool)),U_6398))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6396,tc_HOL_Obool)),U_6397),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6396,tc_HOL_Obool)),U_6398)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6396,tc_HOL_Obool)),U_6397),U_6398) != c_Orderings_Obot__class_Obot(tc_fun(U_6396,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

fof(f_1827_3,plain,
    ( ! [U_6404,U_6402,U_6400] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6400,tc_HOL_Obool)),U_6402),U_6404) = c_Orderings_Obot__class_Obot(tc_fun(U_6400,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6400,tc_HOL_Obool)),U_6402),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6400,tc_HOL_Obool)),U_6404))) )
    & ! [U_6403,U_6401,U_6399] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6399,tc_HOL_Obool)),U_6401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6399,tc_HOL_Obool)),U_6403)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6399,tc_HOL_Obool)),U_6401),U_6403) != c_Orderings_Obot__class_Obot(tc_fun(U_6399,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_1827_2]) ).

cnf(f_1827_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6399,tc_HOL_Obool)),U_6401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6399,tc_HOL_Obool)),U_6403)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6399,tc_HOL_Obool)),U_6401),U_6403) != c_Orderings_Obot__class_Obot(tc_fun(U_6399,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1827_3]) ).

cnf(f_1827_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6400,tc_HOL_Obool)),U_6402),U_6404) = c_Orderings_Obot__class_Obot(tc_fun(U_6400,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6400,tc_HOL_Obool)),U_6402),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6400,tc_HOL_Obool)),U_6404))) ),
    inference(clausify,[status(thm)],[f_1827_3]) ).

fof(f_1828_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_1828_2,plain,
    ! [U_6406,U_6405] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6405,U_6406)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6405),hAPP(c_Int_Onat,U_6406))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6406))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6405)) ),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

cnf(f_1828_3,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6405,U_6406)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6405),hAPP(c_Int_Onat,U_6406))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6406))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6405)) ),
    inference(clausify,[status(thm)],[f_1828_2]) ).

fof(f_1829_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_1829_2,plain,
    ! [U_6408,U_6407] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6407),hAPP(c_Int_Onat,U_6408)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6407,U_6408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6407)) ),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

cnf(f_1829_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6407),hAPP(c_Int_Onat,U_6408)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6407,U_6408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6407)) ),
    inference(clausify,[status(thm)],[f_1829_2]) ).

fof(f_1830_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_1830_2,plain,
    ! [U_6409] : 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_6409))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1830_1]) ).

cnf(f_1830_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_6409))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1830_2]) ).

fof(f_1831_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_1831_2,plain,
    ! [U_6412,U_6411,U_6410] : 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_6410),U_6411)),U_6411)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6410,U_6411))),U_6412) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6410),U_6412),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

cnf(f_1831_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_6410),U_6411)),U_6411)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6410,U_6411))),U_6412) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6410),U_6412),
    inference(clausify,[status(thm)],[f_1831_2]) ).

fof(f_1832_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_1832_2,plain,
    ! [U_6415,U_6414,U_6413] : 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_6413),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6414),U_6413))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6414,U_6413))),U_6415) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6414),U_6415),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

cnf(f_1832_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_6413),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6414),U_6413))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6414,U_6413))),U_6415) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6414),U_6415),
    inference(clausify,[status(thm)],[f_1832_2]) ).

fof(f_1833_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_1833_2,plain,
    ! [U_6418,U_6417,U_6416] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),U_6417)),U_6418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6417),U_6418))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6417,U_6418))),U_6418)),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

cnf(f_1833_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),U_6417)),U_6418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6417),U_6418))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6416),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6417,U_6418))),U_6418)),
    inference(clausify,[status(thm)],[f_1833_2]) ).

fof(f_1834_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_1834_2,plain,
    ! [U_6420,U_6419] : U_6419 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6420),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6419),U_6420))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6419,U_6420)),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

cnf(f_1834_3,plain,
    U_6419 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6420),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6419),U_6420))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6419,U_6420)),
    inference(clausify,[status(thm)],[f_1834_2]) ).

fof(f_1835_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_1835_2,plain,
    ! [U_6421] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6421),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

cnf(f_1835_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6421),
    inference(clausify,[status(thm)],[f_1835_2]) ).

fof(f_1836_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_1836_2,plain,
    ! [U_6423,U_6422] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6422,U_6423) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6422),U_6423)),U_6423)),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

cnf(f_1836_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6422,U_6423) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6422),U_6423)),U_6423)),
    inference(clausify,[status(thm)],[f_1836_2]) ).

fof(f_1837_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_1837_2,plain,
    ! [U_6425,U_6424] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6424),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6425),U_6424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6425),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6425,U_6424)),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

cnf(f_1837_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6424),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6425),U_6424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6425),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6425,U_6424)),
    inference(clausify,[status(thm)],[f_1837_2]) ).

fof(f_1838_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_1838_2,plain,
    ! [U_6427,U_6426] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6426),U_6427))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6426))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6427))),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

cnf(f_1838_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_6426),U_6427))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6426))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6427))),
    inference(clausify,[status(thm)],[f_1838_2]) ).

fof(f_1839_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_1839_2,plain,
    ! [U_6431,U_6430,U_6429,U_6428] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6428),U_6430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6428),U_6431),U_6429))),U_6429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6428),U_6431),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6428),U_6430),U_6429))
      | U_6429 = c_Groups_Ozero__class_Ozero(U_6428)
      | ~ class_Divides_Osemiring__div(U_6428) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

cnf(f_1839_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6428),U_6430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6428),U_6431),U_6429))),U_6429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6428),U_6431),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6428),U_6430),U_6429))
    | U_6429 = c_Groups_Ozero__class_Ozero(U_6428)
    | ~ class_Divides_Osemiring__div(U_6428) ),
    inference(clausify,[status(thm)],[f_1839_2]) ).

fof(f_1840_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_1840_2,plain,
    ! [U_6435,U_6434,U_6433,U_6432] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6432),U_6434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6432),U_6433),U_6435))),U_6433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6432),U_6435),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6432),U_6434),U_6433))
      | U_6433 = c_Groups_Ozero__class_Ozero(U_6432)
      | ~ class_Divides_Osemiring__div(U_6432) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

cnf(f_1840_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6432),U_6434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6432),U_6433),U_6435))),U_6433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6432),U_6435),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6432),U_6434),U_6433))
    | U_6433 = c_Groups_Ozero__class_Ozero(U_6432)
    | ~ class_Divides_Osemiring__div(U_6432) ),
    inference(clausify,[status(thm)],[f_1840_2]) ).

fof(f_1841_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_1841_2,plain,
    ! [U_6438,U_6437,U_6436] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6436),U_6438),U_6437)),U_6437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6436),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6436),U_6438),U_6437)),c_Groups_Oone__class_Oone(U_6436))
      | U_6437 = c_Groups_Ozero__class_Ozero(U_6436)
      | ~ class_Divides_Osemiring__div(U_6436) ),
    inference(variable_rename,[status(thm)],[f_1841_1]) ).

cnf(f_1841_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6436),U_6438),U_6437)),U_6437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6436),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6436),U_6438),U_6437)),c_Groups_Oone__class_Oone(U_6436))
    | U_6437 = c_Groups_Ozero__class_Ozero(U_6436)
    | ~ class_Divides_Osemiring__div(U_6436) ),
    inference(clausify,[status(thm)],[f_1841_2]) ).

fof(f_1842_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_1842_2,plain,
    ! [U_6441,U_6440,U_6439] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6439),U_6440),U_6441)),U_6440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6439),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6439),U_6441),U_6440)),c_Groups_Oone__class_Oone(U_6439))
      | U_6440 = c_Groups_Ozero__class_Ozero(U_6439)
      | ~ class_Divides_Osemiring__div(U_6439) ),
    inference(variable_rename,[status(thm)],[f_1842_1]) ).

cnf(f_1842_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6439),U_6440),U_6441)),U_6440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6439),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6439),U_6441),U_6440)),c_Groups_Oone__class_Oone(U_6439))
    | U_6440 = c_Groups_Ozero__class_Ozero(U_6439)
    | ~ class_Divides_Osemiring__div(U_6439) ),
    inference(clausify,[status(thm)],[f_1842_2]) ).

fof(f_1843_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_1843_2,plain,
    ! [U_6445,U_6444,U_6443,U_6442] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6442),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6442),U_6443),U_6444)),U_6444)),c_Divides_Odiv__class_Omod(U_6442,U_6443,U_6444))),U_6445) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),U_6443),U_6445)
      | ~ class_Divides_Osemiring__div(U_6442) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

cnf(f_1843_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6442),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6442),U_6443),U_6444)),U_6444)),c_Divides_Odiv__class_Omod(U_6442,U_6443,U_6444))),U_6445) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6442),U_6443),U_6445)
    | ~ class_Divides_Osemiring__div(U_6442) ),
    inference(clausify,[status(thm)],[f_1843_2]) ).

fof(f_1844_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_1844_2,plain,
    ! [U_6449,U_6448,U_6447,U_6446] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6446),U_6447),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6446),U_6448),U_6447))),c_Divides_Odiv__class_Omod(U_6446,U_6448,U_6447))),U_6449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),U_6448),U_6449)
      | ~ class_Divides_Osemiring__div(U_6446) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

cnf(f_1844_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6446),U_6447),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6446),U_6448),U_6447))),c_Divides_Odiv__class_Omod(U_6446,U_6448,U_6447))),U_6449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6446),U_6448),U_6449)
    | ~ class_Divides_Osemiring__div(U_6446) ),
    inference(clausify,[status(thm)],[f_1844_2]) ).

fof(f_1845_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_1845_2,plain,
    ! [U_6452,U_6451,U_6450] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6450),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6450),U_6451),U_6452)),U_6452)),c_Divides_Odiv__class_Omod(U_6450,U_6451,U_6452)) = U_6451
      | ~ class_Divides_Osemiring__div(U_6450) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

cnf(f_1845_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6450),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6450),U_6451),U_6452)),U_6452)),c_Divides_Odiv__class_Omod(U_6450,U_6451,U_6452)) = U_6451
    | ~ class_Divides_Osemiring__div(U_6450) ),
    inference(clausify,[status(thm)],[f_1845_2]) ).

fof(f_1846_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_1846_2,plain,
    ! [U_6455,U_6454,U_6453] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6453),U_6454),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6453),U_6455),U_6454))),c_Divides_Odiv__class_Omod(U_6453,U_6455,U_6454)) = U_6455
      | ~ class_Divides_Osemiring__div(U_6453) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

cnf(f_1846_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6453),U_6454),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6453),U_6455),U_6454))),c_Divides_Odiv__class_Omod(U_6453,U_6455,U_6454)) = U_6455
    | ~ class_Divides_Osemiring__div(U_6453) ),
    inference(clausify,[status(thm)],[f_1846_2]) ).

fof(f_1847_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_1847_2,plain,
    ! [U_6458,U_6457,U_6456] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6456),c_Divides_Odiv__class_Omod(U_6456,U_6457,U_6458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6456),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6456),U_6457),U_6458)),U_6458)) = U_6457
      | ~ class_Divides_Osemiring__div(U_6456) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

cnf(f_1847_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6456),c_Divides_Odiv__class_Omod(U_6456,U_6457,U_6458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6456),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6456),U_6457),U_6458)),U_6458)) = U_6457
    | ~ class_Divides_Osemiring__div(U_6456) ),
    inference(clausify,[status(thm)],[f_1847_2]) ).

fof(f_1848_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_1848_2,plain,
    ! [U_6459] :
      ( c_Int_Oiszero(U_6459,hAPP(c_Int_Onumber__class_Onumber__of(U_6459),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_6459) ),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

cnf(f_1848_3,plain,
    ( c_Int_Oiszero(U_6459,hAPP(c_Int_Onumber__class_Onumber__of(U_6459),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_6459) ),
    inference(clausify,[status(thm)],[f_1848_2]) ).

fof(f_1849_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_1849_2,plain,
    ! [U_6461,U_6460] :
      ( ~ c_Int_Oiszero(U_6460,hAPP(c_Int_Onumber__class_Onumber__of(U_6460),c_Int_OBit1(U_6461)))
      | ~ class_Int_Oring__char__0(U_6460)
      | ~ class_Int_Onumber__ring(U_6460) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

cnf(f_1849_3,plain,
    ( ~ c_Int_Oiszero(U_6460,hAPP(c_Int_Onumber__class_Onumber__of(U_6460),c_Int_OBit1(U_6461)))
    | ~ class_Int_Oring__char__0(U_6460)
    | ~ class_Int_Onumber__ring(U_6460) ),
    inference(clausify,[status(thm)],[f_1849_2]) ).

fof(f_1850_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_1850_2,plain,
    ! [U_6463,U_6462] :
      ( ( ( c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),c_Int_OBit0(U_6463)))
          | ~ c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),U_6463)) )
        & ( c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),U_6463))
          | ~ c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),c_Int_OBit0(U_6463))) ) )
      | ~ class_Int_Oring__char__0(U_6462)
      | ~ class_Int_Onumber__ring(U_6462) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

cnf(f_1850_3,plain,
    ( c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),U_6463))
    | ~ c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),c_Int_OBit0(U_6463)))
    | ~ class_Int_Oring__char__0(U_6462)
    | ~ class_Int_Onumber__ring(U_6462) ),
    inference(clausify,[status(thm)],[f_1850_2]) ).

cnf(f_1850_4,plain,
    ( c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),c_Int_OBit0(U_6463)))
    | ~ c_Int_Oiszero(U_6462,hAPP(c_Int_Onumber__class_Onumber__of(U_6462),U_6463))
    | ~ class_Int_Oring__char__0(U_6462)
    | ~ class_Int_Onumber__ring(U_6462) ),
    inference(clausify,[status(thm)],[f_1850_2]) ).

fof(f_1851_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_1851_2,plain,
    ! [U_6464] :
      ( ~ c_Int_Oiszero(U_6464,hAPP(c_Int_Onumber__class_Onumber__of(U_6464),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_6464) ),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

cnf(f_1851_3,plain,
    ( ~ c_Int_Oiszero(U_6464,hAPP(c_Int_Onumber__class_Onumber__of(U_6464),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_6464) ),
    inference(clausify,[status(thm)],[f_1851_2]) ).

fof(f_1852_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_1852_2,plain,
    ! [U_6465] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_6465)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6465)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6465))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_6465))) ) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

fof(f_1852_3,plain,
    ( ! [U_6467] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_6467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6467)) )
    & ! [U_6466] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6466))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_6466))) ) ),
    inference(miniscope,[status(thm)],[f_1852_2]) ).

cnf(f_1852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6466))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_6466))) ),
    inference(clausify,[status(thm)],[f_1852_3]) ).

cnf(f_1852_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_6467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6467)) ),
    inference(clausify,[status(thm)],[f_1852_3]) ).

fof(f_1853_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_1853_2,plain,
    ! [U_6469,U_6468] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6468)),hAPP(c_Int_Onat,U_6469)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),U_6469)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),U_6469))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6468)),hAPP(c_Int_Onat,U_6469))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

cnf(f_1853_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),U_6469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6468)),hAPP(c_Int_Onat,U_6469)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(clausify,[status(thm)],[f_1853_2]) ).

cnf(f_1853_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6468)),hAPP(c_Int_Onat,U_6469)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6468),U_6469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(clausify,[status(thm)],[f_1853_2]) ).

fof(f_1854_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_1854_2,plain,
    ! [U_6471,U_6470] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6470)),hAPP(c_Int_Onat,U_6471)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6470)),hAPP(c_Int_Onat,U_6471))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6470)) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

cnf(f_1854_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6470)),hAPP(c_Int_Onat,U_6471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6470)) ),
    inference(clausify,[status(thm)],[f_1854_2]) ).

cnf(f_1854_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6470)),hAPP(c_Int_Onat,U_6471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6470)) ),
    inference(clausify,[status(thm)],[f_1854_2]) ).

fof(f_1855_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_1855_2,plain,
    ! [U_6473,U_6472] :
      ( ( U_6472 = hAPP(c_Int_Onat,U_6473)
        | ( U_6472 != 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_6473)) )
        | ( U_6473 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6472)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6473)) ) )
      & ( ( ( U_6472 = 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_6473)) )
          & ( U_6473 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6472)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6473)) ) )
        | U_6472 != hAPP(c_Int_Onat,U_6473) ) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

fof(f_1855_3,plain,
    ( ! [U_6477,U_6475] :
        ( U_6475 = hAPP(c_Int_Onat,U_6477)
        | ( U_6475 != 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_6477)) )
        | ( U_6477 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6475)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6477)) ) )
    & ! [U_6476,U_6474] :
        ( ( ( U_6474 = 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_6476)) )
          & ( U_6476 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6474)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6476)) ) )
        | U_6474 != hAPP(c_Int_Onat,U_6476) ) ),
    inference(miniscope,[status(thm)],[f_1855_2]) ).

cnf(f_1855_4,plain,
    ( U_6476 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6474)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6476))
    | U_6474 != hAPP(c_Int_Onat,U_6476) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_5,plain,
    ( U_6474 = 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_6476))
    | U_6474 != hAPP(c_Int_Onat,U_6476) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6477))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6477))
    | U_6475 = hAPP(c_Int_Onat,U_6477) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_7,plain,
    ( U_6475 != 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_6477))
    | U_6475 = hAPP(c_Int_Onat,U_6477) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6477))
    | U_6477 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6475)
    | U_6475 = hAPP(c_Int_Onat,U_6477) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_9,plain,
    ( U_6475 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6477 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6475)
    | U_6475 = hAPP(c_Int_Onat,U_6477) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

fof(f_1856_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_1856_2,plain,
    ! [U_6479,U_6478] :
      ( ( hAPP(c_Int_Onat,U_6478) = U_6479
        | ( U_6479 != 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_6478)) )
        | ( U_6478 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6479)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6478)) ) )
      & ( ( ( U_6479 = 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_6478)) )
          & ( U_6478 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6479)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6478)) ) )
        | hAPP(c_Int_Onat,U_6478) != U_6479 ) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

fof(f_1856_3,plain,
    ( ! [U_6483,U_6481] :
        ( hAPP(c_Int_Onat,U_6481) = U_6483
        | ( U_6483 != 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_6481)) )
        | ( U_6481 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6483)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6481)) ) )
    & ! [U_6482,U_6480] :
        ( ( ( U_6482 = 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_6480)) )
          & ( U_6480 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6482)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6480)) ) )
        | hAPP(c_Int_Onat,U_6480) != U_6482 ) ),
    inference(miniscope,[status(thm)],[f_1856_2]) ).

cnf(f_1856_4,plain,
    ( U_6480 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6482)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6480))
    | hAPP(c_Int_Onat,U_6480) != U_6482 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_5,plain,
    ( U_6482 = 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_6480))
    | hAPP(c_Int_Onat,U_6480) != U_6482 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6481))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6481))
    | hAPP(c_Int_Onat,U_6481) = U_6483 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_7,plain,
    ( U_6483 != 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_6481))
    | hAPP(c_Int_Onat,U_6481) = U_6483 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6481))
    | U_6481 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6483)
    | hAPP(c_Int_Onat,U_6481) = U_6483 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_9,plain,
    ( U_6483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6481 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6483)
    | hAPP(c_Int_Onat,U_6481) = U_6483 ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

fof(f_1857_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_1857_2,plain,
    ! [U_6485,U_6484] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6485))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6484)) ) ),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

cnf(f_1857_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6484)) ),
    inference(clausify,[status(thm)],[f_1857_2]) ).

cnf(f_1857_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6484)) ),
    inference(clausify,[status(thm)],[f_1857_2]) ).

cnf(f_1857_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6485)) ),
    inference(clausify,[status(thm)],[f_1857_2]) ).

cnf(f_1857_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_6484)),hAPP(c_Int_Onat,U_6485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6484),U_6485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6485)) ),
    inference(clausify,[status(thm)],[f_1857_2]) ).

fof(f_1858_1,plain,
    ! [V_i_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_n))
            & V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
      & ( ( ( hBOOL(hAPP(V_Pa_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_Pa_2,B_n))
              | V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
        | ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__nat]) ).

fof(f_1858_2,plain,
    ! [U_6489,U_6488] :
      ( ( hBOOL(hAPP(U_6488,hAPP(c_Int_Onat,U_6489)))
        | ( ~ hBOOL(hAPP(U_6488,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6489),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_6487] :
            ( ~ hBOOL(hAPP(U_6488,U_6487))
            & U_6489 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6487) ) )
      & ( ( ( hBOOL(hAPP(U_6488,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6489),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_6486] :
              ( hBOOL(hAPP(U_6488,U_6486))
              | U_6489 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6486) ) )
        | ~ hBOOL(hAPP(U_6488,hAPP(c_Int_Onat,U_6489))) ) ),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

fof(f_1858_3,plain,
    ( ! [U_6493,U_6491] :
        ( hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493)))
        | ( ~ hBOOL(hAPP(U_6491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6493),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_6487] :
            ( ~ hBOOL(hAPP(U_6491,U_6487))
            & U_6493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6487) ) )
    & ! [U_6492,U_6490] :
        ( ( ( hBOOL(hAPP(U_6490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6492),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_6486] :
              ( hBOOL(hAPP(U_6490,U_6486))
              | U_6492 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6486) ) )
        | ~ hBOOL(hAPP(U_6490,hAPP(c_Int_Onat,U_6492))) ) ),
    inference(miniscope,[status(thm)],[f_1858_2]) ).

fof(f_1858_4,plain,
    ( ! [U_6493,U_6491] :
        ( hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493)))
        | ( ~ hBOOL(hAPP(U_6491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6493),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_6491,sK129(U_6493,U_6491)))
          & U_6493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK129(U_6493,U_6491)) ) )
    & ! [U_6492,U_6490] :
        ( ( ( hBOOL(hAPP(U_6490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6492),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_6486] :
              ( hBOOL(hAPP(U_6490,U_6486))
              | U_6492 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6486) ) )
        | ~ hBOOL(hAPP(U_6490,hAPP(c_Int_Onat,U_6492))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_6487,sK129(U_6493,U_6491))],[f_1858_3]) ).

cnf(f_1858_5,plain,
    ( hBOOL(hAPP(U_6490,U_6486))
    | U_6492 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6486)
    | ~ hBOOL(hAPP(U_6490,hAPP(c_Int_Onat,U_6492))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

cnf(f_1858_6,plain,
    ( hBOOL(hAPP(U_6490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6490,hAPP(c_Int_Onat,U_6492))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

cnf(f_1858_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK129(U_6493,U_6491))
    | hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

cnf(f_1858_8,plain,
    ( ~ hBOOL(hAPP(U_6491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_6493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK129(U_6493,U_6491))
    | hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

cnf(f_1858_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6493),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6491,sK129(U_6493,U_6491)))
    | hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

cnf(f_1858_10,plain,
    ( ~ hBOOL(hAPP(U_6491,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_6491,sK129(U_6493,U_6491)))
    | hBOOL(hAPP(U_6491,hAPP(c_Int_Onat,U_6493))) ),
    inference(clausify,[status(thm)],[f_1858_4]) ).

fof(f_1859_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_1859_2,plain,
    ! [U_6495,U_6494] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6494)),hAPP(c_Int_Onat,U_6495)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6494),U_6495))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6495))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6494)) ),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

cnf(f_1859_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6494)),hAPP(c_Int_Onat,U_6495)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6494),U_6495))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6495))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6494)) ),
    inference(clausify,[status(thm)],[f_1859_2]) ).

fof(f_1860_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_1860_2,plain,
    ! [U_6497,U_6496] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6496),U_6497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6496)),hAPP(c_Int_Onat,U_6497))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6497))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6496)) ),
    inference(variable_rename,[status(thm)],[f_1860_1]) ).

cnf(f_1860_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6496),U_6497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6496)),hAPP(c_Int_Onat,U_6497))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6497))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6496)) ),
    inference(clausify,[status(thm)],[f_1860_2]) ).

fof(f_1861_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_1861_2,plain,
    ! [U_6499,U_6498] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6498) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6499)
        | ~ 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_6499)))
        | U_6498 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6499)) )
      & ( ( 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_6499)))
          & U_6498 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6499)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6498) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6499) ) ),
    inference(variable_rename,[status(thm)],[f_1861_1]) ).

fof(f_1861_3,plain,
    ( ! [U_6503,U_6501] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6501) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6503)
        | ~ 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_6503)))
        | U_6501 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6503)) )
    & ! [U_6502,U_6500] :
        ( ( 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_6502)))
          & U_6500 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6502)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6500) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6502) ) ),
    inference(miniscope,[status(thm)],[f_1861_2]) ).

cnf(f_1861_4,plain,
    ( U_6500 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6502))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6500) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6502) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

cnf(f_1861_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_6502)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6500) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6502) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

cnf(f_1861_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6501) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6503)
    | ~ 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_6503)))
    | U_6501 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6503)) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

fof(f_1862_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_1862_2,plain,
    ! [U_6505,U_6504] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_6504)),hAPP(c_Int_Onat,U_6505)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6504),U_6505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6504)) ),
    inference(variable_rename,[status(thm)],[f_1862_1]) ).

cnf(f_1862_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_6504)),hAPP(c_Int_Onat,U_6505)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6504),U_6505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6504)) ),
    inference(clausify,[status(thm)],[f_1862_2]) ).

fof(f_1863_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_1863_2,plain,
    ! [U_6507,U_6506] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6506),U_6507)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_6506)),hAPP(c_Int_Onat,U_6507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6506)) ),
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

cnf(f_1863_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6506),U_6507)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_6506)),hAPP(c_Int_Onat,U_6507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6506)) ),
    inference(clausify,[status(thm)],[f_1863_2]) ).

fof(f_1864_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_1864_2,plain,
    ! [U_6508] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_6508) = 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_6508)) ),
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

cnf(f_1864_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_6508) = 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_6508)) ),
    inference(clausify,[status(thm)],[f_1864_2]) ).

fof(f_1865_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_1865_2,plain,
    ! [U_6510,U_6509] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6510),U_6509)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6510)),hAPP(c_Int_Onat,U_6509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6509),U_6510))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6509)) ),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

cnf(f_1865_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6510),U_6509)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6510)),hAPP(c_Int_Onat,U_6509))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6509),U_6510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6509)) ),
    inference(clausify,[status(thm)],[f_1865_2]) ).

fof(f_1866_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_1866_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_1866_1]) ).

fof(f_1867_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_1867_2,plain,
    ! [U_6512,U_6511] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6511)),hAPP(c_Int_Onat,U_6512)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_6511,U_6512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6511)) ),
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

cnf(f_1867_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6511)),hAPP(c_Int_Onat,U_6512)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_6511,U_6512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6511)) ),
    inference(clausify,[status(thm)],[f_1867_2]) ).

fof(f_1868_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_1868_2,plain,
    ! [U_6513] :
      ( ( 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_6513)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6513)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6513))
        | ~ 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_6513))) ) ),
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

fof(f_1868_3,plain,
    ( ! [U_6515] :
        ( 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_6515)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6515)) )
    & ! [U_6514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6514))
        | ~ 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_6514))) ) ),
    inference(miniscope,[status(thm)],[f_1868_2]) ).

cnf(f_1868_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6514))
    | ~ 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_6514))) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

cnf(f_1868_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_6515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6515)) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

fof(f_1869_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_1869_2,plain,
    ! [U_6519,U_6518,U_6517,U_6516] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),U_6517) = U_6518
      | U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6519),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6519)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6519),U_6517))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517)) )
      | U_6516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6518)),U_6519) ),
    inference(variable_rename,[status(thm)],[f_1869_1]) ).

cnf(f_1869_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),U_6517) = U_6518
    | U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6518)),U_6519) ),
    inference(clausify,[status(thm)],[f_1869_2]) ).

cnf(f_1869_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6519),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6519))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),U_6517) = U_6518
    | U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6518)),U_6519) ),
    inference(clausify,[status(thm)],[f_1869_2]) ).

cnf(f_1869_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6517))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6519),U_6517))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),U_6517) = U_6518
    | U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6518)),U_6519) ),
    inference(clausify,[status(thm)],[f_1869_2]) ).

cnf(f_1869_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6519),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6517),U_6519))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6519),U_6517))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6519))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),U_6517) = U_6518
    | U_6517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6517),U_6518)),U_6519) ),
    inference(clausify,[status(thm)],[f_1869_2]) ).

fof(f_1870_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_Pa_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_1870_2,plain,
    ! [U_6530,U_6529,U_6528] :
      ( ( hBOOL(hAPP(U_6528,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6529),U_6530)))
        | ( ? [U_6527] :
              ( ~ hBOOL(hAPP(U_6528,U_6527))
              & ? [U_6526] :
                  ( U_6529 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6530),U_6527)),U_6526)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6530),U_6526)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6530),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_6525] :
              ( ~ hBOOL(hAPP(U_6528,U_6525))
              & ? [U_6524] :
                  ( U_6529 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6530),U_6525)),U_6524)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6524),U_6530))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6524)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6530)) )
        | ( ~ hBOOL(hAPP(U_6528,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6528,U_6523))
                | ! [U_6522] :
                    ( U_6529 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6530),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6530),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6530),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6528,U_6521))
                | ! [U_6520] :
                    ( U_6529 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6530),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6530))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6530)) )
          & ( hBOOL(hAPP(U_6528,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6530 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6528,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6529),U_6530))) ) ),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

fof(f_1870_3,plain,
    ( ! [U_6536,U_6534,U_6532] :
        ( hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536)))
        | ( ? [U_6527] :
              ( ~ hBOOL(hAPP(U_6532,U_6527))
              & ? [U_6526] :
                  ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),U_6527)),U_6526)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),U_6526)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_6525] :
              ( ~ hBOOL(hAPP(U_6532,U_6525))
              & ? [U_6524] :
                  ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),U_6525)),U_6524)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6524),U_6536))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6524)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536)) )
        | ( ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6535,U_6533,U_6531] :
        ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6531,U_6523))
                | ! [U_6522] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6531,U_6521))
                | ! [U_6520] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535)) )
          & ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ) ),
    inference(miniscope,[status(thm)],[f_1870_2]) ).

fof(f_1870_4,plain,
    ( ! [U_6536,U_6534,U_6532] :
        ( hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536)))
        | ( ? [U_6527] :
              ( ~ hBOOL(hAPP(U_6532,U_6527))
              & ? [U_6526] :
                  ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),U_6527)),U_6526)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),U_6526)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
          & ? [U_6524] :
              ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),U_6524)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6524),U_6536))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6524)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536)) )
        | ( ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6535,U_6533,U_6531] :
        ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6531,U_6523))
                | ! [U_6522] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6531,U_6521))
                | ! [U_6520] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535)) )
          & ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_6525,sK130(U_6536,U_6534,U_6532))],[f_1870_3]) ).

fof(f_1870_5,plain,
    ( ! [U_6536,U_6534,U_6532] :
        ( hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536)))
        | ( ? [U_6527] :
              ( ~ hBOOL(hAPP(U_6532,U_6527))
              & ? [U_6526] :
                  ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),U_6527)),U_6526)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),U_6526)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
          & U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536)) )
        | ( ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6535,U_6533,U_6531] :
        ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6531,U_6523))
                | ! [U_6522] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6531,U_6521))
                | ! [U_6520] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535)) )
          & ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_6524,sK131(U_6536,U_6534,U_6532))],[f_1870_4]) ).

fof(f_1870_6,plain,
    ( ! [U_6536,U_6534,U_6532] :
        ( hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536)))
        | ( ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
          & ? [U_6526] :
              ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),U_6526)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6526),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),U_6526)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
          & U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536)) )
        | ( ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6535,U_6533,U_6531] :
        ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6531,U_6523))
                | ! [U_6522] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6531,U_6521))
                | ! [U_6520] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535)) )
          & ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6527,sK132(U_6536,U_6534,U_6532))],[f_1870_5]) ).

fof(f_1870_7,plain,
    ( ! [U_6536,U_6534,U_6532] :
        ( hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536)))
        | ( ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
          & U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
          & U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536)) )
        | ( ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6535,U_6533,U_6531] :
        ( ( ( ! [U_6523] :
                ( hBOOL(hAPP(U_6531,U_6523))
                | ! [U_6522] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_6521] :
                ( hBOOL(hAPP(U_6531,U_6521))
                | ! [U_6520] :
                    ( U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535)) )
          & ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6526,sK133(U_6536,U_6534,U_6532))],[f_1870_6]) ).

cnf(f_1870_8,plain,
    ( hBOOL(hAPP(U_6531,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6535 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_9,plain,
    ( hBOOL(hAPP(U_6531,U_6521))
    | U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6521)),U_6520)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6520),U_6535))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6535))
    | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_10,plain,
    ( hBOOL(hAPP(U_6531,U_6523))
    | U_6533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6535),U_6523)),U_6522)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),U_6522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6535),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6533),U_6535))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_14,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_15,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_19,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_20,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_24,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_25,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_29,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_30,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_34,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_35,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_39,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_40,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | U_6536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_44,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_45,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6536),sK133(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_49,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_50,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK133(U_6536,U_6534,U_6532)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_54,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_55,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK132(U_6536,U_6534,U_6532))),sK133(U_6536,U_6534,U_6532))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK131(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK131(U_6536,U_6534,U_6532)),U_6536))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_59,plain,
    ( U_6534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6536),sK130(U_6536,U_6534,U_6532))),sK131(U_6536,U_6534,U_6532))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

cnf(f_1870_60,plain,
    ( ~ hBOOL(hAPP(U_6532,sK130(U_6536,U_6534,U_6532)))
    | ~ hBOOL(hAPP(U_6532,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_6532,sK132(U_6536,U_6534,U_6532)))
    | hBOOL(hAPP(U_6532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6534),U_6536))) ),
    inference(clausify,[status(thm)],[f_1870_7]) ).

fof(f_1871_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_1871_2,plain,
    ! [U_6538,U_6537] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6537)),U_6538))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6537)),U_6538)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6537)) ),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

cnf(f_1871_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6537)),U_6538))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6537)) ),
    inference(clausify,[status(thm)],[f_1871_2]) ).

cnf(f_1871_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_6537)),U_6538))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6537)) ),
    inference(clausify,[status(thm)],[f_1871_2]) ).

fof(f_1872_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_1872_2,plain,
    ! [U_6539] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_6539)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6539)) ),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

cnf(f_1872_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_6539)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6539)) ),
    inference(clausify,[status(thm)],[f_1872_2]) ).

fof(f_1873_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_1873_2,plain,
    ! [U_6542,U_6541,U_6540] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6542),U_6540)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6542),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6541),U_6542),U_6540))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6541,U_6542))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6540)) ),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

cnf(f_1873_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6541,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6542),U_6540)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6542),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6541),U_6542),U_6540))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6541,U_6542))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6540)) ),
    inference(clausify,[status(thm)],[f_1873_2]) ).

fof(f_1874_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_1874_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_1874_1]) ).

fof(f_1875_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_1875_2,plain,
    ! [U_6544,U_6543] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6543),U_6544)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6543))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6544)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6543),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

cnf(f_1875_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6543),U_6544)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6543))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6544)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6543),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1875_2]) ).

fof(f_1876_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_1876_2,plain,
    ! [U_6546,U_6545] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6545)) = 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_6546),U_6545))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6546,U_6545) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6545)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),U_6545))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6546,U_6545) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_6545 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

cnf(f_1876_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6545)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),U_6545))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6546,U_6545) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6545 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1876_2]) ).

cnf(f_1876_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6545)) = 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_6546),U_6545))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6546,U_6545) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6545 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1876_2]) ).

fof(f_1877_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_1877_2,plain,
    ! [U_6548,U_6547] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6548)),U_6547) = 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_6548),U_6547))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6547) = 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_6548)),U_6547) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6548),U_6547))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6547) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_6547 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

cnf(f_1877_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6548)),U_6547) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6548),U_6547))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6547) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6547 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1877_2]) ).

cnf(f_1877_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6548)),U_6547) = 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_6548),U_6547))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6547) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6547 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1877_2]) ).

fof(f_1878_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_1878_2,plain,
    ! [U_6550,U_6549] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6550)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6550)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6550))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6550)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6549)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6550))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6549))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6550)) = 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_6549))) ) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

fof(f_1878_3,plain,
    ( ! [U_6554,U_6552] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6554)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6554)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6552))) )
    & ! [U_6553,U_6551] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6551),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6553)) = 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_6551))) ) ),
    inference(miniscope,[status(thm)],[f_1878_2]) ).

cnf(f_1878_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6551),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6553)) = 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_6551))) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6554)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6552))) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6554)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6552),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6554)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6552))) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

fof(f_1879_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_1879_2,plain,
    ! [U_6555] :
      ( ~ c_Int_Oiszero(U_6555,hAPP(c_Int_Onumber__class_Onumber__of(U_6555),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_6555) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

cnf(f_1879_3,plain,
    ( ~ c_Int_Oiszero(U_6555,hAPP(c_Int_Onumber__class_Onumber__of(U_6555),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_6555) ),
    inference(clausify,[status(thm)],[f_1879_2]) ).

fof(f_1880_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_1880_2,plain,
    ! [U_6558,U_6557,U_6556] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557) = hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558)
          | ~ c_Int_Oiszero(U_6556,hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6558)))) )
        & ( c_Int_Oiszero(U_6556,hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6558))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557) != hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558) ) )
      | ~ class_Int_Onumber__ring(U_6556) ),
    inference(variable_rename,[status(thm)],[f_1880_1]) ).

cnf(f_1880_3,plain,
    ( c_Int_Oiszero(U_6556,hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6558))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557) != hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558)
    | ~ class_Int_Onumber__ring(U_6556) ),
    inference(clausify,[status(thm)],[f_1880_2]) ).

cnf(f_1880_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557) = hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558)
    | ~ c_Int_Oiszero(U_6556,hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6558))))
    | ~ class_Int_Onumber__ring(U_6556) ),
    inference(clausify,[status(thm)],[f_1880_2]) ).

fof(f_1881_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_1881_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_1881_1]) ).

fof(f_1882_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_1882_2,plain,
    ! [U_6560,U_6559] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6559),U_6560) = 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_6559),U_6560)),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_6559)) ),
    inference(variable_rename,[status(thm)],[f_1882_1]) ).

cnf(f_1882_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6559),U_6560) = 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_6559),U_6560)),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_6559)) ),
    inference(clausify,[status(thm)],[f_1882_2]) ).

fof(f_1883_1,plain,
    ! [V_n_2,V_Pa_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_1883_2,plain,
    ! [U_6567,U_6566,U_6565] :
      ( ( ( hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
          | ? [U_6564,U_6563] :
              ( ~ hBOOL(hAPP(hAPP(U_6566,U_6564),U_6563))
              & U_6567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),U_6564)),U_6563)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6563),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6563)) ) )
        & ( ! [U_6562,U_6561] :
              ( hBOOL(hAPP(hAPP(U_6566,U_6562),U_6561))
              | U_6567 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),U_6562)),U_6561)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6561)) )
          | ~ hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1883_1]) ).

fof(f_1883_3,plain,
    ! [U_6567,U_6566,U_6565] :
      ( ( ( hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
          | ? [U_6563] :
              ( ~ hBOOL(hAPP(hAPP(U_6566,sK134(U_6567,U_6566,U_6565)),U_6563))
              & U_6567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),sK134(U_6567,U_6566,U_6565))),U_6563)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6563),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6563)) ) )
        & ( ! [U_6562,U_6561] :
              ( hBOOL(hAPP(hAPP(U_6566,U_6562),U_6561))
              | U_6567 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),U_6562)),U_6561)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6561)) )
          | ~ hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6564,sK134(U_6567,U_6566,U_6565))],[f_1883_2]) ).

fof(f_1883_4,plain,
    ! [U_6567,U_6566,U_6565] :
      ( ( ( hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
          | ( ~ hBOOL(hAPP(hAPP(U_6566,sK134(U_6567,U_6566,U_6565)),sK135(U_6567,U_6566,U_6565)))
            & U_6567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),sK134(U_6567,U_6566,U_6565))),sK135(U_6567,U_6566,U_6565))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK135(U_6567,U_6566,U_6565)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),sK135(U_6567,U_6566,U_6565))) ) )
        & ( ! [U_6562,U_6561] :
              ( hBOOL(hAPP(hAPP(U_6566,U_6562),U_6561))
              | U_6567 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),U_6562)),U_6561)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6561)) )
          | ~ hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6563,sK135(U_6567,U_6566,U_6565))],[f_1883_3]) ).

cnf(f_1883_5,plain,
    ( hBOOL(hAPP(hAPP(U_6566,U_6562),U_6561))
    | U_6567 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),U_6562)),U_6561)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6561),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),U_6561))
    | ~ hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1883_4]) ).

cnf(f_1883_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),sK135(U_6567,U_6566,U_6565)))
    | hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1883_4]) ).

cnf(f_1883_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK135(U_6567,U_6566,U_6565)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1883_4]) ).

cnf(f_1883_8,plain,
    ( U_6567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6565),sK134(U_6567,U_6566,U_6565))),sK135(U_6567,U_6566,U_6565))
    | hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1883_4]) ).

cnf(f_1883_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6566,sK134(U_6567,U_6566,U_6565)),sK135(U_6567,U_6566,U_6565)))
    | hBOOL(hAPP(hAPP(U_6566,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6567),U_6565)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6567,U_6565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1883_4]) ).

fof(f_1884_1,plain,
    ! [V_n_2,V_Pa_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_1884_2,plain,
    ! [U_6574,U_6573,U_6572] :
      ( ( ( hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
          | ? [U_6571,U_6570] :
              ( ~ hBOOL(hAPP(hAPP(U_6573,U_6571),U_6570))
              & U_6574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),U_6571)),U_6570)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6570),U_6572))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6570)) ) )
        & ( ! [U_6569,U_6568] :
              ( hBOOL(hAPP(hAPP(U_6573,U_6569),U_6568))
              | U_6574 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),U_6569)),U_6568)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6572))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6568)) )
          | ~ hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

fof(f_1884_3,plain,
    ! [U_6574,U_6573,U_6572] :
      ( ( ( hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
          | ? [U_6570] :
              ( ~ hBOOL(hAPP(hAPP(U_6573,sK136(U_6574,U_6573,U_6572)),U_6570))
              & U_6574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),sK136(U_6574,U_6573,U_6572))),U_6570)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6570),U_6572))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6570)) ) )
        & ( ! [U_6569,U_6568] :
              ( hBOOL(hAPP(hAPP(U_6573,U_6569),U_6568))
              | U_6574 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),U_6569)),U_6568)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6572))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6568)) )
          | ~ hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6571,sK136(U_6574,U_6573,U_6572))],[f_1884_2]) ).

fof(f_1884_4,plain,
    ! [U_6574,U_6573,U_6572] :
      ( ( ( hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
          | ( ~ hBOOL(hAPP(hAPP(U_6573,sK136(U_6574,U_6573,U_6572)),sK137(U_6574,U_6573,U_6572)))
            & U_6574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),sK136(U_6574,U_6573,U_6572))),sK137(U_6574,U_6573,U_6572))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK137(U_6574,U_6573,U_6572)),U_6572))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK137(U_6574,U_6573,U_6572))) ) )
        & ( ! [U_6569,U_6568] :
              ( hBOOL(hAPP(hAPP(U_6573,U_6569),U_6568))
              | U_6574 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),U_6569)),U_6568)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6572))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6568)) )
          | ~ hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_6570,sK137(U_6574,U_6573,U_6572))],[f_1884_3]) ).

cnf(f_1884_5,plain,
    ( hBOOL(hAPP(hAPP(U_6573,U_6569),U_6568))
    | U_6574 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),U_6569)),U_6568)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6568),U_6572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6568))
    | ~ hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

cnf(f_1884_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK137(U_6574,U_6573,U_6572)))
    | hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

cnf(f_1884_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK137(U_6574,U_6573,U_6572)),U_6572))
    | hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

cnf(f_1884_8,plain,
    ( U_6574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6572),sK136(U_6574,U_6573,U_6572))),sK137(U_6574,U_6573,U_6572))
    | hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

cnf(f_1884_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6573,sK136(U_6574,U_6573,U_6572)),sK137(U_6574,U_6573,U_6572)))
    | hBOOL(hAPP(hAPP(U_6573,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6572)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572)) ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

fof(f_1885_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_1885_2,plain,
    ! [U_6576,U_6575] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6576))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6575))) = 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_6576)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6575))
        | 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_6575))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6576))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6575))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6576)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6575))
        | ~ 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_6575))) ) ),
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

fof(f_1885_3,plain,
    ( ! [U_6580,U_6578] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6580))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6578))) = 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_6580)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6578))
        | 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_6578))) )
    & ! [U_6579,U_6577] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6579))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6577))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6579)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6577))
        | ~ 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_6577))) ) ),
    inference(miniscope,[status(thm)],[f_1885_2]) ).

cnf(f_1885_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_6579))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6577))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6579)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6577))
    | ~ 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_6577))) ),
    inference(clausify,[status(thm)],[f_1885_3]) ).

cnf(f_1885_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_6580))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6578))) = 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_6580)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6578))
    | 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_6578))) ),
    inference(clausify,[status(thm)],[f_1885_3]) ).

fof(f_1886_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_1886_2,plain,
    ! [U_6581] :
      ( ( 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_6581)) = 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_6581)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6581))) )
      & ( 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_6581)) = 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_6581))) ) ),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

fof(f_1886_3,plain,
    ( ! [U_6583] :
        ( 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_6583)) = 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_6583)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6583))) )
    & ! [U_6582] :
        ( 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_6582)) = 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_6582))) ) ),
    inference(miniscope,[status(thm)],[f_1886_2]) ).

cnf(f_1886_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_6582)) = 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_6582))) ),
    inference(clausify,[status(thm)],[f_1886_3]) ).

cnf(f_1886_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_6583)) = 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_6583)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6583))) ),
    inference(clausify,[status(thm)],[f_1886_3]) ).

fof(f_1887_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_1887_2,plain,
    ! [U_6585,U_6584] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6584),U_6585) = c_Groups_Ozero__class_Ozero(U_6584)
          | ~ c_Int_Oiszero(U_6584,hAPP(c_Int_Onumber__class_Onumber__of(U_6584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_6584,hAPP(c_Int_Onumber__class_Onumber__of(U_6584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6584),U_6585) != c_Groups_Ozero__class_Ozero(U_6584) ) )
      | ~ class_Int_Onumber__ring(U_6584) ),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

cnf(f_1887_3,plain,
    ( c_Int_Oiszero(U_6584,hAPP(c_Int_Onumber__class_Onumber__of(U_6584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6584),U_6585) != c_Groups_Ozero__class_Ozero(U_6584)
    | ~ class_Int_Onumber__ring(U_6584) ),
    inference(clausify,[status(thm)],[f_1887_2]) ).

cnf(f_1887_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6584),U_6585) = c_Groups_Ozero__class_Ozero(U_6584)
    | ~ c_Int_Oiszero(U_6584,hAPP(c_Int_Onumber__class_Onumber__of(U_6584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_6584) ),
    inference(clausify,[status(thm)],[f_1887_2]) ).

fof(f_1888_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_1888_2,plain,
    ! [U_6587,U_6586] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_6586) = hAPP(c_Int_Onumber__class_Onumber__of(U_6586),U_6587)
          | ~ c_Int_Oiszero(U_6586,hAPP(c_Int_Onumber__class_Onumber__of(U_6586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587)))) )
        & ( c_Int_Oiszero(U_6586,hAPP(c_Int_Onumber__class_Onumber__of(U_6586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587))))
          | c_Groups_Ozero__class_Ozero(U_6586) != hAPP(c_Int_Onumber__class_Onumber__of(U_6586),U_6587) ) )
      | ~ class_Int_Onumber__ring(U_6586) ),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

cnf(f_1888_3,plain,
    ( c_Int_Oiszero(U_6586,hAPP(c_Int_Onumber__class_Onumber__of(U_6586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587))))
    | c_Groups_Ozero__class_Ozero(U_6586) != hAPP(c_Int_Onumber__class_Onumber__of(U_6586),U_6587)
    | ~ class_Int_Onumber__ring(U_6586) ),
    inference(clausify,[status(thm)],[f_1888_2]) ).

cnf(f_1888_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_6586) = hAPP(c_Int_Onumber__class_Onumber__of(U_6586),U_6587)
    | ~ c_Int_Oiszero(U_6586,hAPP(c_Int_Onumber__class_Onumber__of(U_6586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587))))
    | ~ class_Int_Onumber__ring(U_6586) ),
    inference(clausify,[status(thm)],[f_1888_2]) ).

fof(f_1889_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_1889_2,plain,
    ! [U_6589,U_6588] :
      ( ( c_SMT_Oz3div(U_6589,U_6588) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6589),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6588)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6588)) )
      & ( c_SMT_Oz3div(U_6589,U_6588) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6589),U_6588)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6588)) ) ),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

fof(f_1889_3,plain,
    ( ! [U_6593,U_6591] :
        ( c_SMT_Oz3div(U_6593,U_6591) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6591)) )
    & ! [U_6592,U_6590] :
        ( c_SMT_Oz3div(U_6592,U_6590) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6592),U_6590)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6590)) ) ),
    inference(miniscope,[status(thm)],[f_1889_2]) ).

cnf(f_1889_4,plain,
    ( c_SMT_Oz3div(U_6592,U_6590) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6592),U_6590)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6590)) ),
    inference(clausify,[status(thm)],[f_1889_3]) ).

cnf(f_1889_5,plain,
    ( c_SMT_Oz3div(U_6593,U_6591) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6591)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6591)) ),
    inference(clausify,[status(thm)],[f_1889_3]) ).

fof(f_1890_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_1890_2,plain,
    ! [U_6595,U_6594] : c_Int_Onat__aux(U_6594,U_6595) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6594)),U_6595),
    inference(variable_rename,[status(thm)],[f_1890_1]) ).

cnf(f_1890_3,plain,
    c_Int_Onat__aux(U_6594,U_6595) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_6594)),U_6595),
    inference(clausify,[status(thm)],[f_1890_2]) ).

fof(f_1891_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_1891_2,plain,
    ! [U_6597,U_6596] :
      ( ( c_Code__Numeral_Onat__of__aux(U_6596,U_6597) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6596),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6597))
        | U_6596 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_6596,U_6597) = U_6597
        | U_6596 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

fof(f_1891_3,plain,
    ( ! [U_6601,U_6599] :
        ( c_Code__Numeral_Onat__of__aux(U_6599,U_6601) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6599),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6601))
        | U_6599 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6600,U_6598] :
        ( c_Code__Numeral_Onat__of__aux(U_6598,U_6600) = U_6600
        | U_6598 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1891_2]) ).

cnf(f_1891_4,plain,
    ( c_Code__Numeral_Onat__of__aux(U_6598,U_6600) = U_6600
    | U_6598 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_6599,U_6601) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6599),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6601))
    | U_6599 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

fof(f_1892_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_1892_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_1892_1]) ).

fof(f_1893_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_1893_2,plain,
    ! [U_6603,U_6602] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6602),hAPP(c_Int_Onumber__class_Onumber__of(U_6602),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_6603))) = hAPP(c_Int_Onumber__class_Onumber__of(U_6602),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_6602) ),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

cnf(f_1893_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6602),hAPP(c_Int_Onumber__class_Onumber__of(U_6602),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_6603))) = hAPP(c_Int_Onumber__class_Onumber__of(U_6602),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_6602) ),
    inference(clausify,[status(thm)],[f_1893_2]) ).

fof(f_1894_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_1894_2,plain,
    ! [U_6605,U_6604] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6605)) = U_6605,
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

cnf(f_1894_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6605)) = U_6605,
    inference(clausify,[status(thm)],[f_1894_2]) ).

fof(f_1895_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_1895_2,plain,
    ! [U_6608,U_6607,U_6606] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6606,tc_HOL_Obool)),U_6607) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6606,tc_HOL_Obool)),U_6608)
        | U_6607 != U_6608 )
      & ( U_6607 = U_6608
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6606,tc_HOL_Obool)),U_6607) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6606,tc_HOL_Obool)),U_6608) ) ),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

fof(f_1895_3,plain,
    ( ! [U_6614,U_6612] :
        ( ! [U_6610] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6612) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6614)
        | U_6612 != U_6614 )
    & ! [U_6613,U_6611] :
        ( ! [U_6609] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6609,tc_HOL_Obool)),U_6611) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6609,tc_HOL_Obool)),U_6613)
        | U_6611 = U_6613 ) ),
    inference(miniscope,[status(thm)],[f_1895_2]) ).

cnf(f_1895_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6609,tc_HOL_Obool)),U_6611) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6609,tc_HOL_Obool)),U_6613)
    | U_6611 = U_6613 ),
    inference(clausify,[status(thm)],[f_1895_3]) ).

cnf(f_1895_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6612) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6614)
    | U_6612 != U_6614 ),
    inference(clausify,[status(thm)],[f_1895_3]) ).

fof(f_1896_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_1896_2,plain,
    ! [U_6618,U_6617,U_6616,U_6615] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6615),U_6616),U_6617)),U_6618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6615),hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),U_6616),U_6618)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),U_6617),U_6618))
      | ~ class_Rings_Ocomm__semiring__1(U_6615) ),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

cnf(f_1896_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6615),U_6616),U_6617)),U_6618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6615),hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),U_6616),U_6618)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6615),U_6617),U_6618))
    | ~ class_Rings_Ocomm__semiring__1(U_6615) ),
    inference(clausify,[status(thm)],[f_1896_2]) ).

fof(f_1897_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_1897_2,plain,
    ! [U_6621,U_6620,U_6619] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6619),U_6621)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6620),U_6621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6619),U_6620)) ),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

cnf(f_1897_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_6619),U_6621)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6620),U_6621)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6619),U_6620)) ),
    inference(clausify,[status(thm)],[f_1897_2]) ).

fof(f_1898_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_1898_2,plain,
    ! [U_6623,U_6622] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6622),U_6623)),U_6622)),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

cnf(f_1898_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_6622),U_6623)),U_6622)),
    inference(clausify,[status(thm)],[f_1898_2]) ).

fof(f_1899_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_1899_2,plain,
    ! [U_6625,U_6624] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6624)),U_6625) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6624),U_6625)),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

cnf(f_1899_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6624)),U_6625) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6624),U_6625)),
    inference(clausify,[status(thm)],[f_1899_2]) ).

fof(f_1900_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_1900_2,plain,
    ! [U_6627,U_6626] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6626),U_6627)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6626)),U_6627),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

cnf(f_1900_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6626),U_6627)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6626)),U_6627),
    inference(clausify,[status(thm)],[f_1900_2]) ).

fof(f_1901_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_1901_2,plain,
    ! [U_6629,U_6628] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6628)),U_6629) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6628),U_6629)),
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

cnf(f_1901_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6628)),U_6629) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6628),U_6629)),
    inference(clausify,[status(thm)],[f_1901_2]) ).

fof(f_1902_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_1902_2,plain,
    ! [U_6632,U_6631,U_6630] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6631),U_6632)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6630),U_6631)),U_6632),
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

cnf(f_1902_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6630),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6631),U_6632)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6630),U_6631)),U_6632),
    inference(clausify,[status(thm)],[f_1902_2]) ).

fof(f_1903_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_1903_2,plain,
    ! [U_6636,U_6635,U_6634,U_6633] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),U_6634),U_6635)),U_6636) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),U_6634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6635),U_6636))
      | ~ class_Rings_Ocomm__semiring__1(U_6633) ),
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

cnf(f_1903_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),U_6634),U_6635)),U_6636) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6633),U_6634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6635),U_6636))
    | ~ class_Rings_Ocomm__semiring__1(U_6633) ),
    inference(clausify,[status(thm)],[f_1903_2]) ).

fof(f_1904_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_1904_2,plain,
    ! [U_6639,U_6638,U_6637] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6637),U_6638)),U_6639) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6638),U_6639)),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

cnf(f_1904_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6637),U_6638)),U_6639) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6638),U_6639)),
    inference(clausify,[status(thm)],[f_1904_2]) ).

fof(f_1905_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_1905_2,plain,
    ! [U_6641,U_6640] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6640),U_6641),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6641
      | ~ class_Rings_Ocomm__semiring__1(U_6640) ),
    inference(variable_rename,[status(thm)],[f_1905_1]) ).

cnf(f_1905_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6640),U_6641),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6641
    | ~ class_Rings_Ocomm__semiring__1(U_6640) ),
    inference(clausify,[status(thm)],[f_1905_2]) ).

fof(f_1906_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_1906_2,plain,
    ! [U_6644,U_6643,U_6642] : 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_6642,U_6643)),U_6644),U_6643) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6642),U_6644),U_6643),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

cnf(f_1906_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_6642,U_6643)),U_6644),U_6643) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6642),U_6644),U_6643),
    inference(clausify,[status(thm)],[f_1906_2]) ).

fof(f_1907_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_1907_2,plain,
    ! [U_6646,U_6645] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_6645)),U_6646) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6645),U_6646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6645)) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

cnf(f_1907_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_6645)),U_6646) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6645),U_6646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6645)) ),
    inference(clausify,[status(thm)],[f_1907_2]) ).

fof(f_1908_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_1908_2,plain,
    ! [U_6648,U_6647] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6647),U_6648)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_6647)),U_6648)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6647)) ),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

cnf(f_1908_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6647),U_6648)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_6647)),U_6648)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6647)) ),
    inference(clausify,[status(thm)],[f_1908_2]) ).

fof(f_1909_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_1909_2,plain,
    ! [U_6649] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6649),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6649,
    inference(variable_rename,[status(thm)],[f_1909_1]) ).

cnf(f_1909_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6649),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6649,
    inference(clausify,[status(thm)],[f_1909_2]) ).

fof(f_1910_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_1910_2,plain,
    ! [U_6651,U_6650] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6650),U_6651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6650),U_6651)) ),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

cnf(f_1910_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6650),U_6651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6650),U_6651)) ),
    inference(clausify,[status(thm)],[f_1910_2]) ).

fof(f_1911_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_1911_2,plain,
    ! [U_6654,U_6653,U_6652] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6652),U_6653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6652),U_6654)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6653),U_6654)
        | U_6652 = 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_6652),U_6653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6652),U_6654)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ( ! [U_6660,U_6658,U_6656] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6656),U_6658)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6656),U_6660)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6658),U_6660)
        | U_6656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6659,U_6657,U_6655] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6655),U_6657)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6655),U_6659)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1911_2]) ).

cnf(f_1911_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6655),U_6657)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6655),U_6659)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

cnf(f_1911_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6656),U_6658)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6656),U_6660)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6658),U_6660)
    | U_6656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

fof(f_1912_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_1912_2,plain,
    ! [U_6663,U_6662,U_6661] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6661),U_6662),hAPP(c_Nat_OSuc,U_6663)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),hAPP(hAPP(c_Power_Opower__class_Opower(U_6661),U_6662),U_6663))
      | ~ class_Rings_Ocomm__semiring__1(U_6661) ),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

cnf(f_1912_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6661),U_6662),hAPP(c_Nat_OSuc,U_6663)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),hAPP(hAPP(c_Power_Opower__class_Opower(U_6661),U_6662),U_6663))
    | ~ class_Rings_Ocomm__semiring__1(U_6661) ),
    inference(clausify,[status(thm)],[f_1912_2]) ).

fof(f_1913_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_1913_2,plain,
    ! [U_6666,U_6665,U_6664] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6664),U_6665),hAPP(hAPP(c_Power_Opower__class_Opower(U_6664),U_6665),U_6666)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6664),U_6665),hAPP(c_Nat_OSuc,U_6666))
      | ~ class_Rings_Ocomm__semiring__1(U_6664) ),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

cnf(f_1913_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6664),U_6665),hAPP(hAPP(c_Power_Opower__class_Opower(U_6664),U_6665),U_6666)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6664),U_6665),hAPP(c_Nat_OSuc,U_6666))
    | ~ class_Rings_Ocomm__semiring__1(U_6664) ),
    inference(clausify,[status(thm)],[f_1913_2]) ).

fof(f_1914_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_1914_2,plain,
    ! [U_6669,U_6668,U_6667] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6667),hAPP(hAPP(c_Power_Opower__class_Opower(U_6667),U_6668),U_6669)),U_6668) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6667),U_6668),hAPP(c_Nat_OSuc,U_6669))
      | ~ class_Rings_Ocomm__semiring__1(U_6667) ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

cnf(f_1914_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6667),hAPP(hAPP(c_Power_Opower__class_Opower(U_6667),U_6668),U_6669)),U_6668) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6667),U_6668),hAPP(c_Nat_OSuc,U_6669))
    | ~ class_Rings_Ocomm__semiring__1(U_6667) ),
    inference(clausify,[status(thm)],[f_1914_2]) ).

fof(f_1915_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_1915_2,plain,
    ! [U_6671,U_6670] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6670),U_6671),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6670)
      | ~ class_Rings_Ocomm__semiring__1(U_6670) ),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

cnf(f_1915_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6670),U_6671),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6670)
    | ~ class_Rings_Ocomm__semiring__1(U_6670) ),
    inference(clausify,[status(thm)],[f_1915_2]) ).

fof(f_1916_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_1916_2,plain,
    ! [U_6675,U_6674,U_6673,U_6672] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6672),hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),U_6674)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),U_6675)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6674),U_6675))
      | ~ class_Rings_Ocomm__semiring__1(U_6672) ),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

cnf(f_1916_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6672),hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),U_6674)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),U_6675)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6672),U_6673),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6674),U_6675))
    | ~ class_Rings_Ocomm__semiring__1(U_6672) ),
    inference(clausify,[status(thm)],[f_1916_2]) ).

fof(f_1917_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_1917_2,plain,
    ! [U_6677,U_6676] :
      ( 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_6676),U_6677)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6676)) ),
    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_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6676),U_6677)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6676)) ),
    inference(clausify,[status(thm)],[f_1917_2]) ).

fof(f_1918_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_1918_2,plain,
    ! [U_6680,U_6679,U_6678] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6678),U_6679)),U_6680) = 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_6678),U_6680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6679),U_6680))),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_6678,U_6680)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6679,U_6680))),U_6680)),
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

cnf(f_1918_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6678),U_6679)),U_6680) = 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_6678),U_6680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6679),U_6680))),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_6678,U_6680)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6679,U_6680))),U_6680)),
    inference(clausify,[status(thm)],[f_1918_2]) ).

fof(f_1919_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_1919_2,plain,
    ! [U_6682,U_6681] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6681),U_6682)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6681)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6682)),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

cnf(f_1919_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6681),U_6682)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6681)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6682)),
    inference(clausify,[status(thm)],[f_1919_2]) ).

fof(f_1920_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_1920_2,plain,
    ! [U_6684,U_6683] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6683)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6684)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6683),U_6684)),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

cnf(f_1920_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6683)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6684)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6683),U_6684)),
    inference(clausify,[status(thm)],[f_1920_2]) ).

fof(f_1921_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_1921_2,plain,
    ! [U_6687,U_6686,U_6685] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6686),U_6687)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),U_6686)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),U_6687)),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

cnf(f_1921_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6686),U_6687)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),U_6686)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6685),U_6687)),
    inference(clausify,[status(thm)],[f_1921_2]) ).

fof(f_1922_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_1922_2,plain,
    ! [U_6690,U_6689,U_6688] :
      ( hBOOL(hAPP(hAPP(c_member(U_6688),hAPP(hAPP(c_Power_Opower__class_Opower(U_6688),U_6689),U_6690)),c_Int_Oring__1__class_OInts(U_6688)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6688),U_6689),c_Int_Oring__1__class_OInts(U_6688)))
      | ~ class_Rings_Oring__1(U_6688) ),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

cnf(f_1922_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6688),hAPP(hAPP(c_Power_Opower__class_Opower(U_6688),U_6689),U_6690)),c_Int_Oring__1__class_OInts(U_6688)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6688),U_6689),c_Int_Oring__1__class_OInts(U_6688)))
    | ~ class_Rings_Oring__1(U_6688) ),
    inference(clausify,[status(thm)],[f_1922_2]) ).

fof(f_1923_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_1923_2,plain,
    ! [U_6692,U_6691] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6692)) = 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_6691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6692)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6691))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6692)) = 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_6692))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6691))) ) ),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

fof(f_1923_3,plain,
    ( ! [U_6696,U_6694] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6696)) = 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_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6696)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6694))) )
    & ! [U_6695,U_6693] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6693)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6695)) = 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_6695))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6693))) ) ),
    inference(miniscope,[status(thm)],[f_1923_2]) ).

cnf(f_1923_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6693)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6695)) = 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_6695))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6693))) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

cnf(f_1923_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6696)) = 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_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6696)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6694))) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

fof(f_1924_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_1924_2,plain,
    ! [U_6698,U_6697] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6697)),U_6698) = 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_6697)),U_6698))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6697))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6697)),U_6698) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6698)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6697))) ) ),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

fof(f_1924_3,plain,
    ( ! [U_6702,U_6700] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6700)),U_6702) = 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_6700)),U_6702))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6700))) )
    & ! [U_6701,U_6699] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6699)),U_6701) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6701)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6699))) ) ),
    inference(miniscope,[status(thm)],[f_1924_2]) ).

cnf(f_1924_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6699)),U_6701) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6701)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6699))) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

cnf(f_1924_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6700)),U_6702) = 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_6700)),U_6702))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6700))) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

fof(f_1925_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_1925_2,plain,
    ! [U_6705,U_6704,U_6703] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6705),U_6704)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6705),U_6703)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6703),U_6704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6703)) ),
    inference(variable_rename,[status(thm)],[f_1925_1]) ).

cnf(f_1925_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_6705),U_6704)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6705),U_6703)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6703),U_6704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6703)) ),
    inference(clausify,[status(thm)],[f_1925_2]) ).

fof(f_1926_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_1926_2,plain,
    ! [U_6707,U_6706] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6706),U_6707)),U_6706) = U_6707
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6706)) ),
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

cnf(f_1926_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6706),U_6707)),U_6706) = U_6707
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6706)) ),
    inference(clausify,[status(thm)],[f_1926_2]) ).

fof(f_1927_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_1927_2,plain,
    ! [U_6709,U_6708] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6709),U_6708)),U_6708) = U_6709
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6708)) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

cnf(f_1927_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6709),U_6708)),U_6708) = U_6709
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6708)) ),
    inference(clausify,[status(thm)],[f_1927_2]) ).

fof(f_1928_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_1928_2,plain,
    ! [U_6712,U_6711,U_6710] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6710),U_6711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6710),U_6712)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6711),U_6712)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6710)) ),
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

cnf(f_1928_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6710),U_6711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6710),U_6712)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6711),U_6712)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6710)) ),
    inference(clausify,[status(thm)],[f_1928_2]) ).

fof(f_1929_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_1929_2,plain,
    ! [U_6714,U_6713] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6714),U_6713)),U_6714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6713)) ),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

cnf(f_1929_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6714),U_6713)),U_6714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6713)) ),
    inference(clausify,[status(thm)],[f_1929_2]) ).

fof(f_1930_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_1930_2,plain,
    ! [U_6717,U_6716,U_6715] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6715,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6716),U_6717)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6716),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6715),U_6716),U_6717))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6715,U_6716)),
    inference(variable_rename,[status(thm)],[f_1930_1]) ).

cnf(f_1930_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6715,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6716),U_6717)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6716),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6715),U_6716),U_6717))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6715,U_6716)),
    inference(clausify,[status(thm)],[f_1930_2]) ).

fof(f_1931_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_1931_2,plain,
    ! [U_6720,U_6719,U_6718] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),U_6719)),U_6720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6719),U_6720))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6719,U_6720))),U_6720)),
    inference(variable_rename,[status(thm)],[f_1931_1]) ).

cnf(f_1931_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),U_6719)),U_6720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6719),U_6720))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6718),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6719,U_6720))),U_6720)),
    inference(clausify,[status(thm)],[f_1931_2]) ).

fof(f_1932_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_1932_2,plain,
    ! [U_6722,U_6721] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6721),U_6722)),U_6722) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6721),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6721,U_6722)),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

cnf(f_1932_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6721),U_6722)),U_6722) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6721),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6721,U_6722)),
    inference(clausify,[status(thm)],[f_1932_2]) ).

fof(f_1933_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_1933_2,plain,
    ! [U_6724,U_6723] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6724),U_6723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6724),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6724,U_6723)),
    inference(variable_rename,[status(thm)],[f_1933_1]) ).

cnf(f_1933_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6724),U_6723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6724),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6724,U_6723)),
    inference(clausify,[status(thm)],[f_1933_2]) ).

fof(f_1934_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_1934_2,plain,
    ! [U_6726,U_6725] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6725,U_6726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6725),U_6726)),U_6726)),
    inference(variable_rename,[status(thm)],[f_1934_1]) ).

cnf(f_1934_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6725,U_6726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6725),U_6726)),U_6726)),
    inference(clausify,[status(thm)],[f_1934_2]) ).

fof(f_1935_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_1935_2,plain,
    ! [U_6728,U_6727] : 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_6727)),U_6728))),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

cnf(f_1935_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_6727)),U_6728))),
    inference(clausify,[status(thm)],[f_1935_2]) ).

fof(f_1936_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_1936_2,plain,
    ! [U_6730,U_6729] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6730),U_6729) = 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_6730),U_6729)),U_6729))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6730),U_6729))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6729)) ),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

cnf(f_1936_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6730),U_6729) = 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_6730),U_6729)),U_6729))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6730),U_6729))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6729)) ),
    inference(clausify,[status(thm)],[f_1936_2]) ).

fof(f_1937_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_1937_2,plain,
    ! [U_6732,U_6731] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6732),U_6731) = 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_6732),U_6731)),U_6731))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6732),U_6731)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6732),U_6731) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6732),U_6731)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6731)) ),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

cnf(f_1937_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6732),U_6731) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6732),U_6731))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6731)) ),
    inference(clausify,[status(thm)],[f_1937_2]) ).

cnf(f_1937_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6732),U_6731) = 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_6732),U_6731)),U_6731))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6732),U_6731))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6731)) ),
    inference(clausify,[status(thm)],[f_1937_2]) ).

fof(f_1938_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_Pa_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_1938_2,plain,
    ! [U_6739,U_6738,U_6737] :
      ( ( hBOOL(hAPP(U_6737,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6738),U_6739)))
        | ( ? [U_6736,U_6735] :
              ( ~ hBOOL(hAPP(U_6737,U_6736))
              & U_6738 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6736)),U_6735)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6735),U_6739)) )
          & U_6739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6737,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_6734,U_6733] :
                ( hBOOL(hAPP(U_6737,U_6734))
                | U_6738 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6734)),U_6733)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6733),U_6739)) )
            | U_6739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6737,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6737,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6738),U_6739))) ) ),
    inference(variable_rename,[status(thm)],[f_1938_1]) ).

fof(f_1938_3,plain,
    ( ! [U_6745,U_6743,U_6741] :
        ( hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745)))
        | ( ? [U_6736,U_6735] :
              ( ~ hBOOL(hAPP(U_6741,U_6736))
              & U_6743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6745),U_6736)),U_6735)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6735),U_6745)) )
          & U_6745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6744,U_6742,U_6740] :
        ( ( ( ! [U_6734,U_6733] :
                ( hBOOL(hAPP(U_6740,U_6734))
                | U_6742 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6734)),U_6733)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6733),U_6744)) )
            | U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6740,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6744 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6740,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6742),U_6744))) ) ),
    inference(miniscope,[status(thm)],[f_1938_2]) ).

fof(f_1938_4,plain,
    ( ! [U_6745,U_6743,U_6741] :
        ( hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745)))
        | ( ? [U_6735] :
              ( ~ hBOOL(hAPP(U_6741,sK138(U_6745,U_6743,U_6741)))
              & U_6743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6745),sK138(U_6745,U_6743,U_6741))),U_6735)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6735),U_6745)) )
          & U_6745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6744,U_6742,U_6740] :
        ( ( ( ! [U_6734,U_6733] :
                ( hBOOL(hAPP(U_6740,U_6734))
                | U_6742 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6734)),U_6733)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6733),U_6744)) )
            | U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6740,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6744 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6740,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6742),U_6744))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_6736,sK138(U_6745,U_6743,U_6741))],[f_1938_3]) ).

fof(f_1938_5,plain,
    ( ! [U_6745,U_6743,U_6741] :
        ( hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745)))
        | ( ~ hBOOL(hAPP(U_6741,sK138(U_6745,U_6743,U_6741)))
          & U_6743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6745),sK138(U_6745,U_6743,U_6741))),sK139(U_6745,U_6743,U_6741))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK139(U_6745,U_6743,U_6741)),U_6745))
          & U_6745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6744,U_6742,U_6740] :
        ( ( ( ! [U_6734,U_6733] :
                ( hBOOL(hAPP(U_6740,U_6734))
                | U_6742 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6734)),U_6733)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6733),U_6744)) )
            | U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_6740,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6744 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_6740,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6742),U_6744))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_6735,sK139(U_6745,U_6743,U_6741))],[f_1938_4]) ).

cnf(f_1938_6,plain,
    ( hBOOL(hAPP(U_6740,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_6744 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6740,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6742),U_6744))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_7,plain,
    ( hBOOL(hAPP(U_6740,U_6734))
    | U_6742 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6734)),U_6733)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6733),U_6744))
    | U_6744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6740,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6742),U_6744))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_8,plain,
    ( U_6745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK139(U_6745,U_6743,U_6741)),U_6745))
    | U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_10,plain,
    ( U_6743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6745),sK138(U_6745,U_6743,U_6741))),sK139(U_6745,U_6743,U_6741))
    | U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_11,plain,
    ( ~ hBOOL(hAPP(U_6741,sK138(U_6745,U_6743,U_6741)))
    | U_6745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_12,plain,
    ( U_6745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK139(U_6745,U_6743,U_6741)),U_6745))
    | ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_14,plain,
    ( U_6743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6745),sK138(U_6745,U_6743,U_6741))),sK139(U_6745,U_6743,U_6741))
    | ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

cnf(f_1938_15,plain,
    ( ~ hBOOL(hAPP(U_6741,sK138(U_6745,U_6743,U_6741)))
    | ~ hBOOL(hAPP(U_6741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_6741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6743),U_6745))) ),
    inference(clausify,[status(thm)],[f_1938_5]) ).

fof(f_1939_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_1939_2,plain,
    ! [U_6747,U_6746] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6746)),hAPP(c_Int_Onat,U_6747)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6746),U_6747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6746)) ),
    inference(variable_rename,[status(thm)],[f_1939_1]) ).

cnf(f_1939_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6746)),hAPP(c_Int_Onat,U_6747)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6746),U_6747))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6747))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6746)) ),
    inference(clausify,[status(thm)],[f_1939_2]) ).

fof(f_1940_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_1940_2,plain,
    ! [U_6749,U_6748] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6748),U_6749)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6748)),hAPP(c_Int_Onat,U_6749))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6748)) ),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

cnf(f_1940_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6748),U_6749)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6748)),hAPP(c_Int_Onat,U_6749))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6748)) ),
    inference(clausify,[status(thm)],[f_1940_2]) ).

fof(f_1941_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_1941_2,plain,
    ! [U_6751,U_6750] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6750),U_6751),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_6750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6750),U_6751),U_6751)),U_6751)
      | ~ class_Groups_Omonoid__mult(U_6750) ),
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

cnf(f_1941_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6750),U_6751),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_6750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6750),U_6751),U_6751)),U_6751)
    | ~ class_Groups_Omonoid__mult(U_6750) ),
    inference(clausify,[status(thm)],[f_1941_2]) ).

fof(f_1942_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_1942_2,plain,
    ! [U_6753,U_6752] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6752),hAPP(hAPP(c_Power_Opower__class_Opower(U_6752),hAPP(c_Int_Onumber__class_Onumber__of(U_6752),c_Int_OMin)),U_6753)) = c_Groups_Oone__class_Oone(U_6752)
      | ~ class_Rings_Olinordered__idom(U_6752)
      | ~ class_Int_Onumber__ring(U_6752) ),
    inference(variable_rename,[status(thm)],[f_1942_1]) ).

cnf(f_1942_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6752),hAPP(hAPP(c_Power_Opower__class_Opower(U_6752),hAPP(c_Int_Onumber__class_Onumber__of(U_6752),c_Int_OMin)),U_6753)) = c_Groups_Oone__class_Oone(U_6752)
    | ~ class_Rings_Olinordered__idom(U_6752)
    | ~ class_Int_Onumber__ring(U_6752) ),
    inference(clausify,[status(thm)],[f_1942_2]) ).

fof(f_1943_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_1943_2,plain,
    ! [U_6755,U_6754] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6755),U_6754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6755),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6754),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_6754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6755),U_6754) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_6754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

fof(f_1943_3,plain,
    ( ! [U_6759,U_6757] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6759),U_6757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6759),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6757),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_6757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6758,U_6756] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6758),U_6756) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_6756 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1943_2]) ).

cnf(f_1943_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6758),U_6756) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_6756 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

cnf(f_1943_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6759),U_6757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6759),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6757),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_6757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

fof(f_1944_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_1944_2,plain,
    ! [U_6761,U_6760] :
      ( ( 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_6760)),U_6761)))
        | ( U_6761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6760 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_6761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6760 != 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_6760)),U_6761))) ) ),
    inference(variable_rename,[status(thm)],[f_1944_1]) ).

fof(f_1944_3,plain,
    ( ! [U_6765,U_6763] :
        ( 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_6763)),U_6765)))
        | ( U_6765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6763 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_6764,U_6762] :
        ( U_6764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6762 != 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_6762)),U_6764))) ) ),
    inference(miniscope,[status(thm)],[f_1944_2]) ).

cnf(f_1944_4,plain,
    ( U_6764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6762 != 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_6762)),U_6764))) ),
    inference(clausify,[status(thm)],[f_1944_3]) ).

cnf(f_1944_5,plain,
    ( U_6763 = 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_6763)),U_6765))) ),
    inference(clausify,[status(thm)],[f_1944_3]) ).

cnf(f_1944_6,plain,
    ( U_6765 != 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_6763)),U_6765))) ),
    inference(clausify,[status(thm)],[f_1944_3]) ).

fof(f_1945_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_1945_2,plain,
    ! [U_6767,U_6766] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6767),U_6766) = 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_6767),U_6766)),U_6766))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6766),U_6767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6766)) ),
    inference(variable_rename,[status(thm)],[f_1945_1]) ).

cnf(f_1945_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6767),U_6766) = 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_6767),U_6766)),U_6766))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6766),U_6767))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6766)) ),
    inference(clausify,[status(thm)],[f_1945_2]) ).

fof(f_1946_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_1946_2,plain,
    ! [U_6770,U_6769,U_6768] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),hAPP(c_Nat_OSuc,U_6769))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),U_6769)),U_6770)) )
          | U_6769 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6770),U_6768) )
        & ( U_6769 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6770),U_6768)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),hAPP(c_Nat_OSuc,U_6769))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),U_6769)),U_6770)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6768)) ),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

cnf(f_1946_3,plain,
    ( U_6769 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6770),U_6768)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),hAPP(c_Nat_OSuc,U_6769))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),U_6769)),U_6770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6768)) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

cnf(f_1946_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_6768),U_6769)),U_6770))
    | U_6769 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6770),U_6768)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6768)) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

cnf(f_1946_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6768),hAPP(c_Nat_OSuc,U_6769))))
    | U_6769 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6770),U_6768)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6768)) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

fof(f_1947_1,plain,
    ! [V_n_2,V_m_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_Pa_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_1947_2,plain,
    ! [U_6775,U_6774,U_6773] :
      ( ( hBOOL(hAPP(U_6773,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6774),U_6775)))
        | ( ! [U_6772] :
              ( ~ hBOOL(hAPP(U_6773,U_6772))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6775),hAPP(c_Nat_OSuc,U_6772))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6775),U_6772)),U_6774)) )
          & ( ~ hBOOL(hAPP(U_6773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_6771] :
            ( hBOOL(hAPP(U_6773,U_6771))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6775),hAPP(c_Nat_OSuc,U_6771))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6775),U_6771)),U_6774)) )
        | ( hBOOL(hAPP(U_6773,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_6773,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6774),U_6775))) ) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

fof(f_1947_3,plain,
    ( ! [U_6781,U_6779,U_6777] :
        ( hBOOL(hAPP(U_6777,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6779),U_6781)))
        | ( ! [U_6772] :
              ( ~ hBOOL(hAPP(U_6777,U_6772))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),hAPP(c_Nat_OSuc,U_6772))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),U_6772)),U_6779)) )
          & ( ~ hBOOL(hAPP(U_6777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_6780,U_6778,U_6776] :
        ( ? [U_6771] :
            ( hBOOL(hAPP(U_6776,U_6771))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),hAPP(c_Nat_OSuc,U_6771))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),U_6771)),U_6778)) )
        | ( hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ) ),
    inference(miniscope,[status(thm)],[f_1947_2]) ).

fof(f_1947_4,plain,
    ( ! [U_6781,U_6779,U_6777] :
        ( hBOOL(hAPP(U_6777,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6779),U_6781)))
        | ( ! [U_6772] :
              ( ~ hBOOL(hAPP(U_6777,U_6772))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),hAPP(c_Nat_OSuc,U_6772))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),U_6772)),U_6779)) )
          & ( ~ hBOOL(hAPP(U_6777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_6781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_6780,U_6778,U_6776] :
        ( ( hBOOL(hAPP(U_6776,sK140(U_6780,U_6778,U_6776)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),hAPP(c_Nat_OSuc,sK140(U_6780,U_6778,U_6776)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),sK140(U_6780,U_6778,U_6776))),U_6778)) )
        | ( hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_6780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_6771,sK140(U_6780,U_6778,U_6776))],[f_1947_3]) ).

cnf(f_1947_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_6780),sK140(U_6780,U_6778,U_6776))),U_6778))
    | U_6780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),hAPP(c_Nat_OSuc,sK140(U_6780,U_6778,U_6776)))))
    | U_6780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_7,plain,
    ( hBOOL(hAPP(U_6776,sK140(U_6780,U_6778,U_6776)))
    | U_6780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_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_6780),sK140(U_6780,U_6778,U_6776))),U_6778))
    | hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6780),hAPP(c_Nat_OSuc,sK140(U_6780,U_6778,U_6776)))))
    | hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_10,plain,
    ( hBOOL(hAPP(U_6776,sK140(U_6780,U_6778,U_6776)))
    | hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6778),U_6780))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_11,plain,
    ( ~ hBOOL(hAPP(U_6777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_6781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_6777,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6779),U_6781))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

cnf(f_1947_12,plain,
    ( ~ hBOOL(hAPP(U_6777,U_6772))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),hAPP(c_Nat_OSuc,U_6772))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6781),U_6772)),U_6779))
    | hBOOL(hAPP(U_6777,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6779),U_6781))) ),
    inference(clausify,[status(thm)],[f_1947_4]) ).

fof(f_1948_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_1948_2,plain,
    ! [U_6783,U_6782] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6782),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6783)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6782),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_6783)),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

cnf(f_1948_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6782),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6783)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6782),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_6783)),
    inference(clausify,[status(thm)],[f_1948_2]) ).

fof(f_1949_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_1949_2,plain,
    ! [U_6785,U_6784] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6784)))),U_6785) = 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_6784)),U_6785),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

cnf(f_1949_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_6784)))),U_6785) = 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_6784)),U_6785),
    inference(clausify,[status(thm)],[f_1949_2]) ).

fof(f_1950_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_1950_2,plain,
    ! [U_6787,U_6786] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6786)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6787)) = 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_6786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6787)),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

cnf(f_1950_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_6786)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6787)) = 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_6786)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6787)),
    inference(clausify,[status(thm)],[f_1950_2]) ).

fof(f_1951_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_1951_2,plain,
    ! [U_6788] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6788))),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_6788),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_1951_1]) ).

cnf(f_1951_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_6788))),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_6788),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1951_2]) ).

fof(f_1952_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_1952_2,plain,
    ! [U_6789] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6789),U_6789)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_6789,
    inference(variable_rename,[status(thm)],[f_1952_1]) ).

cnf(f_1952_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6789),U_6789)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_6789,
    inference(clausify,[status(thm)],[f_1952_2]) ).

fof(f_1953_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_1953_2,plain,
    ! [U_6790] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6790),c_Groups_Ozero__class_Ozero(U_6790)),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_6790)
      | ~ class_Rings_Osemiring__1(U_6790) ),
    inference(variable_rename,[status(thm)],[f_1953_1]) ).

cnf(f_1953_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6790),c_Groups_Ozero__class_Ozero(U_6790)),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_6790)
    | ~ class_Rings_Osemiring__1(U_6790) ),
    inference(clausify,[status(thm)],[f_1953_2]) ).

fof(f_1954_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_1954_2,plain,
    ! [U_6792,U_6791] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),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_6791)
          | U_6792 != c_Groups_Ozero__class_Ozero(U_6791) )
        & ( U_6792 = c_Groups_Ozero__class_Ozero(U_6791)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),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_6791) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_6791) ),
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

cnf(f_1954_3,plain,
    ( U_6792 = c_Groups_Ozero__class_Ozero(U_6791)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),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_6791)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6791) ),
    inference(clausify,[status(thm)],[f_1954_2]) ).

cnf(f_1954_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),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_6791)
    | U_6792 != c_Groups_Ozero__class_Ozero(U_6791)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6791) ),
    inference(clausify,[status(thm)],[f_1954_2]) ).

fof(f_1955_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_1955_2,plain,
    ! [U_6794,U_6793] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6793),U_6794),U_6794) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6793),U_6794),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_6793) ),
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

cnf(f_1955_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6793),U_6794),U_6794) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6793),U_6794),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_6793) ),
    inference(clausify,[status(thm)],[f_1955_2]) ).

fof(f_1956_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_1956_2,plain,
    ! [U_6796,U_6795] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6795),U_6796),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_6795),U_6796),U_6796)
      | ~ class_Groups_Omonoid__mult(U_6795) ),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

cnf(f_1956_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6795),U_6796),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_6795),U_6796),U_6796)
    | ~ class_Groups_Omonoid__mult(U_6795) ),
    inference(clausify,[status(thm)],[f_1956_2]) ).

fof(f_1957_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_1957_2,plain,
    ! [U_6797] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),c_Groups_Oone__class_Oone(U_6797)),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_6797)
      | ~ class_Rings_Osemiring__1(U_6797) ),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

cnf(f_1957_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),c_Groups_Oone__class_Oone(U_6797)),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_6797)
    | ~ class_Rings_Osemiring__1(U_6797) ),
    inference(clausify,[status(thm)],[f_1957_2]) ).

fof(f_1958_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_1958_2,plain,
    ! [U_6799,U_6798] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6798),hAPP(c_Groups_Ouminus__class_Ouminus(U_6798),U_6799)),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_6798),U_6799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_6798) ),
    inference(variable_rename,[status(thm)],[f_1958_1]) ).

cnf(f_1958_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6798),hAPP(c_Groups_Ouminus__class_Ouminus(U_6798),U_6799)),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_6798),U_6799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_6798) ),
    inference(clausify,[status(thm)],[f_1958_2]) ).

fof(f_1959_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_1959_2,plain,
    ! [U_6802,U_6801,U_6800] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),U_6801),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_6802)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),U_6801),U_6802)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_6800) ),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

cnf(f_1959_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),U_6801),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_6802)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),hAPP(hAPP(c_Power_Opower__class_Opower(U_6800),U_6801),U_6802)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_6800) ),
    inference(clausify,[status(thm)],[f_1959_2]) ).

fof(f_1960_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_1960_2,plain,
    ! [U_6804,U_6803] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6803),hAPP(hAPP(c_Power_Opower__class_Opower(U_6803),U_6804),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_6803),U_6804),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_6803) ),
    inference(variable_rename,[status(thm)],[f_1960_1]) ).

cnf(f_1960_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6803),hAPP(hAPP(c_Power_Opower__class_Opower(U_6803),U_6804),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_6803),U_6804),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_6803) ),
    inference(clausify,[status(thm)],[f_1960_2]) ).

fof(f_1961_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_1961_2,plain,
    ! [U_6806,U_6805] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6805),hAPP(c_Groups_Oabs__class_Oabs(U_6805),U_6806)),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_6805),U_6806),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_6805) ),
    inference(variable_rename,[status(thm)],[f_1961_1]) ).

cnf(f_1961_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6805),hAPP(c_Groups_Oabs__class_Oabs(U_6805),U_6806)),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_6805),U_6806),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_6805) ),
    inference(clausify,[status(thm)],[f_1961_2]) ).

fof(f_1962_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_1962_2,plain,
    ! [U_6809,U_6808,U_6807] :
      ( U_6808 = U_6809
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),c_Groups_Ozero__class_Ozero(U_6807)),U_6809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),c_Groups_Ozero__class_Ozero(U_6807)),U_6808))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_6807),U_6808),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_6807),U_6809),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_6807) ),
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

cnf(f_1962_3,plain,
    ( U_6808 = U_6809
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),c_Groups_Ozero__class_Ozero(U_6807)),U_6809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),c_Groups_Ozero__class_Ozero(U_6807)),U_6808))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6807),U_6808),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_6807),U_6809),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(U_6807) ),
    inference(clausify,[status(thm)],[f_1962_2]) ).

fof(f_1963_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_1963_2,plain,
    ! [U_6812,U_6811,U_6810] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),U_6811),U_6812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),c_Groups_Ozero__class_Ozero(U_6810)),U_6812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),hAPP(hAPP(c_Power_Opower__class_Opower(U_6810),U_6811),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_6810),U_6812),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_6810) ),
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

cnf(f_1963_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),U_6811),U_6812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),c_Groups_Ozero__class_Ozero(U_6810)),U_6812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),hAPP(hAPP(c_Power_Opower__class_Opower(U_6810),U_6811),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_6810),U_6812),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_6810) ),
    inference(clausify,[status(thm)],[f_1963_2]) ).

fof(f_1964_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_1964_2,plain,
    ! [U_6814,U_6813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6813),c_Groups_Ozero__class_Ozero(U_6813)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6813),U_6814),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_6813) ),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

cnf(f_1964_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6813),c_Groups_Ozero__class_Ozero(U_6813)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6813),U_6814),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_6813) ),
    inference(clausify,[status(thm)],[f_1964_2]) ).

fof(f_1965_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_1965_2,plain,
    ! [U_6816,U_6815] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6815),hAPP(hAPP(c_Power_Opower__class_Opower(U_6815),U_6816),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_6815)))
      | ~ class_Rings_Olinordered__idom(U_6815) ),
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

cnf(f_1965_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6815),hAPP(hAPP(c_Power_Opower__class_Opower(U_6815),U_6816),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_6815)))
    | ~ class_Rings_Olinordered__idom(U_6815) ),
    inference(clausify,[status(thm)],[f_1965_2]) ).

fof(f_1966_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_1966_2,plain,
    ! [U_6818,U_6817] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6817),c_Groups_Ozero__class_Ozero(U_6817)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6817),U_6818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_6818 = c_Groups_Ozero__class_Ozero(U_6817) )
        & ( U_6818 != c_Groups_Ozero__class_Ozero(U_6817)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6817),c_Groups_Ozero__class_Ozero(U_6817)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6817),U_6818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_6817) ),
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

cnf(f_1966_3,plain,
    ( U_6818 != c_Groups_Ozero__class_Ozero(U_6817)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6817),c_Groups_Ozero__class_Ozero(U_6817)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6817),U_6818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_6817) ),
    inference(clausify,[status(thm)],[f_1966_2]) ).

cnf(f_1966_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6817),c_Groups_Ozero__class_Ozero(U_6817)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6817),U_6818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_6818 = c_Groups_Ozero__class_Ozero(U_6817)
    | ~ class_Rings_Olinordered__idom(U_6817) ),
    inference(clausify,[status(thm)],[f_1966_2]) ).

fof(f_1967_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_1967_2,plain,
    ! [U_6821,U_6820,U_6819] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6819),hAPP(hAPP(c_Power_Opower__class_Opower(U_6819),U_6820),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_6819),U_6821),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_6819)
          | U_6821 != c_Groups_Ozero__class_Ozero(U_6819)
          | U_6820 != c_Groups_Ozero__class_Ozero(U_6819) )
        & ( ( U_6821 = c_Groups_Ozero__class_Ozero(U_6819)
            & U_6820 = c_Groups_Ozero__class_Ozero(U_6819) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6819),hAPP(hAPP(c_Power_Opower__class_Opower(U_6819),U_6820),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_6819),U_6821),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_6819) ) )
      | ~ class_Rings_Olinordered__idom(U_6819) ),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

cnf(f_1967_3,plain,
    ( U_6820 = c_Groups_Ozero__class_Ozero(U_6819)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6819),hAPP(hAPP(c_Power_Opower__class_Opower(U_6819),U_6820),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_6819),U_6821),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_6819)
    | ~ class_Rings_Olinordered__idom(U_6819) ),
    inference(clausify,[status(thm)],[f_1967_2]) ).

cnf(f_1967_4,plain,
    ( U_6821 = c_Groups_Ozero__class_Ozero(U_6819)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6819),hAPP(hAPP(c_Power_Opower__class_Opower(U_6819),U_6820),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_6819),U_6821),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_6819)
    | ~ class_Rings_Olinordered__idom(U_6819) ),
    inference(clausify,[status(thm)],[f_1967_2]) ).

cnf(f_1967_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6819),hAPP(hAPP(c_Power_Opower__class_Opower(U_6819),U_6820),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_6819),U_6821),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_6819)
    | U_6821 != c_Groups_Ozero__class_Ozero(U_6819)
    | U_6820 != c_Groups_Ozero__class_Ozero(U_6819)
    | ~ class_Rings_Olinordered__idom(U_6819) ),
    inference(clausify,[status(thm)],[f_1967_2]) ).

fof(f_1968_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_1968_2,plain,
    ! [U_6823,U_6822] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6822),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823)),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_6822),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823)),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823))
      | ~ class_Int_Onumber(U_6822)
      | ~ class_Groups_Omonoid__mult(U_6822) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

cnf(f_1968_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6822),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823)),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_6822),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823)),hAPP(c_Int_Onumber__class_Onumber__of(U_6822),U_6823))
    | ~ class_Int_Onumber(U_6822)
    | ~ class_Groups_Omonoid__mult(U_6822) ),
    inference(clausify,[status(thm)],[f_1968_2]) ).

fof(f_1969_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_1969_2,plain,
    ! [U_6825,U_6824] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6824),U_6825),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_6824)
          | ( U_6825 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6824),c_Groups_Oone__class_Oone(U_6824))
            & U_6825 != c_Groups_Oone__class_Oone(U_6824) ) )
        & ( U_6825 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6824),c_Groups_Oone__class_Oone(U_6824))
          | U_6825 = c_Groups_Oone__class_Oone(U_6824)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6824),U_6825),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_6824) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_6824) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

cnf(f_1969_3,plain,
    ( U_6825 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6824),c_Groups_Oone__class_Oone(U_6824))
    | U_6825 = c_Groups_Oone__class_Oone(U_6824)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6824),U_6825),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_6824)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6824) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

cnf(f_1969_4,plain,
    ( U_6825 != c_Groups_Oone__class_Oone(U_6824)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6824),U_6825),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_6824)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6824) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

cnf(f_1969_5,plain,
    ( U_6825 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6824),c_Groups_Oone__class_Oone(U_6824))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6824),U_6825),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_6824)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6824) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

fof(f_1970_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_1970_2,plain,
    ! [U_6827,U_6826] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6827)) = 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_6826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6827)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6826))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6827)) = 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_6826))) ) ),
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

fof(f_1970_3,plain,
    ( ! [U_6831,U_6829] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6829)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6831)) = 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_6829)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6831)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6829))) )
    & ! [U_6830,U_6828] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6828)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6830)) = 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_6828))) ) ),
    inference(miniscope,[status(thm)],[f_1970_2]) ).

cnf(f_1970_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6828)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6830)) = 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_6828))) ),
    inference(clausify,[status(thm)],[f_1970_3]) ).

cnf(f_1970_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6829)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6831)) = 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_6829)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6831)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6829))) ),
    inference(clausify,[status(thm)],[f_1970_3]) ).

fof(f_1971_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_1971_2,plain,
    ! [U_6834,U_6833,U_6832] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),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_6834)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6832),hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),U_6834)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),U_6834))
      | ~ class_Rings_Ocomm__semiring__1(U_6832) ),
    inference(variable_rename,[status(thm)],[f_1971_1]) ).

cnf(f_1971_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),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_6834)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6832),hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),U_6834)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6832),U_6833),U_6834))
    | ~ class_Rings_Ocomm__semiring__1(U_6832) ),
    inference(clausify,[status(thm)],[f_1971_2]) ).

fof(f_1972_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_1972_2,plain,
    ! [U_6837,U_6836,U_6835] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6835),hAPP(c_Groups_Ouminus__class_Ouminus(U_6835),U_6836)),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_6837)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6835),U_6836),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_6837))
      | ~ class_Rings_Oring__1(U_6835) ),
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

cnf(f_1972_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6835),hAPP(c_Groups_Ouminus__class_Ouminus(U_6835),U_6836)),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_6837)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6835),U_6836),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_6837))
    | ~ class_Rings_Oring__1(U_6835) ),
    inference(clausify,[status(thm)],[f_1972_2]) ).

fof(f_1973_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_1973_2,plain,
    ! [U_6838] :
      ( 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_6838),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_6838)) ),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

cnf(f_1973_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_6838),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_6838)) ),
    inference(clausify,[status(thm)],[f_1973_2]) ).

fof(f_1974_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_1974_2,plain,
    ! [U_6841,U_6840,U_6839] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6839),U_6840),U_6841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6839),c_Groups_Ozero__class_Ozero(U_6839)),U_6841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6839),hAPP(hAPP(c_Power_Opower__class_Opower(U_6839),U_6840),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_6839),U_6841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_6839) ),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

cnf(f_1974_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6839),U_6840),U_6841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6839),c_Groups_Ozero__class_Ozero(U_6839)),U_6841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6839),hAPP(hAPP(c_Power_Opower__class_Opower(U_6839),U_6840),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_6839),U_6841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_6839) ),
    inference(clausify,[status(thm)],[f_1974_2]) ).

fof(f_1975_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_1975_2,plain,
    ! [U_6842] : 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_6842)) = 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_6842))),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

cnf(f_1975_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_6842)) = 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_6842))),
    inference(clausify,[status(thm)],[f_1975_2]) ).

fof(f_1976_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_1976_2,plain,
    ! [U_6845,U_6844,U_6843] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6843),c_Groups_Ozero__class_Ozero(U_6843)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6843),hAPP(hAPP(c_Power_Opower__class_Opower(U_6843),U_6844),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_6843),U_6845),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_6843) ),
    inference(variable_rename,[status(thm)],[f_1976_1]) ).

cnf(f_1976_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6843),c_Groups_Ozero__class_Ozero(U_6843)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6843),hAPP(hAPP(c_Power_Opower__class_Opower(U_6843),U_6844),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_6843),U_6845),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_6843) ),
    inference(clausify,[status(thm)],[f_1976_2]) ).

fof(f_1977_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_1977_2,plain,
    ! [U_6848,U_6847,U_6846] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(hAPP(c_Power_Opower__class_Opower(U_6846),U_6847),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_6846),U_6848),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_6846)))
          | U_6848 != c_Groups_Ozero__class_Ozero(U_6846)
          | U_6847 != c_Groups_Ozero__class_Ozero(U_6846) )
        & ( ( U_6848 = c_Groups_Ozero__class_Ozero(U_6846)
            & U_6847 = c_Groups_Ozero__class_Ozero(U_6846) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(hAPP(c_Power_Opower__class_Opower(U_6846),U_6847),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_6846),U_6848),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_6846))) ) )
      | ~ class_Rings_Olinordered__idom(U_6846) ),
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

cnf(f_1977_3,plain,
    ( U_6847 = c_Groups_Ozero__class_Ozero(U_6846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(hAPP(c_Power_Opower__class_Opower(U_6846),U_6847),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_6846),U_6848),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_6846)))
    | ~ class_Rings_Olinordered__idom(U_6846) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

cnf(f_1977_4,plain,
    ( U_6848 = c_Groups_Ozero__class_Ozero(U_6846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(hAPP(c_Power_Opower__class_Opower(U_6846),U_6847),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_6846),U_6848),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_6846)))
    | ~ class_Rings_Olinordered__idom(U_6846) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

cnf(f_1977_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(hAPP(c_Power_Opower__class_Opower(U_6846),U_6847),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_6846),U_6848),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_6846)))
    | U_6848 != c_Groups_Ozero__class_Ozero(U_6846)
    | U_6847 != c_Groups_Ozero__class_Ozero(U_6846)
    | ~ class_Rings_Olinordered__idom(U_6846) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

fof(f_1978_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_1978_2,plain,
    ! [U_6851,U_6850,U_6849] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6849),c_Groups_Ozero__class_Ozero(U_6849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6849),hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),U_6850),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_6849),U_6851),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_6851 = c_Groups_Ozero__class_Ozero(U_6849)
            & U_6850 = c_Groups_Ozero__class_Ozero(U_6849) ) )
        & ( U_6851 != c_Groups_Ozero__class_Ozero(U_6849)
          | U_6850 != c_Groups_Ozero__class_Ozero(U_6849)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6849),c_Groups_Ozero__class_Ozero(U_6849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6849),hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),U_6850),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_6849),U_6851),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_6849) ),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

cnf(f_1978_3,plain,
    ( U_6851 != c_Groups_Ozero__class_Ozero(U_6849)
    | U_6850 != c_Groups_Ozero__class_Ozero(U_6849)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6849),c_Groups_Ozero__class_Ozero(U_6849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6849),hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),U_6850),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_6849),U_6851),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_6849) ),
    inference(clausify,[status(thm)],[f_1978_2]) ).

cnf(f_1978_4,plain,
    ( U_6850 = c_Groups_Ozero__class_Ozero(U_6849)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6849),c_Groups_Ozero__class_Ozero(U_6849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6849),hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),U_6850),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_6849),U_6851),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_6849) ),
    inference(clausify,[status(thm)],[f_1978_2]) ).

cnf(f_1978_5,plain,
    ( U_6851 = c_Groups_Ozero__class_Ozero(U_6849)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6849),c_Groups_Ozero__class_Ozero(U_6849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6849),hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),U_6850),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_6849),U_6851),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_6849) ),
    inference(clausify,[status(thm)],[f_1978_2]) ).

fof(f_1979_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_1979_2,plain,
    ! [U_6854,U_6853,U_6852] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6852),hAPP(hAPP(c_Power_Opower__class_Opower(U_6852),U_6853),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_6852),U_6854),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_6852)))
      | ~ class_Rings_Olinordered__idom(U_6852) ),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

cnf(f_1979_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6852),hAPP(hAPP(c_Power_Opower__class_Opower(U_6852),U_6853),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_6852),U_6854),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_6852)))
    | ~ class_Rings_Olinordered__idom(U_6852) ),
    inference(clausify,[status(thm)],[f_1979_2]) ).

fof(f_1980_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_1980_2,plain,
    ! [U_6857,U_6856,U_6855] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6855),U_6856),U_6857)),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_6855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6855),hAPP(hAPP(c_Power_Opower__class_Opower(U_6855),U_6856),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_6855),U_6857),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_6855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6855),hAPP(c_Int_Onumber__class_Onumber__of(U_6855),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6856)),U_6857))
      | ~ class_Int_Onumber__ring(U_6855) ),
    inference(variable_rename,[status(thm)],[f_1980_1]) ).

cnf(f_1980_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6855),U_6856),U_6857)),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_6855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6855),hAPP(hAPP(c_Power_Opower__class_Opower(U_6855),U_6856),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_6855),U_6857),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_6855),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6855),hAPP(c_Int_Onumber__class_Onumber__of(U_6855),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6856)),U_6857))
    | ~ class_Int_Onumber__ring(U_6855) ),
    inference(clausify,[status(thm)],[f_1980_2]) ).

fof(f_1981_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_1981_2,plain,
    ! [U_6860,U_6859,U_6858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6858),c_Groups_Ozero__class_Ozero(U_6858)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6858),U_6859),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_6860))))
      | ~ class_Rings_Olinordered__idom(U_6858) ),
    inference(variable_rename,[status(thm)],[f_1981_1]) ).

cnf(f_1981_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6858),c_Groups_Ozero__class_Ozero(U_6858)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6858),U_6859),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_6860))))
    | ~ class_Rings_Olinordered__idom(U_6858) ),
    inference(clausify,[status(thm)],[f_1981_2]) ).

fof(f_1982_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_1982_2,plain,
    ! [U_6863,U_6862,U_6861] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),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_6863))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),U_6862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),U_6863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),U_6863)))
      | ~ class_Rings_Ocomm__semiring__1(U_6861) ),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

cnf(f_1982_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),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_6863))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),U_6862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6861),hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),U_6863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6861),U_6862),U_6863)))
    | ~ class_Rings_Ocomm__semiring__1(U_6861) ),
    inference(clausify,[status(thm)],[f_1982_2]) ).

fof(f_1983_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_1983_2,plain,
    ! [U_6866,U_6865,U_6864] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),U_6865),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_6866))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6864),U_6865),hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),U_6865),U_6866)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_6864) ),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

cnf(f_1983_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),U_6865),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_6866))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6864),U_6865),hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),hAPP(hAPP(c_Power_Opower__class_Opower(U_6864),U_6865),U_6866)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_6864) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

fof(f_1984_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_1984_2,plain,
    ! [U_6868,U_6867] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6867),hAPP(c_Groups_Ouminus__class_Ouminus(U_6867),c_Groups_Oone__class_Oone(U_6867))),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_6868)) = c_Groups_Oone__class_Oone(U_6867)
      | ~ class_Rings_Oring__1(U_6867) ),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

cnf(f_1984_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6867),hAPP(c_Groups_Ouminus__class_Ouminus(U_6867),c_Groups_Oone__class_Oone(U_6867))),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_6868)) = c_Groups_Oone__class_Oone(U_6867)
    | ~ class_Rings_Oring__1(U_6867) ),
    inference(clausify,[status(thm)],[f_1984_2]) ).

fof(f_1985_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_1985_2,plain,
    ! [U_6870,U_6869] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6870),U_6869)),U_6870) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6869),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_6870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6869)) ),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

cnf(f_1985_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6870),U_6869)),U_6870) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6869),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_6870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6869)) ),
    inference(clausify,[status(thm)],[f_1985_2]) ).

fof(f_1986_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_1986_2,plain,
    ! [U_6871] :
      ( 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_6871),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_6871)) ),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

cnf(f_1986_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_6871),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_6871)) ),
    inference(clausify,[status(thm)],[f_1986_2]) ).

fof(f_1987_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_1987_2,plain,
    ! [U_6874,U_6873,U_6872] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6872),U_6873),U_6874)),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_6872),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6872),hAPP(hAPP(c_Power_Opower__class_Opower(U_6872),U_6873),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_6872),U_6874),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_6872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6872),hAPP(c_Int_Onumber__class_Onumber__of(U_6872),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6873)),U_6874))
      | ~ class_Int_Onumber__ring(U_6872) ),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

cnf(f_1987_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6872),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6872),U_6873),U_6874)),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_6872),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6872),hAPP(hAPP(c_Power_Opower__class_Opower(U_6872),U_6873),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_6872),U_6874),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_6872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6872),hAPP(c_Int_Onumber__class_Onumber__of(U_6872),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6873)),U_6874))
    | ~ class_Int_Onumber__ring(U_6872) ),
    inference(clausify,[status(thm)],[f_1987_2]) ).

fof(f_1988_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_1988_2,plain,
    ! [U_6877,U_6876,U_6875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6875),c_Groups_Ozero__class_Ozero(U_6875)),U_6876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6875),c_Groups_Ozero__class_Ozero(U_6875)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6875),U_6876),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_6877)))))
      | ~ class_Rings_Olinordered__idom(U_6875) ),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

cnf(f_1988_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6875),c_Groups_Ozero__class_Ozero(U_6875)),U_6876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6875),c_Groups_Ozero__class_Ozero(U_6875)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6875),U_6876),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_6877)))))
    | ~ class_Rings_Olinordered__idom(U_6875) ),
    inference(clausify,[status(thm)],[f_1988_2]) ).

fof(f_1989_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_1989_2,plain,
    ! [U_6880,U_6879,U_6878] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6878),hAPP(hAPP(c_Power_Opower__class_Opower(U_6878),U_6879),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_6880)))),c_Groups_Ozero__class_Ozero(U_6878)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6878),U_6879),c_Groups_Ozero__class_Ozero(U_6878)))
      | ~ class_Rings_Olinordered__idom(U_6878) ),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

cnf(f_1989_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6878),hAPP(hAPP(c_Power_Opower__class_Opower(U_6878),U_6879),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_6880)))),c_Groups_Ozero__class_Ozero(U_6878)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6878),U_6879),c_Groups_Ozero__class_Ozero(U_6878)))
    | ~ class_Rings_Olinordered__idom(U_6878) ),
    inference(clausify,[status(thm)],[f_1989_2]) ).

fof(f_1990_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_1990_2,plain,
    ! [U_6882,U_6881] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6881),hAPP(c_Groups_Ouminus__class_Ouminus(U_6881),c_Groups_Oone__class_Oone(U_6881))),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_6882))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6881),c_Groups_Oone__class_Oone(U_6881))
      | ~ class_Rings_Oring__1(U_6881) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

cnf(f_1990_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6881),hAPP(c_Groups_Ouminus__class_Ouminus(U_6881),c_Groups_Oone__class_Oone(U_6881))),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_6882))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6881),c_Groups_Oone__class_Oone(U_6881))
    | ~ class_Rings_Oring__1(U_6881) ),
    inference(clausify,[status(thm)],[f_1990_2]) ).

fof(f_1991_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_1991_2,plain,
    ! [U_6884,U_6883] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6883),hAPP(c_Int_Onumber__class_Onumber__of(U_6883),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_6884)) = c_Groups_Oone__class_Oone(U_6883)
      | ~ class_Int_Onumber__ring(U_6883) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

cnf(f_1991_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6883),hAPP(c_Int_Onumber__class_Onumber__of(U_6883),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_6884)) = c_Groups_Oone__class_Oone(U_6883)
    | ~ class_Int_Onumber__ring(U_6883) ),
    inference(clausify,[status(thm)],[f_1991_2]) ).

fof(f_1992_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_1992_2,plain,
    ! [U_6885] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_6885) = 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_6885),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_6885,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_6885) = 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_6885),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_6885,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_6885 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_6885) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6885 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1992_1]) ).

fof(f_1992_3,plain,
    ( ! [U_6887] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_6887) = 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_6887),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_6887,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_6887) = 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_6887),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_6887,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_6887 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6886] :
        ( hAPP(c_Code__Numeral_Oint__of,U_6886) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6886 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1992_2]) ).

cnf(f_1992_4,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_6886) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6886 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1992_3]) ).

cnf(f_1992_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_6887) = 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_6887),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_6887,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_6887 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1992_3]) ).

cnf(f_1992_6,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_6887) = 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_6887),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_6887,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_6887 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1992_3]) ).

fof(f_1993_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_1993_2,plain,
    ! [U_6891,U_6890,U_6889,U_6888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6888),hAPP(hAPP(c_Power_Opower__class_Opower(U_6888),U_6889),U_6891)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6888),U_6890),U_6891)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6891))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6888),c_Groups_Ozero__class_Ozero(U_6888)),U_6889))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6888),U_6889),U_6890))
      | ~ class_Rings_Olinordered__semidom(U_6888) ),
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

cnf(f_1993_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6888),hAPP(hAPP(c_Power_Opower__class_Opower(U_6888),U_6889),U_6891)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6888),U_6890),U_6891)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6888),c_Groups_Ozero__class_Ozero(U_6888)),U_6889))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6888),U_6889),U_6890))
    | ~ class_Rings_Olinordered__semidom(U_6888) ),
    inference(clausify,[status(thm)],[f_1993_2]) ).

fof(f_1994_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_1994_2,plain,
    ! [U_6895,U_6894,U_6893,U_6892] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6895),U_6894)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6892),hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),U_6895)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),U_6894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6894),U_6895))
      | U_6893 = c_Groups_Ozero__class_Ozero(U_6892)
      | ~ class_Fields_Ofield(U_6892) ),
    inference(variable_rename,[status(thm)],[f_1994_1]) ).

cnf(f_1994_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6895),U_6894)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6892),hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),U_6895)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6892),U_6893),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6894),U_6895))
    | U_6893 = c_Groups_Ozero__class_Ozero(U_6892)
    | ~ class_Fields_Ofield(U_6892) ),
    inference(clausify,[status(thm)],[f_1994_2]) ).

fof(f_1995_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_1995_2,plain,
    ! [U_6898,U_6897,U_6896] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6896),c_Groups_Oone__class_Oone(U_6896)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6896),U_6897),U_6898)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6898))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6896),c_Groups_Oone__class_Oone(U_6896)),U_6897))
      | ~ class_Rings_Olinordered__semidom(U_6896) ),
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

cnf(f_1995_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6896),c_Groups_Oone__class_Oone(U_6896)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6896),U_6897),U_6898)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6898))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6896),c_Groups_Oone__class_Oone(U_6896)),U_6897))
    | ~ class_Rings_Olinordered__semidom(U_6896) ),
    inference(clausify,[status(thm)],[f_1995_2]) ).

fof(f_1996_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_1996_2,plain,
    ! [U_6902,U_6901,U_6900,U_6899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6901),U_6902))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6899),hAPP(hAPP(c_Power_Opower__class_Opower(U_6899),U_6900),U_6901)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6899),U_6900),U_6902)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6899),c_Groups_Oone__class_Oone(U_6899)),U_6900))
      | ~ class_Rings_Olinordered__semidom(U_6899) ),
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

cnf(f_1996_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6901),U_6902))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6899),hAPP(hAPP(c_Power_Opower__class_Opower(U_6899),U_6900),U_6901)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6899),U_6900),U_6902)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6899),c_Groups_Oone__class_Oone(U_6899)),U_6900))
    | ~ class_Rings_Olinordered__semidom(U_6899) ),
    inference(clausify,[status(thm)],[f_1996_2]) ).

fof(f_1997_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_1997_2,plain,
    ! [U_6905,U_6904,U_6903] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6903),U_6904),U_6905) != c_Groups_Ozero__class_Ozero(U_6903)
      | U_6904 = c_Groups_Ozero__class_Ozero(U_6903)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_6903) ),
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

cnf(f_1997_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6903),U_6904),U_6905) != c_Groups_Ozero__class_Ozero(U_6903)
    | U_6904 = c_Groups_Ozero__class_Ozero(U_6903)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6903) ),
    inference(clausify,[status(thm)],[f_1997_2]) ).

fof(f_1998_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_1998_2,plain,
    ! [U_6906] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6906) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

cnf(f_1998_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_6906) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1998_2]) ).

fof(f_1999_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_1999_2,plain,
    ! [U_6908,U_6907] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6907),U_6908) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_6907 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_6908 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_6907 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_6908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6907),U_6908) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

fof(f_1999_3,plain,
    ( ! [U_6912,U_6910] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6910),U_6912) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_6910 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6911,U_6909] :
        ( U_6909 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6909),U_6911) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1999_2]) ).

cnf(f_1999_4,plain,
    ( U_6909 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_6911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6909),U_6911) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1999_3]) ).

cnf(f_1999_5,plain,
    ( U_6912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6910),U_6912) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1999_3]) ).

cnf(f_1999_6,plain,
    ( U_6910 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6910),U_6912) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1999_3]) ).

fof(f_2000_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_2000_2,plain,
    ! [U_6914,U_6913] :
      ( ( 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_6913),U_6914)))
        | ( U_6914 != 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_6913)) ) )
      & ( U_6914 = 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_6913))
        | ~ 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_6913),U_6914))) ) ),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

fof(f_2000_3,plain,
    ( ! [U_6918,U_6916] :
        ( 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_6916),U_6918)))
        | ( U_6918 != 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_6916)) ) )
    & ! [U_6917,U_6915] :
        ( U_6917 = 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_6915))
        | ~ 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_6915),U_6917))) ) ),
    inference(miniscope,[status(thm)],[f_2000_2]) ).

cnf(f_2000_4,plain,
    ( U_6917 = 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_6915))
    | ~ 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_6915),U_6917))) ),
    inference(clausify,[status(thm)],[f_2000_3]) ).

cnf(f_2000_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6916))
    | 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_6916),U_6918))) ),
    inference(clausify,[status(thm)],[f_2000_3]) ).

cnf(f_2000_6,plain,
    ( U_6918 != 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_6916),U_6918))) ),
    inference(clausify,[status(thm)],[f_2000_3]) ).

fof(f_2001_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_2001_2,plain,
    ! [U_6921,U_6920,U_6919] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6920),U_6921))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6919),U_6920)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6919),U_6921)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6919)) ),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

cnf(f_2001_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6920),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6919),U_6920)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6919),U_6921)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6919)) ),
    inference(clausify,[status(thm)],[f_2001_2]) ).

fof(f_2002_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_2002_2,plain,
    ! [U_6925,U_6924,U_6923,U_6922] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6922),U_6923),U_6924)),U_6925) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6922),hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),U_6923),U_6925)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),U_6924),U_6925))
      | ~ class_Groups_Ocomm__monoid__mult(U_6922) ),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

cnf(f_2002_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6922),U_6923),U_6924)),U_6925) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6922),hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),U_6923),U_6925)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6922),U_6924),U_6925))
    | ~ class_Groups_Ocomm__monoid__mult(U_6922) ),
    inference(clausify,[status(thm)],[f_2002_2]) ).

fof(f_2003_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_2003_2,plain,
    ! [U_6928,U_6927,U_6926] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6926),hAPP(hAPP(c_Power_Opower__class_Opower(U_6926),U_6927),U_6928)),U_6927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6926),U_6927),hAPP(hAPP(c_Power_Opower__class_Opower(U_6926),U_6927),U_6928))
      | ~ class_Groups_Omonoid__mult(U_6926) ),
    inference(variable_rename,[status(thm)],[f_2003_1]) ).

cnf(f_2003_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6926),hAPP(hAPP(c_Power_Opower__class_Opower(U_6926),U_6927),U_6928)),U_6927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6926),U_6927),hAPP(hAPP(c_Power_Opower__class_Opower(U_6926),U_6927),U_6928))
    | ~ class_Groups_Omonoid__mult(U_6926) ),
    inference(clausify,[status(thm)],[f_2003_2]) ).

fof(f_2004_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_2004_2,plain,
    ! [U_6930,U_6929] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6929),c_Groups_Oone__class_Oone(U_6929)),U_6930) = c_Groups_Oone__class_Oone(U_6929)
      | ~ class_Groups_Omonoid__mult(U_6929) ),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

cnf(f_2004_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6929),c_Groups_Oone__class_Oone(U_6929)),U_6930) = c_Groups_Oone__class_Oone(U_6929)
    | ~ class_Groups_Omonoid__mult(U_6929) ),
    inference(clausify,[status(thm)],[f_2004_2]) ).

fof(f_2005_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_2005_2,plain,
    ! [U_6933,U_6932,U_6931] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6931),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6932),U_6933)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6931),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6931),U_6932)),U_6933)
      | ~ class_Rings_Osemiring__1(U_6931) ),
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

cnf(f_2005_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6931),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6932),U_6933)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6931),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6931),U_6932)),U_6933)
    | ~ class_Rings_Osemiring__1(U_6931) ),
    inference(clausify,[status(thm)],[f_2005_2]) ).

fof(f_2006_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_2006_2,plain,
    ! [U_6937,U_6936,U_6935,U_6934] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),U_6935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6936),U_6937)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),U_6935),U_6936)),U_6937)
      | ~ class_Groups_Omonoid__mult(U_6934) ),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

cnf(f_2006_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),U_6935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6936),U_6937)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),hAPP(hAPP(c_Power_Opower__class_Opower(U_6934),U_6935),U_6936)),U_6937)
    | ~ class_Groups_Omonoid__mult(U_6934) ),
    inference(clausify,[status(thm)],[f_2006_2]) ).

fof(f_2007_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_2007_2,plain,
    ! [U_6941,U_6940,U_6939,U_6938] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6938),U_6939),U_6940)),U_6941) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6938),hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),U_6939),U_6941)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),U_6940),U_6941))
      | ~ class_Fields_Ofield__inverse__zero(U_6938) ),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

cnf(f_2007_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6938),U_6939),U_6940)),U_6941) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6938),hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),U_6939),U_6941)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6938),U_6940),U_6941))
    | ~ class_Fields_Ofield__inverse__zero(U_6938) ),
    inference(clausify,[status(thm)],[f_2007_2]) ).

fof(f_2008_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_2008_2,plain,
    ! [U_6944,U_6943,U_6942] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6942),hAPP(hAPP(c_Power_Opower__class_Opower(U_6942),U_6943),U_6944)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6942),hAPP(c_Groups_Oabs__class_Oabs(U_6942),U_6943)),U_6944)
      | ~ class_Rings_Olinordered__idom(U_6942) ),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

cnf(f_2008_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6942),hAPP(hAPP(c_Power_Opower__class_Opower(U_6942),U_6943),U_6944)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6942),hAPP(c_Groups_Oabs__class_Oabs(U_6942),U_6943)),U_6944)
    | ~ class_Rings_Olinordered__idom(U_6942) ),
    inference(clausify,[status(thm)],[f_2008_2]) ).

fof(f_2009_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_2009_2,plain,
    ! [U_6946,U_6945] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6945),U_6946),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6946
      | ~ class_Groups_Omonoid__mult(U_6945) ),
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

cnf(f_2009_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6945),U_6946),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6946
    | ~ class_Groups_Omonoid__mult(U_6945) ),
    inference(clausify,[status(thm)],[f_2009_2]) ).

fof(f_2010_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_2010_2,plain,
    ! [U_6949,U_6948,U_6947] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6947),c_Groups_Ozero__class_Ozero(U_6947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6947),U_6948),U_6949)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6947),c_Groups_Ozero__class_Ozero(U_6947)),U_6948))
      | ~ class_Rings_Olinordered__semidom(U_6947) ),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

cnf(f_2010_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6947),c_Groups_Ozero__class_Ozero(U_6947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6947),U_6948),U_6949)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6947),c_Groups_Ozero__class_Ozero(U_6947)),U_6948))
    | ~ class_Rings_Olinordered__semidom(U_6947) ),
    inference(clausify,[status(thm)],[f_2010_2]) ).

fof(f_2011_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_2011_2,plain,
    ! [U_6953,U_6952,U_6951,U_6950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),hAPP(hAPP(c_Power_Opower__class_Opower(U_6950),U_6951),U_6953)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6950),U_6952),U_6953)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),c_Groups_Ozero__class_Ozero(U_6950)),U_6951))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),U_6951),U_6952))
      | ~ class_Rings_Olinordered__semidom(U_6950) ),
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

cnf(f_2011_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),hAPP(hAPP(c_Power_Opower__class_Opower(U_6950),U_6951),U_6953)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6950),U_6952),U_6953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),c_Groups_Ozero__class_Ozero(U_6950)),U_6951))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6950),U_6951),U_6952))
    | ~ class_Rings_Olinordered__semidom(U_6950) ),
    inference(clausify,[status(thm)],[f_2011_2]) ).

fof(f_2012_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_2012_2,plain,
    ! [U_6956,U_6955,U_6954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6954),c_Groups_Ozero__class_Ozero(U_6954)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6954),U_6955),U_6956)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6954),c_Groups_Ozero__class_Ozero(U_6954)),U_6955))
      | ~ class_Rings_Olinordered__semidom(U_6954) ),
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

cnf(f_2012_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6954),c_Groups_Ozero__class_Ozero(U_6954)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6954),U_6955),U_6956)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6954),c_Groups_Ozero__class_Ozero(U_6954)),U_6955))
    | ~ class_Rings_Olinordered__semidom(U_6954) ),
    inference(clausify,[status(thm)],[f_2012_2]) ).

fof(f_2013_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_2013_2,plain,
    ! [U_6959,U_6958,U_6957] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6957),U_6958),U_6959) = c_Groups_Ozero__class_Ozero(U_6957)
          | U_6959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_6958 != c_Groups_Ozero__class_Ozero(U_6957) )
        & ( ( U_6959 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_6958 = c_Groups_Ozero__class_Ozero(U_6957) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6957),U_6958),U_6959) != c_Groups_Ozero__class_Ozero(U_6957) ) )
      | ~ class_Rings_Ozero__neq__one(U_6957)
      | ~ class_Rings_Ono__zero__divisors(U_6957)
      | ~ class_Rings_Omult__zero(U_6957)
      | ~ class_Power_Opower(U_6957) ),
    inference(variable_rename,[status(thm)],[f_2013_1]) ).

cnf(f_2013_3,plain,
    ( U_6958 = c_Groups_Ozero__class_Ozero(U_6957)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6957),U_6958),U_6959) != c_Groups_Ozero__class_Ozero(U_6957)
    | ~ class_Rings_Ozero__neq__one(U_6957)
    | ~ class_Rings_Ono__zero__divisors(U_6957)
    | ~ class_Rings_Omult__zero(U_6957)
    | ~ class_Power_Opower(U_6957) ),
    inference(clausify,[status(thm)],[f_2013_2]) ).

cnf(f_2013_4,plain,
    ( U_6959 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6957),U_6958),U_6959) != c_Groups_Ozero__class_Ozero(U_6957)
    | ~ class_Rings_Ozero__neq__one(U_6957)
    | ~ class_Rings_Ono__zero__divisors(U_6957)
    | ~ class_Rings_Omult__zero(U_6957)
    | ~ class_Power_Opower(U_6957) ),
    inference(clausify,[status(thm)],[f_2013_2]) ).

cnf(f_2013_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6957),U_6958),U_6959) = c_Groups_Ozero__class_Ozero(U_6957)
    | U_6959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6958 != c_Groups_Ozero__class_Ozero(U_6957)
    | ~ class_Rings_Ozero__neq__one(U_6957)
    | ~ class_Rings_Ono__zero__divisors(U_6957)
    | ~ class_Rings_Omult__zero(U_6957)
    | ~ class_Power_Opower(U_6957) ),
    inference(clausify,[status(thm)],[f_2013_2]) ).

fof(f_2014_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_2014_2,plain,
    ! [U_6962,U_6961,U_6960] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6960),c_Groups_Oone__class_Oone(U_6960)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6960),U_6961),U_6962)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6960),c_Groups_Oone__class_Oone(U_6960)),U_6961))
      | ~ class_Rings_Olinordered__semidom(U_6960) ),
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

cnf(f_2014_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6960),c_Groups_Oone__class_Oone(U_6960)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6960),U_6961),U_6962)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6960),c_Groups_Oone__class_Oone(U_6960)),U_6961))
    | ~ class_Rings_Olinordered__semidom(U_6960) ),
    inference(clausify,[status(thm)],[f_2014_2]) ).

fof(f_2015_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_2015_2,plain,
    ! [U_6964,U_6963] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6963),c_Groups_Ozero__class_Ozero(U_6963)),hAPP(c_Nat_OSuc,U_6964)) = c_Groups_Ozero__class_Ozero(U_6963)
      | ~ class_Rings_Osemiring__0(U_6963)
      | ~ class_Power_Opower(U_6963) ),
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

cnf(f_2015_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6963),c_Groups_Ozero__class_Ozero(U_6963)),hAPP(c_Nat_OSuc,U_6964)) = c_Groups_Ozero__class_Ozero(U_6963)
    | ~ class_Rings_Osemiring__0(U_6963)
    | ~ class_Power_Opower(U_6963) ),
    inference(clausify,[status(thm)],[f_2015_2]) ).

fof(f_2016_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_2016_2,plain,
    ! [U_6968,U_6967,U_6966,U_6965] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6967) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6968)
          | U_6967 != U_6968 )
        & ( U_6967 = U_6968
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6967) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6968) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6965),c_Groups_Oone__class_Oone(U_6965)),U_6966))
      | ~ class_Rings_Olinordered__semidom(U_6965) ),
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

cnf(f_2016_3,plain,
    ( U_6967 = U_6968
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6967) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6968)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6965),c_Groups_Oone__class_Oone(U_6965)),U_6966))
    | ~ class_Rings_Olinordered__semidom(U_6965) ),
    inference(clausify,[status(thm)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6967) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6965),U_6966),U_6968)
    | U_6967 != U_6968
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6965),c_Groups_Oone__class_Oone(U_6965)),U_6966))
    | ~ class_Rings_Olinordered__semidom(U_6965) ),
    inference(clausify,[status(thm)],[f_2016_2]) ).

fof(f_2017_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_2017_2,plain,
    ! [U_6971,U_6970,U_6969] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6969),U_6970),hAPP(c_Nat_OSuc,U_6971)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6969),U_6970),hAPP(hAPP(c_Power_Opower__class_Opower(U_6969),U_6970),U_6971))
      | ~ class_Power_Opower(U_6969) ),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

cnf(f_2017_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6969),U_6970),hAPP(c_Nat_OSuc,U_6971)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6969),U_6970),hAPP(hAPP(c_Power_Opower__class_Opower(U_6969),U_6970),U_6971))
    | ~ class_Power_Opower(U_6969) ),
    inference(clausify,[status(thm)],[f_2017_2]) ).

fof(f_2018_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_2018_2,plain,
    ! [U_6974,U_6973,U_6972] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6972),U_6973),hAPP(c_Nat_OSuc,U_6974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6972),hAPP(hAPP(c_Power_Opower__class_Opower(U_6972),U_6973),U_6974)),U_6973)
      | ~ class_Groups_Omonoid__mult(U_6972) ),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

cnf(f_2018_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6972),U_6973),hAPP(c_Nat_OSuc,U_6974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6972),hAPP(hAPP(c_Power_Opower__class_Opower(U_6972),U_6973),U_6974)),U_6973)
    | ~ class_Groups_Omonoid__mult(U_6972) ),
    inference(clausify,[status(thm)],[f_2018_2]) ).

fof(f_2019_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_2019_2,plain,
    ! [U_6976,U_6975] :
      ( 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_6975),U_6976)))
      | ~ 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_6975)) ),
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

cnf(f_2019_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_6975),U_6976)))
    | ~ 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_6975)) ),
    inference(clausify,[status(thm)],[f_2019_2]) ).

fof(f_2020_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_2020_2,plain,
    ! [U_6978,U_6977] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6977),U_6978),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6977)
      | ~ class_Power_Opower(U_6977) ),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

cnf(f_2020_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6977),U_6978),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6977)
    | ~ class_Power_Opower(U_6977) ),
    inference(clausify,[status(thm)],[f_2020_2]) ).

fof(f_2021_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_2021_2,plain,
    ! [U_6982,U_6981,U_6980,U_6979] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6981),U_6982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6979),hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),U_6981)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),U_6982))
      | ~ class_Groups_Omonoid__mult(U_6979) ),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

cnf(f_2021_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6981),U_6982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6979),hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),U_6981)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6979),U_6980),U_6982))
    | ~ class_Groups_Omonoid__mult(U_6979) ),
    inference(clausify,[status(thm)],[f_2021_2]) ).

fof(f_2022_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_2022_2,plain,
    ! [U_6986,U_6985,U_6984,U_6983] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6983),U_6985),U_6984)),U_6986) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6983),hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),U_6985),U_6986)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),U_6984),U_6986))
      | U_6984 = c_Groups_Ozero__class_Ozero(U_6983)
      | ~ class_Fields_Ofield(U_6983) ),
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

cnf(f_2022_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6983),U_6985),U_6984)),U_6986) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6983),hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),U_6985),U_6986)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6983),U_6984),U_6986))
    | U_6984 = c_Groups_Ozero__class_Ozero(U_6983)
    | ~ class_Fields_Ofield(U_6983) ),
    inference(clausify,[status(thm)],[f_2022_2]) ).

fof(f_2023_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_2023_2,plain,
    ! [U_6989,U_6988,U_6987] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6987),c_Groups_Oone__class_Oone(U_6987)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6987),U_6988),U_6989)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6987),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6987),c_Groups_Oone__class_Oone(U_6987)),U_6988)),U_6989)
      | ~ class_Fields_Ofield__inverse__zero(U_6987) ),
    inference(variable_rename,[status(thm)],[f_2023_1]) ).

cnf(f_2023_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6987),c_Groups_Oone__class_Oone(U_6987)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6987),U_6988),U_6989)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6987),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6987),c_Groups_Oone__class_Oone(U_6987)),U_6988)),U_6989)
    | ~ class_Fields_Ofield__inverse__zero(U_6987) ),
    inference(clausify,[status(thm)],[f_2023_2]) ).

fof(f_2024_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_2024_2,plain,
    ! [U_6992,U_6991,U_6990] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_6990),hAPP(hAPP(c_Power_Opower__class_Opower(U_6990),hAPP(c_Groups_Ouminus__class_Ouminus(U_6990),U_6991)),U_6992)) = hAPP(c_Groups_Oabs__class_Oabs(U_6990),hAPP(hAPP(c_Power_Opower__class_Opower(U_6990),U_6991),U_6992))
      | ~ class_Rings_Olinordered__idom(U_6990) ),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

cnf(f_2024_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_6990),hAPP(hAPP(c_Power_Opower__class_Opower(U_6990),hAPP(c_Groups_Ouminus__class_Ouminus(U_6990),U_6991)),U_6992)) = hAPP(c_Groups_Oabs__class_Oabs(U_6990),hAPP(hAPP(c_Power_Opower__class_Opower(U_6990),U_6991),U_6992))
    | ~ class_Rings_Olinordered__idom(U_6990) ),
    inference(clausify,[status(thm)],[f_2024_2]) ).

fof(f_2025_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_2025_2,plain,
    ! [U_6996,U_6995,U_6994,U_6993] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),U_6994),U_6996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6993),c_Groups_Ozero__class_Ozero(U_6993)),U_6996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),hAPP(hAPP(c_Power_Opower__class_Opower(U_6993),U_6994),U_6995)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6993),U_6996),U_6995)))
      | ~ class_Rings_Olinordered__semidom(U_6993) ),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

cnf(f_2025_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),U_6994),U_6996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6993),c_Groups_Ozero__class_Ozero(U_6993)),U_6996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6993),hAPP(hAPP(c_Power_Opower__class_Opower(U_6993),U_6994),U_6995)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6993),U_6996),U_6995)))
    | ~ class_Rings_Olinordered__semidom(U_6993) ),
    inference(clausify,[status(thm)],[f_2025_2]) ).

fof(f_2026_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_2026_2,plain,
    ! [U_7000,U_6999,U_6998,U_6997] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),U_6998),U_7000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),c_Groups_Ozero__class_Ozero(U_6997)),U_7000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),hAPP(hAPP(c_Power_Opower__class_Opower(U_6997),U_6998),hAPP(c_Nat_OSuc,U_6999))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6997),U_7000),hAPP(c_Nat_OSuc,U_6999))))
      | ~ class_Rings_Olinordered__semidom(U_6997) ),
    inference(variable_rename,[status(thm)],[f_2026_1]) ).

cnf(f_2026_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),U_6998),U_7000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),c_Groups_Ozero__class_Ozero(U_6997)),U_7000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6997),hAPP(hAPP(c_Power_Opower__class_Opower(U_6997),U_6998),hAPP(c_Nat_OSuc,U_6999))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6997),U_7000),hAPP(c_Nat_OSuc,U_6999))))
    | ~ class_Rings_Olinordered__semidom(U_6997) ),
    inference(clausify,[status(thm)],[f_2026_2]) ).

fof(f_2027_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_2027_2,plain,
    ! [U_7004,U_7003,U_7002,U_7001] :
      ( U_7002 = U_7004
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7001),c_Groups_Ozero__class_Ozero(U_7001)),U_7004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7001),c_Groups_Ozero__class_Ozero(U_7001)),U_7002))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_7001),U_7002),hAPP(c_Nat_OSuc,U_7003)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7001),U_7004),hAPP(c_Nat_OSuc,U_7003))
      | ~ class_Rings_Olinordered__semidom(U_7001) ),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

cnf(f_2027_3,plain,
    ( U_7002 = U_7004
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7001),c_Groups_Ozero__class_Ozero(U_7001)),U_7004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7001),c_Groups_Ozero__class_Ozero(U_7001)),U_7002))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7001),U_7002),hAPP(c_Nat_OSuc,U_7003)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7001),U_7004),hAPP(c_Nat_OSuc,U_7003))
    | ~ class_Rings_Olinordered__semidom(U_7001) ),
    inference(clausify,[status(thm)],[f_2027_2]) ).

fof(f_2028_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_2028_2,plain,
    ! [U_7007,U_7006,U_7005] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7005),c_Groups_Oone__class_Oone(U_7005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7005),U_7006),hAPP(hAPP(c_Power_Opower__class_Opower(U_7005),U_7006),U_7007))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7005),c_Groups_Oone__class_Oone(U_7005)),U_7006))
      | ~ class_Rings_Olinordered__semidom(U_7005) ),
    inference(variable_rename,[status(thm)],[f_2028_1]) ).

cnf(f_2028_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7005),c_Groups_Oone__class_Oone(U_7005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7005),U_7006),hAPP(hAPP(c_Power_Opower__class_Opower(U_7005),U_7006),U_7007))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7005),c_Groups_Oone__class_Oone(U_7005)),U_7006))
    | ~ class_Rings_Olinordered__semidom(U_7005) ),
    inference(clausify,[status(thm)],[f_2028_2]) ).

fof(f_2029_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_2029_2,plain,
    ! [U_7010,U_7009,U_7008] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7008),hAPP(hAPP(c_Power_Opower__class_Opower(U_7008),U_7009),U_7010)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7008),U_7009),hAPP(hAPP(c_Power_Opower__class_Opower(U_7008),U_7009),U_7010))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7008),c_Groups_Oone__class_Oone(U_7008)),U_7009))
      | ~ class_Rings_Olinordered__semidom(U_7008) ),
    inference(variable_rename,[status(thm)],[f_2029_1]) ).

cnf(f_2029_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7008),hAPP(hAPP(c_Power_Opower__class_Opower(U_7008),U_7009),U_7010)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7008),U_7009),hAPP(hAPP(c_Power_Opower__class_Opower(U_7008),U_7009),U_7010))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7008),c_Groups_Oone__class_Oone(U_7008)),U_7009))
    | ~ class_Rings_Olinordered__semidom(U_7008) ),
    inference(clausify,[status(thm)],[f_2029_2]) ).

fof(f_2030_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_2030_2,plain,
    ! [U_7012,U_7011] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7011),c_Groups_Ozero__class_Ozero(U_7011)),U_7012) = c_Groups_Ozero__class_Ozero(U_7011)
          | U_7012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7011),c_Groups_Ozero__class_Ozero(U_7011)),U_7012) = c_Groups_Oone__class_Oone(U_7011)
          | U_7012 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_7011)
      | ~ class_Power_Opower(U_7011) ),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

cnf(f_2030_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7011),c_Groups_Ozero__class_Ozero(U_7011)),U_7012) = c_Groups_Oone__class_Oone(U_7011)
    | U_7012 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_7011)
    | ~ class_Power_Opower(U_7011) ),
    inference(clausify,[status(thm)],[f_2030_2]) ).

cnf(f_2030_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7011),c_Groups_Ozero__class_Ozero(U_7011)),U_7012) = c_Groups_Ozero__class_Ozero(U_7011)
    | U_7012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_7011)
    | ~ class_Power_Opower(U_7011) ),
    inference(clausify,[status(thm)],[f_2030_2]) ).

fof(f_2031_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_2031_2,plain,
    ! [U_7015,U_7014,U_7013] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7013),c_Groups_Oone__class_Oone(U_7013)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7013),U_7014),hAPP(c_Nat_OSuc,U_7015))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7013),c_Groups_Oone__class_Oone(U_7013)),U_7014))
      | ~ class_Rings_Olinordered__semidom(U_7013) ),
    inference(variable_rename,[status(thm)],[f_2031_1]) ).

cnf(f_2031_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7013),c_Groups_Oone__class_Oone(U_7013)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7013),U_7014),hAPP(c_Nat_OSuc,U_7015))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7013),c_Groups_Oone__class_Oone(U_7013)),U_7014))
    | ~ class_Rings_Olinordered__semidom(U_7013) ),
    inference(clausify,[status(thm)],[f_2031_2]) ).

fof(f_2032_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_2032_2,plain,
    ! [U_7019,U_7018,U_7017,U_7016] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7018)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7019)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7018),U_7019)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7018),U_7019))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7018)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7019))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),c_Groups_Oone__class_Oone(U_7016)),U_7017))
      | ~ class_Rings_Olinordered__semidom(U_7016) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

cnf(f_2032_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7018),U_7019))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7018)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7019)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),c_Groups_Oone__class_Oone(U_7016)),U_7017))
    | ~ class_Rings_Olinordered__semidom(U_7016) ),
    inference(clausify,[status(thm)],[f_2032_2]) ).

cnf(f_2032_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7018)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7016),U_7017),U_7019)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7018),U_7019))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7016),c_Groups_Oone__class_Oone(U_7016)),U_7017))
    | ~ class_Rings_Olinordered__semidom(U_7016) ),
    inference(clausify,[status(thm)],[f_2032_2]) ).

fof(f_2033_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_2033_2,plain,
    ! [U_7023,U_7022,U_7021,U_7020] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7022),U_7023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7020),hAPP(hAPP(c_Power_Opower__class_Opower(U_7020),U_7021),U_7022)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7020),U_7021),U_7023)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7020),c_Groups_Oone__class_Oone(U_7020)),U_7021))
      | ~ class_Rings_Olinordered__semidom(U_7020) ),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

cnf(f_2033_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7022),U_7023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7020),hAPP(hAPP(c_Power_Opower__class_Opower(U_7020),U_7021),U_7022)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7020),U_7021),U_7023)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7020),c_Groups_Oone__class_Oone(U_7020)),U_7021))
    | ~ class_Rings_Olinordered__semidom(U_7020) ),
    inference(clausify,[status(thm)],[f_2033_2]) ).

fof(f_2034_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_2034_2,plain,
    ! [U_7027,U_7026,U_7025,U_7024] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7024),hAPP(hAPP(c_Power_Opower__class_Opower(U_7024),U_7027),U_7025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7024),U_7027),U_7026)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7024),c_Groups_Oone__class_Oone(U_7024)),U_7027))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7025),U_7026))
      | ~ class_Rings_Olinordered__semidom(U_7024) ),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

cnf(f_2034_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7024),hAPP(hAPP(c_Power_Opower__class_Opower(U_7024),U_7027),U_7025)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7024),U_7027),U_7026)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7024),c_Groups_Oone__class_Oone(U_7024)),U_7027))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7025),U_7026))
    | ~ class_Rings_Olinordered__semidom(U_7024) ),
    inference(clausify,[status(thm)],[f_2034_2]) ).

fof(f_2035_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_2035_2,plain,
    ! [U_7030,U_7029,U_7028] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),c_Groups_Ozero__class_Ozero(U_7028)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7028),hAPP(c_Groups_Oabs__class_Oabs(U_7028),U_7029)),U_7030)))
      | ~ class_Rings_Olinordered__idom(U_7028) ),
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

cnf(f_2035_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7028),c_Groups_Ozero__class_Ozero(U_7028)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7028),hAPP(c_Groups_Oabs__class_Oabs(U_7028),U_7029)),U_7030)))
    | ~ class_Rings_Olinordered__idom(U_7028) ),
    inference(clausify,[status(thm)],[f_2035_2]) ).

fof(f_2036_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_2036_2,plain,
    ! [U_7034,U_7033,U_7032,U_7031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7031),hAPP(hAPP(c_Power_Opower__class_Opower(U_7031),U_7034),U_7032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7031),U_7034),U_7033)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7031),c_Groups_Oone__class_Oone(U_7031)),U_7034))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7032),U_7033))
      | ~ class_Rings_Olinordered__semidom(U_7031) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

cnf(f_2036_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7031),hAPP(hAPP(c_Power_Opower__class_Opower(U_7031),U_7034),U_7032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7031),U_7034),U_7033)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7031),c_Groups_Oone__class_Oone(U_7031)),U_7034))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7032),U_7033))
    | ~ class_Rings_Olinordered__semidom(U_7031) ),
    inference(clausify,[status(thm)],[f_2036_2]) ).

fof(f_2037_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_2037_2,plain,
    ! [U_7037,U_7036,U_7035] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),hAPP(c_Groups_Ouminus__class_Ouminus(U_7035),U_7036)),U_7037) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7035),hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),hAPP(c_Groups_Ouminus__class_Ouminus(U_7035),c_Groups_Oone__class_Oone(U_7035))),U_7037)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),U_7036),U_7037))
      | ~ class_Rings_Oring__1(U_7035) ),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

cnf(f_2037_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),hAPP(c_Groups_Ouminus__class_Ouminus(U_7035),U_7036)),U_7037) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7035),hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),hAPP(c_Groups_Ouminus__class_Ouminus(U_7035),c_Groups_Oone__class_Oone(U_7035))),U_7037)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7035),U_7036),U_7037))
    | ~ class_Rings_Oring__1(U_7035) ),
    inference(clausify,[status(thm)],[f_2037_2]) ).

fof(f_2038_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_2038_2,plain,
    ! [U_7040,U_7039,U_7038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7038),U_7039),hAPP(hAPP(c_Power_Opower__class_Opower(U_7038),U_7039),U_7040))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7038),U_7039),U_7040)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),U_7039),c_Groups_Oone__class_Oone(U_7038)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),c_Groups_Ozero__class_Ozero(U_7038)),U_7039))
      | ~ class_Rings_Olinordered__semidom(U_7038) ),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

cnf(f_2038_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7038),U_7039),hAPP(hAPP(c_Power_Opower__class_Opower(U_7038),U_7039),U_7040))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7038),U_7039),U_7040)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),U_7039),c_Groups_Oone__class_Oone(U_7038)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),c_Groups_Ozero__class_Ozero(U_7038)),U_7039))
    | ~ class_Rings_Olinordered__semidom(U_7038) ),
    inference(clausify,[status(thm)],[f_2038_2]) ).

fof(f_2039_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_2039_2,plain,
    ! [U_7044,U_7043,U_7042,U_7041] :
      ( U_7042 = U_7044
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7041),c_Groups_Ozero__class_Ozero(U_7041)),U_7044))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7041),c_Groups_Ozero__class_Ozero(U_7041)),U_7042))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_7041),U_7042),U_7043) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7041),U_7044),U_7043)
      | ~ class_Rings_Olinordered__semidom(U_7041) ),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

cnf(f_2039_3,plain,
    ( U_7042 = U_7044
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7041),c_Groups_Ozero__class_Ozero(U_7041)),U_7044))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7041),c_Groups_Ozero__class_Ozero(U_7041)),U_7042))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7041),U_7042),U_7043) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7041),U_7044),U_7043)
    | ~ class_Rings_Olinordered__semidom(U_7041) ),
    inference(clausify,[status(thm)],[f_2039_2]) ).

fof(f_2040_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_2040_2,plain,
    ! [U_7047,U_7046,U_7045] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),hAPP(hAPP(c_Power_Opower__class_Opower(U_7045),U_7046),hAPP(c_Nat_OSuc,U_7047))),c_Groups_Oone__class_Oone(U_7045)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),U_7046),c_Groups_Oone__class_Oone(U_7045)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),c_Groups_Ozero__class_Ozero(U_7045)),U_7046))
      | ~ class_Rings_Olinordered__semidom(U_7045) ),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

cnf(f_2040_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),hAPP(hAPP(c_Power_Opower__class_Opower(U_7045),U_7046),hAPP(c_Nat_OSuc,U_7047))),c_Groups_Oone__class_Oone(U_7045)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),U_7046),c_Groups_Oone__class_Oone(U_7045)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7045),c_Groups_Ozero__class_Ozero(U_7045)),U_7046))
    | ~ class_Rings_Olinordered__semidom(U_7045) ),
    inference(clausify,[status(thm)],[f_2040_2]) ).

fof(f_2041_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_2041_2,plain,
    ! [U_7051,U_7050,U_7049,U_7048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),hAPP(hAPP(c_Power_Opower__class_Opower(U_7048),U_7051),U_7050)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7048),U_7051),U_7049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),U_7051),c_Groups_Oone__class_Oone(U_7048)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),c_Groups_Ozero__class_Ozero(U_7048)),U_7051))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7049),U_7050))
      | ~ class_Rings_Olinordered__semidom(U_7048) ),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

cnf(f_2041_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),hAPP(hAPP(c_Power_Opower__class_Opower(U_7048),U_7051),U_7050)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7048),U_7051),U_7049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),U_7051),c_Groups_Oone__class_Oone(U_7048)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7048),c_Groups_Ozero__class_Ozero(U_7048)),U_7051))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7049),U_7050))
    | ~ class_Rings_Olinordered__semidom(U_7048) ),
    inference(clausify,[status(thm)],[f_2041_2]) ).

fof(f_2042_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_2042_2,plain,
    ! [U_7055,U_7054,U_7053,U_7052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),hAPP(hAPP(c_Power_Opower__class_Opower(U_7052),U_7055),U_7054)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7052),U_7055),U_7053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),U_7055),c_Groups_Oone__class_Oone(U_7052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),c_Groups_Ozero__class_Ozero(U_7052)),U_7055))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7053),U_7054))
      | ~ class_Rings_Olinordered__semidom(U_7052) ),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

cnf(f_2042_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),hAPP(hAPP(c_Power_Opower__class_Opower(U_7052),U_7055),U_7054)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7052),U_7055),U_7053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),U_7055),c_Groups_Oone__class_Oone(U_7052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7052),c_Groups_Ozero__class_Ozero(U_7052)),U_7055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7053),U_7054))
    | ~ class_Rings_Olinordered__semidom(U_7052) ),
    inference(clausify,[status(thm)],[f_2042_2]) ).

fof(f_2043_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_2043_2,plain,
    ! [U_7059,U_7058,U_7057,U_7056] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7056),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7058)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7059)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7058),U_7059)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7058),U_7059))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7056),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7058)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7059))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7056),c_Groups_Oone__class_Oone(U_7056)),U_7057))
      | ~ class_Rings_Olinordered__semidom(U_7056) ),
    inference(variable_rename,[status(thm)],[f_2043_1]) ).

cnf(f_2043_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7058),U_7059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7056),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7058)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7059)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7056),c_Groups_Oone__class_Oone(U_7056)),U_7057))
    | ~ class_Rings_Olinordered__semidom(U_7056) ),
    inference(clausify,[status(thm)],[f_2043_2]) ).

cnf(f_2043_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7056),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7058)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7056),U_7057),U_7059)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7058),U_7059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7056),c_Groups_Oone__class_Oone(U_7056)),U_7057))
    | ~ class_Rings_Olinordered__semidom(U_7056) ),
    inference(clausify,[status(thm)],[f_2043_2]) ).

fof(f_2044_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_2044_2,plain,
    ! [U_7061,U_7060] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_7060,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7060),U_7061)) = 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_7060),U_7061))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7060),U_7061)) ),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

cnf(f_2044_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_7060,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7060),U_7061)) = 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_7060),U_7061))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7060),U_7061)) ),
    inference(clausify,[status(thm)],[f_2044_2]) ).

fof(f_2045_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_2045_2,plain,
    ! [U_7062] :
      ( c_Power_Opower__class_Opower(U_7062) = c_Power_Opower_Opower(U_7062,c_Groups_Oone__class_Oone(U_7062),c_Groups_Otimes__class_Otimes(U_7062))
      | ~ class_Power_Opower(U_7062) ),
    inference(variable_rename,[status(thm)],[f_2045_1]) ).

cnf(f_2045_3,plain,
    ( c_Power_Opower__class_Opower(U_7062) = c_Power_Opower_Opower(U_7062,c_Groups_Oone__class_Oone(U_7062),c_Groups_Otimes__class_Otimes(U_7062))
    | ~ class_Power_Opower(U_7062) ),
    inference(clausify,[status(thm)],[f_2045_2]) ).

fof(f_2046_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_2046_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_2046_1]) ).

fof(f_2047_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_2047_2,plain,
    ! [U_7064,U_7063] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7063),U_7064) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(c_Int_Onat,U_7064))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7064),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_7063),U_7064) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7063),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7064))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7064),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_7063) ),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

cnf(f_2047_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7063),U_7064) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7063),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7064))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_7063) ),
    inference(clausify,[status(thm)],[f_2047_2]) ).

cnf(f_2047_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7063),U_7064) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(c_Int_Onat,U_7064))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_7063) ),
    inference(clausify,[status(thm)],[f_2047_2]) ).

fof(f_2048_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_2048_2,plain,
    ! [U_7066,U_7065] : c_Nitpick_Oint__lcm(U_7065,U_7066) = 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_7065)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7066)))),
    inference(variable_rename,[status(thm)],[f_2048_1]) ).

cnf(f_2048_3,plain,
    c_Nitpick_Oint__lcm(U_7065,U_7066) = 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_7065)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7066)))),
    inference(clausify,[status(thm)],[f_2048_2]) ).

fof(f_2049_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_2049_2,plain,
    ! [U_7069,U_7068,U_7067] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7067,tc_HOL_Obool)),U_7068),hAPP(c_Set_OPow(U_7067),U_7069)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7067,tc_HOL_Obool)),U_7068),U_7069)) ),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

cnf(f_2049_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7067,tc_HOL_Obool)),U_7068),hAPP(c_Set_OPow(U_7067),U_7069)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7067,tc_HOL_Obool)),U_7068),U_7069)) ),
    inference(clausify,[status(thm)],[f_2049_2]) ).

fof(f_2050_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_2050_2,plain,
    ! [U_7072,U_7071,U_7070] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7071) = hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7072)
          | U_7071 != U_7072 )
        & ( U_7071 = U_7072
          | hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7071) != hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7072) ) )
      | ~ class_Int_Oring__char__0(U_7070) ),
    inference(variable_rename,[status(thm)],[f_2050_1]) ).

cnf(f_2050_3,plain,
    ( U_7071 = U_7072
    | hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7071) != hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7072)
    | ~ class_Int_Oring__char__0(U_7070) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

cnf(f_2050_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7071) = hAPP(c_Int_Oring__1__class_Oof__int(U_7070),U_7072)
    | U_7071 != U_7072
    | ~ class_Int_Oring__char__0(U_7070) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

fof(f_2051_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_2051_2,plain,
    ! [U_7074,U_7073] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_7073),U_7074) = hAPP(c_Int_Oring__1__class_Oof__int(U_7073),U_7074)
      | ~ class_Int_Onumber__ring(U_7073) ),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

cnf(f_2051_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7073),U_7074) = hAPP(c_Int_Oring__1__class_Oof__int(U_7073),U_7074)
    | ~ class_Int_Onumber__ring(U_7073) ),
    inference(clausify,[status(thm)],[f_2051_2]) ).

fof(f_2052_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_2052_2,plain,
    ! [U_7075] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7075) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7075),
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

cnf(f_2052_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7075) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7075),
    inference(clausify,[status(thm)],[f_2052_2]) ).

fof(f_2053_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_2053_2,plain,
    ! [U_7076] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7076)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7076),
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

cnf(f_2053_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_7076)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7076),
    inference(clausify,[status(thm)],[f_2053_2]) ).

fof(f_2054_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_2054_2,plain,
    ! [U_7078,U_7077] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_7077,tc_HOL_Obool)),U_7078),hAPP(c_Set_OPow(U_7077),U_7078))),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

cnf(f_2054_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_7077,tc_HOL_Obool)),U_7078),hAPP(c_Set_OPow(U_7077),U_7078))),
    inference(clausify,[status(thm)],[f_2054_2]) ).

fof(f_2055_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_2055_2,plain,
    ! [U_7080,U_7079] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7079,tc_HOL_Obool),hAPP(c_Set_OPow(U_7079),U_7080)) = U_7080,
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

cnf(f_2055_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7079,tc_HOL_Obool),hAPP(c_Set_OPow(U_7079),U_7080)) = U_7080,
    inference(clausify,[status(thm)],[f_2055_2]) ).

fof(f_2056_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_2056_2,plain,
    ! [U_7082,U_7081] : hAPP(c_Set_OPow(U_7081),U_7082) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7081,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

cnf(f_2056_3,plain,
    hAPP(c_Set_OPow(U_7081),U_7082) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7081,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2056_2]) ).

fof(f_2057_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_2057_2,plain,
    ! [U_7083] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7083),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7083)
      | ~ class_Rings_Oring__1(U_7083) ),
    inference(variable_rename,[status(thm)],[f_2057_1]) ).

cnf(f_2057_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7083),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7083)
    | ~ class_Rings_Oring__1(U_7083) ),
    inference(clausify,[status(thm)],[f_2057_2]) ).

fof(f_2058_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_2058_2,plain,
    ! [U_7085,U_7084] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_7084) = hAPP(c_Int_Oring__1__class_Oof__int(U_7084),U_7085)
          | U_7085 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_7085 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_7084) != hAPP(c_Int_Oring__1__class_Oof__int(U_7084),U_7085) ) )
      | ~ class_Int_Oring__char__0(U_7084) ),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

cnf(f_2058_3,plain,
    ( U_7085 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_7084) != hAPP(c_Int_Oring__1__class_Oof__int(U_7084),U_7085)
    | ~ class_Int_Oring__char__0(U_7084) ),
    inference(clausify,[status(thm)],[f_2058_2]) ).

cnf(f_2058_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_7084) = hAPP(c_Int_Oring__1__class_Oof__int(U_7084),U_7085)
    | U_7085 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_7084) ),
    inference(clausify,[status(thm)],[f_2058_2]) ).

fof(f_2059_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_2059_2,plain,
    ! [U_7087,U_7086] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7086),U_7087) = c_Groups_Ozero__class_Ozero(U_7086)
          | U_7087 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_7087 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_7086),U_7087) != c_Groups_Ozero__class_Ozero(U_7086) ) )
      | ~ class_Int_Oring__char__0(U_7086) ),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

cnf(f_2059_3,plain,
    ( U_7087 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_7086),U_7087) != c_Groups_Ozero__class_Ozero(U_7086)
    | ~ class_Int_Oring__char__0(U_7086) ),
    inference(clausify,[status(thm)],[f_2059_2]) ).

cnf(f_2059_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7086),U_7087) = c_Groups_Ozero__class_Ozero(U_7086)
    | U_7087 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_7086) ),
    inference(clausify,[status(thm)],[f_2059_2]) ).

fof(f_2060_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_2060_2,plain,
    ! [U_7090,U_7089,U_7088] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7088),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7089)),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7090)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),U_7090)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),U_7090))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7088),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7089)),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7090))) ) )
      | ~ class_Rings_Olinordered__idom(U_7088) ),
    inference(variable_rename,[status(thm)],[f_2060_1]) ).

cnf(f_2060_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),U_7090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7088),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7089)),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7090)))
    | ~ class_Rings_Olinordered__idom(U_7088) ),
    inference(clausify,[status(thm)],[f_2060_2]) ).

cnf(f_2060_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7088),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7089)),hAPP(c_Int_Oring__1__class_Oof__int(U_7088),U_7090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),U_7090))
    | ~ class_Rings_Olinordered__idom(U_7088) ),
    inference(clausify,[status(thm)],[f_2060_2]) ).

fof(f_2061_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_2061_2,plain,
    ! [U_7093,U_7092,U_7091] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7091),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7092)),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7093)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7093)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7093))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7091),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7092)),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7093))) ) )
      | ~ class_Rings_Olinordered__idom(U_7091) ),
    inference(variable_rename,[status(thm)],[f_2061_1]) ).

cnf(f_2061_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7093))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7091),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7092)),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7093)))
    | ~ class_Rings_Olinordered__idom(U_7091) ),
    inference(clausify,[status(thm)],[f_2061_2]) ).

cnf(f_2061_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7091),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7092)),hAPP(c_Int_Oring__1__class_Oof__int(U_7091),U_7093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7093))
    | ~ class_Rings_Olinordered__idom(U_7091) ),
    inference(clausify,[status(thm)],[f_2061_2]) ).

fof(f_2062_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_2062_2,plain,
    ! [U_7096,U_7095,U_7094] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7095),U_7096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7094),hAPP(c_Int_Oring__1__class_Oof__int(U_7094),U_7095)),hAPP(c_Int_Oring__1__class_Oof__int(U_7094),U_7096))
      | ~ class_Rings_Oring__1(U_7094) ),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

cnf(f_2062_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7095),U_7096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7094),hAPP(c_Int_Oring__1__class_Oof__int(U_7094),U_7095)),hAPP(c_Int_Oring__1__class_Oof__int(U_7094),U_7096))
    | ~ class_Rings_Oring__1(U_7094) ),
    inference(clausify,[status(thm)],[f_2062_2]) ).

fof(f_2063_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_2063_2,plain,
    ! [U_7098,U_7097] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7097),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7098)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7097),U_7098)
      | ~ class_Int_Onumber__ring(U_7097) ),
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

cnf(f_2063_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7097),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7098)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7097),U_7098)
    | ~ class_Int_Onumber__ring(U_7097) ),
    inference(clausify,[status(thm)],[f_2063_2]) ).

fof(f_2064_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_2064_2,plain,
    ! [U_7101,U_7100,U_7099] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7100),U_7101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7099),hAPP(c_Int_Oring__1__class_Oof__int(U_7099),U_7100)),hAPP(c_Int_Oring__1__class_Oof__int(U_7099),U_7101))
      | ~ class_Rings_Oring__1(U_7099) ),
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

cnf(f_2064_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7100),U_7101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7099),hAPP(c_Int_Oring__1__class_Oof__int(U_7099),U_7100)),hAPP(c_Int_Oring__1__class_Oof__int(U_7099),U_7101))
    | ~ class_Rings_Oring__1(U_7099) ),
    inference(clausify,[status(thm)],[f_2064_2]) ).

fof(f_2065_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_2065_2,plain,
    ! [U_7102] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7102),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7102)
      | ~ class_Rings_Oring__1(U_7102) ),
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

cnf(f_2065_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7102),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7102)
    | ~ class_Rings_Oring__1(U_7102) ),
    inference(clausify,[status(thm)],[f_2065_2]) ).

fof(f_2066_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_2066_2,plain,
    ! [U_7105,U_7104,U_7103] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7104),U_7105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7103),hAPP(c_Int_Oring__1__class_Oof__int(U_7103),U_7104)),hAPP(c_Int_Oring__1__class_Oof__int(U_7103),U_7105))
      | ~ class_Rings_Oring__1(U_7103) ),
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

cnf(f_2066_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7104),U_7105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7103),hAPP(c_Int_Oring__1__class_Oof__int(U_7103),U_7104)),hAPP(c_Int_Oring__1__class_Oof__int(U_7103),U_7105))
    | ~ class_Rings_Oring__1(U_7103) ),
    inference(clausify,[status(thm)],[f_2066_2]) ).

fof(f_2067_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_2067_2,plain,
    ! [U_7107,U_7106] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7106),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7107)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7106),U_7107)
      | ~ class_Rings_Oring__1(U_7106) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

cnf(f_2067_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7106),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7107)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7106),U_7107)
    | ~ class_Rings_Oring__1(U_7106) ),
    inference(clausify,[status(thm)],[f_2067_2]) ).

fof(f_2068_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_2068_2,plain,
    ! [U_7109,U_7108] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7108),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7109)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7108),hAPP(c_Int_Oring__1__class_Oof__int(U_7108),U_7109))
      | ~ class_Rings_Oring__1(U_7108) ),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

cnf(f_2068_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7108),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7109)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7108),hAPP(c_Int_Oring__1__class_Oof__int(U_7108),U_7109))
    | ~ class_Rings_Oring__1(U_7108) ),
    inference(clausify,[status(thm)],[f_2068_2]) ).

fof(f_2069_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_2069_2,plain,
    ! [U_7111,U_7110] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_7110,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7110,tc_HOL_Obool))),hAPP(c_Set_OPow(U_7110),U_7111))),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

cnf(f_2069_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_7110,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7110,tc_HOL_Obool))),hAPP(c_Set_OPow(U_7110),U_7111))),
    inference(clausify,[status(thm)],[f_2069_2]) ).

fof(f_2070_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_2070_2,plain,
    ! [U_7114,U_7113,U_7112] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7112,tc_HOL_Obool)),U_7113),hAPP(c_Set_OPow(U_7112),U_7114)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7112,tc_HOL_Obool)),U_7113),U_7114)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7112,tc_HOL_Obool)),U_7113),U_7114))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7112,tc_HOL_Obool)),U_7113),hAPP(c_Set_OPow(U_7112),U_7114))) ) ),
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

fof(f_2070_3,plain,
    ( ! [U_7120,U_7118,U_7116] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7116,tc_HOL_Obool)),U_7118),hAPP(c_Set_OPow(U_7116),U_7120)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7116,tc_HOL_Obool)),U_7118),U_7120)) )
    & ! [U_7119,U_7117,U_7115] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7115,tc_HOL_Obool)),U_7117),U_7119))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7115,tc_HOL_Obool)),U_7117),hAPP(c_Set_OPow(U_7115),U_7119))) ) ),
    inference(miniscope,[status(thm)],[f_2070_2]) ).

cnf(f_2070_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7115,tc_HOL_Obool)),U_7117),U_7119))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7115,tc_HOL_Obool)),U_7117),hAPP(c_Set_OPow(U_7115),U_7119))) ),
    inference(clausify,[status(thm)],[f_2070_3]) ).

cnf(f_2070_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7116,tc_HOL_Obool)),U_7118),hAPP(c_Set_OPow(U_7116),U_7120)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7116,tc_HOL_Obool)),U_7118),U_7120)) ),
    inference(clausify,[status(thm)],[f_2070_3]) ).

fof(f_2071_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_2071_2,plain,
    ! [U_7123,U_7122,U_7121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7121,tc_HOL_Obool)),U_7122),U_7123))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7121,tc_HOL_Obool)),U_7122),hAPP(c_Set_OPow(U_7121),U_7123))) ),
    inference(variable_rename,[status(thm)],[f_2071_1]) ).

cnf(f_2071_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7121,tc_HOL_Obool)),U_7122),U_7123))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7121,tc_HOL_Obool)),U_7122),hAPP(c_Set_OPow(U_7121),U_7123))) ),
    inference(clausify,[status(thm)],[f_2071_2]) ).

fof(f_2072_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_2072_2,plain,
    ! [U_7125,U_7124] :
      ( hBOOL(hAPP(hAPP(c_member(U_7124),hAPP(c_Int_Oring__1__class_Oof__int(U_7124),U_7125)),c_Int_Oring__1__class_OInts(U_7124)))
      | ~ class_Rings_Oring__1(U_7124) ),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

cnf(f_2072_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7124),hAPP(c_Int_Oring__1__class_Oof__int(U_7124),U_7125)),c_Int_Oring__1__class_OInts(U_7124)))
    | ~ class_Rings_Oring__1(U_7124) ),
    inference(clausify,[status(thm)],[f_2072_2]) ).

fof(f_2073_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_2073_2,plain,
    ! [U_7128,U_7127,U_7126] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7126),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7127),U_7128)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7126),hAPP(c_Int_Oring__1__class_Oof__int(U_7126),U_7127)),U_7128)
      | ~ class_Rings_Oring__1(U_7126) ),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

cnf(f_2073_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7126),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7127),U_7128)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7126),hAPP(c_Int_Oring__1__class_Oof__int(U_7126),U_7127)),U_7128)
    | ~ class_Rings_Oring__1(U_7126) ),
    inference(clausify,[status(thm)],[f_2073_2]) ).

fof(f_2074_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_2074_2,plain,
    ! [U_7131,U_7130,U_7129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7129,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7129),U_7130)),hAPP(c_Set_OPow(U_7129),U_7131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7131)) ),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

cnf(f_2074_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7129,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7129),U_7130)),hAPP(c_Set_OPow(U_7129),U_7131)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7131)) ),
    inference(clausify,[status(thm)],[f_2074_2]) ).

fof(f_2075_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_2075_2,plain,
    ! [U_7133,U_7132] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7132,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7132),U_7133)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7132),U_7133)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7132),U_7133))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7132,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7132),U_7133))) ) ),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

fof(f_2075_3,plain,
    ( ! [U_7137,U_7135] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7135,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7135),U_7137)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7135),U_7137)) )
    & ! [U_7136,U_7134] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7134),U_7136))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7134,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7134),U_7136))) ) ),
    inference(miniscope,[status(thm)],[f_2075_2]) ).

cnf(f_2075_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7134),U_7136))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7134,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7134),U_7136))) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

cnf(f_2075_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7135,tc_HOL_Obool)),hAPP(c_Set_OPow(U_7135),U_7137)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7135),U_7137)) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

fof(f_2076_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_2076_2,plain,
    ! [U_7139,U_7138] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7138,tc_HOL_Obool),tc_HOL_Obool)),U_7139),hAPP(c_Set_OPow(U_7138),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7138,tc_HOL_Obool),U_7139)))),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

cnf(f_2076_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7138,tc_HOL_Obool),tc_HOL_Obool)),U_7139),hAPP(c_Set_OPow(U_7138),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7138,tc_HOL_Obool),U_7139)))),
    inference(clausify,[status(thm)],[f_2076_2]) ).

fof(f_2077_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_2077_2,plain,
    ! [U_7143,U_7142,U_7141,U_7140] : hAPP(hAPP(c_Power_Opower_Opower(U_7140,U_7141,U_7142),U_7143),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7141,
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

cnf(f_2077_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_7140,U_7141,U_7142),U_7143),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7141,
    inference(clausify,[status(thm)],[f_2077_2]) ).

fof(f_2078_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_2078_2,plain,
    ! [U_7148,U_7147,U_7146,U_7145,U_7144] : hAPP(hAPP(c_Power_Opower_Opower(U_7144,U_7145,U_7146),U_7147),hAPP(c_Nat_OSuc,U_7148)) = hAPP(hAPP(U_7146,U_7147),hAPP(hAPP(c_Power_Opower_Opower(U_7144,U_7145,U_7146),U_7147),U_7148)),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

cnf(f_2078_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_7144,U_7145,U_7146),U_7147),hAPP(c_Nat_OSuc,U_7148)) = hAPP(hAPP(U_7146,U_7147),hAPP(hAPP(c_Power_Opower_Opower(U_7144,U_7145,U_7146),U_7147),U_7148)),
    inference(clausify,[status(thm)],[f_2078_2]) ).

fof(f_2079_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_2079_2,plain,
    ! [U_7151,U_7150,U_7149] : hAPP(c_Set_OPow(U_7149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7149,tc_HOL_Obool)),U_7150),U_7151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_7149,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7149),U_7150)),hAPP(c_Set_OPow(U_7149),U_7151)),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

cnf(f_2079_3,plain,
    hAPP(c_Set_OPow(U_7149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7149,tc_HOL_Obool)),U_7150),U_7151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_7149,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7149),U_7150)),hAPP(c_Set_OPow(U_7149),U_7151)),
    inference(clausify,[status(thm)],[f_2079_2]) ).

fof(f_2080_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_2080_2,plain,
    ! [U_7152] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7152),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7152),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_7152) ),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

cnf(f_2080_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7152),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7152),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_7152) ),
    inference(clausify,[status(thm)],[f_2080_2]) ).

fof(f_2081_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_2081_2,plain,
    ! [U_7153] : hAPP(c_Set_OPow(U_7153),c_Orderings_Obot__class_Obot(tc_fun(U_7153,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7153,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7153,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7153,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2081_1]) ).

cnf(f_2081_3,plain,
    hAPP(c_Set_OPow(U_7153),c_Orderings_Obot__class_Obot(tc_fun(U_7153,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7153,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7153,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7153,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2081_2]) ).

fof(f_2082_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_2082_2,plain,
    ! [U_7155,U_7154] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),hAPP(c_Int_Oring__1__class_Oof__int(U_7154),U_7155)),c_Groups_Ozero__class_Ozero(U_7154)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7155),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7155),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),hAPP(c_Int_Oring__1__class_Oof__int(U_7154),U_7155)),c_Groups_Ozero__class_Ozero(U_7154))) ) )
      | ~ class_Rings_Olinordered__idom(U_7154) ),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

cnf(f_2082_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7155),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),hAPP(c_Int_Oring__1__class_Oof__int(U_7154),U_7155)),c_Groups_Ozero__class_Ozero(U_7154)))
    | ~ class_Rings_Olinordered__idom(U_7154) ),
    inference(clausify,[status(thm)],[f_2082_2]) ).

cnf(f_2082_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7154),hAPP(c_Int_Oring__1__class_Oof__int(U_7154),U_7155)),c_Groups_Ozero__class_Ozero(U_7154)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7155),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_7154) ),
    inference(clausify,[status(thm)],[f_2082_2]) ).

fof(f_2083_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_2083_2,plain,
    ! [U_7157,U_7156] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7156),c_Groups_Ozero__class_Ozero(U_7156)),hAPP(c_Int_Oring__1__class_Oof__int(U_7156),U_7157)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7156),c_Groups_Ozero__class_Ozero(U_7156)),hAPP(c_Int_Oring__1__class_Oof__int(U_7156),U_7157))) ) )
      | ~ class_Rings_Olinordered__idom(U_7156) ),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

cnf(f_2083_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7156),c_Groups_Ozero__class_Ozero(U_7156)),hAPP(c_Int_Oring__1__class_Oof__int(U_7156),U_7157)))
    | ~ class_Rings_Olinordered__idom(U_7156) ),
    inference(clausify,[status(thm)],[f_2083_2]) ).

cnf(f_2083_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7156),c_Groups_Ozero__class_Ozero(U_7156)),hAPP(c_Int_Oring__1__class_Oof__int(U_7156),U_7157)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7157))
    | ~ class_Rings_Olinordered__idom(U_7156) ),
    inference(clausify,[status(thm)],[f_2083_2]) ).

fof(f_2084_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_2084_2,plain,
    ! [U_7159,U_7158] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7158),c_Groups_Ozero__class_Ozero(U_7158)),hAPP(c_Int_Oring__1__class_Oof__int(U_7158),U_7159)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7159)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7159))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7158),c_Groups_Ozero__class_Ozero(U_7158)),hAPP(c_Int_Oring__1__class_Oof__int(U_7158),U_7159))) ) )
      | ~ class_Rings_Olinordered__idom(U_7158) ),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

cnf(f_2084_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7159))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7158),c_Groups_Ozero__class_Ozero(U_7158)),hAPP(c_Int_Oring__1__class_Oof__int(U_7158),U_7159)))
    | ~ class_Rings_Olinordered__idom(U_7158) ),
    inference(clausify,[status(thm)],[f_2084_2]) ).

cnf(f_2084_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7158),c_Groups_Ozero__class_Ozero(U_7158)),hAPP(c_Int_Oring__1__class_Oof__int(U_7158),U_7159)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7159))
    | ~ class_Rings_Olinordered__idom(U_7158) ),
    inference(clausify,[status(thm)],[f_2084_2]) ).

fof(f_2085_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_2085_2,plain,
    ! [U_7161,U_7160] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7160),hAPP(c_Int_Oring__1__class_Oof__int(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7160),hAPP(c_Int_Oring__1__class_Oof__int(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160))) ) )
      | ~ class_Rings_Olinordered__idom(U_7160) ),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

cnf(f_2085_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7160),hAPP(c_Int_Oring__1__class_Oof__int(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
    | ~ class_Rings_Olinordered__idom(U_7160) ),
    inference(clausify,[status(thm)],[f_2085_2]) ).

cnf(f_2085_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7160),hAPP(c_Int_Oring__1__class_Oof__int(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7161),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_7160) ),
    inference(clausify,[status(thm)],[f_2085_2]) ).

fof(f_2086_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_2086_2,plain,
    ! [U_7163,U_7162] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7162),hAPP(c_Int_Onat,U_7163)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7162),U_7163)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7163))
      | ~ class_Rings_Oring__1(U_7162) ),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

cnf(f_2086_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7162),hAPP(c_Int_Onat,U_7163)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7162),U_7163)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7163))
    | ~ class_Rings_Oring__1(U_7162) ),
    inference(clausify,[status(thm)],[f_2086_2]) ).

fof(f_2087_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_2087_2,plain,
    ! [U_7166,U_7165,U_7164] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7164,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_7164,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7164),U_7165)),hAPP(c_Set_OPow(U_7164),U_7166))),hAPP(c_Set_OPow(U_7164),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165),U_7166)))),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

cnf(f_2087_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7164,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_7164,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_7164),U_7165)),hAPP(c_Set_OPow(U_7164),U_7166))),hAPP(c_Set_OPow(U_7164),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165),U_7166)))),
    inference(clausify,[status(thm)],[f_2087_2]) ).

fof(f_2088_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_2088_2,plain,
    ! [U_7168,U_7167] : c_Nitpick_Onat__lcm(U_7167,U_7168) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7167),U_7168)),c_Nitpick_Onat__gcd(U_7167,U_7168)),
    inference(variable_rename,[status(thm)],[f_2088_1]) ).

cnf(f_2088_3,plain,
    c_Nitpick_Onat__lcm(U_7167,U_7168) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7167),U_7168)),c_Nitpick_Onat__gcd(U_7167,U_7168)),
    inference(clausify,[status(thm)],[f_2088_2]) ).

fof(f_2089_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_2089_2,plain,
    ! [U_7169] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_7169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_7169)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

cnf(f_2089_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_7169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_7169)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2089_2]) ).

fof(f_2090_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_2090_2,plain,
    ! [U_7171] :
      ( ? [U_7170] : U_7171 = 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_7170)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7171),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

fof(f_2090_3,plain,
    ! [U_7171] :
      ( U_7171 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK141(U_7171))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7171),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_7170,sK141(U_7171))],[f_2090_2]) ).

cnf(f_2090_4,plain,
    ( U_7171 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK141(U_7171))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7171),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2090_3]) ).

fof(f_2091_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_2091_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_2091_1]) ).

fof(f_2092_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_2092_2,plain,
    ! [U_7173,U_7172] :
      ( c_Groups_Osgn__class_Osgn(U_7172,U_7173) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7172),c_Groups_Oone__class_Oone(U_7172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7172),U_7173),c_Groups_Ozero__class_Ozero(U_7172)))
      | ~ class_Rings_Olinordered__idom(U_7172) ),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

cnf(f_2092_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7172,U_7173) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7172),c_Groups_Oone__class_Oone(U_7172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7172),U_7173),c_Groups_Ozero__class_Ozero(U_7172)))
    | ~ class_Rings_Olinordered__idom(U_7172) ),
    inference(clausify,[status(thm)],[f_2092_2]) ).

fof(f_2093_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_2093_2,plain,
    ! [U_7175,U_7174] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_7174) = c_Code__Numeral_OSuc__code__numeral(U_7175)
        | U_7174 != U_7175 )
      & ( U_7174 = U_7175
        | c_Code__Numeral_OSuc__code__numeral(U_7174) != c_Code__Numeral_OSuc__code__numeral(U_7175) ) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

fof(f_2093_3,plain,
    ( ! [U_7179,U_7177] :
        ( c_Code__Numeral_OSuc__code__numeral(U_7177) = c_Code__Numeral_OSuc__code__numeral(U_7179)
        | U_7177 != U_7179 )
    & ! [U_7178,U_7176] :
        ( U_7176 = U_7178
        | c_Code__Numeral_OSuc__code__numeral(U_7176) != c_Code__Numeral_OSuc__code__numeral(U_7178) ) ),
    inference(miniscope,[status(thm)],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( U_7176 = U_7178
    | c_Code__Numeral_OSuc__code__numeral(U_7176) != c_Code__Numeral_OSuc__code__numeral(U_7178) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

cnf(f_2093_5,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_7177) = c_Code__Numeral_OSuc__code__numeral(U_7179)
    | U_7177 != U_7179 ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

fof(f_2094_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_2094_2,plain,
    ! [U_7181,U_7180] :
      ( c_Groups_Osgn__class_Osgn(U_7180,c_Groups_Osgn__class_Osgn(U_7180,U_7181)) = c_Groups_Osgn__class_Osgn(U_7180,U_7181)
      | ~ class_Rings_Olinordered__idom(U_7180) ),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

cnf(f_2094_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7180,c_Groups_Osgn__class_Osgn(U_7180,U_7181)) = c_Groups_Osgn__class_Osgn(U_7180,U_7181)
    | ~ class_Rings_Olinordered__idom(U_7180) ),
    inference(clausify,[status(thm)],[f_2094_2]) ).

fof(f_2095_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_2095_2,plain,
    ! [U_7183,U_7182] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_7182,U_7183) = c_Groups_Ozero__class_Ozero(U_7182)
          | U_7183 != c_Groups_Ozero__class_Ozero(U_7182) )
        & ( U_7183 = c_Groups_Ozero__class_Ozero(U_7182)
          | c_Groups_Osgn__class_Osgn(U_7182,U_7183) != c_Groups_Ozero__class_Ozero(U_7182) ) )
      | ~ class_Rings_Olinordered__idom(U_7182) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

cnf(f_2095_3,plain,
    ( U_7183 = c_Groups_Ozero__class_Ozero(U_7182)
    | c_Groups_Osgn__class_Osgn(U_7182,U_7183) != c_Groups_Ozero__class_Ozero(U_7182)
    | ~ class_Rings_Olinordered__idom(U_7182) ),
    inference(clausify,[status(thm)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_7182,U_7183) = c_Groups_Ozero__class_Ozero(U_7182)
    | U_7183 != c_Groups_Ozero__class_Ozero(U_7182)
    | ~ class_Rings_Olinordered__idom(U_7182) ),
    inference(clausify,[status(thm)],[f_2095_2]) ).

fof(f_2096_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_2096_2,plain,
    ! [U_7184] :
      ( c_Groups_Osgn__class_Osgn(U_7184,c_Groups_Ozero__class_Ozero(U_7184)) = c_Groups_Ozero__class_Ozero(U_7184)
      | ~ class_Groups_Osgn__if(U_7184) ),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

cnf(f_2096_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7184,c_Groups_Ozero__class_Ozero(U_7184)) = c_Groups_Ozero__class_Ozero(U_7184)
    | ~ class_Groups_Osgn__if(U_7184) ),
    inference(clausify,[status(thm)],[f_2096_2]) ).

fof(f_2097_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_2097_2,plain,
    ! [U_7187,U_7186,U_7185] :
      ( c_Groups_Osgn__class_Osgn(U_7185,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7185),U_7186),U_7187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7185),c_Groups_Osgn__class_Osgn(U_7185,U_7186)),c_Groups_Osgn__class_Osgn(U_7185,U_7187))
      | ~ class_Rings_Olinordered__idom(U_7185) ),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

cnf(f_2097_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7185,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7185),U_7186),U_7187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7185),c_Groups_Osgn__class_Osgn(U_7185,U_7186)),c_Groups_Osgn__class_Osgn(U_7185,U_7187))
    | ~ class_Rings_Olinordered__idom(U_7185) ),
    inference(clausify,[status(thm)],[f_2097_2]) ).

fof(f_2098_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_2098_2,plain,
    ! [U_7188] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_7188),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

cnf(f_2098_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_7188),
    inference(clausify,[status(thm)],[f_2098_2]) ).

fof(f_2099_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_2099_2,plain,
    ! [U_7189] : c_Code__Numeral_OSuc__code__numeral(U_7189) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

cnf(f_2099_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_7189) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2099_2]) ).

fof(f_2100_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_2100_2,plain,
    ! [U_7191,U_7190] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),c_Groups_Osgn__class_Osgn(U_7190,U_7191)),c_Groups_Ozero__class_Ozero(U_7190)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),U_7191),c_Groups_Ozero__class_Ozero(U_7190))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),U_7191),c_Groups_Ozero__class_Ozero(U_7190)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),c_Groups_Osgn__class_Osgn(U_7190,U_7191)),c_Groups_Ozero__class_Ozero(U_7190))) ) )
      | ~ class_Rings_Olinordered__idom(U_7190) ),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

cnf(f_2100_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),U_7191),c_Groups_Ozero__class_Ozero(U_7190)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),c_Groups_Osgn__class_Osgn(U_7190,U_7191)),c_Groups_Ozero__class_Ozero(U_7190)))
    | ~ class_Rings_Olinordered__idom(U_7190) ),
    inference(clausify,[status(thm)],[f_2100_2]) ).

cnf(f_2100_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),c_Groups_Osgn__class_Osgn(U_7190,U_7191)),c_Groups_Ozero__class_Ozero(U_7190)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7190),U_7191),c_Groups_Ozero__class_Ozero(U_7190)))
    | ~ class_Rings_Olinordered__idom(U_7190) ),
    inference(clausify,[status(thm)],[f_2100_2]) ).

fof(f_2101_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_2101_2,plain,
    ! [U_7193,U_7192] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),c_Groups_Osgn__class_Osgn(U_7192,U_7193)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),U_7193)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),U_7193))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),c_Groups_Osgn__class_Osgn(U_7192,U_7193))) ) )
      | ~ class_Rings_Olinordered__idom(U_7192) ),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

cnf(f_2101_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),U_7193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),c_Groups_Osgn__class_Osgn(U_7192,U_7193)))
    | ~ class_Rings_Olinordered__idom(U_7192) ),
    inference(clausify,[status(thm)],[f_2101_2]) ).

cnf(f_2101_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),c_Groups_Osgn__class_Osgn(U_7192,U_7193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7192),c_Groups_Ozero__class_Ozero(U_7192)),U_7193))
    | ~ class_Rings_Olinordered__idom(U_7192) ),
    inference(clausify,[status(thm)],[f_2101_2]) ).

fof(f_2102_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_2102_2,plain,
    ! [U_7194] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_7194)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2102_1]) ).

cnf(f_2102_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_7194)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2102_2]) ).

fof(f_2103_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_2103_2,plain,
    ! [U_7196,U_7195] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7195),c_Groups_Osgn__class_Osgn(U_7195,U_7196)),hAPP(c_Groups_Oabs__class_Oabs(U_7195),U_7196)) = U_7196
      | ~ class_Rings_Olinordered__idom(U_7195) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

cnf(f_2103_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7195),c_Groups_Osgn__class_Osgn(U_7195,U_7196)),hAPP(c_Groups_Oabs__class_Oabs(U_7195),U_7196)) = U_7196
    | ~ class_Rings_Olinordered__idom(U_7195) ),
    inference(clausify,[status(thm)],[f_2103_2]) ).

fof(f_2104_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_2104_2,plain,
    ! [U_7198,U_7197] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7197),U_7198) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7197),U_7198),c_Groups_Osgn__class_Osgn(U_7197,U_7198))
      | ~ class_Rings_Olinordered__idom(U_7197) ),
    inference(variable_rename,[status(thm)],[f_2104_1]) ).

cnf(f_2104_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7197),U_7198) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7197),U_7198),c_Groups_Osgn__class_Osgn(U_7197,U_7198))
    | ~ class_Rings_Olinordered__idom(U_7197) ),
    inference(clausify,[status(thm)],[f_2104_2]) ).

fof(f_2105_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_2105_2,plain,
    ! [U_7199] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7199)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_7199,
    inference(variable_rename,[status(thm)],[f_2105_1]) ).

cnf(f_2105_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7199)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_7199,
    inference(clausify,[status(thm)],[f_2105_2]) ).

fof(f_2106_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_2106_2,plain,
    ! [U_7201,U_7200] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_7200,U_7201) = c_Groups_Oone__class_Oone(U_7200)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7200),c_Groups_Ozero__class_Ozero(U_7200)),U_7201)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7200),c_Groups_Ozero__class_Ozero(U_7200)),U_7201))
          | c_Groups_Osgn__class_Osgn(U_7200,U_7201) != c_Groups_Oone__class_Oone(U_7200) ) )
      | ~ class_Rings_Olinordered__idom(U_7200) ),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

cnf(f_2106_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7200),c_Groups_Ozero__class_Ozero(U_7200)),U_7201))
    | c_Groups_Osgn__class_Osgn(U_7200,U_7201) != c_Groups_Oone__class_Oone(U_7200)
    | ~ class_Rings_Olinordered__idom(U_7200) ),
    inference(clausify,[status(thm)],[f_2106_2]) ).

cnf(f_2106_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_7200,U_7201) = c_Groups_Oone__class_Oone(U_7200)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7200),c_Groups_Ozero__class_Ozero(U_7200)),U_7201))
    | ~ class_Rings_Olinordered__idom(U_7200) ),
    inference(clausify,[status(thm)],[f_2106_2]) ).

fof(f_2107_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_2107_2,plain,
    ! [U_7203,U_7202] :
      ( c_Groups_Osgn__class_Osgn(U_7202,U_7203) = c_Groups_Oone__class_Oone(U_7202)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7202),c_Groups_Ozero__class_Ozero(U_7202)),U_7203))
      | ~ class_Rings_Olinordered__idom(U_7202) ),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

cnf(f_2107_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7202,U_7203) = c_Groups_Oone__class_Oone(U_7202)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7202),c_Groups_Ozero__class_Ozero(U_7202)),U_7203))
    | ~ class_Rings_Olinordered__idom(U_7202) ),
    inference(clausify,[status(thm)],[f_2107_2]) ).

fof(f_2108_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_2108_2,plain,
    ! [U_7205,U_7204] :
      ( ( c_Nitpick_Onat__gcd(U_7205,U_7204) = c_Nitpick_Onat__gcd(U_7204,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7205,U_7204))
        | U_7204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_7205,U_7204) = U_7205
        | U_7204 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

fof(f_2108_3,plain,
    ( ! [U_7209,U_7207] :
        ( c_Nitpick_Onat__gcd(U_7209,U_7207) = c_Nitpick_Onat__gcd(U_7207,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7209,U_7207))
        | U_7207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7208,U_7206] :
        ( c_Nitpick_Onat__gcd(U_7208,U_7206) = U_7208
        | U_7206 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2108_2]) ).

cnf(f_2108_4,plain,
    ( c_Nitpick_Onat__gcd(U_7208,U_7206) = U_7208
    | U_7206 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

cnf(f_2108_5,plain,
    ( c_Nitpick_Onat__gcd(U_7209,U_7207) = c_Nitpick_Onat__gcd(U_7207,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7209,U_7207))
    | U_7207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

fof(f_2109_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_2109_2,plain,
    ! [U_7210] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7210) = 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_7210)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7210) = 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_7210)) ) )
        | U_7210 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7210) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_7210 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

fof(f_2109_3,plain,
    ( ! [U_7212] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7212) = 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_7212)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7212) = 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_7212)) ) )
        | U_7212 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7211] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_7211 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2109_2]) ).

cnf(f_2109_4,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7211 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

cnf(f_2109_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7212) = 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_7212))
    | U_7212 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

cnf(f_2109_6,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_7212) = 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_7212))
    | U_7212 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

fof(f_2110_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_2110_2,plain,
    ! [U_7214,U_7213] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7213),c_Groups_Oone__class_Oone(U_7213))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7213),c_Groups_Ozero__class_Ozero(U_7213)),U_7214)) )
            & ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = c_Groups_Oone__class_Oone(U_7213)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7213),c_Groups_Ozero__class_Ozero(U_7213)),U_7214)) ) )
          | U_7214 = c_Groups_Ozero__class_Ozero(U_7213) )
        & ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = c_Groups_Ozero__class_Ozero(U_7213)
          | U_7214 != c_Groups_Ozero__class_Ozero(U_7213) ) )
      | ~ class_Groups_Osgn__if(U_7213) ),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

cnf(f_2110_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = c_Groups_Ozero__class_Ozero(U_7213)
    | U_7214 != c_Groups_Ozero__class_Ozero(U_7213)
    | ~ class_Groups_Osgn__if(U_7213) ),
    inference(clausify,[status(thm)],[f_2110_2]) ).

cnf(f_2110_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = c_Groups_Oone__class_Oone(U_7213)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7213),c_Groups_Ozero__class_Ozero(U_7213)),U_7214))
    | U_7214 = c_Groups_Ozero__class_Ozero(U_7213)
    | ~ class_Groups_Osgn__if(U_7213) ),
    inference(clausify,[status(thm)],[f_2110_2]) ).

cnf(f_2110_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_7213,U_7214) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7213),c_Groups_Oone__class_Oone(U_7213))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7213),c_Groups_Ozero__class_Ozero(U_7213)),U_7214))
    | U_7214 = c_Groups_Ozero__class_Ozero(U_7213)
    | ~ class_Groups_Osgn__if(U_7213) ),
    inference(clausify,[status(thm)],[f_2110_2]) ).

fof(f_2111_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_2111_2,plain,
    ! [U_7216,U_7215] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_7215,U_7216) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7215),c_Groups_Oone__class_Oone(U_7215))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7215),U_7216),c_Groups_Ozero__class_Ozero(U_7215))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7215),U_7216),c_Groups_Ozero__class_Ozero(U_7215)))
          | c_Groups_Osgn__class_Osgn(U_7215,U_7216) != hAPP(c_Groups_Ouminus__class_Ouminus(U_7215),c_Groups_Oone__class_Oone(U_7215)) ) )
      | ~ class_Rings_Olinordered__idom(U_7215) ),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

cnf(f_2111_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7215),U_7216),c_Groups_Ozero__class_Ozero(U_7215)))
    | c_Groups_Osgn__class_Osgn(U_7215,U_7216) != hAPP(c_Groups_Ouminus__class_Ouminus(U_7215),c_Groups_Oone__class_Oone(U_7215))
    | ~ class_Rings_Olinordered__idom(U_7215) ),
    inference(clausify,[status(thm)],[f_2111_2]) ).

cnf(f_2111_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_7215,U_7216) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7215),c_Groups_Oone__class_Oone(U_7215))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7215),U_7216),c_Groups_Ozero__class_Ozero(U_7215)))
    | ~ class_Rings_Olinordered__idom(U_7215) ),
    inference(clausify,[status(thm)],[f_2111_2]) ).

fof(f_2112_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_2112_2,plain,
    ! [U_7218,U_7217] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_7217),U_7218) = 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_7217)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7218)))),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

cnf(f_2112_3,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_7217),U_7218) = 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_7217)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7218)))),
    inference(clausify,[status(thm)],[f_2112_2]) ).

fof(f_2113_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_2113_2,plain,
    ! [U_7222,U_7221,U_7220,U_7219] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7219,U_7220,U_7221,c_Code__Numeral_OSuc__code__numeral(U_7222)) = hAPP(U_7221,U_7222),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

cnf(f_2113_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7219,U_7220,U_7221,c_Code__Numeral_OSuc__code__numeral(U_7222)) = hAPP(U_7221,U_7222),
    inference(clausify,[status(thm)],[f_2113_2]) ).

fof(f_2114_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_2114_2,plain,
    ! [U_7225,U_7224,U_7223] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7223),U_7224) = U_7225
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7223),U_7224),U_7225) != c_Orderings_Otop__class_Otop(U_7223)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7223),U_7224),U_7225) != c_Orderings_Obot__class_Obot(U_7223)
      | ~ class_Lattices_Oboolean__algebra(U_7223) ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

cnf(f_2114_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7223),U_7224) = U_7225
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7223),U_7224),U_7225) != c_Orderings_Otop__class_Otop(U_7223)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7223),U_7224),U_7225) != c_Orderings_Obot__class_Obot(U_7223)
    | ~ class_Lattices_Oboolean__algebra(U_7223) ),
    inference(clausify,[status(thm)],[f_2114_2]) ).

fof(f_2115_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_2115_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_2115_1]) ).

fof(f_2116_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_2116_2,plain,
    ! [U_7228,U_7227,U_7226] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7226,U_7227,U_7228,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7227,
    inference(variable_rename,[status(thm)],[f_2116_1]) ).

cnf(f_2116_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7226,U_7227,U_7228,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7227,
    inference(clausify,[status(thm)],[f_2116_2]) ).

fof(f_2117_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_2117_2,plain,
    ! [U_7230,U_7229] : hBOOL(hAPP(hAPP(c_member(U_7229),U_7230),c_Orderings_Otop__class_Otop(tc_fun(U_7229,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2117_1]) ).

cnf(f_2117_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_7229),U_7230),c_Orderings_Otop__class_Otop(tc_fun(U_7229,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2117_2]) ).

fof(f_2118_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_2118_2,plain,
    ! [U_7232,U_7231] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7232),c_Orderings_Otop__class_Otop(tc_fun(U_7232,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7231,U_7232)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7231,U_7232),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

fof(f_2118_3,plain,
    ! [U_7232] :
      ( ! [U_7231] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7231,U_7232)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7231,U_7232),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_7232),c_Orderings_Otop__class_Otop(tc_fun(U_7232,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_2118_2]) ).

cnf(f_2118_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7231,U_7232)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7231,U_7232),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_7232),c_Orderings_Otop__class_Otop(tc_fun(U_7232,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

fof(f_2119_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_2119_2,plain,
    ! [U_7233] : c_Orderings_Otop__class_Otop(tc_fun(U_7233,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_7233,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

cnf(f_2119_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_7233,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_7233,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2119_2]) ).

fof(f_2120_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_2120_2,plain,
    ! [U_7234] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7234),c_Orderings_Otop__class_Otop(tc_fun(U_7234,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_7234) ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

cnf(f_2120_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7234),c_Orderings_Otop__class_Otop(tc_fun(U_7234,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_7234) ),
    inference(clausify,[status(thm)],[f_2120_2]) ).

fof(f_2121_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_2121_2,plain,
    ! [U_7236,U_7235] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7235,tc_HOL_Obool)),U_7236),c_Orderings_Otop__class_Otop(tc_fun(U_7235,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2121_1]) ).

cnf(f_2121_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7235,tc_HOL_Obool)),U_7236),c_Orderings_Otop__class_Otop(tc_fun(U_7235,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2121_2]) ).

fof(f_2122_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_2122_2,plain,
    ! [U_7239,U_7238,U_7237] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_7238,U_7237)),U_7239) = c_Orderings_Otop__class_Otop(U_7237)
      | ~ class_Orderings_Otop(U_7237) ),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

cnf(f_2122_3,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_7238,U_7237)),U_7239) = c_Orderings_Otop__class_Otop(U_7237)
    | ~ class_Orderings_Otop(U_7237) ),
    inference(clausify,[status(thm)],[f_2122_2]) ).

fof(f_2123_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_2123_2,plain,
    ! [U_7240] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7240,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7240,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7240,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

cnf(f_2123_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7240,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7240,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7240,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2123_2]) ).

fof(f_2124_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_2124_2,plain,
    ! [U_7241] :
      ( c_Complete__Lattice_OSup__class_OSup(U_7241,c_Orderings_Otop__class_Otop(tc_fun(U_7241,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_7241)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7241) ),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

cnf(f_2124_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_7241,c_Orderings_Otop__class_Otop(tc_fun(U_7241,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_7241)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7241) ),
    inference(clausify,[status(thm)],[f_2124_2]) ).

fof(f_2125_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_2125_2,plain,
    ! [U_7242] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7242)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7242),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7242),c_Orderings_Otop__class_Otop(tc_fun(U_7242,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7242),c_Orderings_Otop__class_Otop(tc_fun(U_7242,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7242)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7242),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

fof(f_2125_3,plain,
    ( ! [U_7244] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7244)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7244),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7244),c_Orderings_Otop__class_Otop(tc_fun(U_7244,tc_HOL_Obool)))) )
    & ! [U_7243] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7243),c_Orderings_Otop__class_Otop(tc_fun(U_7243,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7243)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7243),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2125_2]) ).

cnf(f_2125_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7243),c_Orderings_Otop__class_Otop(tc_fun(U_7243,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7243)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7243),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2125_3]) ).

cnf(f_2125_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_7244)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_7244),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7244),c_Orderings_Otop__class_Otop(tc_fun(U_7244,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2125_3]) ).

fof(f_2126_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_2126_2,plain,
    ! [U_7246,U_7245] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_7245,U_7246)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_7245,U_7246),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7246),c_Orderings_Otop__class_Otop(tc_fun(U_7246,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7245),c_Orderings_Otop__class_Otop(tc_fun(U_7245,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

cnf(f_2126_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_7245,U_7246)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_7245,U_7246),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7246),c_Orderings_Otop__class_Otop(tc_fun(U_7246,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7245),c_Orderings_Otop__class_Otop(tc_fun(U_7245,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2126_2]) ).

fof(f_2127_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_2127_2,plain,
    ! [U_7248,U_7247] : c_Sum__Type_OPlus(U_7247,U_7248,c_Orderings_Otop__class_Otop(tc_fun(U_7247,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7248,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7247,U_7248),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2127_1]) ).

cnf(f_2127_3,plain,
    c_Sum__Type_OPlus(U_7247,U_7248,c_Orderings_Otop__class_Otop(tc_fun(U_7247,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7248,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7247,U_7248),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2127_2]) ).

fof(f_2128_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_2128_2,plain,
    ! [U_7250,U_7249] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7249,tc_HOL_Obool)),U_7250),c_Orderings_Otop__class_Otop(tc_fun(U_7249,tc_HOL_Obool))) = U_7250,
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

cnf(f_2128_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7249,tc_HOL_Obool)),U_7250),c_Orderings_Otop__class_Otop(tc_fun(U_7249,tc_HOL_Obool))) = U_7250,
    inference(clausify,[status(thm)],[f_2128_2]) ).

fof(f_2129_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_2129_2,plain,
    ! [U_7252,U_7251] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7251,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7251,tc_HOL_Obool))),U_7252) = U_7252,
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

cnf(f_2129_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7251,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7251,tc_HOL_Obool))),U_7252) = U_7252,
    inference(clausify,[status(thm)],[f_2129_2]) ).

fof(f_2130_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_2130_2,plain,
    ! [U_7254,U_7253] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7253,tc_HOL_Obool)),U_7254),c_Orderings_Otop__class_Otop(tc_fun(U_7253,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7253,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

cnf(f_2130_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7253,tc_HOL_Obool)),U_7254),c_Orderings_Otop__class_Otop(tc_fun(U_7253,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7253,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2130_2]) ).

fof(f_2131_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_2131_2,plain,
    ! [U_7256,U_7255] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7255,tc_HOL_Obool))),U_7256) = c_Orderings_Otop__class_Otop(tc_fun(U_7255,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

cnf(f_2131_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7255,tc_HOL_Obool))),U_7256) = c_Orderings_Otop__class_Otop(tc_fun(U_7255,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2131_2]) ).

fof(f_2132_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_2132_2,plain,
    ! [U_7257] : hAPP(c_Set_OPow(U_7257),c_Orderings_Otop__class_Otop(tc_fun(U_7257,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7257,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

cnf(f_2132_3,plain,
    hAPP(c_Set_OPow(U_7257),c_Orderings_Otop__class_Otop(tc_fun(U_7257,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7257,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2132_2]) ).

fof(f_2133_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_2133_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_2133_1]) ).

fof(f_2134_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_2134_2,plain,
    ! [U_7259,U_7258] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7258,U_7259)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7258,U_7259),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7259),c_Orderings_Otop__class_Otop(tc_fun(U_7259,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7258),c_Orderings_Otop__class_Otop(tc_fun(U_7258,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7259),c_Orderings_Otop__class_Otop(tc_fun(U_7259,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_7258),c_Orderings_Otop__class_Otop(tc_fun(U_7258,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7258,U_7259)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7258,U_7259),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

fof(f_2134_3,plain,
    ( ! [U_7263,U_7261] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7261,U_7263)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7261,U_7263),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7263),c_Orderings_Otop__class_Otop(tc_fun(U_7263,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7261),c_Orderings_Otop__class_Otop(tc_fun(U_7261,tc_HOL_Obool)))) )
    & ! [U_7262,U_7260] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7262),c_Orderings_Otop__class_Otop(tc_fun(U_7262,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_7260),c_Orderings_Otop__class_Otop(tc_fun(U_7260,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7260,U_7262)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7260,U_7262),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2134_2]) ).

cnf(f_2134_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7260),c_Orderings_Otop__class_Otop(tc_fun(U_7260,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7260,U_7262)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7260,U_7262),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

cnf(f_2134_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7262),c_Orderings_Otop__class_Otop(tc_fun(U_7262,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7260,U_7262)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7260,U_7262),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

cnf(f_2134_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7261,U_7263)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7261,U_7263),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7263),c_Orderings_Otop__class_Otop(tc_fun(U_7263,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7261),c_Orderings_Otop__class_Otop(tc_fun(U_7261,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

fof(f_2135_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_2135_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2135_1]) ).

fof(f_2136_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_2136_2,plain,
    ! [U_7265,U_7264] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7264),U_7265))
      | ~ c_Nat__Transfer_Ois__nat(U_7265)
      | ~ c_Nat__Transfer_Ois__nat(U_7264) ),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

cnf(f_2136_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7264),U_7265))
    | ~ c_Nat__Transfer_Ois__nat(U_7265)
    | ~ c_Nat__Transfer_Ois__nat(U_7264) ),
    inference(clausify,[status(thm)],[f_2136_2]) ).

fof(f_2137_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_2137_2,plain,
    ! [U_7266] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7266)),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

cnf(f_2137_3,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7266)),
    inference(clausify,[status(thm)],[f_2137_2]) ).

fof(f_2138_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_2138_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2138_1]) ).

fof(f_2139_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_2139_2,plain,
    ! [U_7268,U_7267] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7267),U_7268))
      | ~ c_Nat__Transfer_Ois__nat(U_7268)
      | ~ c_Nat__Transfer_Ois__nat(U_7267) ),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

cnf(f_2139_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7267),U_7268))
    | ~ c_Nat__Transfer_Ois__nat(U_7268)
    | ~ c_Nat__Transfer_Ois__nat(U_7267) ),
    inference(clausify,[status(thm)],[f_2139_2]) ).

fof(f_2140_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_2140_2,plain,
    ! [U_7270,U_7269] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7269,U_7270))
      | ~ c_Nat__Transfer_Ois__nat(U_7270)
      | ~ c_Nat__Transfer_Ois__nat(U_7269) ),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

cnf(f_2140_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7269,U_7270))
    | ~ c_Nat__Transfer_Ois__nat(U_7270)
    | ~ c_Nat__Transfer_Ois__nat(U_7269) ),
    inference(clausify,[status(thm)],[f_2140_2]) ).

fof(f_2141_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_2141_2,plain,
    ! [U_7272,U_7271] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7271),U_7272))
      | ~ c_Nat__Transfer_Ois__nat(U_7272)
      | ~ c_Nat__Transfer_Ois__nat(U_7271) ),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

cnf(f_2141_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7271),U_7272))
    | ~ c_Nat__Transfer_Ois__nat(U_7272)
    | ~ c_Nat__Transfer_Ois__nat(U_7271) ),
    inference(clausify,[status(thm)],[f_2141_2]) ).

fof(f_2142_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_2142_2,plain,
    ! [U_7274,U_7273] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7273),U_7274),c_Orderings_Otop__class_Otop(U_7273)))
      | ~ class_Orderings_Otop(U_7273) ),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

cnf(f_2142_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7273),U_7274),c_Orderings_Otop__class_Otop(U_7273)))
    | ~ class_Orderings_Otop(U_7273) ),
    inference(clausify,[status(thm)],[f_2142_2]) ).

fof(f_2143_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_2143_2,plain,
    ! [U_7276,U_7275] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7275),U_7276),c_Orderings_Otop__class_Otop(U_7275)) = c_Orderings_Otop__class_Otop(U_7275)
      | ~ class_Lattices_Obounded__lattice__top(U_7275) ),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

cnf(f_2143_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7275),U_7276),c_Orderings_Otop__class_Otop(U_7275)) = c_Orderings_Otop__class_Otop(U_7275)
    | ~ class_Lattices_Obounded__lattice__top(U_7275) ),
    inference(clausify,[status(thm)],[f_2143_2]) ).

fof(f_2144_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_2144_2,plain,
    ! [U_7278,U_7277] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7277),c_Orderings_Otop__class_Otop(U_7277)),U_7278) = c_Orderings_Otop__class_Otop(U_7277)
      | ~ class_Lattices_Obounded__lattice__top(U_7277) ),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

cnf(f_2144_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7277),c_Orderings_Otop__class_Otop(U_7277)),U_7278) = c_Orderings_Otop__class_Otop(U_7277)
    | ~ class_Lattices_Obounded__lattice__top(U_7277) ),
    inference(clausify,[status(thm)],[f_2144_2]) ).

fof(f_2145_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_2145_2,plain,
    ! [U_7280,U_7279] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7279),c_Orderings_Otop__class_Otop(U_7279)),U_7280) = U_7280
      | ~ class_Lattices_Obounded__lattice__top(U_7279) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

cnf(f_2145_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7279),c_Orderings_Otop__class_Otop(U_7279)),U_7280) = U_7280
    | ~ class_Lattices_Obounded__lattice__top(U_7279) ),
    inference(clausify,[status(thm)],[f_2145_2]) ).

fof(f_2146_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_2146_2,plain,
    ! [U_7282,U_7281] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7281),U_7282),c_Orderings_Otop__class_Otop(U_7281)) = U_7282
      | ~ class_Lattices_Obounded__lattice__top(U_7281) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

cnf(f_2146_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7281),U_7282),c_Orderings_Otop__class_Otop(U_7281)) = U_7282
    | ~ class_Lattices_Obounded__lattice__top(U_7281) ),
    inference(clausify,[status(thm)],[f_2146_2]) ).

fof(f_2147_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_2147_2,plain,
    ! [U_7285,U_7284,U_7283] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7283),U_7284),U_7285) = c_Orderings_Otop__class_Otop(U_7283)
          | U_7285 != c_Orderings_Otop__class_Otop(U_7283)
          | U_7284 != c_Orderings_Otop__class_Otop(U_7283) )
        & ( ( U_7285 = c_Orderings_Otop__class_Otop(U_7283)
            & U_7284 = c_Orderings_Otop__class_Otop(U_7283) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7283),U_7284),U_7285) != c_Orderings_Otop__class_Otop(U_7283) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_7283) ),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

cnf(f_2147_3,plain,
    ( U_7284 = c_Orderings_Otop__class_Otop(U_7283)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7283),U_7284),U_7285) != c_Orderings_Otop__class_Otop(U_7283)
    | ~ class_Lattices_Obounded__lattice__top(U_7283) ),
    inference(clausify,[status(thm)],[f_2147_2]) ).

cnf(f_2147_4,plain,
    ( U_7285 = c_Orderings_Otop__class_Otop(U_7283)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7283),U_7284),U_7285) != c_Orderings_Otop__class_Otop(U_7283)
    | ~ class_Lattices_Obounded__lattice__top(U_7283) ),
    inference(clausify,[status(thm)],[f_2147_2]) ).

cnf(f_2147_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7283),U_7284),U_7285) = c_Orderings_Otop__class_Otop(U_7283)
    | U_7285 != c_Orderings_Otop__class_Otop(U_7283)
    | U_7284 != c_Orderings_Otop__class_Otop(U_7283)
    | ~ class_Lattices_Obounded__lattice__top(U_7283) ),
    inference(clausify,[status(thm)],[f_2147_2]) ).

fof(f_2148_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_2148_2,plain,
    ! [U_7287,U_7286] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7286),U_7287))
      | ~ c_Nat__Transfer_Ois__nat(U_7286) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

cnf(f_2148_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7286),U_7287))
    | ~ c_Nat__Transfer_Ois__nat(U_7286) ),
    inference(clausify,[status(thm)],[f_2148_2]) ).

fof(f_2149_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_2149_2,plain,
    ! [U_7289,U_7288] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7288,tc_HOL_Obool)),U_7289),c_Orderings_Otop__class_Otop(tc_fun(U_7288,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7288,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

cnf(f_2149_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7288,tc_HOL_Obool)),U_7289),c_Orderings_Otop__class_Otop(tc_fun(U_7288,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7288,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2149_2]) ).

fof(f_2150_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_2150_2,plain,
    ! [U_7291,U_7290] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7290,U_7291))
      | ~ c_Nat__Transfer_Ois__nat(U_7291)
      | ~ c_Nat__Transfer_Ois__nat(U_7290) ),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

cnf(f_2150_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7290,U_7291))
    | ~ c_Nat__Transfer_Ois__nat(U_7291)
    | ~ c_Nat__Transfer_Ois__nat(U_7290) ),
    inference(clausify,[status(thm)],[f_2150_2]) ).

fof(f_2151_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_2151_2,plain,
    ! [U_7293,U_7292] :
      ( U_7293 = c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_7292),U_7293) != hAPP(c_Finite__Set_Ocard(U_7292),c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7292),c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

cnf(f_2151_3,plain,
    ( U_7293 = c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_7292),U_7293) != hAPP(c_Finite__Set_Ocard(U_7292),c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7292),c_Orderings_Otop__class_Otop(tc_fun(U_7292,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2151_2]) ).

fof(f_2152_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_2152_2,plain,
    ! [U_7294] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7294,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7294,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7294,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

cnf(f_2152_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7294,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7294,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7294,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2152_2]) ).

fof(f_2153_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_2153_2,plain,
    ! [U_7295] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7295,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7295,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

cnf(f_2153_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7295,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7295,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7295,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2153_2]) ).

fof(f_2154_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_2154_2,plain,
    ! [U_7297,U_7296] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7296,tc_HOL_Obool)),U_7297)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),c_Orderings_Otop__class_Otop(tc_fun(U_7296,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),c_Orderings_Otop__class_Otop(tc_fun(U_7296,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7296,tc_HOL_Obool)),U_7297))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),U_7297)) ),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

cnf(f_2154_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),c_Orderings_Otop__class_Otop(tc_fun(U_7296,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7296,tc_HOL_Obool)),U_7297)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),U_7297)) ),
    inference(clausify,[status(thm)],[f_2154_2]) ).

cnf(f_2154_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7296,tc_HOL_Obool)),U_7297)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),c_Orderings_Otop__class_Otop(tc_fun(U_7296,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7296),U_7297)) ),
    inference(clausify,[status(thm)],[f_2154_2]) ).

fof(f_2155_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_2155_2,plain,
    ! [U_7299,U_7298] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7298,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7298,tc_HOL_Obool)),U_7299)),U_7299) = c_Orderings_Otop__class_Otop(tc_fun(U_7298,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2155_1]) ).

cnf(f_2155_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7298,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7298,tc_HOL_Obool)),U_7299)),U_7299) = c_Orderings_Otop__class_Otop(tc_fun(U_7298,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2155_2]) ).

fof(f_2156_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_2156_2,plain,
    ! [U_7301,U_7300] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7300,tc_HOL_Obool)),U_7301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7300,tc_HOL_Obool)),U_7301)) = c_Orderings_Otop__class_Otop(tc_fun(U_7300,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

cnf(f_2156_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7300,tc_HOL_Obool)),U_7301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7300,tc_HOL_Obool)),U_7301)) = c_Orderings_Otop__class_Otop(tc_fun(U_7300,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2156_2]) ).

fof(f_2157_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_2157_2,plain,
    ! [U_7303,U_7302] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7302,tc_HOL_Obool)),U_7303) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7302,tc_HOL_Obool))),U_7303),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

cnf(f_2157_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7302,tc_HOL_Obool)),U_7303) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7302,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7302,tc_HOL_Obool))),U_7303),
    inference(clausify,[status(thm)],[f_2157_2]) ).

fof(f_2158_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_2158_2,plain,
    ! [U_7304] :
      ( ( c_Nat__Transfer_Ois__nat(U_7304)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7304)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7304))
        | ~ c_Nat__Transfer_Ois__nat(U_7304) ) ),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

fof(f_2158_3,plain,
    ( ! [U_7306] :
        ( c_Nat__Transfer_Ois__nat(U_7306)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7306)) )
    & ! [U_7305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7305))
        | ~ c_Nat__Transfer_Ois__nat(U_7305) ) ),
    inference(miniscope,[status(thm)],[f_2158_2]) ).

cnf(f_2158_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7305))
    | ~ c_Nat__Transfer_Ois__nat(U_7305) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

cnf(f_2158_5,plain,
    ( c_Nat__Transfer_Ois__nat(U_7306)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7306)) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

fof(f_2159_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_2159_2,plain,
    ! [U_7307] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7307),c_Orderings_Obot__class_Obot(U_7307)) = c_Orderings_Otop__class_Otop(U_7307)
      | ~ class_Lattices_Oboolean__algebra(U_7307) ),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

cnf(f_2159_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7307),c_Orderings_Obot__class_Obot(U_7307)) = c_Orderings_Otop__class_Otop(U_7307)
    | ~ class_Lattices_Oboolean__algebra(U_7307) ),
    inference(clausify,[status(thm)],[f_2159_2]) ).

fof(f_2160_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_2160_2,plain,
    ! [U_7308] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7308),c_Orderings_Otop__class_Otop(U_7308)) = c_Orderings_Obot__class_Obot(U_7308)
      | ~ class_Lattices_Oboolean__algebra(U_7308) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

cnf(f_2160_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_7308),c_Orderings_Otop__class_Otop(U_7308)) = c_Orderings_Obot__class_Obot(U_7308)
    | ~ class_Lattices_Oboolean__algebra(U_7308) ),
    inference(clausify,[status(thm)],[f_2160_2]) ).

fof(f_2161_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_2161_2,plain,
    ! [U_7310,U_7309] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7309),U_7310),hAPP(c_Groups_Ouminus__class_Ouminus(U_7309),U_7310)) = c_Orderings_Otop__class_Otop(U_7309)
      | ~ class_Lattices_Oboolean__algebra(U_7309) ),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

cnf(f_2161_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7309),U_7310),hAPP(c_Groups_Ouminus__class_Ouminus(U_7309),U_7310)) = c_Orderings_Otop__class_Otop(U_7309)
    | ~ class_Lattices_Oboolean__algebra(U_7309) ),
    inference(clausify,[status(thm)],[f_2161_2]) ).

fof(f_2162_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_2162_2,plain,
    ! [U_7312,U_7311] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7311),hAPP(c_Groups_Ouminus__class_Ouminus(U_7311),U_7312)),U_7312) = c_Orderings_Otop__class_Otop(U_7311)
      | ~ class_Lattices_Oboolean__algebra(U_7311) ),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

cnf(f_2162_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7311),hAPP(c_Groups_Ouminus__class_Ouminus(U_7311),U_7312)),U_7312) = c_Orderings_Otop__class_Otop(U_7311)
    | ~ class_Lattices_Oboolean__algebra(U_7311) ),
    inference(clausify,[status(thm)],[f_2162_2]) ).

fof(f_2163_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_2163_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_2163_1]) ).

fof(f_2164_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_2164_2,plain,
    ! [U_7313] :
      ( 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_7313),c_Orderings_Otop__class_Otop(tc_fun(U_7313,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7313),c_Orderings_Otop__class_Otop(tc_fun(U_7313,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

cnf(f_2164_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_7313),c_Orderings_Otop__class_Otop(tc_fun(U_7313,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7313),c_Orderings_Otop__class_Otop(tc_fun(U_7313,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2164_2]) ).

fof(f_2165_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_2165_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_2165_1]) ).

fof(f_2166_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_2166_2,plain,
    ! [U_7315,U_7314] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7314),c_Orderings_Otop__class_Otop(tc_fun(U_7314,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_7315),c_Orderings_Otop__class_Otop(tc_fun(U_7315,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7314,U_7315)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7314,U_7315),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

cnf(f_2166_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7314),c_Orderings_Otop__class_Otop(tc_fun(U_7314,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_7315),c_Orderings_Otop__class_Otop(tc_fun(U_7315,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7314,U_7315)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7314,U_7315),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2166_2]) ).

fof(f_2167_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_2167_2,plain,
    ! [U_7317,U_7316] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7316,U_7317) = hAPP(hAPP(c_Finite__Set_Ofold(U_7316,U_7316,c_Lattices_Osemilattice__inf__class_Oinf(U_7316)),c_Orderings_Otop__class_Otop(U_7316)),U_7317)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7316),U_7317))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7316) ),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

cnf(f_2167_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7316,U_7317) = hAPP(hAPP(c_Finite__Set_Ofold(U_7316,U_7316,c_Lattices_Osemilattice__inf__class_Oinf(U_7316)),c_Orderings_Otop__class_Otop(U_7316)),U_7317)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7316),U_7317))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7316) ),
    inference(clausify,[status(thm)],[f_2167_2]) ).

fof(f_2168_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_2168_2,plain,
    ! [U_7321,U_7320,U_7319] :
      ( ? [U_7318] : U_7319 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7320),U_7318))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7321),U_7319))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7319,U_7320) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7321,U_7320) ),
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

fof(f_2168_3,plain,
    ! [U_7321,U_7320,U_7319] :
      ( U_7319 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7320),sK142(U_7321,U_7320,U_7319)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7321),U_7319))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7319,U_7320) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7321,U_7320) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_7318,sK142(U_7321,U_7320,U_7319))],[f_2168_2]) ).

cnf(f_2168_4,plain,
    ( U_7319 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7320),sK142(U_7321,U_7320,U_7319)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7321),U_7319))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7319,U_7320) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7321,U_7320) ),
    inference(clausify,[status(thm)],[f_2168_3]) ).

fof(f_2169_1,plain,
    ! [V_i_2,V_Pa_2,V_p_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,V_i_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
          & hBOOL(hAPP(V_Pa_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_2169_2,plain,
    ! [U_7325,U_7324,U_7323] :
      ( hBOOL(hAPP(U_7324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7325),U_7323))
      | ~ hBOOL(hAPP(U_7324,U_7325))
      | ? [U_7322] :
          ( ~ hBOOL(hAPP(U_7324,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7322),U_7323)))
          & hBOOL(hAPP(U_7324,U_7322))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7322),U_7323)) ) ),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

fof(f_2169_3,plain,
    ! [U_7325,U_7324,U_7323] :
      ( hBOOL(hAPP(U_7324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7325),U_7323))
      | ~ hBOOL(hAPP(U_7324,U_7325))
      | ( ~ hBOOL(hAPP(U_7324,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK143(U_7325,U_7324,U_7323)),U_7323)))
        & hBOOL(hAPP(U_7324,sK143(U_7325,U_7324,U_7323)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK143(U_7325,U_7324,U_7323)),U_7323)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_7322,sK143(U_7325,U_7324,U_7323))],[f_2169_2]) ).

cnf(f_2169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK143(U_7325,U_7324,U_7323)),U_7323))
    | hBOOL(hAPP(U_7324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7325),U_7323))
    | ~ hBOOL(hAPP(U_7324,U_7325)) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

cnf(f_2169_5,plain,
    ( hBOOL(hAPP(U_7324,sK143(U_7325,U_7324,U_7323)))
    | hBOOL(hAPP(U_7324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7325),U_7323))
    | ~ hBOOL(hAPP(U_7324,U_7325)) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

cnf(f_2169_6,plain,
    ( ~ hBOOL(hAPP(U_7324,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK143(U_7325,U_7324,U_7323)),U_7323)))
    | hBOOL(hAPP(U_7324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7325),U_7323))
    | ~ hBOOL(hAPP(U_7324,U_7325)) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

fof(f_2170_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_2170_2,plain,
    ! [U_7327,U_7326] :
      ( ( c_Random_Olog(U_7326,U_7327) = 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_7326,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7327),U_7326)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7327),U_7326))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7326),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_7326,U_7327) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7327),U_7326))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7326),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

fof(f_2170_3,plain,
    ( ! [U_7331,U_7329] :
        ( c_Random_Olog(U_7329,U_7331) = 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_7329,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7331),U_7329)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7331),U_7329))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7329),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_7330,U_7328] :
        ( c_Random_Olog(U_7328,U_7330) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7330),U_7328))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7328),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_2170_2]) ).

cnf(f_2170_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7328),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | c_Random_Olog(U_7328,U_7330) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

cnf(f_2170_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7330),U_7328))
    | c_Random_Olog(U_7328,U_7330) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

cnf(f_2170_6,plain,
    ( c_Random_Olog(U_7329,U_7331) = 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_7329,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7331),U_7329)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7331),U_7329))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7329),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

fof(f_2171_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_2171_2,plain,
    ! [U_7334,U_7333] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7333),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7333,tc_HOL_Obool),U_7334)))
      | ! [U_7332] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7333),U_7332))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7333,tc_HOL_Obool)),U_7332),U_7334)) ) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

cnf(f_2171_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7333),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7333,tc_HOL_Obool),U_7334)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7333),U_7332))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7333,tc_HOL_Obool)),U_7332),U_7334)) ),
    inference(clausify,[status(thm)],[f_2171_2]) ).

fof(f_2172_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_2172_2,plain,
    ! [U_7336,U_7335] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_7335,tc_HOL_Obool)),U_7336)),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

cnf(f_2172_3,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_7335,tc_HOL_Obool)),U_7336)),
    inference(clausify,[status(thm)],[f_2172_2]) ).

fof(f_2173_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_2173_2,plain,
    ! [U_7340,U_7339,U_7338,U_7337] :
      ( hBOOL(hAPP(hAPP(c_member(U_7337),U_7338),U_7340))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7337,tc_HOL_Obool)),U_7340),U_7339))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7337),U_7338),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7337,tc_HOL_Obool),U_7339))) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

cnf(f_2173_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7337),U_7338),U_7340))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7337,tc_HOL_Obool)),U_7340),U_7339))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7337),U_7338),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7337,tc_HOL_Obool),U_7339))) ),
    inference(clausify,[status(thm)],[f_2173_2]) ).

fof(f_2174_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_2174_2,plain,
    ! [U_7344,U_7343,U_7342,U_7341] :
      ( hBOOL(hAPP(hAPP(c_member(U_7341),U_7342),U_7344))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7341,tc_HOL_Obool)),U_7344),U_7343))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7341),U_7342),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7341,tc_HOL_Obool),U_7343))) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

cnf(f_2174_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7341),U_7342),U_7344))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7341,tc_HOL_Obool)),U_7344),U_7343))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7341),U_7342),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7341,tc_HOL_Obool),U_7343))) ),
    inference(clausify,[status(thm)],[f_2174_2]) ).

fof(f_2175_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_2175_2,plain,
    ! [U_7345] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7345,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7345,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

cnf(f_2175_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7345,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_7345,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7345,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2175_2]) ).

fof(f_2176_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_2176_2,plain,
    ! [U_7346] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7346,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7346,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7346,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

cnf(f_2176_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7346,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7346,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_7346,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2176_2]) ).

fof(f_2177_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_2177_2,plain,
    ! [U_7351,U_7350,U_7349] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351)))
          | ? [U_7348] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),U_7348))
              & hBOOL(hAPP(hAPP(c_member(U_7349),U_7348),U_7351)) ) )
        & ( ! [U_7347] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),U_7347))
              | ~ hBOOL(hAPP(hAPP(c_member(U_7349),U_7347),U_7351)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7349) ),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

fof(f_2177_3,plain,
    ! [U_7351,U_7350,U_7349] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),sK144(U_7351,U_7350,U_7349)))
            & hBOOL(hAPP(hAPP(c_member(U_7349),sK144(U_7351,U_7350,U_7349)),U_7351)) ) )
        & ( ! [U_7347] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),U_7347))
              | ~ hBOOL(hAPP(hAPP(c_member(U_7349),U_7347),U_7351)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7349) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_7348,sK144(U_7351,U_7350,U_7349))],[f_2177_2]) ).

cnf(f_2177_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),U_7347))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7349),U_7347),U_7351))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7349) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7349),sK144(U_7351,U_7350,U_7349)),U_7351))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7349) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),sK144(U_7351,U_7350,U_7349)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7349),U_7350),c_Complete__Lattice_OInf__class_OInf(U_7349,U_7351)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7349) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

fof(f_2178_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_2178_2,plain,
    ! [U_7356,U_7355,U_7354] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356))
          | ! [U_7353] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),U_7353),U_7356))
              | ~ hBOOL(hAPP(hAPP(c_member(U_7354),U_7353),U_7355)) ) )
        & ( ? [U_7352] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),U_7352),U_7356))
              & hBOOL(hAPP(hAPP(c_member(U_7354),U_7352),U_7355)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356)) ) )
      | ~ class_Orderings_Olinorder(U_7354)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7354) ),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

fof(f_2178_3,plain,
    ! [U_7356,U_7355,U_7354] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356))
          | ! [U_7353] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),U_7353),U_7356))
              | ~ hBOOL(hAPP(hAPP(c_member(U_7354),U_7353),U_7355)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),sK145(U_7356,U_7355,U_7354)),U_7356))
            & hBOOL(hAPP(hAPP(c_member(U_7354),sK145(U_7356,U_7355,U_7354)),U_7355)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356)) ) )
      | ~ class_Orderings_Olinorder(U_7354)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7354) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_7352,sK145(U_7356,U_7355,U_7354))],[f_2178_2]) ).

cnf(f_2178_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7354),sK145(U_7356,U_7355,U_7354)),U_7355))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356))
    | ~ class_Orderings_Olinorder(U_7354)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7354) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

cnf(f_2178_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),sK145(U_7356,U_7355,U_7354)),U_7356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356))
    | ~ class_Orderings_Olinorder(U_7354)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7354) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

cnf(f_2178_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),c_Complete__Lattice_OInf__class_OInf(U_7354,U_7355)),U_7356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7354),U_7353),U_7356))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7354),U_7353),U_7355))
    | ~ class_Orderings_Olinorder(U_7354)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7354) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

fof(f_2179_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_2179_2,plain,
    ! [U_7357] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7357,c_Orderings_Otop__class_Otop(tc_fun(U_7357,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_7357)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7357) ),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

cnf(f_2179_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7357,c_Orderings_Otop__class_Otop(tc_fun(U_7357,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_7357)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7357) ),
    inference(clausify,[status(thm)],[f_2179_2]) ).

fof(f_2180_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_2180_2,plain,
    ! [U_7360,U_7359,U_7358] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7358,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7358,tc_HOL_Obool),U_7360)),U_7359))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7358,tc_HOL_Obool)),U_7359),U_7360)) ),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

cnf(f_2180_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7358,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7358,tc_HOL_Obool),U_7360)),U_7359))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7358,tc_HOL_Obool)),U_7359),U_7360)) ),
    inference(clausify,[status(thm)],[f_2180_2]) ).

fof(f_2181_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_2181_2,plain,
    ! [U_7363,U_7362,U_7361] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7361,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7361,tc_HOL_Obool),U_7363)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7361,tc_HOL_Obool),U_7362)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7361,tc_HOL_Obool),tc_HOL_Obool)),U_7362),U_7363)) ),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

cnf(f_2181_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7361,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7361,tc_HOL_Obool),U_7363)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7361,tc_HOL_Obool),U_7362)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7361,tc_HOL_Obool),tc_HOL_Obool)),U_7362),U_7363)) ),
    inference(clausify,[status(thm)],[f_2181_2]) ).

fof(f_2182_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_2182_2,plain,
    ! [U_7366,U_7365,U_7364] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7364,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7364,tc_HOL_Obool)),U_7365),U_7366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7364,tc_HOL_Obool)),U_7365),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7364,tc_HOL_Obool),U_7366)),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

cnf(f_2182_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7364,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7364,tc_HOL_Obool)),U_7365),U_7366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7364,tc_HOL_Obool)),U_7365),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7364,tc_HOL_Obool),U_7366)),
    inference(clausify,[status(thm)],[f_2182_2]) ).

fof(f_2183_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_2183_2,plain,
    ! [U_7369,U_7368,U_7367] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7367),c_Complete__Lattice_OInf__class_OInf(U_7367,U_7369)),U_7368))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7367),U_7368),U_7369))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7367) ),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

cnf(f_2183_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7367),c_Complete__Lattice_OInf__class_OInf(U_7367,U_7369)),U_7368))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7367),U_7368),U_7369))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7367) ),
    inference(clausify,[status(thm)],[f_2183_2]) ).

fof(f_2184_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_2184_2,plain,
    ! [U_7372,U_7371,U_7370] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_7370,tc_HOL_Obool),tc_HOL_Obool)),U_7371),U_7372)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7370,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),U_7371)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),U_7372)),
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

cnf(f_2184_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_7370,tc_HOL_Obool),tc_HOL_Obool)),U_7371),U_7372)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7370,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),U_7371)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7370,tc_HOL_Obool),U_7372)),
    inference(clausify,[status(thm)],[f_2184_2]) ).

fof(f_2185_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_2185_2,plain,
    ! [U_7374,U_7373] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7373,hAPP(hAPP(c_Set_Oinsert(U_7373),U_7374),c_Orderings_Obot__class_Obot(tc_fun(U_7373,tc_HOL_Obool)))) = U_7374
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7373) ),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

cnf(f_2185_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7373,hAPP(hAPP(c_Set_Oinsert(U_7373),U_7374),c_Orderings_Obot__class_Obot(tc_fun(U_7373,tc_HOL_Obool)))) = U_7374
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7373) ),
    inference(clausify,[status(thm)],[f_2185_2]) ).

fof(f_2186_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_2186_2,plain,
    ! [U_7375] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7375,c_Orderings_Obot__class_Obot(tc_fun(U_7375,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_7375)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7375) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

cnf(f_2186_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7375,c_Orderings_Obot__class_Obot(tc_fun(U_7375,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_7375)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7375) ),
    inference(clausify,[status(thm)],[f_2186_2]) ).

fof(f_2187_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_2187_2,plain,
    ! [U_7378,U_7377,U_7376] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7376,hAPP(hAPP(c_Set_Oinsert(U_7376),U_7377),U_7378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7376),U_7377),c_Complete__Lattice_OInf__class_OInf(U_7376,U_7378))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7376) ),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

cnf(f_2187_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7376,hAPP(hAPP(c_Set_Oinsert(U_7376),U_7377),U_7378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7376),U_7377),c_Complete__Lattice_OInf__class_OInf(U_7376,U_7378))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7376) ),
    inference(clausify,[status(thm)],[f_2187_2]) ).

fof(f_2188_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_2188_2,plain,
    ! [U_7381,U_7380,U_7379] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7379,tc_HOL_Obool)),U_7380),U_7381) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7379,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7379,tc_HOL_Obool)),U_7380),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7379,tc_HOL_Obool)),U_7381),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7379,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2188_1]) ).

cnf(f_2188_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7379,tc_HOL_Obool)),U_7380),U_7381) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7379,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7379,tc_HOL_Obool)),U_7380),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_7379,tc_HOL_Obool)),U_7381),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7379,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2188_2]) ).

fof(f_2189_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_2189_2,plain,
    ! [U_7384,U_7383,U_7382] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7382,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7382,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),U_7383)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),U_7384))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_7382,tc_HOL_Obool),tc_HOL_Obool)),U_7383),U_7384)))),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

cnf(f_2189_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7382,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7382,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),U_7383)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),U_7384))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7382,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_7382,tc_HOL_Obool),tc_HOL_Obool)),U_7383),U_7384)))),
    inference(clausify,[status(thm)],[f_2189_2]) ).

fof(f_2190_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_2190_2,plain,
    ! [U_7387,U_7386,U_7385] :
      ( c_Complete__Lattice_OInf__class_OInf(U_7385,hAPP(hAPP(c_Set_Oinsert(U_7385),U_7386),hAPP(hAPP(c_Set_Oinsert(U_7385),U_7387),c_Orderings_Obot__class_Obot(tc_fun(U_7385,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7385),U_7386),U_7387)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7385) ),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

cnf(f_2190_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_7385,hAPP(hAPP(c_Set_Oinsert(U_7385),U_7386),hAPP(hAPP(c_Set_Oinsert(U_7385),U_7387),c_Orderings_Obot__class_Obot(tc_fun(U_7385,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7385),U_7386),U_7387)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7385) ),
    inference(clausify,[status(thm)],[f_2190_2]) ).

fof(f_2191_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_2191_2,plain,
    ! [U_7390,U_7389,U_7388] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7388),U_7390),c_Complete__Lattice_OInf__class_OInf(U_7388,U_7389)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7388,U_7388,c_Lattices_Osemilattice__inf__class_Oinf(U_7388)),U_7390),U_7389)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7388),U_7389))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7388) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

cnf(f_2191_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7388),U_7390),c_Complete__Lattice_OInf__class_OInf(U_7388,U_7389)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7388,U_7388,c_Lattices_Osemilattice__inf__class_Oinf(U_7388)),U_7390),U_7389)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7388),U_7389))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7388) ),
    inference(clausify,[status(thm)],[f_2191_2]) ).

fof(f_2192_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_2192_2,plain,
    ! [U_7392,U_7391] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_7391,U_7392) = c_Complete__Lattice_OInf__class_OInf(U_7391,U_7392)
      | U_7392 = c_Orderings_Obot__class_Obot(tc_fun(U_7391,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7391),U_7392))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_7391) ),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

cnf(f_2192_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_7391,U_7392) = c_Complete__Lattice_OInf__class_OInf(U_7391,U_7392)
    | U_7392 = c_Orderings_Obot__class_Obot(tc_fun(U_7391,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7391),U_7392))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_7391) ),
    inference(clausify,[status(thm)],[f_2192_2]) ).

fof(f_2193_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_2193_2,plain,
    ! [U_7395,U_7394,U_7393] :
      ( ( c_Random_Ominus__shift(U_7395,U_7393,U_7394) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7393),U_7394)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7393),U_7394)) )
      & ( c_Random_Ominus__shift(U_7395,U_7393,U_7394) = 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_7395),U_7393)),U_7394)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7393),U_7394)) ) ),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

fof(f_2193_3,plain,
    ( ! [U_7401,U_7399,U_7397] :
        ( c_Random_Ominus__shift(U_7401,U_7397,U_7399) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7397),U_7399)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7397),U_7399)) )
    & ! [U_7400,U_7398,U_7396] :
        ( c_Random_Ominus__shift(U_7400,U_7396,U_7398) = 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_7400),U_7396)),U_7398)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7396),U_7398)) ) ),
    inference(miniscope,[status(thm)],[f_2193_2]) ).

cnf(f_2193_4,plain,
    ( c_Random_Ominus__shift(U_7400,U_7396,U_7398) = 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_7400),U_7396)),U_7398)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7396),U_7398)) ),
    inference(clausify,[status(thm)],[f_2193_3]) ).

cnf(f_2193_5,plain,
    ( c_Random_Ominus__shift(U_7401,U_7397,U_7399) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7397),U_7399)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7397),U_7399)) ),
    inference(clausify,[status(thm)],[f_2193_3]) ).

fof(f_2194_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_2194_2,plain,
    ! [U_7403,U_7402] :
      ( ( c_Random_Oinc__shift(U_7402,U_7403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7403),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_7402 = U_7403 )
      & ( c_Random_Oinc__shift(U_7402,U_7403) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_7402 != U_7403 ) ),
    inference(variable_rename,[status(thm)],[f_2194_1]) ).

fof(f_2194_3,plain,
    ( ! [U_7407,U_7405] :
        ( c_Random_Oinc__shift(U_7405,U_7407) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7407),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_7405 = U_7407 )
    & ! [U_7406,U_7404] :
        ( c_Random_Oinc__shift(U_7404,U_7406) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_7404 != U_7406 ) ),
    inference(miniscope,[status(thm)],[f_2194_2]) ).

cnf(f_2194_4,plain,
    ( c_Random_Oinc__shift(U_7404,U_7406) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_7404 != U_7406 ),
    inference(clausify,[status(thm)],[f_2194_3]) ).

cnf(f_2194_5,plain,
    ( c_Random_Oinc__shift(U_7405,U_7407) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7407),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_7405 = U_7407 ),
    inference(clausify,[status(thm)],[f_2194_3]) ).

fof(f_2195_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_2195_2,plain,
    ! [U_7409,U_7408] : hBOOL(hAPP(hAPP(c_member(U_7408),U_7409),c_Orderings_Otop__class_Otop(tc_fun(U_7408,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

cnf(f_2195_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_7408),U_7409),c_Orderings_Otop__class_Otop(tc_fun(U_7408,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2195_2]) ).

fof(f_2196_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_2196_2,plain,
    ! [U_7412,U_7411,U_7410] :
      ( U_7411 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7410),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7410),U_7411),U_7412)),U_7412)),c_Divides_Odiv__class_Omod(U_7410,U_7411,U_7412))
      | ~ class_Divides_Osemiring__div(U_7410) ),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

cnf(f_2196_3,plain,
    ( U_7411 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7410),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7410),U_7411),U_7412)),U_7412)),c_Divides_Odiv__class_Omod(U_7410,U_7411,U_7412))
    | ~ class_Divides_Osemiring__div(U_7410) ),
    inference(clausify,[status(thm)],[f_2196_2]) ).

fof(f_2197_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_2197_2,plain,
    ! [U_7416,U_7415,U_7414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7414,tc_HOL_Obool),U_7415)),U_7416))
      | U_7415 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7414,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_7413] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),U_7413),U_7416))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_7414,tc_HOL_Obool)),U_7413),U_7415)) ) ),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

fof(f_2197_3,plain,
    ! [U_7416,U_7415,U_7414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7414,tc_HOL_Obool),U_7415)),U_7416))
      | U_7415 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7414,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),sK146(U_7416,U_7415,U_7414)),U_7416))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_7414,tc_HOL_Obool)),sK146(U_7416,U_7415,U_7414)),U_7415)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_7413,sK146(U_7416,U_7415,U_7414))],[f_2197_2]) ).

cnf(f_2197_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7414,tc_HOL_Obool)),sK146(U_7416,U_7415,U_7414)),U_7415))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7414,tc_HOL_Obool),U_7415)),U_7416))
    | U_7415 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7414,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

cnf(f_2197_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),sK146(U_7416,U_7415,U_7414)),U_7416))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7414,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7414,tc_HOL_Obool),U_7415)),U_7416))
    | U_7415 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_7414,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2197_3]) ).

fof(f_2198_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_2198_2,plain,
    ! [U_7420,U_7419,U_7418] :
      ( hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7418,tc_HOL_Obool),U_7419)))
      | ? [U_7417] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),U_7417))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_7418,tc_HOL_Obool)),U_7417),U_7419)) ) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

fof(f_2198_3,plain,
    ! [U_7420,U_7419,U_7418] :
      ( hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7418,tc_HOL_Obool),U_7419)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),sK147(U_7420,U_7419,U_7418)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_7418,tc_HOL_Obool)),sK147(U_7420,U_7419,U_7418)),U_7419)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_7417,sK147(U_7420,U_7419,U_7418))],[f_2198_2]) ).

cnf(f_2198_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7418,tc_HOL_Obool)),sK147(U_7420,U_7419,U_7418)),U_7419))
    | hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7418,tc_HOL_Obool),U_7419))) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),sK147(U_7420,U_7419,U_7418)))
    | hBOOL(hAPP(hAPP(c_member(U_7418),U_7420),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_7418,tc_HOL_Obool),U_7419))) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

fof(f_2199_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_2199_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2199_1]) ).

fof(f_2200_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_2200_2,plain,
    ! [U_7422,U_7421] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7421),U_7422) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_7421),U_7422),
    inference(variable_rename,[status(thm)],[f_2200_1]) ).

cnf(f_2200_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7421),U_7422) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_7421),U_7422),
    inference(clausify,[status(thm)],[f_2200_2]) ).

fof(f_2201_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_2201_2,plain,
    ! [U_7423] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)),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_7423))))
          | 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_7423)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)) = 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_7423)))
          | ~ 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_7423)))) ) )
      | ~ 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_7423))) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

cnf(f_2201_3,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)) = 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_7423)))
    | ~ 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_7423))))
    | ~ 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_7423))) ),
    inference(clausify,[status(thm)],[f_2201_2]) ).

cnf(f_2201_4,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7423)),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_7423))))
    | 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_7423))))
    | ~ 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_7423))) ),
    inference(clausify,[status(thm)],[f_2201_2]) ).

fof(f_2202_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_2202_2,plain,
    ! [U_7424] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_7424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_7424)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

cnf(f_2202_3,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_7424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_7424)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2202_2]) ).

fof(f_2203_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_2203_2,plain,
    ! [U_7426,U_7425] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7426)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7425)) = 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_7426),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7425)))),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_7425),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7426)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7425)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7426)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7425),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

fof(f_2203_3,plain,
    ( ! [U_7430,U_7428] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7430)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7428)) = 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_7430),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7428)))),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_7428),c_Int_OPls)) )
    & ! [U_7429,U_7427] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7427)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7429)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7427),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2203_2]) ).

cnf(f_2203_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7427)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7429)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7427),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2203_3]) ).

cnf(f_2203_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7430)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7428)) = 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_7430),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7428)))),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_7428),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2203_3]) ).

fof(f_2204_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_2204_2,plain,
    ! [U_7434,U_7433,U_7432,U_7431] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7431,U_7432,U_7433,c_Code__Numeral_OSuc__code__numeral(U_7434)) = hAPP(hAPP(U_7433,U_7434),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7431,U_7432,U_7433,U_7434)),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

cnf(f_2204_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7431,U_7432,U_7433,c_Code__Numeral_OSuc__code__numeral(U_7434)) = hAPP(hAPP(U_7433,U_7434),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7431,U_7432,U_7433,U_7434)),
    inference(clausify,[status(thm)],[f_2204_2]) ).

fof(f_2205_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_2205_2,plain,
    ! [U_7438,U_7437,U_7436,U_7435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7435),hAPP(c_Groups_Oabs__class_Oabs(U_7435),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7436,U_7435),U_7437),U_7438))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7436,U_7435),hAPP(hAPP(c_COMBB(U_7435,U_7435,U_7436),c_Groups_Oabs__class_Oabs(U_7435)),U_7437)),U_7438)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7435) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

cnf(f_2205_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7435),hAPP(c_Groups_Oabs__class_Oabs(U_7435),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7436,U_7435),U_7437),U_7438))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7436,U_7435),hAPP(hAPP(c_COMBB(U_7435,U_7435,U_7436),c_Groups_Oabs__class_Oabs(U_7435)),U_7437)),U_7438)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7435) ),
    inference(clausify,[status(thm)],[f_2205_2]) ).

fof(f_2206_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_2206_2,plain,
    ! [U_7442,U_7441,U_7440,U_7439] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7439),c_Groups_Ozero__class_Ozero(U_7439)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7440,U_7439),hAPP(hAPP(c_COMBB(U_7439,U_7439,U_7440),c_Groups_Oabs__class_Oabs(U_7439)),U_7441)),U_7442)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7439) ),
    inference(variable_rename,[status(thm)],[f_2206_1]) ).

cnf(f_2206_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7439),c_Groups_Ozero__class_Ozero(U_7439)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7440,U_7439),hAPP(hAPP(c_COMBB(U_7439,U_7439,U_7440),c_Groups_Oabs__class_Oabs(U_7439)),U_7441)),U_7442)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7439) ),
    inference(clausify,[status(thm)],[f_2206_2]) ).

fof(f_2207_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_2207_2,plain,
    ! [U_7447,U_7446,U_7445,U_7444,U_7443] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),hAPP(hAPP(c_COMBS(U_7444,U_7443,U_7443),hAPP(hAPP(c_COMBB(U_7443,tc_fun(U_7443,U_7443),U_7444),c_Groups_Oplus__class_Oplus(U_7443)),U_7446)),U_7447)),U_7445) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7443),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),U_7446),U_7445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),U_7447),U_7445))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7444),U_7445))
      | ~ class_Groups_Ocomm__monoid__add(U_7443) ),
    inference(variable_rename,[status(thm)],[f_2207_1]) ).

cnf(f_2207_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),hAPP(hAPP(c_COMBS(U_7444,U_7443,U_7443),hAPP(hAPP(c_COMBB(U_7443,tc_fun(U_7443,U_7443),U_7444),c_Groups_Oplus__class_Oplus(U_7443)),U_7446)),U_7447)),U_7445) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7443),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),U_7446),U_7445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7444,U_7443),U_7447),U_7445))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7444),U_7445))
    | ~ class_Groups_Ocomm__monoid__add(U_7443) ),
    inference(clausify,[status(thm)],[f_2207_2]) ).

fof(f_2208_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_2208_2,plain,
    ! [U_7452,U_7451,U_7450,U_7449,U_7448] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),hAPP(hAPP(c_COMBS(U_7449,U_7448,U_7448),hAPP(hAPP(c_COMBB(U_7448,tc_fun(U_7448,U_7448),U_7449),c_Groups_Oplus__class_Oplus(U_7448)),U_7450)),U_7451)),U_7452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7448),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),U_7450),U_7452)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),U_7451),U_7452))
      | ~ class_Groups_Ocomm__monoid__add(U_7448) ),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

cnf(f_2208_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),hAPP(hAPP(c_COMBS(U_7449,U_7448,U_7448),hAPP(hAPP(c_COMBB(U_7448,tc_fun(U_7448,U_7448),U_7449),c_Groups_Oplus__class_Oplus(U_7448)),U_7450)),U_7451)),U_7452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7448),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),U_7450),U_7452)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7449,U_7448),U_7451),U_7452))
    | ~ class_Groups_Ocomm__monoid__add(U_7448) ),
    inference(clausify,[status(thm)],[f_2208_2]) ).

fof(f_2209_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_2209_2,plain,
    ! [U_7456,U_7455,U_7454,U_7453] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7453,tc_fun(U_7454,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7453,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),U_7453),c_COMBC(U_7454,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_prod(U_7453,U_7454)),tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),U_7453),hAPP(c_COMBB(tc_prod(U_7453,U_7454),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool),U_7454),c_member(tc_prod(U_7453,U_7454)))),c_Product__Type_OPair(U_7453,U_7454)))),U_7455)),hAPP(hAPP(c_COMBC(U_7453,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),U_7453),c_COMBC(U_7454,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_prod(U_7453,U_7454)),tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),U_7453),hAPP(c_COMBB(tc_prod(U_7453,U_7454),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool),U_7454),c_member(tc_prod(U_7453,U_7454)))),c_Product__Type_OPair(U_7453,U_7454)))),U_7456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool)),U_7455),U_7456)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool)),U_7455),U_7456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7453,tc_fun(U_7454,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7453,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),U_7453),c_COMBC(U_7454,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_prod(U_7453,U_7454)),tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),U_7453),hAPP(c_COMBB(tc_prod(U_7453,U_7454),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool),U_7454),c_member(tc_prod(U_7453,U_7454)))),c_Product__Type_OPair(U_7453,U_7454)))),U_7455)),hAPP(hAPP(c_COMBC(U_7453,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool)),U_7453),c_COMBC(U_7454,tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_prod(U_7453,U_7454)),tc_fun(U_7454,tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool)),U_7453),hAPP(c_COMBB(tc_prod(U_7453,U_7454),tc_fun(tc_fun(tc_prod(U_7453,U_7454),tc_HOL_Obool),tc_HOL_Obool),U_7454),c_member(tc_prod(U_7453,U_7454)))),c_Product__Type_OPair(U_7453,U_7454)))),U_7456))) ) ),
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

fof(f_2209_3,plain,
    ( ! [U_7464,U_7462,U_7460,U_7458] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7458,tc_fun(U_7460,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7458,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),U_7458),c_COMBC(U_7460,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_prod(U_7458,U_7460)),tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),U_7458),hAPP(c_COMBB(tc_prod(U_7458,U_7460),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool),U_7460),c_member(tc_prod(U_7458,U_7460)))),c_Product__Type_OPair(U_7458,U_7460)))),U_7462)),hAPP(hAPP(c_COMBC(U_7458,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),U_7458),c_COMBC(U_7460,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_prod(U_7458,U_7460)),tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),U_7458),hAPP(c_COMBB(tc_prod(U_7458,U_7460),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool),U_7460),c_member(tc_prod(U_7458,U_7460)))),c_Product__Type_OPair(U_7458,U_7460)))),U_7464)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool)),U_7462),U_7464)) )
    & ! [U_7463,U_7461,U_7459,U_7457] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool)),U_7461),U_7463))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7457,tc_fun(U_7459,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7457,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),U_7457),c_COMBC(U_7459,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_prod(U_7457,U_7459)),tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),U_7457),hAPP(c_COMBB(tc_prod(U_7457,U_7459),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool),U_7459),c_member(tc_prod(U_7457,U_7459)))),c_Product__Type_OPair(U_7457,U_7459)))),U_7461)),hAPP(hAPP(c_COMBC(U_7457,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),U_7457),c_COMBC(U_7459,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_prod(U_7457,U_7459)),tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),U_7457),hAPP(c_COMBB(tc_prod(U_7457,U_7459),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool),U_7459),c_member(tc_prod(U_7457,U_7459)))),c_Product__Type_OPair(U_7457,U_7459)))),U_7463))) ) ),
    inference(miniscope,[status(thm)],[f_2209_2]) ).

cnf(f_2209_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool)),U_7461),U_7463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7457,tc_fun(U_7459,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7457,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),U_7457),c_COMBC(U_7459,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_prod(U_7457,U_7459)),tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),U_7457),hAPP(c_COMBB(tc_prod(U_7457,U_7459),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool),U_7459),c_member(tc_prod(U_7457,U_7459)))),c_Product__Type_OPair(U_7457,U_7459)))),U_7461)),hAPP(hAPP(c_COMBC(U_7457,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_fun(U_7459,tc_HOL_Obool)),U_7457),c_COMBC(U_7459,tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7459,tc_prod(U_7457,U_7459)),tc_fun(U_7459,tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool)),U_7457),hAPP(c_COMBB(tc_prod(U_7457,U_7459),tc_fun(tc_fun(tc_prod(U_7457,U_7459),tc_HOL_Obool),tc_HOL_Obool),U_7459),c_member(tc_prod(U_7457,U_7459)))),c_Product__Type_OPair(U_7457,U_7459)))),U_7463))) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

cnf(f_2209_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7458,tc_fun(U_7460,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7458,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),U_7458),c_COMBC(U_7460,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_prod(U_7458,U_7460)),tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),U_7458),hAPP(c_COMBB(tc_prod(U_7458,U_7460),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool),U_7460),c_member(tc_prod(U_7458,U_7460)))),c_Product__Type_OPair(U_7458,U_7460)))),U_7462)),hAPP(hAPP(c_COMBC(U_7458,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_fun(U_7460,tc_HOL_Obool)),U_7458),c_COMBC(U_7460,tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7460,tc_prod(U_7458,U_7460)),tc_fun(U_7460,tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool)),U_7458),hAPP(c_COMBB(tc_prod(U_7458,U_7460),tc_fun(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool),tc_HOL_Obool),U_7460),c_member(tc_prod(U_7458,U_7460)))),c_Product__Type_OPair(U_7458,U_7460)))),U_7464)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7458,U_7460),tc_HOL_Obool)),U_7462),U_7464)) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

fof(f_2210_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_2210_2,plain,
    ! [U_7467,U_7466,U_7465] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7465,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7465,tc_fun(U_7465,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7465)),U_7466)),hAPP(hAPP(c_COMBC(U_7465,tc_fun(U_7465,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7465)),U_7467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7465,tc_HOL_Obool)),U_7466),U_7467)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7465,tc_HOL_Obool)),U_7466),U_7467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7465,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7465,tc_fun(U_7465,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7465)),U_7466)),hAPP(hAPP(c_COMBC(U_7465,tc_fun(U_7465,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7465)),U_7467))) ) ),
    inference(variable_rename,[status(thm)],[f_2210_1]) ).

fof(f_2210_3,plain,
    ( ! [U_7473,U_7471,U_7469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7469,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7469,tc_fun(U_7469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7469)),U_7471)),hAPP(hAPP(c_COMBC(U_7469,tc_fun(U_7469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7469)),U_7473)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7469,tc_HOL_Obool)),U_7471),U_7473)) )
    & ! [U_7472,U_7470,U_7468] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7468,tc_HOL_Obool)),U_7470),U_7472))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7468,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7468,tc_fun(U_7468,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7468)),U_7470)),hAPP(hAPP(c_COMBC(U_7468,tc_fun(U_7468,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7468)),U_7472))) ) ),
    inference(miniscope,[status(thm)],[f_2210_2]) ).

cnf(f_2210_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7468,tc_HOL_Obool)),U_7470),U_7472))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7468,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7468,tc_fun(U_7468,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7468)),U_7470)),hAPP(hAPP(c_COMBC(U_7468,tc_fun(U_7468,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7468)),U_7472))) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7469,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7469,tc_fun(U_7469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7469)),U_7471)),hAPP(hAPP(c_COMBC(U_7469,tc_fun(U_7469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7469)),U_7473)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7469,tc_HOL_Obool)),U_7471),U_7473)) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

fof(f_2211_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_2211_2,plain,
    ! [U_7477,U_7476,U_7475,U_7474] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7474),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7475,tc_Int_Oint),U_7476),U_7477)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7475,U_7474),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7474,U_7475),c_Int_Oring__1__class_Oof__int(U_7474)),U_7476)),U_7477)
      | ~ class_Rings_Oring__1(U_7474)
      | ~ class_Groups_Ocomm__monoid__mult(U_7474) ),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

cnf(f_2211_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7474),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7475,tc_Int_Oint),U_7476),U_7477)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7475,U_7474),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7474,U_7475),c_Int_Oring__1__class_Oof__int(U_7474)),U_7476)),U_7477)
    | ~ class_Rings_Oring__1(U_7474)
    | ~ class_Groups_Ocomm__monoid__mult(U_7474) ),
    inference(clausify,[status(thm)],[f_2211_2]) ).

fof(f_2212_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_2212_2,plain,
    ! [U_7481,U_7480,U_7479,U_7478] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_7478),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7479,tc_Int_Oint),U_7480),U_7481)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7479,U_7478),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7478,U_7479),c_Int_Oring__1__class_Oof__int(U_7478)),U_7480)),U_7481)
      | ~ class_Rings_Oring__1(U_7478) ),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

cnf(f_2212_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_7478),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7479,tc_Int_Oint),U_7480),U_7481)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7479,U_7478),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_7478,U_7479),c_Int_Oring__1__class_Oof__int(U_7478)),U_7480)),U_7481)
    | ~ class_Rings_Oring__1(U_7478) ),
    inference(clausify,[status(thm)],[f_2212_2]) ).

fof(f_2213_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_2213_2,plain,
    ! [U_7486,U_7485,U_7484,U_7483,U_7482] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),hAPP(hAPP(c_COMBS(U_7483,U_7482,U_7482),hAPP(hAPP(c_COMBB(U_7482,tc_fun(U_7482,U_7482),U_7483),c_Groups_Ominus__class_Ominus(U_7482)),U_7484)),U_7485)),U_7486) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7482),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),U_7484),U_7486)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),U_7485),U_7486))
      | ~ class_Groups_Oab__group__add(U_7482) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

cnf(f_2213_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),hAPP(hAPP(c_COMBS(U_7483,U_7482,U_7482),hAPP(hAPP(c_COMBB(U_7482,tc_fun(U_7482,U_7482),U_7483),c_Groups_Ominus__class_Ominus(U_7482)),U_7484)),U_7485)),U_7486) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7482),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),U_7484),U_7486)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7483,U_7482),U_7485),U_7486))
    | ~ class_Groups_Oab__group__add(U_7482) ),
    inference(clausify,[status(thm)],[f_2213_2]) ).

fof(f_2214_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_2214_2,plain,
    ! [U_7491,U_7490,U_7489,U_7488,U_7487] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7488,U_7487)),U_7489),U_7490),U_7491) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7487),hAPP(U_7489,U_7491)),hAPP(U_7490,U_7491))
      | ~ class_Groups_Ominus(U_7487) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

cnf(f_2214_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7488,U_7487)),U_7489),U_7490),U_7491) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7487),hAPP(U_7489,U_7491)),hAPP(U_7490,U_7491))
    | ~ class_Groups_Ominus(U_7487) ),
    inference(clausify,[status(thm)],[f_2214_2]) ).

fof(f_2215_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_2215_2,plain,
    ! [U_7494,U_7493,U_7492] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7493,U_7492),hAPP(c_COMBK(U_7492,U_7493),c_Groups_Ozero__class_Ozero(U_7492))),U_7494) = c_Groups_Ozero__class_Ozero(U_7492)
      | ~ class_Groups_Ocomm__monoid__add(U_7492) ),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

cnf(f_2215_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7493,U_7492),hAPP(c_COMBK(U_7492,U_7493),c_Groups_Ozero__class_Ozero(U_7492))),U_7494) = c_Groups_Ozero__class_Ozero(U_7492)
    | ~ class_Groups_Ocomm__monoid__add(U_7492) ),
    inference(clausify,[status(thm)],[f_2215_2]) ).

fof(f_2216_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_2216_2,plain,
    ! [U_7497,U_7496,U_7495] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7495,tc_Nat_Onat),U_7496),U_7497)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7495,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7495),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7496)),U_7497),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

cnf(f_2216_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7495,tc_Nat_Onat),U_7496),U_7497)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7495,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7495),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7496)),U_7497),
    inference(clausify,[status(thm)],[f_2216_2]) ).

fof(f_2217_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_2217_2,plain,
    ! [U_7501,U_7500,U_7499,U_7498] : hAPP(c_Finite__Set_Ofold__image(U_7498,U_7499,U_7500),U_7501) = c_Finite__Set_Ofold(U_7499,U_7498,hAPP(hAPP(c_COMBB(U_7498,tc_fun(U_7498,U_7498),U_7499),U_7500),U_7501)),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

cnf(f_2217_3,plain,
    hAPP(c_Finite__Set_Ofold__image(U_7498,U_7499,U_7500),U_7501) = c_Finite__Set_Ofold(U_7499,U_7498,hAPP(hAPP(c_COMBB(U_7498,tc_fun(U_7498,U_7498),U_7499),U_7500),U_7501)),
    inference(clausify,[status(thm)],[f_2217_2]) ).

fof(f_2218_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_2218_2,plain,
    ! [U_7506,U_7505,U_7504,U_7503,U_7502] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),hAPP(hAPP(c_COMBS(U_7503,U_7502,U_7502),hAPP(hAPP(c_COMBB(U_7502,tc_fun(U_7502,U_7502),U_7503),c_Groups_Otimes__class_Otimes(U_7502)),U_7504)),U_7505)),U_7506) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7502),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),U_7504),U_7506)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),U_7505),U_7506))
      | ~ class_Groups_Ocomm__monoid__mult(U_7502) ),
    inference(variable_rename,[status(thm)],[f_2218_1]) ).

cnf(f_2218_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),hAPP(hAPP(c_COMBS(U_7503,U_7502,U_7502),hAPP(hAPP(c_COMBB(U_7502,tc_fun(U_7502,U_7502),U_7503),c_Groups_Otimes__class_Otimes(U_7502)),U_7504)),U_7505)),U_7506) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7502),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),U_7504),U_7506)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7503,U_7502),U_7505),U_7506))
    | ~ class_Groups_Ocomm__monoid__mult(U_7502) ),
    inference(clausify,[status(thm)],[f_2218_2]) ).

fof(f_2219_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_2219_2,plain,
    ! [U_7511,U_7510,U_7509,U_7508,U_7507] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7507),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7508,U_7507),U_7509),U_7510)),U_7511) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7508,U_7507),hAPP(hAPP(c_COMBC(U_7508,U_7507,U_7507),hAPP(hAPP(c_COMBB(U_7507,tc_fun(U_7507,U_7507),U_7508),c_Rings_Oinverse__class_Odivide(U_7507)),U_7509)),U_7511)),U_7510)
      | ~ class_Fields_Ofield(U_7507) ),
    inference(variable_rename,[status(thm)],[f_2219_1]) ).

cnf(f_2219_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7507),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7508,U_7507),U_7509),U_7510)),U_7511) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7508,U_7507),hAPP(hAPP(c_COMBC(U_7508,U_7507,U_7507),hAPP(hAPP(c_COMBB(U_7507,tc_fun(U_7507,U_7507),U_7508),c_Rings_Oinverse__class_Odivide(U_7507)),U_7509)),U_7511)),U_7510)
    | ~ class_Fields_Ofield(U_7507) ),
    inference(clausify,[status(thm)],[f_2219_2]) ).

fof(f_2220_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_2220_2,plain,
    ! [U_7513,U_7512] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7512,tc_HOL_Obool)),U_7513))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7512),U_7513),c_Orderings_Obot__class_Obot(tc_fun(U_7512,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7512),U_7513),c_Orderings_Obot__class_Obot(tc_fun(U_7512,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7512,tc_HOL_Obool)),U_7513)) ) ),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

fof(f_2220_3,plain,
    ( ! [U_7517,U_7515] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7515,tc_HOL_Obool)),U_7517))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7515),U_7517),c_Orderings_Obot__class_Obot(tc_fun(U_7515,tc_HOL_Obool)))) )
    & ! [U_7516,U_7514] :
        ( hBOOL(hAPP(hAPP(c_member(U_7514),U_7516),c_Orderings_Obot__class_Obot(tc_fun(U_7514,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7514,tc_HOL_Obool)),U_7516)) ) ),
    inference(miniscope,[status(thm)],[f_2220_2]) ).

cnf(f_2220_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7514),U_7516),c_Orderings_Obot__class_Obot(tc_fun(U_7514,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7514,tc_HOL_Obool)),U_7516)) ),
    inference(clausify,[status(thm)],[f_2220_3]) ).

cnf(f_2220_5,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7515,tc_HOL_Obool)),U_7517))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7515),U_7517),c_Orderings_Obot__class_Obot(tc_fun(U_7515,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2220_3]) ).

fof(f_2221_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_2221_2,plain,
    ! [U_7520,U_7519,U_7518] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7519,U_7518)),U_7520) = c_Orderings_Obot__class_Obot(U_7518)
      | ~ class_Orderings_Obot(U_7518) ),
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

cnf(f_2221_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7519,U_7518)),U_7520) = c_Orderings_Obot__class_Obot(U_7518)
    | ~ class_Orderings_Obot(U_7518) ),
    inference(clausify,[status(thm)],[f_2221_2]) ).

fof(f_2222_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_2222_2,plain,
    ! [U_7524,U_7523,U_7522,U_7521] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7521,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7521,tc_fun(U_7521,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7521)),U_7522)),hAPP(hAPP(c_COMBC(U_7521,tc_fun(U_7521,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7521)),U_7523)),U_7524))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7521),U_7524),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7521,tc_HOL_Obool)),U_7522),U_7523))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7521),U_7524),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7521,tc_HOL_Obool)),U_7522),U_7523)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7521,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7521,tc_fun(U_7521,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7521)),U_7522)),hAPP(hAPP(c_COMBC(U_7521,tc_fun(U_7521,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7521)),U_7523)),U_7524)) ) ),
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

fof(f_2222_3,plain,
    ( ! [U_7532,U_7530,U_7528,U_7526] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7526,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7526,tc_fun(U_7526,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7526)),U_7528)),hAPP(hAPP(c_COMBC(U_7526,tc_fun(U_7526,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7526)),U_7530)),U_7532))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7526),U_7532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7526,tc_HOL_Obool)),U_7528),U_7530))) )
    & ! [U_7531,U_7529,U_7527,U_7525] :
        ( hBOOL(hAPP(hAPP(c_member(U_7525),U_7531),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7525,tc_HOL_Obool)),U_7527),U_7529)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7525,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7525,tc_fun(U_7525,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7525)),U_7527)),hAPP(hAPP(c_COMBC(U_7525,tc_fun(U_7525,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7525)),U_7529)),U_7531)) ) ),
    inference(miniscope,[status(thm)],[f_2222_2]) ).

cnf(f_2222_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7525),U_7531),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7525,tc_HOL_Obool)),U_7527),U_7529)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7525,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7525,tc_fun(U_7525,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7525)),U_7527)),hAPP(hAPP(c_COMBC(U_7525,tc_fun(U_7525,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7525)),U_7529)),U_7531)) ),
    inference(clausify,[status(thm)],[f_2222_3]) ).

cnf(f_2222_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7526,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7526,tc_fun(U_7526,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7526)),U_7528)),hAPP(hAPP(c_COMBC(U_7526,tc_fun(U_7526,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7526)),U_7530)),U_7532))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7526),U_7532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7526,tc_HOL_Obool)),U_7528),U_7530))) ),
    inference(clausify,[status(thm)],[f_2222_3]) ).

fof(f_2223_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_2223_2,plain,
    ! [U_7536,U_7535,U_7534,U_7533] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7533,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7533,tc_fun(U_7533,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7533)),U_7534)),hAPP(hAPP(c_COMBC(U_7533,tc_fun(U_7533,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7533)),U_7535)),U_7536))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7533,tc_HOL_Obool)),U_7534),U_7535))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7533),U_7536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7533,tc_HOL_Obool)),U_7534),U_7535)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7533,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7533,tc_fun(U_7533,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7533)),U_7534)),hAPP(hAPP(c_COMBC(U_7533,tc_fun(U_7533,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7533)),U_7535)),U_7536)) ) ),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

fof(f_2223_3,plain,
    ( ! [U_7544,U_7542,U_7540,U_7538] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7538,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7538,tc_fun(U_7538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7538)),U_7540)),hAPP(hAPP(c_COMBC(U_7538,tc_fun(U_7538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7538)),U_7542)),U_7544))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7538),U_7544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7538,tc_HOL_Obool)),U_7540),U_7542))) )
    & ! [U_7543,U_7541,U_7539,U_7537] :
        ( hBOOL(hAPP(hAPP(c_member(U_7537),U_7543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7537,tc_HOL_Obool)),U_7539),U_7541)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7537,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7537,tc_fun(U_7537,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7537)),U_7539)),hAPP(hAPP(c_COMBC(U_7537,tc_fun(U_7537,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7537)),U_7541)),U_7543)) ) ),
    inference(miniscope,[status(thm)],[f_2223_2]) ).

cnf(f_2223_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7537),U_7543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7537,tc_HOL_Obool)),U_7539),U_7541)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7537,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7537,tc_fun(U_7537,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7537)),U_7539)),hAPP(hAPP(c_COMBC(U_7537,tc_fun(U_7537,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7537)),U_7541)),U_7543)) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

cnf(f_2223_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7538,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_7538,tc_fun(U_7538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7538)),U_7540)),hAPP(hAPP(c_COMBC(U_7538,tc_fun(U_7538,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7538)),U_7542)),U_7544))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7538),U_7544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7538,tc_HOL_Obool)),U_7540),U_7542))) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

fof(f_2224_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_2224_2,plain,
    ! [U_7550,U_7549,U_7548,U_7547,U_7546,U_7545] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7545,tc_fun(U_7546,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7545,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),U_7545),c_COMBC(U_7546,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_prod(U_7545,U_7546)),tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),U_7545),hAPP(c_COMBB(tc_prod(U_7545,U_7546),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool),U_7546),c_member(tc_prod(U_7545,U_7546)))),c_Product__Type_OPair(U_7545,U_7546)))),U_7547)),hAPP(hAPP(c_COMBC(U_7545,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),U_7545),c_COMBC(U_7546,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_prod(U_7545,U_7546)),tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),U_7545),hAPP(c_COMBB(tc_prod(U_7545,U_7546),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool),U_7546),c_member(tc_prod(U_7545,U_7546)))),c_Product__Type_OPair(U_7545,U_7546)))),U_7548)),U_7549),U_7550))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7545,U_7546)),hAPP(hAPP(c_Product__Type_OPair(U_7545,U_7546),U_7549),U_7550)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool)),U_7547),U_7548))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7545,U_7546)),hAPP(hAPP(c_Product__Type_OPair(U_7545,U_7546),U_7549),U_7550)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool)),U_7547),U_7548)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7545,tc_fun(U_7546,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7545,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),U_7545),c_COMBC(U_7546,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_prod(U_7545,U_7546)),tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),U_7545),hAPP(c_COMBB(tc_prod(U_7545,U_7546),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool),U_7546),c_member(tc_prod(U_7545,U_7546)))),c_Product__Type_OPair(U_7545,U_7546)))),U_7547)),hAPP(hAPP(c_COMBC(U_7545,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_fun(U_7546,tc_HOL_Obool)),U_7545),c_COMBC(U_7546,tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7546,tc_prod(U_7545,U_7546)),tc_fun(U_7546,tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool)),U_7545),hAPP(c_COMBB(tc_prod(U_7545,U_7546),tc_fun(tc_fun(tc_prod(U_7545,U_7546),tc_HOL_Obool),tc_HOL_Obool),U_7546),c_member(tc_prod(U_7545,U_7546)))),c_Product__Type_OPair(U_7545,U_7546)))),U_7548)),U_7549),U_7550)) ) ),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

fof(f_2224_3,plain,
    ( ! [U_7562,U_7560,U_7558,U_7556,U_7554,U_7552] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7552,tc_fun(U_7554,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7552,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),U_7552),c_COMBC(U_7554,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_prod(U_7552,U_7554)),tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),U_7552),hAPP(c_COMBB(tc_prod(U_7552,U_7554),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool),U_7554),c_member(tc_prod(U_7552,U_7554)))),c_Product__Type_OPair(U_7552,U_7554)))),U_7556)),hAPP(hAPP(c_COMBC(U_7552,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),U_7552),c_COMBC(U_7554,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_prod(U_7552,U_7554)),tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),U_7552),hAPP(c_COMBB(tc_prod(U_7552,U_7554),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool),U_7554),c_member(tc_prod(U_7552,U_7554)))),c_Product__Type_OPair(U_7552,U_7554)))),U_7558)),U_7560),U_7562))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7552,U_7554)),hAPP(hAPP(c_Product__Type_OPair(U_7552,U_7554),U_7560),U_7562)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool)),U_7556),U_7558))) )
    & ! [U_7561,U_7559,U_7557,U_7555,U_7553,U_7551] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7551,U_7553)),hAPP(hAPP(c_Product__Type_OPair(U_7551,U_7553),U_7559),U_7561)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool)),U_7555),U_7557)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7551,tc_fun(U_7553,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7551,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),U_7551),c_COMBC(U_7553,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_prod(U_7551,U_7553)),tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),U_7551),hAPP(c_COMBB(tc_prod(U_7551,U_7553),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool),U_7553),c_member(tc_prod(U_7551,U_7553)))),c_Product__Type_OPair(U_7551,U_7553)))),U_7555)),hAPP(hAPP(c_COMBC(U_7551,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),U_7551),c_COMBC(U_7553,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_prod(U_7551,U_7553)),tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),U_7551),hAPP(c_COMBB(tc_prod(U_7551,U_7553),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool),U_7553),c_member(tc_prod(U_7551,U_7553)))),c_Product__Type_OPair(U_7551,U_7553)))),U_7557)),U_7559),U_7561)) ) ),
    inference(miniscope,[status(thm)],[f_2224_2]) ).

cnf(f_2224_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7551,U_7553)),hAPP(hAPP(c_Product__Type_OPair(U_7551,U_7553),U_7559),U_7561)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool)),U_7555),U_7557)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7551,tc_fun(U_7553,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7551,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),U_7551),c_COMBC(U_7553,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_prod(U_7551,U_7553)),tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),U_7551),hAPP(c_COMBB(tc_prod(U_7551,U_7553),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool),U_7553),c_member(tc_prod(U_7551,U_7553)))),c_Product__Type_OPair(U_7551,U_7553)))),U_7555)),hAPP(hAPP(c_COMBC(U_7551,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_fun(U_7553,tc_HOL_Obool)),U_7551),c_COMBC(U_7553,tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7553,tc_prod(U_7551,U_7553)),tc_fun(U_7553,tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool)),U_7551),hAPP(c_COMBB(tc_prod(U_7551,U_7553),tc_fun(tc_fun(tc_prod(U_7551,U_7553),tc_HOL_Obool),tc_HOL_Obool),U_7553),c_member(tc_prod(U_7551,U_7553)))),c_Product__Type_OPair(U_7551,U_7553)))),U_7557)),U_7559),U_7561)) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

cnf(f_2224_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7552,tc_fun(U_7554,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7552,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),U_7552),c_COMBC(U_7554,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_prod(U_7552,U_7554)),tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),U_7552),hAPP(c_COMBB(tc_prod(U_7552,U_7554),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool),U_7554),c_member(tc_prod(U_7552,U_7554)))),c_Product__Type_OPair(U_7552,U_7554)))),U_7556)),hAPP(hAPP(c_COMBC(U_7552,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_fun(U_7554,tc_HOL_Obool)),U_7552),c_COMBC(U_7554,tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7554,tc_prod(U_7552,U_7554)),tc_fun(U_7554,tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool)),U_7552),hAPP(c_COMBB(tc_prod(U_7552,U_7554),tc_fun(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool),tc_HOL_Obool),U_7554),c_member(tc_prod(U_7552,U_7554)))),c_Product__Type_OPair(U_7552,U_7554)))),U_7558)),U_7560),U_7562))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7552,U_7554)),hAPP(hAPP(c_Product__Type_OPair(U_7552,U_7554),U_7560),U_7562)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_7552,U_7554),tc_HOL_Obool)),U_7556),U_7558))) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

fof(f_2225_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_2225_2,plain,
    ! [U_7566,U_7565,U_7564,U_7563] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_fun(U_7564,tc_HOL_Obool))),U_7565),U_7566))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7563,U_7564)),hAPP(hAPP(c_Product__Type_OPair(U_7563,U_7564),U_7565),U_7566)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7563,U_7564),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7563,U_7564)),hAPP(hAPP(c_Product__Type_OPair(U_7563,U_7564),U_7565),U_7566)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7563,U_7564),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7563,tc_fun(U_7564,tc_HOL_Obool))),U_7565),U_7566)) ) ),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

fof(f_2225_3,plain,
    ( ! [U_7574,U_7572,U_7570,U_7568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7568,tc_fun(U_7570,tc_HOL_Obool))),U_7572),U_7574))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7568,U_7570)),hAPP(hAPP(c_Product__Type_OPair(U_7568,U_7570),U_7572),U_7574)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7568,U_7570),tc_HOL_Obool)))) )
    & ! [U_7573,U_7571,U_7569,U_7567] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7567,U_7569)),hAPP(hAPP(c_Product__Type_OPair(U_7567,U_7569),U_7571),U_7573)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7567,U_7569),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7567,tc_fun(U_7569,tc_HOL_Obool))),U_7571),U_7573)) ) ),
    inference(miniscope,[status(thm)],[f_2225_2]) ).

cnf(f_2225_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7567,U_7569)),hAPP(hAPP(c_Product__Type_OPair(U_7567,U_7569),U_7571),U_7573)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7567,U_7569),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7567,tc_fun(U_7569,tc_HOL_Obool))),U_7571),U_7573)) ),
    inference(clausify,[status(thm)],[f_2225_3]) ).

cnf(f_2225_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7568,tc_fun(U_7570,tc_HOL_Obool))),U_7572),U_7574))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7568,U_7570)),hAPP(hAPP(c_Product__Type_OPair(U_7568,U_7570),U_7572),U_7574)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7568,U_7570),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2225_3]) ).

fof(f_2226_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_2226_2,plain,
    ! [U_7580,U_7579,U_7578,U_7577,U_7576,U_7575] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7575,tc_fun(U_7576,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7575,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),U_7575),c_COMBC(U_7576,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_prod(U_7575,U_7576)),tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),U_7575),hAPP(c_COMBB(tc_prod(U_7575,U_7576),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool),U_7576),c_member(tc_prod(U_7575,U_7576)))),c_Product__Type_OPair(U_7575,U_7576)))),U_7577)),hAPP(hAPP(c_COMBC(U_7575,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),U_7575),c_COMBC(U_7576,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_prod(U_7575,U_7576)),tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),U_7575),hAPP(c_COMBB(tc_prod(U_7575,U_7576),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool),U_7576),c_member(tc_prod(U_7575,U_7576)))),c_Product__Type_OPair(U_7575,U_7576)))),U_7578)),U_7579),U_7580))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7575,U_7576)),hAPP(hAPP(c_Product__Type_OPair(U_7575,U_7576),U_7579),U_7580)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool)),U_7577),U_7578))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7575,U_7576)),hAPP(hAPP(c_Product__Type_OPair(U_7575,U_7576),U_7579),U_7580)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool)),U_7577),U_7578)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7575,tc_fun(U_7576,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7575,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),U_7575),c_COMBC(U_7576,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_prod(U_7575,U_7576)),tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),U_7575),hAPP(c_COMBB(tc_prod(U_7575,U_7576),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool),U_7576),c_member(tc_prod(U_7575,U_7576)))),c_Product__Type_OPair(U_7575,U_7576)))),U_7577)),hAPP(hAPP(c_COMBC(U_7575,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_fun(U_7576,tc_HOL_Obool)),U_7575),c_COMBC(U_7576,tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7576,tc_prod(U_7575,U_7576)),tc_fun(U_7576,tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool)),U_7575),hAPP(c_COMBB(tc_prod(U_7575,U_7576),tc_fun(tc_fun(tc_prod(U_7575,U_7576),tc_HOL_Obool),tc_HOL_Obool),U_7576),c_member(tc_prod(U_7575,U_7576)))),c_Product__Type_OPair(U_7575,U_7576)))),U_7578)),U_7579),U_7580)) ) ),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

fof(f_2226_3,plain,
    ( ! [U_7592,U_7590,U_7588,U_7586,U_7584,U_7582] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7582,tc_fun(U_7584,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7582,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),U_7582),c_COMBC(U_7584,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_prod(U_7582,U_7584)),tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),U_7582),hAPP(c_COMBB(tc_prod(U_7582,U_7584),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool),U_7584),c_member(tc_prod(U_7582,U_7584)))),c_Product__Type_OPair(U_7582,U_7584)))),U_7586)),hAPP(hAPP(c_COMBC(U_7582,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),U_7582),c_COMBC(U_7584,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_prod(U_7582,U_7584)),tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),U_7582),hAPP(c_COMBB(tc_prod(U_7582,U_7584),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool),U_7584),c_member(tc_prod(U_7582,U_7584)))),c_Product__Type_OPair(U_7582,U_7584)))),U_7588)),U_7590),U_7592))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7582,U_7584)),hAPP(hAPP(c_Product__Type_OPair(U_7582,U_7584),U_7590),U_7592)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool)),U_7586),U_7588))) )
    & ! [U_7591,U_7589,U_7587,U_7585,U_7583,U_7581] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7581,U_7583)),hAPP(hAPP(c_Product__Type_OPair(U_7581,U_7583),U_7589),U_7591)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool)),U_7585),U_7587)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7581,tc_fun(U_7583,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7581,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),U_7581),c_COMBC(U_7583,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_prod(U_7581,U_7583)),tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),U_7581),hAPP(c_COMBB(tc_prod(U_7581,U_7583),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool),U_7583),c_member(tc_prod(U_7581,U_7583)))),c_Product__Type_OPair(U_7581,U_7583)))),U_7585)),hAPP(hAPP(c_COMBC(U_7581,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),U_7581),c_COMBC(U_7583,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_prod(U_7581,U_7583)),tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),U_7581),hAPP(c_COMBB(tc_prod(U_7581,U_7583),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool),U_7583),c_member(tc_prod(U_7581,U_7583)))),c_Product__Type_OPair(U_7581,U_7583)))),U_7587)),U_7589),U_7591)) ) ),
    inference(miniscope,[status(thm)],[f_2226_2]) ).

cnf(f_2226_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7581,U_7583)),hAPP(hAPP(c_Product__Type_OPair(U_7581,U_7583),U_7589),U_7591)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool)),U_7585),U_7587)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7581,tc_fun(U_7583,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7581,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),U_7581),c_COMBC(U_7583,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_prod(U_7581,U_7583)),tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),U_7581),hAPP(c_COMBB(tc_prod(U_7581,U_7583),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool),U_7583),c_member(tc_prod(U_7581,U_7583)))),c_Product__Type_OPair(U_7581,U_7583)))),U_7585)),hAPP(hAPP(c_COMBC(U_7581,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_fun(U_7583,tc_HOL_Obool)),U_7581),c_COMBC(U_7583,tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7583,tc_prod(U_7581,U_7583)),tc_fun(U_7583,tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool)),U_7581),hAPP(c_COMBB(tc_prod(U_7581,U_7583),tc_fun(tc_fun(tc_prod(U_7581,U_7583),tc_HOL_Obool),tc_HOL_Obool),U_7583),c_member(tc_prod(U_7581,U_7583)))),c_Product__Type_OPair(U_7581,U_7583)))),U_7587)),U_7589),U_7591)) ),
    inference(clausify,[status(thm)],[f_2226_3]) ).

cnf(f_2226_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7582,tc_fun(U_7584,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7582,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),U_7582),c_COMBC(U_7584,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_prod(U_7582,U_7584)),tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),U_7582),hAPP(c_COMBB(tc_prod(U_7582,U_7584),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool),U_7584),c_member(tc_prod(U_7582,U_7584)))),c_Product__Type_OPair(U_7582,U_7584)))),U_7586)),hAPP(hAPP(c_COMBC(U_7582,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_fun(U_7584,tc_HOL_Obool)),U_7582),c_COMBC(U_7584,tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7584,tc_prod(U_7582,U_7584)),tc_fun(U_7584,tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool)),U_7582),hAPP(c_COMBB(tc_prod(U_7582,U_7584),tc_fun(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool),tc_HOL_Obool),U_7584),c_member(tc_prod(U_7582,U_7584)))),c_Product__Type_OPair(U_7582,U_7584)))),U_7588)),U_7590),U_7592))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7582,U_7584)),hAPP(hAPP(c_Product__Type_OPair(U_7582,U_7584),U_7590),U_7592)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_7582,U_7584),tc_HOL_Obool)),U_7586),U_7588))) ),
    inference(clausify,[status(thm)],[f_2226_3]) ).

fof(f_2227_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_2227_2,plain,
    ! [U_7598,U_7597,U_7596,U_7595,U_7594,U_7593] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),hAPP(hAPP(c_COMBC(U_7594,tc_fun(U_7595,tc_HOL_Obool),U_7593),hAPP(hAPP(c_COMBB(tc_fun(U_7595,U_7593),tc_fun(tc_fun(U_7595,tc_HOL_Obool),U_7593),U_7594),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7595,U_7593)),U_7596)),U_7597)),U_7598) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7595,U_7593),hAPP(hAPP(c_COMBC(U_7595,tc_fun(U_7594,tc_HOL_Obool),U_7593),hAPP(hAPP(c_COMBB(tc_fun(U_7594,U_7593),tc_fun(tc_fun(U_7594,tc_HOL_Obool),U_7593),U_7595),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593)),hAPP(c_COMBC(U_7594,U_7595,U_7593),U_7596))),U_7598)),U_7597)
      | ~ class_Groups_Ocomm__monoid__add(U_7593) ),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

cnf(f_2227_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),hAPP(hAPP(c_COMBC(U_7594,tc_fun(U_7595,tc_HOL_Obool),U_7593),hAPP(hAPP(c_COMBB(tc_fun(U_7595,U_7593),tc_fun(tc_fun(U_7595,tc_HOL_Obool),U_7593),U_7594),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7595,U_7593)),U_7596)),U_7597)),U_7598) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7595,U_7593),hAPP(hAPP(c_COMBC(U_7595,tc_fun(U_7594,tc_HOL_Obool),U_7593),hAPP(hAPP(c_COMBB(tc_fun(U_7594,U_7593),tc_fun(tc_fun(U_7594,tc_HOL_Obool),U_7593),U_7595),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593)),hAPP(c_COMBC(U_7594,U_7595,U_7593),U_7596))),U_7598)),U_7597)
    | ~ class_Groups_Ocomm__monoid__add(U_7593) ),
    inference(clausify,[status(thm)],[f_2227_2]) ).

fof(f_2228_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_2228_2,plain,
    ! [U_7603,U_7602,U_7601,U_7600,U_7599] :
      ( c_Finite__Set_Ofun__left__comm(U_7602,U_7600,hAPP(hAPP(c_COMBB(U_7599,tc_fun(U_7600,U_7600),U_7602),U_7601),U_7603))
      | ~ c_Finite__Set_Ofun__left__comm(U_7599,U_7600,U_7601) ),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

cnf(f_2228_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_7602,U_7600,hAPP(hAPP(c_COMBB(U_7599,tc_fun(U_7600,U_7600),U_7602),U_7601),U_7603))
    | ~ c_Finite__Set_Ofun__left__comm(U_7599,U_7600,U_7601) ),
    inference(clausify,[status(thm)],[f_2228_2]) ).

fof(f_2229_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_2229_2,plain,
    ! [U_7607,U_7606,U_7605,U_7604] :
      ( ( hAPP(hAPP(c_COMBC(U_7604,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),U_7604),c_COMBC(U_7605,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_prod(U_7604,U_7605)),tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),U_7604),hAPP(c_COMBB(tc_prod(U_7604,U_7605),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool),U_7605),c_member(tc_prod(U_7604,U_7605)))),c_Product__Type_OPair(U_7604,U_7605)))),U_7606) = hAPP(hAPP(c_COMBC(U_7604,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),U_7604),c_COMBC(U_7605,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_prod(U_7604,U_7605)),tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),U_7604),hAPP(c_COMBB(tc_prod(U_7604,U_7605),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool),U_7605),c_member(tc_prod(U_7604,U_7605)))),c_Product__Type_OPair(U_7604,U_7605)))),U_7607)
        | U_7606 != U_7607 )
      & ( U_7606 = U_7607
        | hAPP(hAPP(c_COMBC(U_7604,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),U_7604),c_COMBC(U_7605,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_prod(U_7604,U_7605)),tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),U_7604),hAPP(c_COMBB(tc_prod(U_7604,U_7605),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool),U_7605),c_member(tc_prod(U_7604,U_7605)))),c_Product__Type_OPair(U_7604,U_7605)))),U_7606) != hAPP(hAPP(c_COMBC(U_7604,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_fun(U_7605,tc_HOL_Obool)),U_7604),c_COMBC(U_7605,tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7605,tc_prod(U_7604,U_7605)),tc_fun(U_7605,tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool)),U_7604),hAPP(c_COMBB(tc_prod(U_7604,U_7605),tc_fun(tc_fun(tc_prod(U_7604,U_7605),tc_HOL_Obool),tc_HOL_Obool),U_7605),c_member(tc_prod(U_7604,U_7605)))),c_Product__Type_OPair(U_7604,U_7605)))),U_7607) ) ),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

fof(f_2229_3,plain,
    ( ! [U_7615,U_7613] :
        ( ! [U_7611,U_7609] : hAPP(hAPP(c_COMBC(U_7609,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),U_7609),c_COMBC(U_7611,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_prod(U_7609,U_7611)),tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),U_7609),hAPP(c_COMBB(tc_prod(U_7609,U_7611),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool),U_7611),c_member(tc_prod(U_7609,U_7611)))),c_Product__Type_OPair(U_7609,U_7611)))),U_7613) = hAPP(hAPP(c_COMBC(U_7609,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),U_7609),c_COMBC(U_7611,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_prod(U_7609,U_7611)),tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),U_7609),hAPP(c_COMBB(tc_prod(U_7609,U_7611),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool),U_7611),c_member(tc_prod(U_7609,U_7611)))),c_Product__Type_OPair(U_7609,U_7611)))),U_7615)
        | U_7613 != U_7615 )
    & ! [U_7614,U_7612] :
        ( ! [U_7610,U_7608] : hAPP(hAPP(c_COMBC(U_7608,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),U_7608),c_COMBC(U_7610,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_prod(U_7608,U_7610)),tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),U_7608),hAPP(c_COMBB(tc_prod(U_7608,U_7610),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool),U_7610),c_member(tc_prod(U_7608,U_7610)))),c_Product__Type_OPair(U_7608,U_7610)))),U_7612) != hAPP(hAPP(c_COMBC(U_7608,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),U_7608),c_COMBC(U_7610,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_prod(U_7608,U_7610)),tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),U_7608),hAPP(c_COMBB(tc_prod(U_7608,U_7610),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool),U_7610),c_member(tc_prod(U_7608,U_7610)))),c_Product__Type_OPair(U_7608,U_7610)))),U_7614)
        | U_7612 = U_7614 ) ),
    inference(miniscope,[status(thm)],[f_2229_2]) ).

cnf(f_2229_4,plain,
    ( hAPP(hAPP(c_COMBC(U_7608,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),U_7608),c_COMBC(U_7610,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_prod(U_7608,U_7610)),tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),U_7608),hAPP(c_COMBB(tc_prod(U_7608,U_7610),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool),U_7610),c_member(tc_prod(U_7608,U_7610)))),c_Product__Type_OPair(U_7608,U_7610)))),U_7612) != hAPP(hAPP(c_COMBC(U_7608,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_fun(U_7610,tc_HOL_Obool)),U_7608),c_COMBC(U_7610,tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7610,tc_prod(U_7608,U_7610)),tc_fun(U_7610,tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool)),U_7608),hAPP(c_COMBB(tc_prod(U_7608,U_7610),tc_fun(tc_fun(tc_prod(U_7608,U_7610),tc_HOL_Obool),tc_HOL_Obool),U_7610),c_member(tc_prod(U_7608,U_7610)))),c_Product__Type_OPair(U_7608,U_7610)))),U_7614)
    | U_7612 = U_7614 ),
    inference(clausify,[status(thm)],[f_2229_3]) ).

cnf(f_2229_5,plain,
    ( hAPP(hAPP(c_COMBC(U_7609,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),U_7609),c_COMBC(U_7611,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_prod(U_7609,U_7611)),tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),U_7609),hAPP(c_COMBB(tc_prod(U_7609,U_7611),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool),U_7611),c_member(tc_prod(U_7609,U_7611)))),c_Product__Type_OPair(U_7609,U_7611)))),U_7613) = hAPP(hAPP(c_COMBC(U_7609,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_fun(U_7611,tc_HOL_Obool)),U_7609),c_COMBC(U_7611,tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7611,tc_prod(U_7609,U_7611)),tc_fun(U_7611,tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool)),U_7609),hAPP(c_COMBB(tc_prod(U_7609,U_7611),tc_fun(tc_fun(tc_prod(U_7609,U_7611),tc_HOL_Obool),tc_HOL_Obool),U_7611),c_member(tc_prod(U_7609,U_7611)))),c_Product__Type_OPair(U_7609,U_7611)))),U_7615)
    | U_7613 != U_7615 ),
    inference(clausify,[status(thm)],[f_2229_3]) ).

fof(f_2230_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_2230_2,plain,
    ! [U_7618,U_7617,U_7616] :
      ( ( hAPP(hAPP(c_COMBC(U_7616,tc_fun(U_7616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7616)),U_7617) = hAPP(hAPP(c_COMBC(U_7616,tc_fun(U_7616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7616)),U_7618)
        | U_7617 != U_7618 )
      & ( U_7617 = U_7618
        | hAPP(hAPP(c_COMBC(U_7616,tc_fun(U_7616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7616)),U_7617) != hAPP(hAPP(c_COMBC(U_7616,tc_fun(U_7616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7616)),U_7618) ) ),
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

fof(f_2230_3,plain,
    ( ! [U_7624,U_7622] :
        ( ! [U_7620] : hAPP(hAPP(c_COMBC(U_7620,tc_fun(U_7620,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7620)),U_7622) = hAPP(hAPP(c_COMBC(U_7620,tc_fun(U_7620,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7620)),U_7624)
        | U_7622 != U_7624 )
    & ! [U_7623,U_7621] :
        ( ! [U_7619] : hAPP(hAPP(c_COMBC(U_7619,tc_fun(U_7619,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7619)),U_7621) != hAPP(hAPP(c_COMBC(U_7619,tc_fun(U_7619,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7619)),U_7623)
        | U_7621 = U_7623 ) ),
    inference(miniscope,[status(thm)],[f_2230_2]) ).

cnf(f_2230_4,plain,
    ( hAPP(hAPP(c_COMBC(U_7619,tc_fun(U_7619,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7619)),U_7621) != hAPP(hAPP(c_COMBC(U_7619,tc_fun(U_7619,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7619)),U_7623)
    | U_7621 = U_7623 ),
    inference(clausify,[status(thm)],[f_2230_3]) ).

cnf(f_2230_5,plain,
    ( hAPP(hAPP(c_COMBC(U_7620,tc_fun(U_7620,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7620)),U_7622) = hAPP(hAPP(c_COMBC(U_7620,tc_fun(U_7620,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7620)),U_7624)
    | U_7622 != U_7624 ),
    inference(clausify,[status(thm)],[f_2230_3]) ).

fof(f_2231_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_2231_2,plain,
    ! [U_7629,U_7628,U_7627,U_7626,U_7625] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_7628,U_7626,hAPP(hAPP(c_COMBB(U_7625,tc_fun(U_7626,U_7626),U_7628),U_7627),U_7629))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_7625,U_7626,U_7627) ),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

cnf(f_2231_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_7628,U_7626,hAPP(hAPP(c_COMBB(U_7625,tc_fun(U_7626,U_7626),U_7628),U_7627),U_7629))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_7625,U_7626,U_7627) ),
    inference(clausify,[status(thm)],[f_2231_2]) ).

fof(f_2232_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_2232_2,plain,
    ! [U_7634,U_7633,U_7632,U_7631,U_7630] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7631,U_7630)),U_7632),U_7633),U_7634) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7630),hAPP(U_7632,U_7634)),hAPP(U_7633,U_7634))
      | ~ class_Lattices_Olattice(U_7630) ),
    inference(variable_rename,[status(thm)],[f_2232_1]) ).

cnf(f_2232_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7631,U_7630)),U_7632),U_7633),U_7634) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_7630),hAPP(U_7632,U_7634)),hAPP(U_7633,U_7634))
    | ~ class_Lattices_Olattice(U_7630) ),
    inference(clausify,[status(thm)],[f_2232_2]) ).

fof(f_2233_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_2233_2,plain,
    ! [U_7639,U_7638,U_7637,U_7636,U_7635] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7636,U_7635)),U_7637),U_7638),U_7639) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7635),hAPP(U_7637,U_7639)),hAPP(U_7638,U_7639))
      | ~ class_Lattices_Olattice(U_7635) ),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

cnf(f_2233_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7636,U_7635)),U_7637),U_7638),U_7639) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7635),hAPP(U_7637,U_7639)),hAPP(U_7638,U_7639))
    | ~ class_Lattices_Olattice(U_7635) ),
    inference(clausify,[status(thm)],[f_2233_2]) ).

fof(f_2234_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_2234_2,plain,
    ! [U_7646,U_7645,U_7644,U_7643,U_7642,U_7641,U_7640] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7640),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7641,U_7640),U_7642),U_7643)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7644,U_7640),U_7645),U_7646)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7641,U_7640),hAPP(hAPP(c_COMBC(U_7641,tc_fun(U_7644,tc_HOL_Obool),U_7640),hAPP(hAPP(c_COMBB(tc_fun(U_7644,U_7640),tc_fun(tc_fun(U_7644,tc_HOL_Obool),U_7640),U_7641),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7644,U_7640)),hAPP(hAPP(c_COMBC(U_7641,tc_fun(U_7644,U_7640),tc_fun(U_7644,U_7640)),hAPP(hAPP(c_COMBB(tc_fun(U_7640,U_7640),tc_fun(tc_fun(U_7644,U_7640),tc_fun(U_7644,U_7640)),U_7641),c_COMBB(U_7640,U_7640,U_7644)),hAPP(hAPP(c_COMBB(U_7640,tc_fun(U_7640,U_7640),U_7641),c_Groups_Otimes__class_Otimes(U_7640)),U_7642))),U_7645))),U_7646)),U_7643)
      | ~ class_Rings_Osemiring__0(U_7640) ),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

cnf(f_2234_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7640),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7641,U_7640),U_7642),U_7643)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7644,U_7640),U_7645),U_7646)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7641,U_7640),hAPP(hAPP(c_COMBC(U_7641,tc_fun(U_7644,tc_HOL_Obool),U_7640),hAPP(hAPP(c_COMBB(tc_fun(U_7644,U_7640),tc_fun(tc_fun(U_7644,tc_HOL_Obool),U_7640),U_7641),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7644,U_7640)),hAPP(hAPP(c_COMBC(U_7641,tc_fun(U_7644,U_7640),tc_fun(U_7644,U_7640)),hAPP(hAPP(c_COMBB(tc_fun(U_7640,U_7640),tc_fun(tc_fun(U_7644,U_7640),tc_fun(U_7644,U_7640)),U_7641),c_COMBB(U_7640,U_7640,U_7644)),hAPP(hAPP(c_COMBB(U_7640,tc_fun(U_7640,U_7640),U_7641),c_Groups_Otimes__class_Otimes(U_7640)),U_7642))),U_7645))),U_7646)),U_7643)
    | ~ class_Rings_Osemiring__0(U_7640) ),
    inference(clausify,[status(thm)],[f_2234_2]) ).

fof(f_2235_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_2235_2,plain,
    ! [U_7651,U_7650,U_7649,U_7648,U_7647] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7647),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7648,U_7647),U_7649),U_7650)),U_7651) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7648,U_7647),hAPP(hAPP(c_COMBC(U_7648,U_7647,U_7647),hAPP(hAPP(c_COMBB(U_7647,tc_fun(U_7647,U_7647),U_7648),c_Groups_Otimes__class_Otimes(U_7647)),U_7649)),U_7651)),U_7650)
      | ~ class_Rings_Osemiring__0(U_7647) ),
    inference(variable_rename,[status(thm)],[f_2235_1]) ).

cnf(f_2235_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7647),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7648,U_7647),U_7649),U_7650)),U_7651) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7648,U_7647),hAPP(hAPP(c_COMBC(U_7648,U_7647,U_7647),hAPP(hAPP(c_COMBB(U_7647,tc_fun(U_7647,U_7647),U_7648),c_Groups_Otimes__class_Otimes(U_7647)),U_7649)),U_7651)),U_7650)
    | ~ class_Rings_Osemiring__0(U_7647) ),
    inference(clausify,[status(thm)],[f_2235_2]) ).

fof(f_2236_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_2236_2,plain,
    ! [U_7656,U_7655,U_7654,U_7653,U_7652] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7652),U_7653),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7654,U_7652),U_7655),U_7656)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7654,U_7652),hAPP(hAPP(c_COMBB(U_7652,U_7652,U_7654),hAPP(c_Groups_Otimes__class_Otimes(U_7652),U_7653)),U_7655)),U_7656)
      | ~ class_Rings_Osemiring__0(U_7652) ),
    inference(variable_rename,[status(thm)],[f_2236_1]) ).

cnf(f_2236_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7652),U_7653),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7654,U_7652),U_7655),U_7656)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7654,U_7652),hAPP(hAPP(c_COMBB(U_7652,U_7652,U_7654),hAPP(c_Groups_Otimes__class_Otimes(U_7652),U_7653)),U_7655)),U_7656)
    | ~ class_Rings_Osemiring__0(U_7652) ),
    inference(clausify,[status(thm)],[f_2236_2]) ).

fof(f_2237_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_2237_2,plain,
    ! [U_7660,U_7659,U_7658,U_7657] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7657),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7658,U_7657),U_7659),U_7660)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7658,U_7657),hAPP(hAPP(c_COMBB(U_7657,U_7657,U_7658),c_Groups_Oabs__class_Oabs(U_7657)),U_7659)),U_7660)
      | ~ class_Fields_Olinordered__field(U_7657) ),
    inference(variable_rename,[status(thm)],[f_2237_1]) ).

cnf(f_2237_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7657),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7658,U_7657),U_7659),U_7660)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7658,U_7657),hAPP(hAPP(c_COMBB(U_7657,U_7657,U_7658),c_Groups_Oabs__class_Oabs(U_7657)),U_7659)),U_7660)
    | ~ class_Fields_Olinordered__field(U_7657) ),
    inference(clausify,[status(thm)],[f_2237_2]) ).

fof(f_2238_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_2238_2,plain,
    ! [U_7664,U_7663,U_7662,U_7661] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_7661),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7662,U_7661),hAPP(hAPP(c_COMBB(U_7661,U_7661,U_7662),c_Groups_Oabs__class_Oabs(U_7661)),U_7663)),U_7664)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7662,U_7661),hAPP(hAPP(c_COMBB(U_7661,U_7661,U_7662),c_Groups_Oabs__class_Oabs(U_7661)),U_7663)),U_7664)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_7661) ),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

cnf(f_2238_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_7661),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7662,U_7661),hAPP(hAPP(c_COMBB(U_7661,U_7661,U_7662),c_Groups_Oabs__class_Oabs(U_7661)),U_7663)),U_7664)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7662,U_7661),hAPP(hAPP(c_COMBB(U_7661,U_7661,U_7662),c_Groups_Oabs__class_Oabs(U_7661)),U_7663)),U_7664)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_7661) ),
    inference(clausify,[status(thm)],[f_2238_2]) ).

fof(f_2239_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_2239_2,plain,
    ! [U_7667,U_7666,U_7665] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7666,U_7665),hAPP(c_COMBK(U_7665,U_7666),c_Groups_Oone__class_Oone(U_7665))),U_7667) = c_Groups_Oone__class_Oone(U_7665)
      | ~ class_Groups_Ocomm__monoid__mult(U_7665) ),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

cnf(f_2239_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7666,U_7665),hAPP(c_COMBK(U_7665,U_7666),c_Groups_Oone__class_Oone(U_7665))),U_7667) = c_Groups_Oone__class_Oone(U_7665)
    | ~ class_Groups_Ocomm__monoid__mult(U_7665) ),
    inference(clausify,[status(thm)],[f_2239_2]) ).

fof(f_2240_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_2240_2,plain,
    ! [U_7670,U_7669,U_7668] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7668,tc_Nat_Onat),U_7669),U_7670)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7668,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7668),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7669)),U_7670),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

cnf(f_2240_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7668,tc_Nat_Onat),U_7669),U_7670)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7668,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7668),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7669)),U_7670),
    inference(clausify,[status(thm)],[f_2240_2]) ).

fof(f_2241_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_2241_2,plain,
    ! [U_7674,U_7673,U_7672,U_7671] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7672,U_7671)),U_7673),U_7674) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7671),hAPP(U_7673,U_7674))
      | ~ class_Groups_Ouminus(U_7671) ),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

cnf(f_2241_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7672,U_7671)),U_7673),U_7674) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7671),hAPP(U_7673,U_7674))
    | ~ class_Groups_Ouminus(U_7671) ),
    inference(clausify,[status(thm)],[f_2241_2]) ).

fof(f_2242_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_2242_2,plain,
    ! [U_7678,U_7677,U_7676,U_7675] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7676,U_7675),hAPP(hAPP(c_COMBB(U_7675,U_7675,U_7676),c_Groups_Ouminus__class_Ouminus(U_7675)),U_7677)),U_7678) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7675),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7676,U_7675),U_7677),U_7678))
      | ~ class_Groups_Oab__group__add(U_7675) ),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

cnf(f_2242_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7676,U_7675),hAPP(hAPP(c_COMBB(U_7675,U_7675,U_7676),c_Groups_Ouminus__class_Ouminus(U_7675)),U_7677)),U_7678) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7675),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7676,U_7675),U_7677),U_7678))
    | ~ class_Groups_Oab__group__add(U_7675) ),
    inference(clausify,[status(thm)],[f_2242_2]) ).

fof(f_2243_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_2243_2,plain,
    ! [U_7683,U_7682,U_7681,U_7680,U_7679] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),hAPP(hAPP(c_COMBS(U_7680,U_7679,U_7679),hAPP(hAPP(c_COMBB(U_7679,tc_fun(U_7679,U_7679),U_7680),c_Groups_Otimes__class_Otimes(U_7679)),U_7682)),U_7683)),U_7681) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7679),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),U_7682),U_7681)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),U_7683),U_7681))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7680),U_7681))
      | ~ class_Groups_Ocomm__monoid__mult(U_7679) ),
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

cnf(f_2243_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),hAPP(hAPP(c_COMBS(U_7680,U_7679,U_7679),hAPP(hAPP(c_COMBB(U_7679,tc_fun(U_7679,U_7679),U_7680),c_Groups_Otimes__class_Otimes(U_7679)),U_7682)),U_7683)),U_7681) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7679),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),U_7682),U_7681)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7680,U_7679),U_7683),U_7681))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7680),U_7681))
    | ~ class_Groups_Ocomm__monoid__mult(U_7679) ),
    inference(clausify,[status(thm)],[f_2243_2]) ).

fof(f_2244_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_2244_2,plain,
    ! [U_7684] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7684) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7684)),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

cnf(f_2244_3,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7684) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7684)),
    inference(clausify,[status(thm)],[f_2244_2]) ).

fof(f_2245_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_2245_2,plain,
    ! [U_7685] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7685)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7685)),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_2245_1]) ).

cnf(f_2245_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7685)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7685)),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_2245_2]) ).

fof(f_2246_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_2246_2,plain,
    ! [U_7690,U_7689,U_7688,U_7687,U_7686] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),hAPP(hAPP(c_COMBS(U_7687,U_7686,U_7686),hAPP(hAPP(c_COMBB(U_7686,tc_fun(U_7686,U_7686),U_7687),c_Rings_Oinverse__class_Odivide(U_7686)),U_7689)),U_7690)),U_7688) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),U_7689),U_7688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),U_7690),U_7688))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7688))
      | ~ class_Fields_Ofield__inverse__zero(U_7686) ),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

cnf(f_2246_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),hAPP(hAPP(c_COMBS(U_7687,U_7686,U_7686),hAPP(hAPP(c_COMBB(U_7686,tc_fun(U_7686,U_7686),U_7687),c_Rings_Oinverse__class_Odivide(U_7686)),U_7689)),U_7690)),U_7688) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),U_7689),U_7688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7687,U_7686),U_7690),U_7688))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7688))
    | ~ class_Fields_Ofield__inverse__zero(U_7686) ),
    inference(clausify,[status(thm)],[f_2246_2]) ).

fof(f_2247_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_2247_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_2247_1]) ).

fof(f_2248_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_2248_2,plain,
    ! [U_7694,U_7693,U_7692,U_7691] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7692,tc_Nat_Onat),U_7693),U_7694)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7692,U_7691),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7691,U_7692),c_Nat_Osemiring__1__class_Oof__nat(U_7691)),U_7693)),U_7694)
      | ~ class_Rings_Osemiring__1(U_7691) ),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

cnf(f_2248_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7692,tc_Nat_Onat),U_7693),U_7694)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7692,U_7691),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7691,U_7692),c_Nat_Osemiring__1__class_Oof__nat(U_7691)),U_7693)),U_7694)
    | ~ class_Rings_Osemiring__1(U_7691) ),
    inference(clausify,[status(thm)],[f_2248_2]) ).

fof(f_2249_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_2249_2,plain,
    ! [U_7697,U_7696,U_7695] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7695,tc_Nat_Onat),U_7696),U_7697) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7695,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7695),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7696)),U_7697)),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

cnf(f_2249_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7695,tc_Nat_Onat),U_7696),U_7697) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7695,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7695),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7696)),U_7697)),
    inference(clausify,[status(thm)],[f_2249_2]) ).

fof(f_2250_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_2250_2,plain,
    ! [U_7699,U_7698] : hAPP(c_Finite__Set_Ocard(U_7698),U_7699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7698,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_7698),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_7699),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

cnf(f_2250_3,plain,
    hAPP(c_Finite__Set_Ocard(U_7698),U_7699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7698,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_7698),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_7699),
    inference(clausify,[status(thm)],[f_2250_2]) ).

fof(f_2251_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_2251_2,plain,
    ! [U_7703,U_7702,U_7701,U_7700] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7700),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7701,tc_Nat_Onat),U_7702),U_7703)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7701,U_7700),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7700,U_7701),c_Nat_Osemiring__1__class_Oof__nat(U_7700)),U_7702)),U_7703)
      | ~ class_Rings_Osemiring__1(U_7700)
      | ~ class_Groups_Ocomm__monoid__mult(U_7700) ),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

cnf(f_2251_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7700),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7701,tc_Nat_Onat),U_7702),U_7703)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7701,U_7700),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7700,U_7701),c_Nat_Osemiring__1__class_Oof__nat(U_7700)),U_7702)),U_7703)
    | ~ class_Rings_Osemiring__1(U_7700)
    | ~ class_Groups_Ocomm__monoid__mult(U_7700) ),
    inference(clausify,[status(thm)],[f_2251_2]) ).

fof(f_2252_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_2252_2,plain,
    ! [U_7706,U_7705,U_7704] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7704,tc_Nat_Onat),U_7705),U_7706) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7704,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7704),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7705)),U_7706)),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

cnf(f_2252_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7704,tc_Nat_Onat),U_7705),U_7706) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7704,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7704),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7705)),U_7706)),
    inference(clausify,[status(thm)],[f_2252_2]) ).

fof(f_2253_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_2253_2,plain,
    ! [U_7711,U_7710,U_7709,U_7708,U_7707] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7708,U_7707),hAPP(hAPP(c_COMBC(U_7708,U_7707,U_7707),hAPP(hAPP(c_COMBS(U_7708,U_7707,tc_fun(U_7707,U_7707)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7707,tc_fun(U_7707,U_7707)),U_7708),c_If(U_7707)),hAPP(hAPP(c_COMBC(U_7708,U_7708,tc_HOL_Obool),c_fequal),U_7710))),U_7711)),c_Groups_Ozero__class_Ozero(U_7707))),U_7709) = c_Groups_Ozero__class_Ozero(U_7707)
          | hBOOL(hAPP(hAPP(c_member(U_7708),U_7710),U_7709)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7708,U_7707),hAPP(hAPP(c_COMBC(U_7708,U_7707,U_7707),hAPP(hAPP(c_COMBS(U_7708,U_7707,tc_fun(U_7707,U_7707)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7707,tc_fun(U_7707,U_7707)),U_7708),c_If(U_7707)),hAPP(hAPP(c_COMBC(U_7708,U_7708,tc_HOL_Obool),c_fequal),U_7710))),U_7711)),c_Groups_Ozero__class_Ozero(U_7707))),U_7709) = hAPP(U_7711,U_7710)
          | ~ hBOOL(hAPP(hAPP(c_member(U_7708),U_7710),U_7709)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7708),U_7709))
      | ~ class_Groups_Ocomm__monoid__add(U_7707) ),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

cnf(f_2253_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7708,U_7707),hAPP(hAPP(c_COMBC(U_7708,U_7707,U_7707),hAPP(hAPP(c_COMBS(U_7708,U_7707,tc_fun(U_7707,U_7707)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7707,tc_fun(U_7707,U_7707)),U_7708),c_If(U_7707)),hAPP(hAPP(c_COMBC(U_7708,U_7708,tc_HOL_Obool),c_fequal),U_7710))),U_7711)),c_Groups_Ozero__class_Ozero(U_7707))),U_7709) = hAPP(U_7711,U_7710)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7708),U_7710),U_7709))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7708),U_7709))
    | ~ class_Groups_Ocomm__monoid__add(U_7707) ),
    inference(clausify,[status(thm)],[f_2253_2]) ).

cnf(f_2253_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7708,U_7707),hAPP(hAPP(c_COMBC(U_7708,U_7707,U_7707),hAPP(hAPP(c_COMBS(U_7708,U_7707,tc_fun(U_7707,U_7707)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7707,tc_fun(U_7707,U_7707)),U_7708),c_If(U_7707)),hAPP(hAPP(c_COMBC(U_7708,U_7708,tc_HOL_Obool),c_fequal),U_7710))),U_7711)),c_Groups_Ozero__class_Ozero(U_7707))),U_7709) = c_Groups_Ozero__class_Ozero(U_7707)
    | hBOOL(hAPP(hAPP(c_member(U_7708),U_7710),U_7709))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7708),U_7709))
    | ~ class_Groups_Ocomm__monoid__add(U_7707) ),
    inference(clausify,[status(thm)],[f_2253_2]) ).

fof(f_2254_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_2254_2,plain,
    ! [U_7716,U_7715,U_7714,U_7713,U_7712] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7713,U_7712),hAPP(hAPP(c_COMBC(U_7713,U_7712,U_7712),hAPP(hAPP(c_COMBS(U_7713,U_7712,tc_fun(U_7712,U_7712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7712,tc_fun(U_7712,U_7712)),U_7713),c_If(U_7712)),hAPP(c_fequal,U_7715))),U_7716)),c_Groups_Ozero__class_Ozero(U_7712))),U_7714) = c_Groups_Ozero__class_Ozero(U_7712)
          | hBOOL(hAPP(hAPP(c_member(U_7713),U_7715),U_7714)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7713,U_7712),hAPP(hAPP(c_COMBC(U_7713,U_7712,U_7712),hAPP(hAPP(c_COMBS(U_7713,U_7712,tc_fun(U_7712,U_7712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7712,tc_fun(U_7712,U_7712)),U_7713),c_If(U_7712)),hAPP(c_fequal,U_7715))),U_7716)),c_Groups_Ozero__class_Ozero(U_7712))),U_7714) = hAPP(U_7716,U_7715)
          | ~ hBOOL(hAPP(hAPP(c_member(U_7713),U_7715),U_7714)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),U_7714))
      | ~ class_Groups_Ocomm__monoid__add(U_7712) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

cnf(f_2254_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7713,U_7712),hAPP(hAPP(c_COMBC(U_7713,U_7712,U_7712),hAPP(hAPP(c_COMBS(U_7713,U_7712,tc_fun(U_7712,U_7712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7712,tc_fun(U_7712,U_7712)),U_7713),c_If(U_7712)),hAPP(c_fequal,U_7715))),U_7716)),c_Groups_Ozero__class_Ozero(U_7712))),U_7714) = hAPP(U_7716,U_7715)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7713),U_7715),U_7714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),U_7714))
    | ~ class_Groups_Ocomm__monoid__add(U_7712) ),
    inference(clausify,[status(thm)],[f_2254_2]) ).

cnf(f_2254_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7713,U_7712),hAPP(hAPP(c_COMBC(U_7713,U_7712,U_7712),hAPP(hAPP(c_COMBS(U_7713,U_7712,tc_fun(U_7712,U_7712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7712,tc_fun(U_7712,U_7712)),U_7713),c_If(U_7712)),hAPP(c_fequal,U_7715))),U_7716)),c_Groups_Ozero__class_Ozero(U_7712))),U_7714) = c_Groups_Ozero__class_Ozero(U_7712)
    | hBOOL(hAPP(hAPP(c_member(U_7713),U_7715),U_7714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),U_7714))
    | ~ class_Groups_Ocomm__monoid__add(U_7712) ),
    inference(clausify,[status(thm)],[f_2254_2]) ).

fof(f_2255_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_2255_2,plain,
    ! [U_7721,U_7720,U_7719,U_7718,U_7717] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7718,U_7717),hAPP(hAPP(c_COMBC(U_7718,U_7717,U_7717),hAPP(hAPP(c_COMBS(U_7718,U_7717,tc_fun(U_7717,U_7717)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7717,tc_fun(U_7717,U_7717)),U_7718),c_If(U_7717)),hAPP(c_fequal,U_7720))),U_7721)),c_Groups_Oone__class_Oone(U_7717))),U_7719) = c_Groups_Oone__class_Oone(U_7717)
          | hBOOL(hAPP(hAPP(c_member(U_7718),U_7720),U_7719)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7718,U_7717),hAPP(hAPP(c_COMBC(U_7718,U_7717,U_7717),hAPP(hAPP(c_COMBS(U_7718,U_7717,tc_fun(U_7717,U_7717)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7717,tc_fun(U_7717,U_7717)),U_7718),c_If(U_7717)),hAPP(c_fequal,U_7720))),U_7721)),c_Groups_Oone__class_Oone(U_7717))),U_7719) = hAPP(U_7721,U_7720)
          | ~ hBOOL(hAPP(hAPP(c_member(U_7718),U_7720),U_7719)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),U_7719))
      | ~ class_Groups_Ocomm__monoid__mult(U_7717) ),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

cnf(f_2255_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7718,U_7717),hAPP(hAPP(c_COMBC(U_7718,U_7717,U_7717),hAPP(hAPP(c_COMBS(U_7718,U_7717,tc_fun(U_7717,U_7717)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7717,tc_fun(U_7717,U_7717)),U_7718),c_If(U_7717)),hAPP(c_fequal,U_7720))),U_7721)),c_Groups_Oone__class_Oone(U_7717))),U_7719) = hAPP(U_7721,U_7720)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7718),U_7720),U_7719))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),U_7719))
    | ~ class_Groups_Ocomm__monoid__mult(U_7717) ),
    inference(clausify,[status(thm)],[f_2255_2]) ).

cnf(f_2255_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7718,U_7717),hAPP(hAPP(c_COMBC(U_7718,U_7717,U_7717),hAPP(hAPP(c_COMBS(U_7718,U_7717,tc_fun(U_7717,U_7717)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7717,tc_fun(U_7717,U_7717)),U_7718),c_If(U_7717)),hAPP(c_fequal,U_7720))),U_7721)),c_Groups_Oone__class_Oone(U_7717))),U_7719) = c_Groups_Oone__class_Oone(U_7717)
    | hBOOL(hAPP(hAPP(c_member(U_7718),U_7720),U_7719))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),U_7719))
    | ~ class_Groups_Ocomm__monoid__mult(U_7717) ),
    inference(clausify,[status(thm)],[f_2255_2]) ).

fof(f_2256_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_2256_2,plain,
    ! [U_7726,U_7725,U_7724,U_7723,U_7722] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7723,U_7722),hAPP(hAPP(c_COMBC(U_7723,U_7722,U_7722),hAPP(hAPP(c_COMBS(U_7723,U_7722,tc_fun(U_7722,U_7722)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7722,tc_fun(U_7722,U_7722)),U_7723),c_If(U_7722)),hAPP(hAPP(c_COMBC(U_7723,U_7723,tc_HOL_Obool),c_fequal),U_7725))),U_7726)),c_Groups_Oone__class_Oone(U_7722))),U_7724) = c_Groups_Oone__class_Oone(U_7722)
          | hBOOL(hAPP(hAPP(c_member(U_7723),U_7725),U_7724)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7723,U_7722),hAPP(hAPP(c_COMBC(U_7723,U_7722,U_7722),hAPP(hAPP(c_COMBS(U_7723,U_7722,tc_fun(U_7722,U_7722)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7722,tc_fun(U_7722,U_7722)),U_7723),c_If(U_7722)),hAPP(hAPP(c_COMBC(U_7723,U_7723,tc_HOL_Obool),c_fequal),U_7725))),U_7726)),c_Groups_Oone__class_Oone(U_7722))),U_7724) = hAPP(U_7726,U_7725)
          | ~ hBOOL(hAPP(hAPP(c_member(U_7723),U_7725),U_7724)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7723),U_7724))
      | ~ class_Groups_Ocomm__monoid__mult(U_7722) ),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

cnf(f_2256_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7723,U_7722),hAPP(hAPP(c_COMBC(U_7723,U_7722,U_7722),hAPP(hAPP(c_COMBS(U_7723,U_7722,tc_fun(U_7722,U_7722)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7722,tc_fun(U_7722,U_7722)),U_7723),c_If(U_7722)),hAPP(hAPP(c_COMBC(U_7723,U_7723,tc_HOL_Obool),c_fequal),U_7725))),U_7726)),c_Groups_Oone__class_Oone(U_7722))),U_7724) = hAPP(U_7726,U_7725)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7723),U_7725),U_7724))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7723),U_7724))
    | ~ class_Groups_Ocomm__monoid__mult(U_7722) ),
    inference(clausify,[status(thm)],[f_2256_2]) ).

cnf(f_2256_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7723,U_7722),hAPP(hAPP(c_COMBC(U_7723,U_7722,U_7722),hAPP(hAPP(c_COMBS(U_7723,U_7722,tc_fun(U_7722,U_7722)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7722,tc_fun(U_7722,U_7722)),U_7723),c_If(U_7722)),hAPP(hAPP(c_COMBC(U_7723,U_7723,tc_HOL_Obool),c_fequal),U_7725))),U_7726)),c_Groups_Oone__class_Oone(U_7722))),U_7724) = c_Groups_Oone__class_Oone(U_7722)
    | hBOOL(hAPP(hAPP(c_member(U_7723),U_7725),U_7724))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7723),U_7724))
    | ~ class_Groups_Ocomm__monoid__mult(U_7722) ),
    inference(clausify,[status(thm)],[f_2256_2]) ).

fof(f_2257_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_2257_2,plain,
    ! [U_7730,U_7729,U_7728,U_7727] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7728,U_7727),hAPP(c_COMBK(U_7727,U_7728),U_7729)),U_7730) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7727),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7727),hAPP(c_Finite__Set_Ocard(U_7728),U_7730))),U_7729)
      | ~ class_Rings_Osemiring__1(U_7727) ),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

cnf(f_2257_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7728,U_7727),hAPP(c_COMBK(U_7727,U_7728),U_7729)),U_7730) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7727),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7727),hAPP(c_Finite__Set_Ocard(U_7728),U_7730))),U_7729)
    | ~ class_Rings_Osemiring__1(U_7727) ),
    inference(clausify,[status(thm)],[f_2257_2]) ).

fof(f_2258_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_2258_2,plain,
    ! [U_7733,U_7732,U_7731] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7731),U_7732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7733))) = hAPP(hAPP(c_HOL_OLet(U_7731,U_7731),hAPP(hAPP(c_Power_Opower__class_Opower(U_7731),U_7732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7733))),hAPP(hAPP(c_COMBS(U_7731,U_7731,U_7731),c_Groups_Otimes__class_Otimes(U_7731)),c_COMBI(U_7731)))
      | ~ class_Int_Onumber__ring(U_7731) ),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

cnf(f_2258_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7731),U_7732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7733))) = hAPP(hAPP(c_HOL_OLet(U_7731,U_7731),hAPP(hAPP(c_Power_Opower__class_Opower(U_7731),U_7732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7733))),hAPP(hAPP(c_COMBS(U_7731,U_7731,U_7731),c_Groups_Otimes__class_Otimes(U_7731)),c_COMBI(U_7731)))
    | ~ class_Int_Onumber__ring(U_7731) ),
    inference(clausify,[status(thm)],[f_2258_2]) ).

fof(f_2259_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_2259_2,plain,
    ! [U_7738,U_7737,U_7736,U_7735,U_7734] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),hAPP(hAPP(c_COMBS(U_7735,U_7734,U_7734),hAPP(hAPP(c_COMBB(U_7734,tc_fun(U_7734,U_7734),U_7735),c_Groups_Otimes__class_Otimes(U_7734)),U_7737)),U_7738)),c_Groups_Oone__class_Oone(U_7734)),U_7736) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7734),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),U_7737),c_Groups_Oone__class_Oone(U_7734)),U_7736)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),U_7738),c_Groups_Oone__class_Oone(U_7734)),U_7736))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7735),U_7736))
      | ~ class_Groups_Ocomm__monoid__mult(U_7734) ),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

cnf(f_2259_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),hAPP(hAPP(c_COMBS(U_7735,U_7734,U_7734),hAPP(hAPP(c_COMBB(U_7734,tc_fun(U_7734,U_7734),U_7735),c_Groups_Otimes__class_Otimes(U_7734)),U_7737)),U_7738)),c_Groups_Oone__class_Oone(U_7734)),U_7736) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7734),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),U_7737),c_Groups_Oone__class_Oone(U_7734)),U_7736)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7734,U_7735,c_Groups_Otimes__class_Otimes(U_7734)),U_7738),c_Groups_Oone__class_Oone(U_7734)),U_7736))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7735),U_7736))
    | ~ class_Groups_Ocomm__monoid__mult(U_7734) ),
    inference(clausify,[status(thm)],[f_2259_2]) ).

fof(f_2260_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_2260_2,plain,
    ! [U_7742,U_7741,U_7740,U_7739] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7740,U_7739),hAPP(c_COMBK(U_7739,U_7740),U_7742)),U_7741) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7739),U_7742),hAPP(c_Finite__Set_Ocard(U_7740),U_7741))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7740),U_7741))
      | ~ class_Groups_Ocomm__monoid__mult(U_7739) ),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

cnf(f_2260_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7740,U_7739),hAPP(c_COMBK(U_7739,U_7740),U_7742)),U_7741) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7739),U_7742),hAPP(c_Finite__Set_Ocard(U_7740),U_7741))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7740),U_7741))
    | ~ class_Groups_Ocomm__monoid__mult(U_7739) ),
    inference(clausify,[status(thm)],[f_2260_2]) ).

fof(f_2261_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_2261_2,plain,
    ! [U_7744,U_7743] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7744))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744))),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_2261_1]) ).

cnf(f_2261_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7744))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7743),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7744))),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_2261_2]) ).

fof(f_2262_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_2262_2,plain,
    ! [U_7747,U_7746,U_7745] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_7745,hAPP(hAPP(c_COMBC(U_7745,tc_fun(U_7745,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7745)),U_7746)),U_7747))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7745,tc_HOL_Obool)),U_7747),hAPP(c_Set_OPow(U_7745),U_7746))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7745,tc_HOL_Obool)),U_7747),hAPP(c_Set_OPow(U_7745),U_7746)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7745,hAPP(hAPP(c_COMBC(U_7745,tc_fun(U_7745,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7745)),U_7746)),U_7747)) ) ),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

fof(f_2262_3,plain,
    ( ! [U_7753,U_7751,U_7749] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_7749,hAPP(hAPP(c_COMBC(U_7749,tc_fun(U_7749,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7749)),U_7751)),U_7753))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7749,tc_HOL_Obool)),U_7753),hAPP(c_Set_OPow(U_7749),U_7751))) )
    & ! [U_7752,U_7750,U_7748] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7748,tc_HOL_Obool)),U_7752),hAPP(c_Set_OPow(U_7748),U_7750)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7748,hAPP(hAPP(c_COMBC(U_7748,tc_fun(U_7748,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7748)),U_7750)),U_7752)) ) ),
    inference(miniscope,[status(thm)],[f_2262_2]) ).

cnf(f_2262_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7748,tc_HOL_Obool)),U_7752),hAPP(c_Set_OPow(U_7748),U_7750)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7748,hAPP(hAPP(c_COMBC(U_7748,tc_fun(U_7748,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7748)),U_7750)),U_7752)) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

cnf(f_2262_5,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_7749,hAPP(hAPP(c_COMBC(U_7749,tc_fun(U_7749,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7749)),U_7751)),U_7753))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_7749,tc_HOL_Obool)),U_7753),hAPP(c_Set_OPow(U_7749),U_7751))) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

fof(f_2263_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_2263_2,plain,
    ! [U_7758,U_7757,U_7756,U_7755,U_7754] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7755,U_7754),U_7757),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7755,tc_HOL_Obool)),U_7756),U_7758)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7755,U_7754),hAPP(hAPP(c_COMBC(U_7755,U_7754,U_7754),hAPP(hAPP(c_COMBS(U_7755,U_7754,tc_fun(U_7754,U_7754)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7754,tc_fun(U_7754,U_7754)),U_7755),c_If(U_7754)),hAPP(hAPP(c_COMBC(U_7755,tc_fun(U_7755,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7755)),U_7758))),U_7757)),c_Groups_Ozero__class_Ozero(U_7754))),U_7756)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7755),U_7756))
      | ~ class_Groups_Ocomm__monoid__add(U_7754) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

cnf(f_2263_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7755,U_7754),U_7757),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7755,tc_HOL_Obool)),U_7756),U_7758)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7755,U_7754),hAPP(hAPP(c_COMBC(U_7755,U_7754,U_7754),hAPP(hAPP(c_COMBS(U_7755,U_7754,tc_fun(U_7754,U_7754)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7754,tc_fun(U_7754,U_7754)),U_7755),c_If(U_7754)),hAPP(hAPP(c_COMBC(U_7755,tc_fun(U_7755,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7755)),U_7758))),U_7757)),c_Groups_Ozero__class_Ozero(U_7754))),U_7756)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7755),U_7756))
    | ~ class_Groups_Ocomm__monoid__add(U_7754) ),
    inference(clausify,[status(thm)],[f_2263_2]) ).

fof(f_2264_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_2264_2,plain,
    ! [U_7761,U_7760,U_7759] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7759),hAPP(c_Int_Onumber__class_Onumber__of(U_7759),U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7761))) = hAPP(hAPP(c_HOL_OLet(U_7759,U_7759),hAPP(hAPP(c_Power_Opower__class_Opower(U_7759),hAPP(c_Int_Onumber__class_Onumber__of(U_7759),U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7761))),hAPP(hAPP(c_COMBS(U_7759,U_7759,U_7759),c_Groups_Otimes__class_Otimes(U_7759)),c_COMBI(U_7759)))
      | ~ class_Int_Onumber__ring(U_7759) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

cnf(f_2264_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7759),hAPP(c_Int_Onumber__class_Onumber__of(U_7759),U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_7761))) = hAPP(hAPP(c_HOL_OLet(U_7759,U_7759),hAPP(hAPP(c_Power_Opower__class_Opower(U_7759),hAPP(c_Int_Onumber__class_Onumber__of(U_7759),U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7761))),hAPP(hAPP(c_COMBS(U_7759,U_7759,U_7759),c_Groups_Otimes__class_Otimes(U_7759)),c_COMBI(U_7759)))
    | ~ class_Int_Onumber__ring(U_7759) ),
    inference(clausify,[status(thm)],[f_2264_2]) ).

fof(f_2265_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_2265_2,plain,
    ! [U_7763,U_7762] :
      ( hAPP(c_Finite__Set_Ocard(U_7762),U_7763) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_7762,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_7762),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7763)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7762),U_7763)) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

cnf(f_2265_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7762),U_7763) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_7762,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_7762),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7763)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7762),U_7763)) ),
    inference(clausify,[status(thm)],[f_2265_2]) ).

fof(f_2266_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_2266_2,plain,
    ! [U_7765,U_7764] :
      ( ( hAPP(c_Finite__Set_Ocard(U_7764),U_7765) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_7764),U_7765)) )
      & ( hAPP(c_Finite__Set_Ocard(U_7764),U_7765) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_7764,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_7764),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7765)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7764),U_7765)) ) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

fof(f_2266_3,plain,
    ( ! [U_7769,U_7767] :
        ( hAPP(c_Finite__Set_Ocard(U_7767),U_7769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_7767),U_7769)) )
    & ! [U_7768,U_7766] :
        ( hAPP(c_Finite__Set_Ocard(U_7766),U_7768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_7766,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_7766),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7768)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7766),U_7768)) ) ),
    inference(miniscope,[status(thm)],[f_2266_2]) ).

cnf(f_2266_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7766),U_7768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_7766,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_7766),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7768)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7766),U_7768)) ),
    inference(clausify,[status(thm)],[f_2266_3]) ).

cnf(f_2266_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_7767),U_7769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_7767),U_7769)) ),
    inference(clausify,[status(thm)],[f_2266_3]) ).

fof(f_2267_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_2267_2,plain,
    ! [U_7770] : c_Finite__Set_Ofun__left__comm__idem(U_7770,tc_fun(U_7770,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7770,tc_HOL_Obool),tc_fun(tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),U_7770),hAPP(c_COMBC(tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_7770,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_7770,tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),c_Set_Oinsert(U_7770)),c_Orderings_Obot__class_Obot(tc_fun(U_7770,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

cnf(f_2267_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_7770,tc_fun(U_7770,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7770,tc_HOL_Obool),tc_fun(tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),U_7770),hAPP(c_COMBC(tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_7770,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_7770,tc_fun(U_7770,tc_HOL_Obool),tc_fun(U_7770,tc_HOL_Obool)),c_Set_Oinsert(U_7770)),c_Orderings_Obot__class_Obot(tc_fun(U_7770,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2267_2]) ).

fof(f_2268_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_2268_2,plain,
    ! [U_7772,U_7771] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7772)),hAPP(c_Int_Onat,U_7771)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7772),U_7771)),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_7771)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7772)),hAPP(c_Int_Onat,U_7771)) = hAPP(c_Int_Onat,U_7772)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7771)) ) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

fof(f_2268_3,plain,
    ( ! [U_7776,U_7774] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7776)),hAPP(c_Int_Onat,U_7774)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7776),U_7774)),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_7774)) )
    & ! [U_7775,U_7773] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7775)),hAPP(c_Int_Onat,U_7773)) = hAPP(c_Int_Onat,U_7775)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7773)) ) ),
    inference(miniscope,[status(thm)],[f_2268_2]) ).

cnf(f_2268_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7775)),hAPP(c_Int_Onat,U_7773)) = hAPP(c_Int_Onat,U_7775)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7773)) ),
    inference(clausify,[status(thm)],[f_2268_3]) ).

cnf(f_2268_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7776)),hAPP(c_Int_Onat,U_7774)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7776),U_7774)),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_7774)) ),
    inference(clausify,[status(thm)],[f_2268_3]) ).

fof(f_2269_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_2269_2,plain,
    ! [U_7778,U_7777] :
      ( c_Divides_OnegDivAlg(U_7777,U_7778) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7777),U_7778)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7777,U_7778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

cnf(f_2269_3,plain,
    ( c_Divides_OnegDivAlg(U_7777,U_7778) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7777),U_7778)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7777,U_7778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2269_2]) ).

fof(f_2270_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_2270_2,plain,
    ! [U_7779] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_7779) = 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_7779),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

cnf(f_2270_3,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_7779) = 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_7779),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2270_2]) ).

fof(f_2271_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_2271_2,plain,
    ! [U_7782,U_7781,U_7780] : hAPP(c_Divides_Oadjust(U_7780),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_7781),U_7782)) = 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_7782),U_7780)),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_7781)),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_7781)),U_7782))),
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

cnf(f_2271_3,plain,
    hAPP(c_Divides_Oadjust(U_7780),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_7781),U_7782)) = 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_7782),U_7780)),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_7781)),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_7781)),U_7782))),
    inference(clausify,[status(thm)],[f_2271_2]) ).

fof(f_2272_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_2272_2,plain,
    ! [U_7785,U_7784,U_7783] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7783,tc_HOL_Obool)),U_7785),U_7784) = hAPP(hAPP(c_Finite__Set_Ofold(U_7783,tc_fun(U_7783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7783,tc_HOL_Obool),tc_fun(tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),U_7783),hAPP(c_COMBC(tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_7783,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_7783,tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),c_Set_Oinsert(U_7783)),c_Orderings_Obot__class_Obot(tc_fun(U_7783,tc_HOL_Obool))))),U_7785),U_7784)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7783),U_7784)) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

cnf(f_2272_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7783,tc_HOL_Obool)),U_7785),U_7784) = hAPP(hAPP(c_Finite__Set_Ofold(U_7783,tc_fun(U_7783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7783,tc_HOL_Obool),tc_fun(tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),U_7783),hAPP(c_COMBC(tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_7783,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_7783,tc_fun(U_7783,tc_HOL_Obool),tc_fun(U_7783,tc_HOL_Obool)),c_Set_Oinsert(U_7783)),c_Orderings_Obot__class_Obot(tc_fun(U_7783,tc_HOL_Obool))))),U_7785),U_7784)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7783),U_7784)) ),
    inference(clausify,[status(thm)],[f_2272_2]) ).

fof(f_2273_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_2273_2,plain,
    ! [U_7787,U_7786] :
      ( ( hAPP(c_Nat_OSuc,U_7786) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7787)
        | ~ 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_7787))),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_7786))))) )
      & ( 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_7787))),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_7786)))))
        | hAPP(c_Nat_OSuc,U_7786) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7787) ) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

fof(f_2273_3,plain,
    ( ! [U_7791,U_7789] :
        ( hAPP(c_Nat_OSuc,U_7789) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7791)
        | ~ 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_7791))),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_7789))))) )
    & ! [U_7790,U_7788] :
        ( 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_7790))),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_7788)))))
        | hAPP(c_Nat_OSuc,U_7788) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7790) ) ),
    inference(miniscope,[status(thm)],[f_2273_2]) ).

cnf(f_2273_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_7790))),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_7788)))))
    | hAPP(c_Nat_OSuc,U_7788) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7790) ),
    inference(clausify,[status(thm)],[f_2273_3]) ).

cnf(f_2273_5,plain,
    ( hAPP(c_Nat_OSuc,U_7789) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7791)
    | ~ 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_7791))),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_7789))))) ),
    inference(clausify,[status(thm)],[f_2273_3]) ).

fof(f_2274_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_2274_2,plain,
    ! [U_7793,U_7792] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7792) = hAPP(c_Nat_OSuc,U_7793)
        | ~ 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_7792))),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_7793))))) )
      & ( 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_7792))),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_7793)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7792) != hAPP(c_Nat_OSuc,U_7793) ) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

fof(f_2274_3,plain,
    ( ! [U_7797,U_7795] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7795) = hAPP(c_Nat_OSuc,U_7797)
        | ~ 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_7795))),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_7797))))) )
    & ! [U_7796,U_7794] :
        ( 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_7794))),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_7796)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7794) != hAPP(c_Nat_OSuc,U_7796) ) ),
    inference(miniscope,[status(thm)],[f_2274_2]) ).

cnf(f_2274_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_7794))),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_7796)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7794) != hAPP(c_Nat_OSuc,U_7796) ),
    inference(clausify,[status(thm)],[f_2274_3]) ).

cnf(f_2274_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7795) = hAPP(c_Nat_OSuc,U_7797)
    | ~ 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_7795))),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_7797))))) ),
    inference(clausify,[status(thm)],[f_2274_3]) ).

fof(f_2275_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_2275_2,plain,
    ! [U_7798] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7798)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7798)),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_7798))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7798)) = 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_7798))) ) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

fof(f_2275_3,plain,
    ( ! [U_7800] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7800)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7800)),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_7800))) )
    & ! [U_7799] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7799)) = 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_7799))) ) ),
    inference(miniscope,[status(thm)],[f_2275_2]) ).

cnf(f_2275_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7799)) = 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_7799))) ),
    inference(clausify,[status(thm)],[f_2275_3]) ).

cnf(f_2275_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7800)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7800)),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_7800))) ),
    inference(clausify,[status(thm)],[f_2275_3]) ).

fof(f_2276_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_2276_2,plain,
    ! [U_7802,U_7801] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7801)),hAPP(c_Nat_OSuc,U_7802)))
        | ~ 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_7801))),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_7802)))) )
      & ( 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_7801))),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_7802))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7801)),hAPP(c_Nat_OSuc,U_7802))) ) ),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

fof(f_2276_3,plain,
    ( ! [U_7806,U_7804] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7804)),hAPP(c_Nat_OSuc,U_7806)))
        | ~ 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_7804))),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_7806)))) )
    & ! [U_7805,U_7803] :
        ( 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_7803))),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_7805))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7803)),hAPP(c_Nat_OSuc,U_7805))) ) ),
    inference(miniscope,[status(thm)],[f_2276_2]) ).

cnf(f_2276_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_7803))),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_7805))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7803)),hAPP(c_Nat_OSuc,U_7805))) ),
    inference(clausify,[status(thm)],[f_2276_3]) ).

cnf(f_2276_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7804)),hAPP(c_Nat_OSuc,U_7806)))
    | ~ 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_7804))),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_7806)))) ),
    inference(clausify,[status(thm)],[f_2276_3]) ).

fof(f_2277_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_2277_2,plain,
    ! [U_7808,U_7807] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7807)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7808)))
        | ~ 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_7808))),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_7807)),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_7808))),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_7807)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7807)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7808))) ) ),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

fof(f_2277_3,plain,
    ( ! [U_7812,U_7810] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7810)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7812)))
        | ~ 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_7812))),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_7810)),c_Int_Onat))))) )
    & ! [U_7811,U_7809] :
        ( 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_7811))),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_7809)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7809)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7811))) ) ),
    inference(miniscope,[status(thm)],[f_2277_2]) ).

cnf(f_2277_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_7811))),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_7809)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7809)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7811))) ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

cnf(f_2277_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7810)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7812)))
    | ~ 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_7812))),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_7810)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

fof(f_2278_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_2278_2,plain,
    ! [U_7814,U_7813] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7813)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7814)))
        | ~ 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_7814))),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_7813)),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_7814))),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_7813)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7813)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7814))) ) ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

fof(f_2278_3,plain,
    ( ! [U_7818,U_7816] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7816)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7818)))
        | ~ 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_7818))),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_7816)),c_Int_Onat))))) )
    & ! [U_7817,U_7815] :
        ( 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_7817))),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_7815)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7817))) ) ),
    inference(miniscope,[status(thm)],[f_2278_2]) ).

cnf(f_2278_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_7817))),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_7815)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7817))) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

cnf(f_2278_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7816)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7818)))
    | ~ 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_7818))),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_7816)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

fof(f_2279_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_2279_2,plain,
    ! [U_7820,U_7819] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7819)),hAPP(c_Nat_OSuc,U_7820)))
        | ~ 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_7819))),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_7820)))) )
      & ( 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_7819))),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_7820))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7819)),hAPP(c_Nat_OSuc,U_7820))) ) ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

fof(f_2279_3,plain,
    ( ! [U_7824,U_7822] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7822)),hAPP(c_Nat_OSuc,U_7824)))
        | ~ 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_7822))),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_7824)))) )
    & ! [U_7823,U_7821] :
        ( 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_7821))),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_7823))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7821)),hAPP(c_Nat_OSuc,U_7823))) ) ),
    inference(miniscope,[status(thm)],[f_2279_2]) ).

cnf(f_2279_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_7821))),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_7823))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7821)),hAPP(c_Nat_OSuc,U_7823))) ),
    inference(clausify,[status(thm)],[f_2279_3]) ).

cnf(f_2279_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_7822)),hAPP(c_Nat_OSuc,U_7824)))
    | ~ 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_7822))),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_7824)))) ),
    inference(clausify,[status(thm)],[f_2279_3]) ).

fof(f_2280_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_2280_2,plain,
    ! [U_7827,U_7826,U_7825] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7826))) = c_Groups_Oone__class_Oone(U_7825)
          | 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_7826))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7826))) = hAPP(hAPP(c_HOL_OLet(U_7825,U_7825),hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7826))),hAPP(hAPP(c_COMBS(U_7825,U_7825,U_7825),hAPP(hAPP(c_COMBB(U_7825,tc_fun(U_7825,U_7825),U_7825),c_Groups_Otimes__class_Otimes(U_7825)),hAPP(c_Groups_Otimes__class_Otimes(U_7825),U_7827))),c_COMBI(U_7825)))
          | ~ 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_7826))) ) )
      | ~ class_Int_Onumber__ring(U_7825) ),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

cnf(f_2280_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7826))) = hAPP(hAPP(c_HOL_OLet(U_7825,U_7825),hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7826))),hAPP(hAPP(c_COMBS(U_7825,U_7825,U_7825),hAPP(hAPP(c_COMBB(U_7825,tc_fun(U_7825,U_7825),U_7825),c_Groups_Otimes__class_Otimes(U_7825)),hAPP(c_Groups_Otimes__class_Otimes(U_7825),U_7827))),c_COMBI(U_7825)))
    | ~ 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_7826)))
    | ~ class_Int_Onumber__ring(U_7825) ),
    inference(clausify,[status(thm)],[f_2280_2]) ).

cnf(f_2280_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7825),U_7827),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7826))) = c_Groups_Oone__class_Oone(U_7825)
    | 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_7826)))
    | ~ class_Int_Onumber__ring(U_7825) ),
    inference(clausify,[status(thm)],[f_2280_2]) ).

fof(f_2281_1,plain,
    ! [V_ca_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_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_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_ca_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_ca_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_2281_2,plain,
    ! [U_7833,U_7832,U_7831,U_7830,U_7829,U_7828] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7829,U_7828),hAPP(hAPP(c_COMBC(U_7829,U_7828,U_7828),hAPP(hAPP(c_COMBS(U_7829,U_7828,tc_fun(U_7828,U_7828)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7828,tc_fun(U_7828,U_7828)),U_7829),c_If(U_7828)),hAPP(hAPP(c_COMBC(U_7829,U_7829,tc_HOL_Obool),c_fequal),U_7831))),U_7832)),U_7833)),U_7830) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7828),U_7833),hAPP(c_Finite__Set_Ocard(U_7829),U_7830))
          | hBOOL(hAPP(hAPP(c_member(U_7829),U_7831),U_7830)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7829,U_7828),hAPP(hAPP(c_COMBC(U_7829,U_7828,U_7828),hAPP(hAPP(c_COMBS(U_7829,U_7828,tc_fun(U_7828,U_7828)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7828,tc_fun(U_7828,U_7828)),U_7829),c_If(U_7828)),hAPP(hAPP(c_COMBC(U_7829,U_7829,tc_HOL_Obool),c_fequal),U_7831))),U_7832)),U_7833)),U_7830) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7828),hAPP(U_7832,U_7831)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7828),U_7833),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7829),U_7830)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_7829),U_7831),U_7830)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7829),U_7830))
      | ~ class_Groups_Ocomm__monoid__mult(U_7828) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

cnf(f_2281_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7829,U_7828),hAPP(hAPP(c_COMBC(U_7829,U_7828,U_7828),hAPP(hAPP(c_COMBS(U_7829,U_7828,tc_fun(U_7828,U_7828)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7828,tc_fun(U_7828,U_7828)),U_7829),c_If(U_7828)),hAPP(hAPP(c_COMBC(U_7829,U_7829,tc_HOL_Obool),c_fequal),U_7831))),U_7832)),U_7833)),U_7830) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7828),hAPP(U_7832,U_7831)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7828),U_7833),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7829),U_7830)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7829),U_7831),U_7830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7829),U_7830))
    | ~ class_Groups_Ocomm__monoid__mult(U_7828) ),
    inference(clausify,[status(thm)],[f_2281_2]) ).

cnf(f_2281_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7829,U_7828),hAPP(hAPP(c_COMBC(U_7829,U_7828,U_7828),hAPP(hAPP(c_COMBS(U_7829,U_7828,tc_fun(U_7828,U_7828)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7828,tc_fun(U_7828,U_7828)),U_7829),c_If(U_7828)),hAPP(hAPP(c_COMBC(U_7829,U_7829,tc_HOL_Obool),c_fequal),U_7831))),U_7832)),U_7833)),U_7830) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7828),U_7833),hAPP(c_Finite__Set_Ocard(U_7829),U_7830))
    | hBOOL(hAPP(hAPP(c_member(U_7829),U_7831),U_7830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7829),U_7830))
    | ~ class_Groups_Ocomm__monoid__mult(U_7828) ),
    inference(clausify,[status(thm)],[f_2281_2]) ).

fof(f_2282_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_2282_2,plain,
    ! [U_7835,U_7834] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7835),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7834))) = 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_7834))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7835),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7834))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7835),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7834))),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_7835))),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_7834))) ) ),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

fof(f_2282_3,plain,
    ( ! [U_7839,U_7837] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7839),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7837))) = 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_7837))) )
    & ! [U_7838,U_7836] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7836))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7836))),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_7838))),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_7836))) ) ),
    inference(miniscope,[status(thm)],[f_2282_2]) ).

cnf(f_2282_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7836))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7838),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7836))),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_7838))),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_7836))) ),
    inference(clausify,[status(thm)],[f_2282_3]) ).

cnf(f_2282_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7839),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7837))) = 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_7837))) ),
    inference(clausify,[status(thm)],[f_2282_3]) ).

fof(f_2283_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_2283_2,plain,
    ! [U_7841,U_7840] :
      ( ( c_Divides_OnegDivAlg(U_7840,U_7841) = hAPP(c_Divides_Oadjust(U_7841),c_Divides_OnegDivAlg(U_7840,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_7841)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7841),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_7840),U_7841))) )
      & ( c_Divides_OnegDivAlg(U_7840,U_7841) = 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_7840),U_7841))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7841),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_7840),U_7841))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

fof(f_2283_3,plain,
    ( ! [U_7845,U_7843] :
        ( c_Divides_OnegDivAlg(U_7843,U_7845) = hAPP(c_Divides_Oadjust(U_7845),c_Divides_OnegDivAlg(U_7843,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_7845)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7845),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_7843),U_7845))) )
    & ! [U_7844,U_7842] :
        ( c_Divides_OnegDivAlg(U_7842,U_7844) = 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_7842),U_7844))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7844),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_7842),U_7844))) ) ) ),
    inference(miniscope,[status(thm)],[f_2283_2]) ).

cnf(f_2283_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_7842),U_7844)))
    | c_Divides_OnegDivAlg(U_7842,U_7844) = 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_7842),U_7844)) ),
    inference(clausify,[status(thm)],[f_2283_3]) ).

cnf(f_2283_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7844),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_7842,U_7844) = 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_7842),U_7844)) ),
    inference(clausify,[status(thm)],[f_2283_3]) ).

cnf(f_2283_6,plain,
    ( c_Divides_OnegDivAlg(U_7843,U_7845) = hAPP(c_Divides_Oadjust(U_7845),c_Divides_OnegDivAlg(U_7843,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_7845)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7845),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_7843),U_7845))) ),
    inference(clausify,[status(thm)],[f_2283_3]) ).

fof(f_2284_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_2284_2,plain,
    ! [U_7847,U_7846] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7846)),hAPP(c_Nat_OSuc,U_7847)) = 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_7846))),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_7847)))),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

cnf(f_2284_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7846)),hAPP(c_Nat_OSuc,U_7847)) = 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_7846))),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_7847)))),
    inference(clausify,[status(thm)],[f_2284_2]) ).

fof(f_2285_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_2285_2,plain,
    ! [U_7849,U_7848] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7848)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7849)) = 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_7849))),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_7848)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

cnf(f_2285_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7848)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7849)) = 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_7849))),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_7848)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2285_2]) ).

fof(f_2286_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_2286_2,plain,
    ! [U_7852,U_7851,U_7850] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7851))) = c_Groups_Oone__class_Oone(U_7850)
          | 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_7851))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7851))) = hAPP(hAPP(c_HOL_OLet(U_7850,U_7850),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7851))),hAPP(hAPP(c_COMBS(U_7850,U_7850,U_7850),hAPP(hAPP(c_COMBB(U_7850,tc_fun(U_7850,U_7850),U_7850),c_Groups_Otimes__class_Otimes(U_7850)),hAPP(c_Groups_Otimes__class_Otimes(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)))),c_COMBI(U_7850)))
          | ~ 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_7851))) ) )
      | ~ class_Int_Onumber__ring(U_7850) ),
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

cnf(f_2286_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7851))) = hAPP(hAPP(c_HOL_OLet(U_7850,U_7850),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7851))),hAPP(hAPP(c_COMBS(U_7850,U_7850,U_7850),hAPP(hAPP(c_COMBB(U_7850,tc_fun(U_7850,U_7850),U_7850),c_Groups_Otimes__class_Otimes(U_7850)),hAPP(c_Groups_Otimes__class_Otimes(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)))),c_COMBI(U_7850)))
    | ~ 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_7851)))
    | ~ class_Int_Onumber__ring(U_7850) ),
    inference(clausify,[status(thm)],[f_2286_2]) ).

cnf(f_2286_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(c_Int_Onumber__class_Onumber__of(U_7850),U_7852)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_7851))) = c_Groups_Oone__class_Oone(U_7850)
    | 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_7851)))
    | ~ class_Int_Onumber__ring(U_7850) ),
    inference(clausify,[status(thm)],[f_2286_2]) ).

fof(f_2287_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_2287_2,plain,
    ! [U_7855,U_7854,U_7853] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7853,U_7854,U_7855,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7854,
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

cnf(f_2287_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_7853,U_7854,U_7855,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7854,
    inference(clausify,[status(thm)],[f_2287_2]) ).

fof(f_2288_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_2288_2,plain,
    ! [U_7857,U_7856] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),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_7856))))
          | 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)) = 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)))
          | ~ 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)))) ) )
      | ~ 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_7856))) ),
    inference(variable_rename,[status(thm)],[f_2288_1]) ).

cnf(f_2288_3,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)) = 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)))
    | ~ 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856))))
    | ~ 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_7856))) ),
    inference(clausify,[status(thm)],[f_2288_2]) ).

cnf(f_2288_4,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7857),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_7856))))
    | 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_7857)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7856))))
    | ~ 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_7856))) ),
    inference(clausify,[status(thm)],[f_2288_2]) ).

fof(f_2289_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_2289_2,plain,
    ! [U_7859,U_7858] :
      ( ( ( c_Divides_OnegDivAlg(U_7859,U_7858) = hAPP(c_Divides_Oadjust(U_7858),c_Divides_OnegDivAlg(U_7859,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_7858)))
          | 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_7859),U_7858))) )
        & ( c_Divides_OnegDivAlg(U_7859,U_7858) = 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_7859),U_7858))
          | ~ 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_7859),U_7858))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7858)) ),
    inference(variable_rename,[status(thm)],[f_2289_1]) ).

cnf(f_2289_3,plain,
    ( c_Divides_OnegDivAlg(U_7859,U_7858) = 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_7859),U_7858))
    | ~ 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_7859),U_7858)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7858)) ),
    inference(clausify,[status(thm)],[f_2289_2]) ).

cnf(f_2289_4,plain,
    ( c_Divides_OnegDivAlg(U_7859,U_7858) = hAPP(c_Divides_Oadjust(U_7858),c_Divides_OnegDivAlg(U_7859,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_7858)))
    | 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_7859),U_7858)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7858)) ),
    inference(clausify,[status(thm)],[f_2289_2]) ).

fof(f_2290_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_2290_2,plain,
    ! [U_7861,U_7860] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_7861,U_7860) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_7861),U_7860)),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_7861))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7860)))
            | U_7860 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_7861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_7861,U_7860) = 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_7860 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_7861 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7860),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_7861,U_7860) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7860),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2290_1]) ).

fof(f_2290_3,plain,
    ( ! [U_7865,U_7863] :
        ( ( ( c_Nitpick_Onorm__frac(U_7865,U_7863) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_7865),U_7863)),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_7865))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7863)))
            | U_7863 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_7865 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_7865,U_7863) = 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_7863 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_7865 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7863),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7864,U_7862] :
        ( c_Nitpick_Onorm__frac(U_7864,U_7862) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7862))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7862),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2290_2]) ).

cnf(f_2290_4,plain,
    ( c_Nitpick_Onorm__frac(U_7864,U_7862) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7862))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7862),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

cnf(f_2290_5,plain,
    ( U_7865 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_7865,U_7863) = 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_7863),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

cnf(f_2290_6,plain,
    ( U_7863 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_7865,U_7863) = 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_7863),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

cnf(f_2290_7,plain,
    ( c_Nitpick_Onorm__frac(U_7865,U_7863) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_7865),U_7863)),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_7865))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7863)))
    | U_7863 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7865 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7863),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

fof(f_2291_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_2291_2,plain,
    ! [U_7870,U_7869,U_7868,U_7867,U_7866] : c_Nat_Onat_Onat__case(U_7866,U_7867,U_7868,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7869)),U_7870)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_7866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7869))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_7866,U_7866),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_7866,tc_fun(U_7866,U_7866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7866,tc_fun(U_7866,U_7866)),tc_Int_Oint),c_If(U_7866)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_7866,U_7867,U_7868,U_7870))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7866,tc_Int_Oint),U_7868),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_7870)))),
    inference(variable_rename,[status(thm)],[f_2291_1]) ).

cnf(f_2291_3,plain,
    c_Nat_Onat_Onat__case(U_7866,U_7867,U_7868,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7869)),U_7870)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_7866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7869))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_7866,U_7866),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_7866,tc_fun(U_7866,U_7866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7866,tc_fun(U_7866,U_7866)),tc_Int_Oint),c_If(U_7866)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_7866,U_7867,U_7868,U_7870))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7866,tc_Int_Oint),U_7868),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_7870)))),
    inference(clausify,[status(thm)],[f_2291_2]) ).

fof(f_2292_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_2292_2,plain,
    ! [U_7871] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)),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_7871))))
          | 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_7871))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)) = 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_7871))) ) )
      | ~ 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_7871))) ),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

cnf(f_2292_3,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)) = 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_7871)))
    | ~ 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_7871))) ),
    inference(clausify,[status(thm)],[f_2292_2]) ).

cnf(f_2292_4,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7871)),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_7871))))
    | 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_7871)))
    | ~ 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_7871))) ),
    inference(clausify,[status(thm)],[f_2292_2]) ).

fof(f_2293_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_2293_2,plain,
    ! [U_7873,U_7872] :
      ( ( c_Divides_OposDivAlg(U_7872,U_7873) = hAPP(c_Divides_Oadjust(U_7873),c_Divides_OposDivAlg(U_7872,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_7873)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7873),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7872),U_7873)) )
      & ( c_Divides_OposDivAlg(U_7872,U_7873) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7872)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7873),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7872),U_7873)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

fof(f_2293_3,plain,
    ( ! [U_7877,U_7875] :
        ( c_Divides_OposDivAlg(U_7875,U_7877) = hAPP(c_Divides_Oadjust(U_7877),c_Divides_OposDivAlg(U_7875,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_7877)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7875),U_7877)) )
    & ! [U_7876,U_7874] :
        ( c_Divides_OposDivAlg(U_7874,U_7876) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7874)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7876),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7874),U_7876)) ) ) ),
    inference(miniscope,[status(thm)],[f_2293_2]) ).

cnf(f_2293_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7874),U_7876))
    | c_Divides_OposDivAlg(U_7874,U_7876) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7874) ),
    inference(clausify,[status(thm)],[f_2293_3]) ).

cnf(f_2293_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7876),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_7874,U_7876) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7874) ),
    inference(clausify,[status(thm)],[f_2293_3]) ).

cnf(f_2293_6,plain,
    ( c_Divides_OposDivAlg(U_7875,U_7877) = hAPP(c_Divides_Oadjust(U_7877),c_Divides_OposDivAlg(U_7875,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_7877)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7875),U_7877)) ),
    inference(clausify,[status(thm)],[f_2293_3]) ).

fof(f_2294_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_2294_2,plain,
    ! [U_7883,U_7882,U_7881,U_7880,U_7879,U_7878] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7882,tc_fun(U_7883,tc_HOL_Obool))),U_7881),U_7878),U_7879),U_7880))
      | ( ~ hBOOL(hAPP(hAPP(U_7881,U_7879),U_7880))
        & ~ hBOOL(hAPP(hAPP(U_7878,U_7879),U_7880)) ) ),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

cnf(f_2294_3,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7878,U_7879),U_7880))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7882,tc_fun(U_7883,tc_HOL_Obool))),U_7881),U_7878),U_7879),U_7880)) ),
    inference(clausify,[status(thm)],[f_2294_2]) ).

cnf(f_2294_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7881,U_7879),U_7880))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7882,tc_fun(U_7883,tc_HOL_Obool))),U_7881),U_7878),U_7879),U_7880)) ),
    inference(clausify,[status(thm)],[f_2294_2]) ).

fof(f_2295_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_2295_2,plain,
    ! [U_7889,U_7888,U_7887,U_7886,U_7885,U_7884] :
      ( hBOOL(hAPP(hAPP(U_7887,U_7888),U_7889))
      | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7889))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7884,tc_fun(U_7885,tc_HOL_Obool))),U_7886),U_7887),U_7888),U_7889)) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

fof(f_2295_3,plain,
    ! [U_7889,U_7888,U_7887,U_7886] :
      ( ! [U_7885,U_7884] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7884,tc_fun(U_7885,tc_HOL_Obool))),U_7886),U_7887),U_7888),U_7889))
      | hBOOL(hAPP(hAPP(U_7887,U_7888),U_7889))
      | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7889)) ),
    inference(miniscope,[status(thm)],[f_2295_2]) ).

cnf(f_2295_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7884,tc_fun(U_7885,tc_HOL_Obool))),U_7886),U_7887),U_7888),U_7889))
    | hBOOL(hAPP(hAPP(U_7887,U_7888),U_7889))
    | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7889)) ),
    inference(clausify,[status(thm)],[f_2295_3]) ).

fof(f_2296_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_2296_2,plain,
    ! [U_7895,U_7894,U_7893,U_7892,U_7891,U_7890] :
      ( ( hBOOL(hAPP(hAPP(U_7893,U_7894),U_7895))
        & hBOOL(hAPP(hAPP(U_7892,U_7894),U_7895)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7890,tc_fun(U_7891,tc_HOL_Obool))),U_7892),U_7893),U_7894),U_7895)) ),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

fof(f_2296_3,plain,
    ! [U_7895,U_7894,U_7893,U_7892] :
      ( ! [U_7891,U_7890] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7890,tc_fun(U_7891,tc_HOL_Obool))),U_7892),U_7893),U_7894),U_7895))
      | ( hBOOL(hAPP(hAPP(U_7893,U_7894),U_7895))
        & hBOOL(hAPP(hAPP(U_7892,U_7894),U_7895)) ) ),
    inference(miniscope,[status(thm)],[f_2296_2]) ).

cnf(f_2296_4,plain,
    ( hBOOL(hAPP(hAPP(U_7892,U_7894),U_7895))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7890,tc_fun(U_7891,tc_HOL_Obool))),U_7892),U_7893),U_7894),U_7895)) ),
    inference(clausify,[status(thm)],[f_2296_3]) ).

cnf(f_2296_5,plain,
    ( hBOOL(hAPP(hAPP(U_7893,U_7894),U_7895))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7890,tc_fun(U_7891,tc_HOL_Obool))),U_7892),U_7893),U_7894),U_7895)) ),
    inference(clausify,[status(thm)],[f_2296_3]) ).

fof(f_2297_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_2297_2,plain,
    ! [U_7901,U_7900,U_7899,U_7898,U_7897,U_7896] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7900,tc_fun(U_7901,tc_HOL_Obool))),U_7896),U_7899),U_7897),U_7898))
      | ~ hBOOL(hAPP(hAPP(U_7899,U_7897),U_7898))
      | ~ hBOOL(hAPP(hAPP(U_7896,U_7897),U_7898)) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

cnf(f_2297_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7900,tc_fun(U_7901,tc_HOL_Obool))),U_7896),U_7899),U_7897),U_7898))
    | ~ hBOOL(hAPP(hAPP(U_7899,U_7897),U_7898))
    | ~ hBOOL(hAPP(hAPP(U_7896,U_7897),U_7898)) ),
    inference(clausify,[status(thm)],[f_2297_2]) ).

fof(f_2298_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_2298_2,plain,
    ! [U_7905,U_7904,U_7903,U_7902] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7902,tc_fun(U_7903,tc_HOL_Obool))),U_7904),U_7905)),
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

cnf(f_2298_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7902,tc_fun(U_7903,tc_HOL_Obool))),U_7904),U_7905)),
    inference(clausify,[status(thm)],[f_2298_2]) ).

fof(f_2299_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_2299_2,plain,
    ! [U_7911,U_7910,U_7909,U_7908,U_7907,U_7906] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7909,tc_fun(U_7910,tc_HOL_Obool))),U_7911),U_7906),U_7907),U_7908))
      | ~ hBOOL(hAPP(hAPP(U_7906,U_7907),U_7908)) ),
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

cnf(f_2299_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7909,tc_fun(U_7910,tc_HOL_Obool))),U_7911),U_7906),U_7907),U_7908))
    | ~ hBOOL(hAPP(hAPP(U_7906,U_7907),U_7908)) ),
    inference(clausify,[status(thm)],[f_2299_2]) ).

fof(f_2300_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_2300_2,plain,
    ! [U_7917,U_7916,U_7915,U_7914,U_7913,U_7912] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7915,tc_fun(U_7916,tc_HOL_Obool))),U_7912),U_7917),U_7913),U_7914))
      | ~ hBOOL(hAPP(hAPP(U_7912,U_7913),U_7914)) ),
    inference(variable_rename,[status(thm)],[f_2300_1]) ).

cnf(f_2300_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7915,tc_fun(U_7916,tc_HOL_Obool))),U_7912),U_7917),U_7913),U_7914))
    | ~ hBOOL(hAPP(hAPP(U_7912,U_7913),U_7914)) ),
    inference(clausify,[status(thm)],[f_2300_2]) ).

fof(f_2301_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_2301_2,plain,
    ! [U_7923,U_7922,U_7921,U_7920,U_7919,U_7918] :
      ( hBOOL(hAPP(hAPP(U_7921,U_7922),U_7923))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7918,tc_fun(U_7919,tc_HOL_Obool))),U_7920),U_7921),U_7922),U_7923)) ),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

fof(f_2301_3,plain,
    ! [U_7923,U_7922,U_7921] :
      ( ! [U_7920,U_7919,U_7918] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7918,tc_fun(U_7919,tc_HOL_Obool))),U_7920),U_7921),U_7922),U_7923))
      | hBOOL(hAPP(hAPP(U_7921,U_7922),U_7923)) ),
    inference(miniscope,[status(thm)],[f_2301_2]) ).

cnf(f_2301_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7918,tc_fun(U_7919,tc_HOL_Obool))),U_7920),U_7921),U_7922),U_7923))
    | hBOOL(hAPP(hAPP(U_7921,U_7922),U_7923)) ),
    inference(clausify,[status(thm)],[f_2301_3]) ).

fof(f_2302_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_2302_2,plain,
    ! [U_7929,U_7928,U_7927,U_7926,U_7925,U_7924] :
      ( hBOOL(hAPP(hAPP(U_7926,U_7928),U_7929))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7924,tc_fun(U_7925,tc_HOL_Obool))),U_7926),U_7927),U_7928),U_7929)) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

fof(f_2302_3,plain,
    ! [U_7929,U_7928,U_7927,U_7926] :
      ( ! [U_7925,U_7924] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7924,tc_fun(U_7925,tc_HOL_Obool))),U_7926),U_7927),U_7928),U_7929))
      | hBOOL(hAPP(hAPP(U_7926,U_7928),U_7929)) ),
    inference(miniscope,[status(thm)],[f_2302_2]) ).

cnf(f_2302_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7924,tc_fun(U_7925,tc_HOL_Obool))),U_7926),U_7927),U_7928),U_7929))
    | hBOOL(hAPP(hAPP(U_7926,U_7928),U_7929)) ),
    inference(clausify,[status(thm)],[f_2302_3]) ).

fof(f_2303_1,plain,
    ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).

fof(f_2303_2,plain,
    ! [U_7935,U_7934,U_7933,U_7932,U_7931,U_7930] :
      ( hBOOL(hAPP(hAPP(U_7933,U_7934),U_7935))
      | ~ hBOOL(hAPP(hAPP(U_7932,U_7934),U_7935))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7930,tc_fun(U_7931,tc_HOL_Obool))),U_7932),U_7933)) ),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

fof(f_2303_3,plain,
    ! [U_7935,U_7934,U_7933,U_7932] :
      ( ! [U_7931,U_7930] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7930,tc_fun(U_7931,tc_HOL_Obool))),U_7932),U_7933))
      | hBOOL(hAPP(hAPP(U_7933,U_7934),U_7935))
      | ~ hBOOL(hAPP(hAPP(U_7932,U_7934),U_7935)) ),
    inference(miniscope,[status(thm)],[f_2303_2]) ).

cnf(f_2303_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7930,tc_fun(U_7931,tc_HOL_Obool))),U_7932),U_7933))
    | hBOOL(hAPP(hAPP(U_7933,U_7934),U_7935))
    | ~ hBOOL(hAPP(hAPP(U_7932,U_7934),U_7935)) ),
    inference(clausify,[status(thm)],[f_2303_3]) ).

fof(f_2304_1,plain,
    ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Qa_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_Pa_2),V_Qa_2))
      | ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).

fof(f_2304_2,plain,
    ! [U_7941,U_7940,U_7939,U_7938,U_7937,U_7936] :
      ( hBOOL(hAPP(hAPP(U_7941,U_7937),U_7938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7939,tc_fun(U_7940,tc_HOL_Obool))),U_7936),U_7941))
      | ~ hBOOL(hAPP(hAPP(U_7936,U_7937),U_7938)) ),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

cnf(f_2304_3,plain,
    ( hBOOL(hAPP(hAPP(U_7941,U_7937),U_7938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7939,tc_fun(U_7940,tc_HOL_Obool))),U_7936),U_7941))
    | ~ hBOOL(hAPP(hAPP(U_7936,U_7937),U_7938)) ),
    inference(clausify,[status(thm)],[f_2304_2]) ).

fof(f_2305_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_2305_2,plain,
    ! [U_7944,U_7943,U_7942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7943,U_7943),tc_HOL_Obool)),U_7942),U_7944))
      | U_7942 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7943,U_7943),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

cnf(f_2305_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_7943,U_7943),tc_HOL_Obool)),U_7942),U_7944))
    | U_7942 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_7943,U_7943),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2305_2]) ).

fof(f_2306_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_2306_2,plain,
    ! [U_7947,U_7946,U_7945] : c_Nat_Onat_Onat__case(U_7945,U_7946,U_7947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7946,
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

cnf(f_2306_3,plain,
    c_Nat_Onat_Onat__case(U_7945,U_7946,U_7947,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7946,
    inference(clausify,[status(thm)],[f_2306_2]) ).

fof(f_2307_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_2307_2,plain,
    ! [U_7951,U_7950,U_7949,U_7948] : c_Nat_Onat_Onat__case(U_7948,U_7949,U_7950,hAPP(c_Nat_OSuc,U_7951)) = hAPP(U_7950,U_7951),
    inference(variable_rename,[status(thm)],[f_2307_1]) ).

cnf(f_2307_3,plain,
    c_Nat_Onat_Onat__case(U_7948,U_7949,U_7950,hAPP(c_Nat_OSuc,U_7951)) = hAPP(U_7950,U_7951),
    inference(clausify,[status(thm)],[f_2307_2]) ).

fof(f_2308_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_2308_2,plain,
    ! [U_7952] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_7952) = 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_2308_1]) ).

cnf(f_2308_3,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_7952) = 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_2308_2]) ).

fof(f_2309_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_2309_2,plain,
    ! [U_7954,U_7953] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7953)),U_7954))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7953),U_7954)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7953),U_7954))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7953)),U_7954)) ) ),
    inference(variable_rename,[status(thm)],[f_2309_1]) ).

fof(f_2309_3,plain,
    ( ! [U_7958,U_7956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7956)),U_7958))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7956),U_7958)) )
    & ! [U_7957,U_7955] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7955),U_7957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7955)),U_7957)) ) ),
    inference(miniscope,[status(thm)],[f_2309_2]) ).

cnf(f_2309_4,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7955),U_7957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7955)),U_7957)) ),
    inference(clausify,[status(thm)],[f_2309_3]) ).

cnf(f_2309_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7956)),U_7958))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7956),U_7958)) ),
    inference(clausify,[status(thm)],[f_2309_3]) ).

fof(f_2310_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_2310_2,plain,
    ! [U_7960,U_7959] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7959),hAPP(c_Nat_OSuc,U_7960)) = 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_7959),U_7960)),
    inference(variable_rename,[status(thm)],[f_2310_1]) ).

cnf(f_2310_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7959),hAPP(c_Nat_OSuc,U_7960)) = 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_7959),U_7960)),
    inference(clausify,[status(thm)],[f_2310_2]) ).

fof(f_2311_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_2311_2,plain,
    ! [U_7962,U_7961] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_7961),hAPP(c_Nat_OSuc,U_7962)) = 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_7962)),U_7961),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

cnf(f_2311_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_7961),hAPP(c_Nat_OSuc,U_7962)) = 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_7962)),U_7961),
    inference(clausify,[status(thm)],[f_2311_2]) ).

fof(f_2312_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_2312_2,plain,
    ! [U_7964,U_7963] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7963)),U_7964) = 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_7963)),U_7964),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

cnf(f_2312_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7963)),U_7964) = 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_7963)),U_7964),
    inference(clausify,[status(thm)],[f_2312_2]) ).

fof(f_2313_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_2313_2,plain,
    ! [U_7966,U_7965] :
      ( c_Divides_OposDivAlg(U_7965,U_7966) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7965),U_7966)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7965,U_7966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7965)) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

cnf(f_2313_3,plain,
    ( c_Divides_OposDivAlg(U_7965,U_7966) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7965),U_7966)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7965,U_7966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7965)) ),
    inference(clausify,[status(thm)],[f_2313_2]) ).

fof(f_2314_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_2314_2,plain,
    ! [U_7970,U_7969,U_7968,U_7967] : c_Nat_Onat_Onat__case(U_7967,U_7968,U_7969,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7970)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_7967),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_7967,U_7967),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_7967,tc_fun(U_7967,U_7967)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7967,tc_fun(U_7967,U_7967)),tc_Int_Oint),c_If(U_7967)),c_Nat__Numeral_Oneg)),U_7968)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7967,tc_Int_Oint),U_7969),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

cnf(f_2314_3,plain,
    c_Nat_Onat_Onat__case(U_7967,U_7968,U_7969,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7970)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_7967),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_7970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_7967,U_7967),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_7967,tc_fun(U_7967,U_7967)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_7967,tc_fun(U_7967,U_7967)),tc_Int_Oint),c_If(U_7967)),c_Nat__Numeral_Oneg)),U_7968)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7967,tc_Int_Oint),U_7969),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_2314_2]) ).

fof(f_2315_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_2315_2,plain,
    ! [U_7972,U_7971] :
      ( ( ( c_Divides_OposDivAlg(U_7972,U_7971) = hAPP(c_Divides_Oadjust(U_7971),c_Divides_OposDivAlg(U_7972,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_7971)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7972),U_7971)) )
        & ( c_Divides_OposDivAlg(U_7972,U_7971) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7972)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7972),U_7971)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971)) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

cnf(f_2315_3,plain,
    ( c_Divides_OposDivAlg(U_7972,U_7971) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7972)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7972),U_7971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971)) ),
    inference(clausify,[status(thm)],[f_2315_2]) ).

cnf(f_2315_4,plain,
    ( c_Divides_OposDivAlg(U_7972,U_7971) = hAPP(c_Divides_Oadjust(U_7971),c_Divides_OposDivAlg(U_7972,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_7971)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7972),U_7971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971)) ),
    inference(clausify,[status(thm)],[f_2315_2]) ).

fof(f_2316_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_2316_2,plain,
    ! [U_7974,U_7973] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),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_7973))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)) = 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_7974))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973))) ) )
      | ~ 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_7973))) ),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

cnf(f_2316_3,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)) = 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_7974))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)))
    | ~ 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_7973))) ),
    inference(clausify,[status(thm)],[f_2316_2]) ).

cnf(f_2316_4,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974),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_7973))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7974)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7973)))
    | ~ 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_7973))) ),
    inference(clausify,[status(thm)],[f_2316_2]) ).

fof(f_2317_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_2317_2,plain,
    ! [U_7979,U_7978,U_7977,U_7976,U_7975] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7975,U_7976,U_7977),U_7978),U_7979))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7975,U_7976)),hAPP(hAPP(c_Product__Type_OPair(U_7975,U_7976),U_7978),U_7979)),U_7977)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7975,U_7976)),hAPP(hAPP(c_Product__Type_OPair(U_7975,U_7976),U_7978),U_7979)),U_7977))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7975,U_7976,U_7977),U_7978),U_7979)) ) ),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

fof(f_2317_3,plain,
    ( ! [U_7989,U_7987,U_7985,U_7983,U_7981] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7981,U_7983,U_7985),U_7987),U_7989))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7981,U_7983)),hAPP(hAPP(c_Product__Type_OPair(U_7981,U_7983),U_7987),U_7989)),U_7985)) )
    & ! [U_7988,U_7986,U_7984,U_7982,U_7980] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7980,U_7982)),hAPP(hAPP(c_Product__Type_OPair(U_7980,U_7982),U_7986),U_7988)),U_7984))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7980,U_7982,U_7984),U_7986),U_7988)) ) ),
    inference(miniscope,[status(thm)],[f_2317_2]) ).

cnf(f_2317_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7980,U_7982)),hAPP(hAPP(c_Product__Type_OPair(U_7980,U_7982),U_7986),U_7988)),U_7984))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7980,U_7982,U_7984),U_7986),U_7988)) ),
    inference(clausify,[status(thm)],[f_2317_3]) ).

cnf(f_2317_5,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_7981,U_7983,U_7985),U_7987),U_7989))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7981,U_7983)),hAPP(hAPP(c_Product__Type_OPair(U_7981,U_7983),U_7987),U_7989)),U_7985)) ),
    inference(clausify,[status(thm)],[f_2317_3]) ).

fof(f_2318_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_2318_2,plain,
    ! [U_7991,U_7990] : c_Code__Numeral_Odiv__mod__code__numeral(U_7990,U_7991) = 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_7990),U_7991)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_7990,U_7991)),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

cnf(f_2318_3,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_7990,U_7991) = 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_7990),U_7991)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_7990,U_7991)),
    inference(clausify,[status(thm)],[f_2318_2]) ).

fof(f_2319_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_2319_2,plain,
    ! [U_7995,U_7994] :
      ( ( c_Nitpick_Orefl_H(U_7994,U_7995)
        | ? [U_7993] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7994,U_7994)),hAPP(hAPP(c_Product__Type_OPair(U_7994,U_7994),U_7993),U_7993)),U_7995)) )
      & ( ! [U_7992] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7994,U_7994)),hAPP(hAPP(c_Product__Type_OPair(U_7994,U_7994),U_7992),U_7992)),U_7995))
        | ~ c_Nitpick_Orefl_H(U_7994,U_7995) ) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

fof(f_2319_3,plain,
    ( ! [U_7999,U_7997] :
        ( c_Nitpick_Orefl_H(U_7997,U_7999)
        | ? [U_7993] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7997,U_7997)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7997),U_7993),U_7993)),U_7999)) )
    & ! [U_7998,U_7996] :
        ( ! [U_7992] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7996,U_7996)),hAPP(hAPP(c_Product__Type_OPair(U_7996,U_7996),U_7992),U_7992)),U_7998))
        | ~ c_Nitpick_Orefl_H(U_7996,U_7998) ) ),
    inference(miniscope,[status(thm)],[f_2319_2]) ).

fof(f_2319_4,plain,
    ( ! [U_7999,U_7997] :
        ( c_Nitpick_Orefl_H(U_7997,U_7999)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7997,U_7997)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7997),sK148(U_7999,U_7997)),sK148(U_7999,U_7997))),U_7999)) )
    & ! [U_7998,U_7996] :
        ( ! [U_7992] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7996,U_7996)),hAPP(hAPP(c_Product__Type_OPair(U_7996,U_7996),U_7992),U_7992)),U_7998))
        | ~ c_Nitpick_Orefl_H(U_7996,U_7998) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_7993,sK148(U_7999,U_7997))],[f_2319_3]) ).

cnf(f_2319_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7996,U_7996)),hAPP(hAPP(c_Product__Type_OPair(U_7996,U_7996),U_7992),U_7992)),U_7998))
    | ~ c_Nitpick_Orefl_H(U_7996,U_7998) ),
    inference(clausify,[status(thm)],[f_2319_4]) ).

cnf(f_2319_6,plain,
    ( c_Nitpick_Orefl_H(U_7997,U_7999)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7997,U_7997)),hAPP(hAPP(c_Product__Type_OPair(U_7997,U_7997),sK148(U_7999,U_7997)),sK148(U_7999,U_7997))),U_7999)) ),
    inference(clausify,[status(thm)],[f_2319_4]) ).

fof(f_2320_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_2320_2,plain,
    ! [U_8000] : c_Divides_Oadjust(U_8000) = 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_8000))))),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_8000))))),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_2320_1]) ).

cnf(f_2320_3,plain,
    c_Divides_Oadjust(U_8000) = 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_8000))))),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_8000))))),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_2320_2]) ).

fof(f_2321_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_2321_2,plain,
    ! [U_8002,U_8001] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_8001),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_8001,U_8001)),tc_fun(tc_Int_Oint,U_8001)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8001,U_8001),U_8001),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_8001,U_8001)),tc_fun(tc_Int_Oint,U_8001)),tc_Int_Oint),c_COMBB(tc_fun(U_8001,U_8001),U_8001,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_8001,tc_fun(tc_fun(U_8001,U_8001),U_8001),tc_Int_Oint),c_HOL_OLet(U_8001,U_8001)),c_Int_Oring__1__class_Oof__int(U_8001)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_8001,U_8001),tc_fun(U_8001,U_8001)),hAPP(hAPP(c_COMBB(tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_fun(tc_fun(U_8001,U_8001),tc_fun(U_8001,U_8001)),tc_Int_Oint),c_COMBS(U_8001,U_8001,U_8001)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_8001,U_8001),tc_fun(U_8001,tc_fun(U_8001,U_8001))),hAPP(hAPP(c_COMBB(tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_fun(tc_fun(U_8001,U_8001),tc_fun(U_8001,tc_fun(U_8001,U_8001))),tc_Int_Oint),c_COMBB(U_8001,tc_fun(U_8001,U_8001),U_8001)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_Int_Oint),c_If(U_8001)),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_8001,U_8001,U_8001),c_Groups_Oplus__class_Oplus(U_8001)),c_COMBI(U_8001))))),hAPP(hAPP(c_COMBC(U_8001,U_8001,U_8001),hAPP(hAPP(c_COMBB(U_8001,tc_fun(U_8001,U_8001),U_8001),c_Groups_Oplus__class_Oplus(U_8001)),hAPP(hAPP(c_COMBS(U_8001,U_8001,U_8001),c_Groups_Oplus__class_Oplus(U_8001)),c_COMBI(U_8001)))),c_Groups_Oone__class_Oone(U_8001))))),c_Divides_Odivmod__int(U_8002,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_8002),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8001),hAPP(c_Int_Oring__1__class_Oof__int(U_8001),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8002)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8002),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_8002 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = c_Groups_Ozero__class_Ozero(U_8001)
          | U_8002 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_8001) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

cnf(f_2321_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = c_Groups_Ozero__class_Ozero(U_8001)
    | U_8002 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_8001) ),
    inference(clausify,[status(thm)],[f_2321_2]) ).

cnf(f_2321_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8001),hAPP(c_Int_Oring__1__class_Oof__int(U_8001),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8002)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8002),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_8002 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_8001) ),
    inference(clausify,[status(thm)],[f_2321_2]) ).

cnf(f_2321_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8001),U_8002) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_8001),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_8001,U_8001)),tc_fun(tc_Int_Oint,U_8001)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8001,U_8001),U_8001),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_8001,U_8001)),tc_fun(tc_Int_Oint,U_8001)),tc_Int_Oint),c_COMBB(tc_fun(U_8001,U_8001),U_8001,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_8001,tc_fun(tc_fun(U_8001,U_8001),U_8001),tc_Int_Oint),c_HOL_OLet(U_8001,U_8001)),c_Int_Oring__1__class_Oof__int(U_8001)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_8001,U_8001),tc_fun(U_8001,U_8001)),hAPP(hAPP(c_COMBB(tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_fun(tc_fun(U_8001,U_8001),tc_fun(U_8001,U_8001)),tc_Int_Oint),c_COMBS(U_8001,U_8001,U_8001)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_8001,U_8001),tc_fun(U_8001,tc_fun(U_8001,U_8001))),hAPP(hAPP(c_COMBB(tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_fun(tc_fun(U_8001,U_8001),tc_fun(U_8001,tc_fun(U_8001,U_8001))),tc_Int_Oint),c_COMBB(U_8001,tc_fun(U_8001,U_8001),U_8001)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8001,tc_fun(U_8001,U_8001)),tc_Int_Oint),c_If(U_8001)),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_8001,U_8001,U_8001),c_Groups_Oplus__class_Oplus(U_8001)),c_COMBI(U_8001))))),hAPP(hAPP(c_COMBC(U_8001,U_8001,U_8001),hAPP(hAPP(c_COMBB(U_8001,tc_fun(U_8001,U_8001),U_8001),c_Groups_Oplus__class_Oplus(U_8001)),hAPP(hAPP(c_COMBS(U_8001,U_8001,U_8001),c_Groups_Oplus__class_Oplus(U_8001)),c_COMBI(U_8001)))),c_Groups_Oone__class_Oone(U_8001))))),c_Divides_Odivmod__int(U_8002,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_8002),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_8002 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_8001) ),
    inference(clausify,[status(thm)],[f_2321_2]) ).

fof(f_2322_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_2322_2,plain,
    ! [U_8004,U_8003] :
      ( c_Divides_Odivmod__nat(U_8004,U_8003) = 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_8004),U_8003)),U_8003))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8004),U_8003),U_8003))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8003),U_8004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8003)) ),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

cnf(f_2322_3,plain,
    ( c_Divides_Odivmod__nat(U_8004,U_8003) = 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_8004),U_8003)),U_8003))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8004),U_8003),U_8003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8003),U_8004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8003)) ),
    inference(clausify,[status(thm)],[f_2322_2]) ).

fof(f_2323_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_2323_2,plain,
    ! [U_8009,U_8008,U_8007,U_8006,U_8005] : hAPP(c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8008)),U_8009)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_8005),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_8008))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8005,U_8005),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_8005,tc_fun(U_8005,U_8005)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8005,tc_fun(U_8005,U_8005)),tc_Int_Oint),c_If(U_8005)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007),U_8009))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8005,U_8005),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8005,U_8005),tc_Int_Oint),U_8007),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_8009))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8005,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007)),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_8009))))),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

cnf(f_2323_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8008)),U_8009)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_8005),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_8008))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8005,U_8005),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_8005,tc_fun(U_8005,U_8005)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8005,tc_fun(U_8005,U_8005)),tc_Int_Oint),c_If(U_8005)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007),U_8009))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8005,U_8005),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8005,U_8005),tc_Int_Oint),U_8007),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_8009))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8005,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_8005,U_8006,U_8007)),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_8009))))),
    inference(clausify,[status(thm)],[f_2323_2]) ).

fof(f_2324_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_2324_2,plain,
    ! [U_8011,U_8010] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8010),U_8011) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_8010,hAPP(hAPP(c_COMBC(U_8010,U_8010,U_8010),c_Groups_Oplus__class_Oplus(U_8010)),c_Groups_Oone__class_Oone(U_8010)),U_8011,c_Groups_Ozero__class_Ozero(U_8010))
      | ~ class_Rings_Osemiring__1(U_8010) ),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

cnf(f_2324_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8010),U_8011) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_8010,hAPP(hAPP(c_COMBC(U_8010,U_8010,U_8010),c_Groups_Oplus__class_Oplus(U_8010)),c_Groups_Oone__class_Oone(U_8010)),U_8011,c_Groups_Ozero__class_Ozero(U_8010))
    | ~ class_Rings_Osemiring__1(U_8010) ),
    inference(clausify,[status(thm)],[f_2324_2]) ).

fof(f_2325_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_2325_2,plain,
    ! [U_8014,U_8013,U_8012] : hAPP(c_Nat_Onat_Onat__rec(U_8012,U_8013,U_8014),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8013,
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

cnf(f_2325_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_8012,U_8013,U_8014),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8013,
    inference(clausify,[status(thm)],[f_2325_2]) ).

fof(f_2326_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_2326_2,plain,
    ! [U_8018,U_8017,U_8016,U_8015] : hAPP(c_Nat_Onat_Onat__rec(U_8015,U_8016,U_8017),hAPP(c_Nat_OSuc,U_8018)) = hAPP(hAPP(U_8017,U_8018),hAPP(c_Nat_Onat_Onat__rec(U_8015,U_8016,U_8017),U_8018)),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

cnf(f_2326_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_8015,U_8016,U_8017),hAPP(c_Nat_OSuc,U_8018)) = hAPP(hAPP(U_8017,U_8018),hAPP(c_Nat_Onat_Onat__rec(U_8015,U_8016,U_8017),U_8018)),
    inference(clausify,[status(thm)],[f_2326_2]) ).

fof(f_2327_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_2327_2,plain,
    ! [U_8019] : c_Divides_Odivmod__nat(U_8019,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_8019),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

cnf(f_2327_3,plain,
    c_Divides_Odivmod__nat(U_8019,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_8019),
    inference(clausify,[status(thm)],[f_2327_2]) ).

fof(f_2328_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_2328_2,plain,
    ! [U_8022,U_8021,U_8020] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_8020,U_8021,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8022) = U_8022
      | ~ class_Rings_Osemiring__1(U_8020) ),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

cnf(f_2328_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_8020,U_8021,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8022) = U_8022
    | ~ class_Rings_Osemiring__1(U_8020) ),
    inference(clausify,[status(thm)],[f_2328_2]) ).

fof(f_2329_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_2329_2,plain,
    ! [U_8026,U_8025,U_8024,U_8023] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_8023,U_8024,hAPP(c_Nat_OSuc,U_8025),U_8026) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_8023,U_8024,U_8025,hAPP(U_8024,U_8026))
      | ~ class_Rings_Osemiring__1(U_8023) ),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

cnf(f_2329_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_8023,U_8024,hAPP(c_Nat_OSuc,U_8025),U_8026) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_8023,U_8024,U_8025,hAPP(U_8024,U_8026))
    | ~ class_Rings_Osemiring__1(U_8023) ),
    inference(clausify,[status(thm)],[f_2329_2]) ).

fof(f_2330_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_2330_2,plain,
    ! [U_8028,U_8027] :
      ( c_Divides_Odivmod__nat(U_8027,U_8028) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8027)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8027),U_8028)) ),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

cnf(f_2330_3,plain,
    ( c_Divides_Odivmod__nat(U_8027,U_8028) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8027)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8027),U_8028)) ),
    inference(clausify,[status(thm)],[f_2330_2]) ).

fof(f_2331_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_2331_2,plain,
    ! [U_8030,U_8029] : c_Divides_Odivmod__nat(U_8029,U_8030) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8029),U_8030)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8029,U_8030)),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

cnf(f_2331_3,plain,
    c_Divides_Odivmod__nat(U_8029,U_8030) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8029),U_8030)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8029,U_8030)),
    inference(clausify,[status(thm)],[f_2331_2]) ).

fof(f_2332_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_2332_2,plain,
    ! [U_8032,U_8031] : c_Divides_Odivmod__int(U_8031,U_8032) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8031),U_8032)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8031,U_8032)),
    inference(variable_rename,[status(thm)],[f_2332_1]) ).

cnf(f_2332_3,plain,
    c_Divides_Odivmod__int(U_8031,U_8032) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8031),U_8032)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8031,U_8032)),
    inference(clausify,[status(thm)],[f_2332_2]) ).

fof(f_2333_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_2333_2,plain,
    ! [U_8036,U_8035,U_8034,U_8033] : hAPP(c_Nat_Onat_Onat__rec(U_8033,U_8034,U_8035),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8036)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_8033),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_8036))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8033,U_8033),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_8033,tc_fun(U_8033,U_8033)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8033,tc_fun(U_8033,U_8033)),tc_Int_Oint),c_If(U_8033)),c_Nat__Numeral_Oneg)),U_8034)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8033,U_8033),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8033,U_8033),tc_Int_Oint),U_8035),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8033,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_8033,U_8034,U_8035)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

cnf(f_2333_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_8033,U_8034,U_8035),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8036)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_8033),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_8036))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8033,U_8033),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_8033,tc_fun(U_8033,U_8033)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8033,tc_fun(U_8033,U_8033)),tc_Int_Oint),c_If(U_8033)),c_Nat__Numeral_Oneg)),U_8034)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_8033,U_8033),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8033,U_8033),tc_Int_Oint),U_8035),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8033,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_8033,U_8034,U_8035)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2333_2]) ).

fof(f_2334_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_2334_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_2334_1]) ).

fof(f_2335_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_2335_2,plain,
    ! [U_8038,U_8037] :
      ( ( ( ( c_Divides_Odivmod__int(U_8037,U_8038) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8037),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8038)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) )
          & ( c_Divides_Odivmod__int(U_8037,U_8038) = c_Divides_OnegDivAlg(U_8037,U_8038)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8037)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_8037,U_8038) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8037),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8038)))
                | U_8037 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_8037,U_8038) = 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_8037 != 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_8038)) )
          & ( c_Divides_Odivmod__int(U_8037,U_8038) = c_Divides_OposDivAlg(U_8037,U_8038)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8037)) ) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

fof(f_2335_3,plain,
    ( ! [U_8042,U_8040] :
        ( ( ( c_Divides_Odivmod__int(U_8040,U_8042) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8040),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8042)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042)) )
          & ( c_Divides_Odivmod__int(U_8040,U_8042) = c_Divides_OnegDivAlg(U_8040,U_8042)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8040)) )
    & ! [U_8041,U_8039] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_8039,U_8041) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8041)))
                | U_8039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_8039,U_8041) = 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_8039 != 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_8041)) )
          & ( c_Divides_Odivmod__int(U_8039,U_8041) = c_Divides_OposDivAlg(U_8039,U_8041)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8041)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039)) ) ),
    inference(miniscope,[status(thm)],[f_2335_2]) ).

cnf(f_2335_4,plain,
    ( c_Divides_Odivmod__int(U_8039,U_8041) = c_Divides_OposDivAlg(U_8039,U_8041)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8041))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

cnf(f_2335_5,plain,
    ( c_Divides_Odivmod__int(U_8039,U_8041) = 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_8039 != 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_8041))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

cnf(f_2335_6,plain,
    ( c_Divides_Odivmod__int(U_8039,U_8041) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8041)))
    | U_8039 = 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_8041))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

cnf(f_2335_7,plain,
    ( c_Divides_Odivmod__int(U_8040,U_8042) = c_Divides_OnegDivAlg(U_8040,U_8042)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8040)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

cnf(f_2335_8,plain,
    ( c_Divides_Odivmod__int(U_8040,U_8042) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8040),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8042)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8040)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

fof(f_2336_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_2336_2,plain,
    ! [U_8044,U_8043] :
      ( ( ( ( c_Divides_Odivmod__int(U_8043,U_8044) = 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_8044))),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_8044)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8043))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8044),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8043),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_8043,U_8044)),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_8044))))),c_Divides_Opdivmod(U_8043,U_8044))))
            | U_8044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_8043,U_8044) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8043)
            | U_8044 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_8043 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_8043,U_8044) = 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_8043 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

fof(f_2336_3,plain,
    ( ! [U_8048,U_8046] :
        ( ( ( c_Divides_Odivmod__int(U_8046,U_8048) = 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_8048))),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_8048)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8046))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8048),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8046),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_8046,U_8048)),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_8048))))),c_Divides_Opdivmod(U_8046,U_8048))))
            | U_8048 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_8046,U_8048) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8046)
            | U_8048 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_8046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8047,U_8045] :
        ( c_Divides_Odivmod__int(U_8045,U_8047) = 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_8045 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2336_2]) ).

cnf(f_2336_4,plain,
    ( c_Divides_Odivmod__int(U_8045,U_8047) = 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_8045 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2336_3]) ).

cnf(f_2336_5,plain,
    ( c_Divides_Odivmod__int(U_8046,U_8048) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8046)
    | U_8048 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2336_3]) ).

cnf(f_2336_6,plain,
    ( c_Divides_Odivmod__int(U_8046,U_8048) = 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_8048))),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_8048)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8046))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8048),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8046),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_8046,U_8048)),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_8048))))),c_Divides_Opdivmod(U_8046,U_8048))))
    | U_8048 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2336_3]) ).

fof(f_2337_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_2337_2,plain,
    ! [U_8053,U_8052,U_8051,U_8050,U_8049] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8049,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8050),U_8053)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8051),U_8053)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8050),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8051,U_8053))),U_8052))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8050))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8049,U_8050),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8051),U_8052))) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

cnf(f_2337_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8049,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8050),U_8053)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8051),U_8053)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8050),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8051,U_8053))),U_8052))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8053))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8050))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8049,U_8050),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8051),U_8052))) ),
    inference(clausify,[status(thm)],[f_2337_2]) ).

fof(f_2338_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_2338_2,plain,
    ! [U_8057,U_8056,U_8055,U_8054] :
      ( U_8056 = U_8057
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8054,U_8055),U_8057))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8054,U_8055),U_8056)) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

cnf(f_2338_3,plain,
    ( U_8056 = U_8057
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8054,U_8055),U_8057))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8054,U_8055),U_8056)) ),
    inference(clausify,[status(thm)],[f_2338_2]) ).

fof(f_2339_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_2339_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_2339_1]) ).

fof(f_2340_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_2340_2,plain,
    ! [U_8059,U_8058] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8058,U_8059),c_Divides_Odivmod__nat(U_8058,U_8059))),
    inference(variable_rename,[status(thm)],[f_2340_1]) ).

cnf(f_2340_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8058,U_8059),c_Divides_Odivmod__nat(U_8058,U_8059))),
    inference(clausify,[status(thm)],[f_2340_2]) ).

fof(f_2341_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_2341_2,plain,
    ! [U_8062,U_8061,U_8060] :
      ( c_Divides_Odivmod__nat(U_8060,U_8061) = U_8062
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8060,U_8061),U_8062)) ),
    inference(variable_rename,[status(thm)],[f_2341_1]) ).

cnf(f_2341_3,plain,
    ( c_Divides_Odivmod__nat(U_8060,U_8061) = U_8062
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8060,U_8061),U_8062)) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

fof(f_2342_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_2342_2,plain,
    ! [U_8066,U_8065,U_8064,U_8063] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8063,U_8064) = U_8066
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8063,U_8064),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8065),U_8066))) ),
    inference(variable_rename,[status(thm)],[f_2342_1]) ).

cnf(f_2342_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8063,U_8064) = U_8066
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8063,U_8064),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8065),U_8066))) ),
    inference(clausify,[status(thm)],[f_2342_2]) ).

fof(f_2343_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_2343_2,plain,
    ! [U_8070,U_8069,U_8068,U_8067] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8067),U_8068) = U_8069
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8067,U_8068),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8069),U_8070))) ),
    inference(variable_rename,[status(thm)],[f_2343_1]) ).

cnf(f_2343_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8067),U_8068) = U_8069
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8067,U_8068),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8069),U_8070))) ),
    inference(clausify,[status(thm)],[f_2343_2]) ).

fof(f_2344_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_2344_2,plain,
    ! [U_8072,U_8071] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8071),U_8072)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8072)),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

cnf(f_2344_3,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8071),U_8072)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8072)),
    inference(clausify,[status(thm)],[f_2344_2]) ).

fof(f_2345_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_2345_2,plain,
    ! [U_8074,U_8073] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8073,U_8074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8073),U_8074)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8073,U_8074)))),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

cnf(f_2345_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8073,U_8074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8073),U_8074)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8073,U_8074)))),
    inference(clausify,[status(thm)],[f_2345_2]) ).

fof(f_2346_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_2346_2,plain,
    ! [U_8081,U_8080,U_8079,U_8078,U_8077,U_8076,U_8075] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8075),U_8079),U_8076),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_8077),U_8080)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8078),U_8081)),U_8076))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8078),U_8081),U_8076))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8076))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8079,U_8076),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8080),U_8081)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8075,U_8076),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8077),U_8078))) ),
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

cnf(f_2346_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8075),U_8079),U_8076),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_8077),U_8080)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8078),U_8081)),U_8076))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8078),U_8081),U_8076))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8076))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8079,U_8076),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8080),U_8081)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8075,U_8076),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8077),U_8078))) ),
    inference(clausify,[status(thm)],[f_2346_2]) ).

fof(f_2347_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_2347_2,plain,
    ! [U_8083,U_8082] : c_Divides_Opdivmod(U_8082,U_8083) = 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_8082)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8083))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8082),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8083))),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

cnf(f_2347_3,plain,
    c_Divides_Opdivmod(U_8082,U_8083) = 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_8082)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8083))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8082),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8083))),
    inference(clausify,[status(thm)],[f_2347_2]) ).

fof(f_2348_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_2348_2,plain,
    ! [U_8085,U_8084] :
      ( ( c_Divides_Opdivmod(U_8085,U_8084) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8085),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8084))
        | U_8084 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_8085,U_8084) = 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_8085))
        | U_8084 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

fof(f_2348_3,plain,
    ( ! [U_8089,U_8087] :
        ( c_Divides_Opdivmod(U_8089,U_8087) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8089),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8087))
        | U_8087 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8088,U_8086] :
        ( c_Divides_Opdivmod(U_8088,U_8086) = 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_8088))
        | U_8086 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2348_2]) ).

cnf(f_2348_4,plain,
    ( c_Divides_Opdivmod(U_8088,U_8086) = 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_8088))
    | U_8086 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

cnf(f_2348_5,plain,
    ( c_Divides_Opdivmod(U_8089,U_8087) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8089),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8087))
    | U_8087 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

fof(f_2349_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_2349_2,plain,
    ! [U_8091,U_8090] :
      ( ( ( ( c_Divides_Odivmod__int(U_8090,U_8091) = 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_8091))),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_8090)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_8091))),c_Divides_Opdivmod(U_8090,U_8091)),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_8091))))),c_Divides_Opdivmod(U_8090,U_8091))))
            | U_8091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_8090,U_8091) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8090)
            | U_8091 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_8090 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_8090,U_8091) = 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_8090 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

fof(f_2349_3,plain,
    ( ! [U_8095,U_8093] :
        ( ( ( c_Divides_Odivmod__int(U_8093,U_8095) = 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_8095))),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_8093)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_8095))),c_Divides_Opdivmod(U_8093,U_8095)),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_8095))))),c_Divides_Opdivmod(U_8093,U_8095))))
            | U_8095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_8093,U_8095) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8093)
            | U_8095 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_8093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8094,U_8092] :
        ( c_Divides_Odivmod__int(U_8092,U_8094) = 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_8092 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2349_2]) ).

cnf(f_2349_4,plain,
    ( c_Divides_Odivmod__int(U_8092,U_8094) = 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_8092 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_5,plain,
    ( c_Divides_Odivmod__int(U_8093,U_8095) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8093)
    | U_8095 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_6,plain,
    ( c_Divides_Odivmod__int(U_8093,U_8095) = 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_8095))),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_8093)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_8095))),c_Divides_Opdivmod(U_8093,U_8095)),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_8095))))),c_Divides_Opdivmod(U_8093,U_8095))))
    | U_8095 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

fof(f_2350_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_2350_2,plain,
    ! [U_8100,U_8099,U_8098,U_8097,U_8096] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8096),U_8097),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_8100),U_8098)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8099)),U_8097))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8099),U_8097))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8097))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8096,U_8097),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8098),U_8099))) ),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

cnf(f_2350_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8096),U_8097),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_8100),U_8098)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8099)),U_8097))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8100),U_8099),U_8097))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8097))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8096,U_8097),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8098),U_8099))) ),
    inference(clausify,[status(thm)],[f_2350_2]) ).

fof(f_2351_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_2351_2,plain,
    ! [U_8105,U_8104,U_8103,U_8102,U_8101] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8104,U_8105,tc_HOL_Obool),U_8101),hAPP(hAPP(c_Product__Type_OPair(U_8104,U_8105),U_8102),U_8103)))
      | ~ hBOOL(hAPP(hAPP(U_8101,U_8102),U_8103)) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

cnf(f_2351_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8104,U_8105,tc_HOL_Obool),U_8101),hAPP(hAPP(c_Product__Type_OPair(U_8104,U_8105),U_8102),U_8103)))
    | ~ hBOOL(hAPP(hAPP(U_8101,U_8102),U_8103)) ),
    inference(clausify,[status(thm)],[f_2351_2]) ).

fof(f_2352_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_2352_2,plain,
    ! [U_8110,U_8109,U_8108,U_8107,U_8106] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8109,U_8110,tc_HOL_Obool),U_8106),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8110),U_8107),U_8108)))
      | ~ hBOOL(hAPP(hAPP(U_8106,U_8107),U_8108)) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

cnf(f_2352_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8109,U_8110,tc_HOL_Obool),U_8106),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8110),U_8107),U_8108)))
    | ~ hBOOL(hAPP(hAPP(U_8106,U_8107),U_8108)) ),
    inference(clausify,[status(thm)],[f_2352_2]) ).

fof(f_2353_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_2353_2,plain,
    ! [U_8112,U_8111] :
      ( ( ( c_Divides_OnegDivAlg(U_8111,U_8112) = hAPP(c_Divides_Oadjust(U_8112),c_Divides_OnegDivAlg(U_8111,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_8112)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8112),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_8111),U_8112))) )
        & ( c_Divides_OnegDivAlg(U_8111,U_8112) = 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_8111),U_8112))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8112),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_8111),U_8112))) ) ) )
      | ~ 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_8111),U_8112))) ),
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

cnf(f_2353_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_8111),U_8112)))
    | c_Divides_OnegDivAlg(U_8111,U_8112) = 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_8111),U_8112))
    | ~ 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_8111),U_8112))) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

cnf(f_2353_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8112),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_8111,U_8112) = 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_8111),U_8112))
    | ~ 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_8111),U_8112))) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

cnf(f_2353_5,plain,
    ( c_Divides_OnegDivAlg(U_8111,U_8112) = hAPP(c_Divides_Oadjust(U_8112),c_Divides_OnegDivAlg(U_8111,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_8112)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8112),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_8111),U_8112)))
    | ~ 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_8111),U_8112))) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

fof(f_2354_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_2354_2,plain,
    ! [U_8113] :
      ( c_Orderings_Oord_Omax(U_8113,hAPP(c_COMBC(U_8113,U_8113,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_8113))) = c_Orderings_Oord__class_Omin(U_8113)
      | ~ class_Orderings_Olinorder(U_8113) ),
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

cnf(f_2354_3,plain,
    ( c_Orderings_Oord_Omax(U_8113,hAPP(c_COMBC(U_8113,U_8113,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_8113))) = c_Orderings_Oord__class_Omin(U_8113)
    | ~ class_Orderings_Olinorder(U_8113) ),
    inference(clausify,[status(thm)],[f_2354_2]) ).

fof(f_2355_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_2355_2,plain,
    ! [U_8117,U_8116,U_8115,U_8114] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8114,U_8115),U_8117))
      | ~ hBOOL(hAPP(hAPP(U_8115,U_8117),U_8116))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8114,U_8115),U_8116)) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

cnf(f_2355_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8114,U_8115),U_8117))
    | ~ hBOOL(hAPP(hAPP(U_8115,U_8117),U_8116))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8114,U_8115),U_8116)) ),
    inference(clausify,[status(thm)],[f_2355_2]) ).

fof(f_2356_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_2356_2,plain,
    ! [U_8122,U_8121,U_8120] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8120,U_8121),U_8122))
        | ? [U_8119] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8120,U_8121),U_8119))
            & hBOOL(hAPP(hAPP(U_8121,U_8119),U_8122)) ) )
      & ( ! [U_8118] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8120,U_8121),U_8118))
            | ~ hBOOL(hAPP(hAPP(U_8121,U_8118),U_8122)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8120,U_8121),U_8122)) ) ),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

fof(f_2356_3,plain,
    ( ! [U_8128,U_8126,U_8124] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),U_8128))
        | ? [U_8119] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),U_8119))
            & hBOOL(hAPP(hAPP(U_8126,U_8119),U_8128)) ) )
    & ! [U_8127,U_8125,U_8123] :
        ( ! [U_8118] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8118))
            | ~ hBOOL(hAPP(hAPP(U_8125,U_8118),U_8127)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8127)) ) ),
    inference(miniscope,[status(thm)],[f_2356_2]) ).

fof(f_2356_4,plain,
    ( ! [U_8128,U_8126,U_8124] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),U_8128))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),sK149(U_8128,U_8126,U_8124)))
          & hBOOL(hAPP(hAPP(U_8126,sK149(U_8128,U_8126,U_8124)),U_8128)) ) )
    & ! [U_8127,U_8125,U_8123] :
        ( ! [U_8118] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8118))
            | ~ hBOOL(hAPP(hAPP(U_8125,U_8118),U_8127)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8127)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_8119,sK149(U_8128,U_8126,U_8124))],[f_2356_3]) ).

cnf(f_2356_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8118))
    | ~ hBOOL(hAPP(hAPP(U_8125,U_8118),U_8127))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8123,U_8125),U_8127)) ),
    inference(clausify,[status(thm)],[f_2356_4]) ).

cnf(f_2356_6,plain,
    ( hBOOL(hAPP(hAPP(U_8126,sK149(U_8128,U_8126,U_8124)),U_8128))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),U_8128)) ),
    inference(clausify,[status(thm)],[f_2356_4]) ).

cnf(f_2356_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),sK149(U_8128,U_8126,U_8124)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_8124,U_8126),U_8128)) ),
    inference(clausify,[status(thm)],[f_2356_4]) ).

fof(f_2357_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_2357_2,plain,
    ! [U_8133,U_8132,U_8131] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8131,U_8132),U_8133))
        | ? [U_8130] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8131,U_8132),U_8130))
            & hBOOL(hAPP(hAPP(U_8132,U_8130),U_8133)) ) )
      & ( ! [U_8129] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8131,U_8132),U_8129))
            | ~ hBOOL(hAPP(hAPP(U_8132,U_8129),U_8133)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8131,U_8132),U_8133)) ) ),
    inference(variable_rename,[status(thm)],[f_2357_1]) ).

fof(f_2357_3,plain,
    ( ! [U_8139,U_8137,U_8135] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),U_8139))
        | ? [U_8130] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),U_8130))
            & hBOOL(hAPP(hAPP(U_8137,U_8130),U_8139)) ) )
    & ! [U_8138,U_8136,U_8134] :
        ( ! [U_8129] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8129))
            | ~ hBOOL(hAPP(hAPP(U_8136,U_8129),U_8138)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8138)) ) ),
    inference(miniscope,[status(thm)],[f_2357_2]) ).

fof(f_2357_4,plain,
    ( ! [U_8139,U_8137,U_8135] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),U_8139))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),sK150(U_8139,U_8137,U_8135)))
          & hBOOL(hAPP(hAPP(U_8137,sK150(U_8139,U_8137,U_8135)),U_8139)) ) )
    & ! [U_8138,U_8136,U_8134] :
        ( ! [U_8129] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8129))
            | ~ hBOOL(hAPP(hAPP(U_8136,U_8129),U_8138)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8138)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_8130,sK150(U_8139,U_8137,U_8135))],[f_2357_3]) ).

cnf(f_2357_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8129))
    | ~ hBOOL(hAPP(hAPP(U_8136,U_8129),U_8138))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8134,U_8136),U_8138)) ),
    inference(clausify,[status(thm)],[f_2357_4]) ).

cnf(f_2357_6,plain,
    ( hBOOL(hAPP(hAPP(U_8137,sK150(U_8139,U_8137,U_8135)),U_8139))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),U_8139)) ),
    inference(clausify,[status(thm)],[f_2357_4]) ).

cnf(f_2357_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),sK150(U_8139,U_8137,U_8135)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_8135,U_8137),U_8139)) ),
    inference(clausify,[status(thm)],[f_2357_4]) ).

fof(f_2358_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_2358_2,plain,
    ! [U_8142,U_8141,U_8140] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8140,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_8140,U_8142)),c_Wellfounded_Oaccp(U_8140,U_8141)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8140,tc_fun(U_8140,tc_HOL_Obool))),U_8141),U_8142)) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

cnf(f_2358_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8140,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_8140,U_8142)),c_Wellfounded_Oaccp(U_8140,U_8141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8140,tc_fun(U_8140,tc_HOL_Obool))),U_8141),U_8142)) ),
    inference(clausify,[status(thm)],[f_2358_2]) ).

fof(f_2359_1,plain,
    ! [T_c,T_b,V_Pa_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ? [B_a,B_b] : ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
      & ( ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
        | ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).

fof(f_2359_2,plain,
    ! [U_8151,U_8150,U_8149] :
      ( ( ! [U_8148] : hBOOL(hAPP(U_8149,U_8148))
        | ? [U_8147,U_8146] : ~ hBOOL(hAPP(U_8149,hAPP(hAPP(c_Product__Type_OPair(U_8150,U_8151),U_8147),U_8146))) )
      & ( ! [U_8145,U_8144] : hBOOL(hAPP(U_8149,hAPP(hAPP(c_Product__Type_OPair(U_8150,U_8151),U_8145),U_8144)))
        | ? [U_8143] : ~ hBOOL(hAPP(U_8149,U_8143)) ) ),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

fof(f_2359_3,plain,
    ( ! [U_8157,U_8155,U_8153] :
        ( ! [U_8148] : hBOOL(hAPP(U_8153,U_8148))
        | ? [U_8147,U_8146] : ~ hBOOL(hAPP(U_8153,hAPP(hAPP(c_Product__Type_OPair(U_8155,U_8157),U_8147),U_8146))) )
    & ! [U_8156,U_8154,U_8152] :
        ( ! [U_8145,U_8144] : hBOOL(hAPP(U_8152,hAPP(hAPP(c_Product__Type_OPair(U_8154,U_8156),U_8145),U_8144)))
        | ? [U_8143] : ~ hBOOL(hAPP(U_8152,U_8143)) ) ),
    inference(miniscope,[status(thm)],[f_2359_2]) ).

fof(f_2359_4,plain,
    ( ! [U_8157,U_8155,U_8153] :
        ( ! [U_8148] : hBOOL(hAPP(U_8153,U_8148))
        | ? [U_8147,U_8146] : ~ hBOOL(hAPP(U_8153,hAPP(hAPP(c_Product__Type_OPair(U_8155,U_8157),U_8147),U_8146))) )
    & ! [U_8156,U_8154,U_8152] :
        ( ! [U_8145,U_8144] : hBOOL(hAPP(U_8152,hAPP(hAPP(c_Product__Type_OPair(U_8154,U_8156),U_8145),U_8144)))
        | ~ hBOOL(hAPP(U_8152,sK151(U_8156,U_8154,U_8152))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_8143,sK151(U_8156,U_8154,U_8152))],[f_2359_3]) ).

fof(f_2359_5,plain,
    ( ! [U_8157,U_8155,U_8153] :
        ( ! [U_8148] : hBOOL(hAPP(U_8153,U_8148))
        | ? [U_8146] : ~ hBOOL(hAPP(U_8153,hAPP(hAPP(c_Product__Type_OPair(U_8155,U_8157),sK152(U_8157,U_8155,U_8153)),U_8146))) )
    & ! [U_8156,U_8154,U_8152] :
        ( ! [U_8145,U_8144] : hBOOL(hAPP(U_8152,hAPP(hAPP(c_Product__Type_OPair(U_8154,U_8156),U_8145),U_8144)))
        | ~ hBOOL(hAPP(U_8152,sK151(U_8156,U_8154,U_8152))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_8147,sK152(U_8157,U_8155,U_8153))],[f_2359_4]) ).

fof(f_2359_6,plain,
    ( ! [U_8157,U_8155,U_8153] :
        ( ! [U_8148] : hBOOL(hAPP(U_8153,U_8148))
        | ~ hBOOL(hAPP(U_8153,hAPP(hAPP(c_Product__Type_OPair(U_8155,U_8157),sK152(U_8157,U_8155,U_8153)),sK153(U_8157,U_8155,U_8153)))) )
    & ! [U_8156,U_8154,U_8152] :
        ( ! [U_8145,U_8144] : hBOOL(hAPP(U_8152,hAPP(hAPP(c_Product__Type_OPair(U_8154,U_8156),U_8145),U_8144)))
        | ~ hBOOL(hAPP(U_8152,sK151(U_8156,U_8154,U_8152))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_8146,sK153(U_8157,U_8155,U_8153))],[f_2359_5]) ).

cnf(f_2359_7,plain,
    ( hBOOL(hAPP(U_8152,hAPP(hAPP(c_Product__Type_OPair(U_8154,U_8156),U_8145),U_8144)))
    | ~ hBOOL(hAPP(U_8152,sK151(U_8156,U_8154,U_8152))) ),
    inference(clausify,[status(thm)],[f_2359_6]) ).

cnf(f_2359_8,plain,
    ( hBOOL(hAPP(U_8153,U_8148))
    | ~ hBOOL(hAPP(U_8153,hAPP(hAPP(c_Product__Type_OPair(U_8155,U_8157),sK152(U_8157,U_8155,U_8153)),sK153(U_8157,U_8155,U_8153)))) ),
    inference(clausify,[status(thm)],[f_2359_6]) ).

fof(f_2360_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_2360_2,plain,
    ! [U_8163,U_8162,U_8161,U_8160,U_8159,U_8158] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_8158,U_8159),U_8160),U_8161) = hAPP(hAPP(c_Product__Type_OPair(U_8158,U_8159),U_8162),U_8163)
        | U_8161 != U_8163
        | U_8160 != U_8162 )
      & ( ( U_8161 = U_8163
          & U_8160 = U_8162 )
        | hAPP(hAPP(c_Product__Type_OPair(U_8158,U_8159),U_8160),U_8161) != hAPP(hAPP(c_Product__Type_OPair(U_8158,U_8159),U_8162),U_8163) ) ),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

fof(f_2360_3,plain,
    ( ! [U_8175,U_8173,U_8171,U_8169] :
        ( ! [U_8167,U_8165] : hAPP(hAPP(c_Product__Type_OPair(U_8165,U_8167),U_8169),U_8171) = hAPP(hAPP(c_Product__Type_OPair(U_8165,U_8167),U_8173),U_8175)
        | U_8171 != U_8175
        | U_8169 != U_8173 )
    & ! [U_8174,U_8172,U_8170,U_8168] :
        ( ! [U_8166,U_8164] : hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8168),U_8170) != hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8172),U_8174)
        | ( U_8170 = U_8174
          & U_8168 = U_8172 ) ) ),
    inference(miniscope,[status(thm)],[f_2360_2]) ).

cnf(f_2360_4,plain,
    ( U_8168 = U_8172
    | hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8168),U_8170) != hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8172),U_8174) ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

cnf(f_2360_5,plain,
    ( U_8170 = U_8174
    | hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8168),U_8170) != hAPP(hAPP(c_Product__Type_OPair(U_8164,U_8166),U_8172),U_8174) ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

cnf(f_2360_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_8165,U_8167),U_8169),U_8171) = hAPP(hAPP(c_Product__Type_OPair(U_8165,U_8167),U_8173),U_8175)
    | U_8171 != U_8175
    | U_8169 != U_8173 ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

fof(f_2361_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_2361_2,plain,
    ! [U_8181,U_8180,U_8179,U_8178,U_8177,U_8176] :
      ( ( U_8179 = U_8181
        & U_8178 = U_8180 )
      | hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8178),U_8179) != hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8180),U_8181) ),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

fof(f_2361_3,plain,
    ! [U_8181,U_8180,U_8179,U_8178] :
      ( ! [U_8177,U_8176] : hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8178),U_8179) != hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8180),U_8181)
      | ( U_8179 = U_8181
        & U_8178 = U_8180 ) ),
    inference(miniscope,[status(thm)],[f_2361_2]) ).

cnf(f_2361_4,plain,
    ( U_8178 = U_8180
    | hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8178),U_8179) != hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8180),U_8181) ),
    inference(clausify,[status(thm)],[f_2361_3]) ).

cnf(f_2361_5,plain,
    ( U_8179 = U_8181
    | hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8178),U_8179) != hAPP(hAPP(c_Product__Type_OPair(U_8176,U_8177),U_8180),U_8181) ),
    inference(clausify,[status(thm)],[f_2361_3]) ).

fof(f_2362_1,plain,
    ! [V_ca_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_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2)
      | V_p_2 != V_q_2 ),
    inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).

fof(f_2362_2,plain,
    ! [U_8187,U_8186,U_8185,U_8184,U_8183,U_8182] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8184,U_8185,U_8186),U_8187),U_8182) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8184,U_8185,U_8186),U_8187),U_8183)
      | U_8182 != U_8183 ),
    inference(variable_rename,[status(thm)],[f_2362_1]) ).

cnf(f_2362_3,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8184,U_8185,U_8186),U_8187),U_8182) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8184,U_8185,U_8186),U_8187),U_8183)
    | U_8182 != U_8183 ),
    inference(clausify,[status(thm)],[f_2362_2]) ).

fof(f_2363_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_2363_2,plain,
    ! [U_8193,U_8192,U_8191,U_8190,U_8189,U_8188] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8188,U_8189,U_8190),U_8191),hAPP(hAPP(c_Product__Type_OPair(U_8188,U_8189),U_8192),U_8193)) = hAPP(hAPP(U_8191,U_8192),U_8193),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

cnf(f_2363_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8188,U_8189,U_8190),U_8191),hAPP(hAPP(c_Product__Type_OPair(U_8188,U_8189),U_8192),U_8193)) = hAPP(hAPP(U_8191,U_8192),U_8193),
    inference(clausify,[status(thm)],[f_2363_2]) ).

fof(f_2364_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_2364_2,plain,
    ! [U_8199,U_8198,U_8197,U_8196,U_8195,U_8194] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8194,U_8195,U_8196),U_8197),hAPP(hAPP(c_Product__Type_OPair(U_8194,U_8195),U_8198),U_8199)) = hAPP(hAPP(U_8197,U_8198),U_8199),
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

cnf(f_2364_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8194,U_8195,U_8196),U_8197),hAPP(hAPP(c_Product__Type_OPair(U_8194,U_8195),U_8198),U_8199)) = hAPP(hAPP(U_8197,U_8198),U_8199),
    inference(clausify,[status(thm)],[f_2364_2]) ).

fof(f_2365_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_2365_2,plain,
    ! [U_8204,U_8203,U_8202,U_8201,U_8200] :
      ( hBOOL(hAPP(hAPP(U_8202,U_8203),U_8204))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8200,U_8201,tc_HOL_Obool),U_8202),hAPP(hAPP(c_Product__Type_OPair(U_8200,U_8201),U_8203),U_8204))) ),
    inference(variable_rename,[status(thm)],[f_2365_1]) ).

fof(f_2365_3,plain,
    ! [U_8204,U_8203,U_8202] :
      ( ! [U_8201,U_8200] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8200,U_8201,tc_HOL_Obool),U_8202),hAPP(hAPP(c_Product__Type_OPair(U_8200,U_8201),U_8203),U_8204)))
      | hBOOL(hAPP(hAPP(U_8202,U_8203),U_8204)) ),
    inference(miniscope,[status(thm)],[f_2365_2]) ).

cnf(f_2365_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8200,U_8201,tc_HOL_Obool),U_8202),hAPP(hAPP(c_Product__Type_OPair(U_8200,U_8201),U_8203),U_8204)))
    | hBOOL(hAPP(hAPP(U_8202,U_8203),U_8204)) ),
    inference(clausify,[status(thm)],[f_2365_3]) ).

fof(f_2366_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_2366_2,plain,
    ! [U_8210,U_8209,U_8208,U_8207,U_8206,U_8205] : hAPP(c_Product__Type_Oapsnd(U_8205,U_8206,U_8207,U_8208),hAPP(hAPP(c_Product__Type_OPair(U_8207,U_8205),U_8209),U_8210)) = hAPP(hAPP(c_Product__Type_OPair(U_8207,U_8206),U_8209),hAPP(U_8208,U_8210)),
    inference(variable_rename,[status(thm)],[f_2366_1]) ).

cnf(f_2366_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_8205,U_8206,U_8207,U_8208),hAPP(hAPP(c_Product__Type_OPair(U_8207,U_8205),U_8209),U_8210)) = hAPP(hAPP(c_Product__Type_OPair(U_8207,U_8206),U_8209),hAPP(U_8208,U_8210)),
    inference(clausify,[status(thm)],[f_2366_2]) ).

fof(f_2367_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_2367_2,plain,
    ! [U_8214,U_8213,U_8212,U_8211] : hAPP(c_Product__Type_Oprod_Oprod__case(U_8211,U_8212,U_8213),hAPP(hAPP(c_COMBB(tc_fun(U_8212,tc_prod(U_8211,U_8212)),tc_fun(U_8212,U_8213),U_8211),hAPP(c_COMBB(tc_prod(U_8211,U_8212),U_8213,U_8212),U_8214)),c_Product__Type_OPair(U_8211,U_8212))) = U_8214,
    inference(variable_rename,[status(thm)],[f_2367_1]) ).

cnf(f_2367_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_8211,U_8212,U_8213),hAPP(hAPP(c_COMBB(tc_fun(U_8212,tc_prod(U_8211,U_8212)),tc_fun(U_8212,U_8213),U_8211),hAPP(c_COMBB(tc_prod(U_8211,U_8212),U_8213,U_8212),U_8214)),c_Product__Type_OPair(U_8211,U_8212))) = U_8214,
    inference(clausify,[status(thm)],[f_2367_2]) ).

fof(f_2368_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_2368_2,plain,
    ! [U_8222,U_8221,U_8220,U_8219,U_8218,U_8217,U_8216,U_8215] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8215,U_8216,U_8217),U_8218),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8219,U_8220,tc_prod(U_8215,U_8216)),U_8221),U_8222)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8219,U_8220,U_8217),hAPP(hAPP(c_COMBB(tc_fun(U_8220,tc_prod(U_8215,U_8216)),tc_fun(U_8220,U_8217),U_8219),hAPP(c_COMBB(tc_prod(U_8215,U_8216),U_8217,U_8220),hAPP(c_Product__Type_Oprod_Oprod__case(U_8215,U_8216,U_8217),U_8218))),U_8221)),U_8222),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

cnf(f_2368_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8215,U_8216,U_8217),U_8218),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8219,U_8220,tc_prod(U_8215,U_8216)),U_8221),U_8222)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8219,U_8220,U_8217),hAPP(hAPP(c_COMBB(tc_fun(U_8220,tc_prod(U_8215,U_8216)),tc_fun(U_8220,U_8217),U_8219),hAPP(c_COMBB(tc_prod(U_8215,U_8216),U_8217,U_8220),hAPP(c_Product__Type_Oprod_Oprod__case(U_8215,U_8216,U_8217),U_8218))),U_8221)),U_8222),
    inference(clausify,[status(thm)],[f_2368_2]) ).

fof(f_2369_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_2369_2,plain,
    ! [U_8224,U_8223] :
      ( ( ( c_Divides_OposDivAlg(U_8223,U_8224) = hAPP(c_Divides_Oadjust(U_8224),c_Divides_OposDivAlg(U_8223,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_8224)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8224),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8223),U_8224)) )
        & ( c_Divides_OposDivAlg(U_8223,U_8224) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8223)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8224),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8223),U_8224)) ) ) )
      | ~ 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_8223),U_8224))) ),
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

cnf(f_2369_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8223),U_8224))
    | c_Divides_OposDivAlg(U_8223,U_8224) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8223)
    | ~ 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_8223),U_8224))) ),
    inference(clausify,[status(thm)],[f_2369_2]) ).

cnf(f_2369_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8224),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_8223,U_8224) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8223)
    | ~ 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_8223),U_8224))) ),
    inference(clausify,[status(thm)],[f_2369_2]) ).

cnf(f_2369_5,plain,
    ( c_Divides_OposDivAlg(U_8223,U_8224) = hAPP(c_Divides_Oadjust(U_8224),c_Divides_OposDivAlg(U_8223,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_8224)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8224),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8223),U_8224))
    | ~ 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_8223),U_8224))) ),
    inference(clausify,[status(thm)],[f_2369_2]) ).

fof(f_2370_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_2370_2,plain,
    ! [U_8226,U_8225] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_8225,U_8226) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_8225),U_8226)),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_8225))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8226)))
              | U_8226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_8225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_8225,U_8226) = 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_8226 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_8225 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8226),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_8225,U_8226) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8225),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8226))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8226),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_8225),U_8226))) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

cnf(f_2370_3,plain,
    ( c_Nitpick_Onorm__frac(U_8225,U_8226) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8225),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8226),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_8225),U_8226))) ),
    inference(clausify,[status(thm)],[f_2370_2]) ).

cnf(f_2370_4,plain,
    ( U_8225 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_8225,U_8226) = 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_8226),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_8225),U_8226))) ),
    inference(clausify,[status(thm)],[f_2370_2]) ).

cnf(f_2370_5,plain,
    ( U_8226 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_8225,U_8226) = 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_8226),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_8225),U_8226))) ),
    inference(clausify,[status(thm)],[f_2370_2]) ).

cnf(f_2370_6,plain,
    ( c_Nitpick_Onorm__frac(U_8225,U_8226) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_8225),U_8226)),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_8225))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8226)))
    | U_8226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8226),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_8225),U_8226))) ),
    inference(clausify,[status(thm)],[f_2370_2]) ).

fof(f_2371_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_2371_2,plain,
    ! [U_8231,U_8230,U_8229] :
      ( hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
      | ? [U_8228,U_8227] :
          ( ~ hBOOL(hAPP(hAPP(U_8231,U_8228),U_8227))
          & ( hBOOL(hAPP(hAPP(U_8231,U_8228),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_8227)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8227),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_8228),U_8227))) )
          & 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_8228),U_8227))) )
      | ~ 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_8229),U_8230))) ),
    inference(variable_rename,[status(thm)],[f_2371_1]) ).

fof(f_2371_3,plain,
    ! [U_8231,U_8230,U_8229] :
      ( hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
      | ? [U_8227] :
          ( ~ hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),U_8227))
          & ( hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),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_8227)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8227),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),sK154(U_8231,U_8230,U_8229)),U_8227))) )
          & 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),sK154(U_8231,U_8230,U_8229)),U_8227))) )
      | ~ 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_8229),U_8230))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_8228,sK154(U_8231,U_8230,U_8229))],[f_2371_2]) ).

fof(f_2371_4,plain,
    ! [U_8231,U_8230,U_8229] :
      ( hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
      | ( ~ hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229)))
        & ( hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),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)))),sK155(U_8231,U_8230,U_8229))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK155(U_8231,U_8230,U_8229)),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),sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229)))) )
        & 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),sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229)))) )
      | ~ 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_8229),U_8230))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_8227,sK155(U_8231,U_8230,U_8229))],[f_2371_3]) ).

cnf(f_2371_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),sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229))))
    | hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
    | ~ 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_8229),U_8230))) ),
    inference(clausify,[status(thm)],[f_2371_4]) ).

cnf(f_2371_6,plain,
    ( hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),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)))),sK155(U_8231,U_8230,U_8229))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK155(U_8231,U_8230,U_8229)),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),sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229))))
    | hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
    | ~ 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_8229),U_8230))) ),
    inference(clausify,[status(thm)],[f_2371_4]) ).

cnf(f_2371_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8231,sK154(U_8231,U_8230,U_8229)),sK155(U_8231,U_8230,U_8229)))
    | hBOOL(hAPP(hAPP(U_8231,U_8229),U_8230))
    | ~ 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_8229),U_8230))) ),
    inference(clausify,[status(thm)],[f_2371_4]) ).

fof(f_2372_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_2372_2,plain,
    ! [U_8236,U_8235,U_8234,U_8233,U_8232] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8232,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8233),U_8236)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8234),U_8236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8233),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8234,U_8236))),U_8235))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8236))
      | U_8233 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8232,U_8233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8234),U_8235))) ),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

cnf(f_2372_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8232,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8233),U_8236)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8234),U_8236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8233),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8234,U_8236))),U_8235))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8236))
    | U_8233 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8232,U_8233),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8234),U_8235))) ),
    inference(clausify,[status(thm)],[f_2372_2]) ).

fof(f_2373_1,plain,
    ! [T_d,T_c,V_b_2,V_a_2,V_ca_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_ca_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_ca_2,V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).

fof(f_2373_2,plain,
    ! [U_8243,U_8242,U_8241,U_8240,U_8239,U_8238,U_8237] :
      ( hBOOL(hAPP(hAPP(c_member(U_8237),U_8238),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8242,U_8243,tc_fun(U_8237,tc_HOL_Obool)),U_8239),hAPP(hAPP(c_Product__Type_OPair(U_8242,U_8243),U_8240),U_8241))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8237),U_8238),hAPP(hAPP(U_8239,U_8240),U_8241))) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

cnf(f_2373_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8237),U_8238),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8242,U_8243,tc_fun(U_8237,tc_HOL_Obool)),U_8239),hAPP(hAPP(c_Product__Type_OPair(U_8242,U_8243),U_8240),U_8241))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8237),U_8238),hAPP(hAPP(U_8239,U_8240),U_8241))) ),
    inference(clausify,[status(thm)],[f_2373_2]) ).

fof(f_2374_1,plain,
    ! [V_ca_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_ca_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_ca_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).

fof(f_2374_2,plain,
    ! [U_8250,U_8249,U_8248,U_8247,U_8246,U_8245,U_8244] :
      ( hBOOL(hAPP(hAPP(hAPP(U_8247,U_8248),U_8249),U_8250))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8244,U_8245,tc_fun(U_8246,tc_HOL_Obool)),U_8247),hAPP(hAPP(c_Product__Type_OPair(U_8244,U_8245),U_8248),U_8249)),U_8250)) ),
    inference(variable_rename,[status(thm)],[f_2374_1]) ).

fof(f_2374_3,plain,
    ! [U_8250,U_8249,U_8248,U_8247] :
      ( ! [U_8246,U_8245,U_8244] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8244,U_8245,tc_fun(U_8246,tc_HOL_Obool)),U_8247),hAPP(hAPP(c_Product__Type_OPair(U_8244,U_8245),U_8248),U_8249)),U_8250))
      | hBOOL(hAPP(hAPP(hAPP(U_8247,U_8248),U_8249),U_8250)) ),
    inference(miniscope,[status(thm)],[f_2374_2]) ).

cnf(f_2374_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8244,U_8245,tc_fun(U_8246,tc_HOL_Obool)),U_8247),hAPP(hAPP(c_Product__Type_OPair(U_8244,U_8245),U_8248),U_8249)),U_8250))
    | hBOOL(hAPP(hAPP(hAPP(U_8247,U_8248),U_8249),U_8250)) ),
    inference(clausify,[status(thm)],[f_2374_3]) ).

fof(f_2375_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_2375_2,plain,
    ! [U_8256,U_8255,U_8254,U_8253,U_8252,U_8251] :
      ( U_8254 = U_8256
      | U_8252 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8251,U_8252),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8255),U_8256)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8251,U_8252),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8253),U_8254))) ),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

cnf(f_2375_3,plain,
    ( U_8254 = U_8256
    | U_8252 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8251,U_8252),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8255),U_8256)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8251,U_8252),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8253),U_8254))) ),
    inference(clausify,[status(thm)],[f_2375_2]) ).

fof(f_2376_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_2376_2,plain,
    ! [U_8262,U_8261,U_8260,U_8259,U_8258,U_8257] :
      ( U_8259 = U_8261
      | U_8258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8257,U_8258),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8261),U_8262)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8257,U_8258),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8259),U_8260))) ),
    inference(variable_rename,[status(thm)],[f_2376_1]) ).

cnf(f_2376_3,plain,
    ( U_8259 = U_8261
    | U_8258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8257,U_8258),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8261),U_8262)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8257,U_8258),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8259),U_8260))) ),
    inference(clausify,[status(thm)],[f_2376_2]) ).

fof(f_2377_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_2377_2,plain,
    ! [U_8265,U_8264,U_8263] :
      ( U_8265 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_8263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8263,U_8263),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8264),U_8265))) ),
    inference(variable_rename,[status(thm)],[f_2377_1]) ).

cnf(f_2377_3,plain,
    ( U_8265 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8263,U_8263),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8264),U_8265))) ),
    inference(clausify,[status(thm)],[f_2377_2]) ).

fof(f_2378_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_2378_2,plain,
    ! [U_8266] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8266),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_8266 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2378_1]) ).

cnf(f_2378_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8266),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_8266 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2378_2]) ).

fof(f_2379_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_2379_2,plain,
    ! [U_8269,U_8268,U_8267] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8267,U_8268),hAPP(c_Divides_OnegateSnd,U_8269)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8267),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8268)),U_8269)) ),
    inference(variable_rename,[status(thm)],[f_2379_1]) ).

cnf(f_2379_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8267,U_8268),hAPP(c_Divides_OnegateSnd,U_8269)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8267),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8268)),U_8269)) ),
    inference(clausify,[status(thm)],[f_2379_2]) ).

fof(f_2380_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_2380_2,plain,
    ! [U_8271,U_8270] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8271,U_8270),c_Divides_Odivmod__int(U_8271,U_8270)))
      | U_8270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2380_1]) ).

cnf(f_2380_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8271,U_8270),c_Divides_Odivmod__int(U_8271,U_8270)))
    | U_8270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2380_2]) ).

fof(f_2381_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_2381_2,plain,
    ! [U_8274,U_8273,U_8272] :
      ( U_8273 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_8272 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8272,U_8272),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8273),U_8274))) ),
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

cnf(f_2381_3,plain,
    ( U_8273 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_8272 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8272,U_8272),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8273),U_8274))) ),
    inference(clausify,[status(thm)],[f_2381_2]) ).

fof(f_2382_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_2382_2,plain,
    ! [U_8278,U_8277,U_8276,U_8275] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8275,U_8276) = U_8278
      | U_8276 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8275,U_8276),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8277),U_8278))) ),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

cnf(f_2382_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8275,U_8276) = U_8278
    | U_8276 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8275,U_8276),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8277),U_8278))) ),
    inference(clausify,[status(thm)],[f_2382_2]) ).

fof(f_2383_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_2383_2,plain,
    ! [U_8282,U_8281,U_8280,U_8279] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8279),U_8280) = U_8281
      | U_8280 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8279,U_8280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8281),U_8282))) ),
    inference(variable_rename,[status(thm)],[f_2383_1]) ).

cnf(f_2383_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8279),U_8280) = U_8281
    | U_8280 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8279,U_8280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8281),U_8282))) ),
    inference(clausify,[status(thm)],[f_2383_2]) ).

fof(f_2384_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_2384_2,plain,
    ! [U_8284,U_8283] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8283,U_8284),c_Divides_OnegDivAlg(U_8283,U_8284)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8283),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2384_1]) ).

cnf(f_2384_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8283,U_8284),c_Divides_OnegDivAlg(U_8283,U_8284)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8283),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2384_2]) ).

fof(f_2385_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_2385_2,plain,
    ! [U_8286,U_8285] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8286,U_8285),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8286),U_8285)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8286,U_8285))))
      | U_8285 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

cnf(f_2385_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8286,U_8285),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8286),U_8285)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8286,U_8285))))
    | U_8285 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2385_2]) ).

fof(f_2386_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_2386_2,plain,
    ! [U_8288,U_8287] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8287,U_8288),c_Divides_OposDivAlg(U_8287,U_8288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8287)) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

cnf(f_2386_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8287,U_8288),c_Divides_OposDivAlg(U_8287,U_8288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8287)) ),
    inference(clausify,[status(thm)],[f_2386_2]) ).

fof(f_2387_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_2387_2,plain,
    ! [U_8295,U_8294,U_8293,U_8292,U_8291,U_8290,U_8289] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8289),U_8293),U_8290),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_8291),U_8294)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8292),U_8295)),U_8290))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8292),U_8295),U_8290))))
      | U_8290 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8293,U_8290),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8294),U_8295)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8289,U_8290),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8291),U_8292))) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

cnf(f_2387_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8289),U_8293),U_8290),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_8291),U_8294)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8292),U_8295)),U_8290))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8292),U_8295),U_8290))))
    | U_8290 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8293,U_8290),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8294),U_8295)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8289,U_8290),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8291),U_8292))) ),
    inference(clausify,[status(thm)],[f_2387_2]) ).

fof(f_2388_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_2388_2,plain,
    ! [U_8299,U_8298,U_8297,U_8296] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8296),U_8297),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_8299),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8298)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8298)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_8299),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_8297),U_8299)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8296,U_8297),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8298),U_8299))) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

cnf(f_2388_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8296),U_8297),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_8299),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8298)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8298)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_8299),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_8297),U_8299)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8296,U_8297),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8298),U_8299))) ),
    inference(clausify,[status(thm)],[f_2388_2]) ).

fof(f_2389_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_2389_2,plain,
    ! [U_8301,U_8300] :
      ( ( c_Divides_Odivmod__nat(U_8301,U_8300) = 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_8301),U_8300),U_8300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8301),U_8300))
        | U_8300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_8301,U_8300) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8301)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8301),U_8300))
          & U_8300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

fof(f_2389_3,plain,
    ( ! [U_8305,U_8303] :
        ( c_Divides_Odivmod__nat(U_8305,U_8303) = 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_8305),U_8303),U_8303))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8305),U_8303))
        | U_8303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_8304,U_8302] :
        ( c_Divides_Odivmod__nat(U_8304,U_8302) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8304)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8304),U_8302))
          & U_8302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_2389_2]) ).

cnf(f_2389_4,plain,
    ( U_8302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Divides_Odivmod__nat(U_8304,U_8302) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8304) ),
    inference(clausify,[status(thm)],[f_2389_3]) ).

cnf(f_2389_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8304),U_8302))
    | c_Divides_Odivmod__nat(U_8304,U_8302) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8304) ),
    inference(clausify,[status(thm)],[f_2389_3]) ).

cnf(f_2389_6,plain,
    ( c_Divides_Odivmod__nat(U_8305,U_8303) = 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_8305),U_8303),U_8303))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8305),U_8303))
    | U_8303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2389_3]) ).

fof(f_2390_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_2390_2,plain,
    ! [U_8309,U_8308,U_8307,U_8306] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8306,U_8307),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8308),U_8309)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8307),U_8309)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8307))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307)) )
      | U_8306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8307),U_8308)),U_8309) ),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

cnf(f_2390_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8306,U_8307),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8308),U_8309)))
    | U_8306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8307),U_8308)),U_8309) ),
    inference(clausify,[status(thm)],[f_2390_2]) ).

cnf(f_2390_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8307),U_8309))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8306,U_8307),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8308),U_8309)))
    | U_8306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8307),U_8308)),U_8309) ),
    inference(clausify,[status(thm)],[f_2390_2]) ).

cnf(f_2390_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8307))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8307))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8306,U_8307),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8308),U_8309)))
    | U_8306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8307),U_8308)),U_8309) ),
    inference(clausify,[status(thm)],[f_2390_2]) ).

cnf(f_2390_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8307),U_8309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8307))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8306,U_8307),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8308),U_8309)))
    | U_8306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8307),U_8308)),U_8309) ),
    inference(clausify,[status(thm)],[f_2390_2]) ).

fof(f_2391_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_2391_2,plain,
    ! [U_8314,U_8313,U_8312,U_8311,U_8310] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8310),U_8311),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_8314),U_8312)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8313)),U_8311))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8313),U_8311))))
      | U_8311 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8310,U_8311),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8312),U_8313))) ),
    inference(variable_rename,[status(thm)],[f_2391_1]) ).

cnf(f_2391_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8310),U_8311),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_8314),U_8312)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8313)),U_8311))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8314),U_8313),U_8311))))
    | U_8311 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_8310,U_8311),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_8312),U_8313))) ),
    inference(clausify,[status(thm)],[f_2391_2]) ).

fof(f_2392_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_2392_2,plain,
    ! [U_8316,U_8315] : c_Divides_Odivmod__int__rel(U_8315,U_8316) = 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_8315))),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_8316)))))),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_8316))),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_8316))))),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_8316)))),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_8316))),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_2392_1]) ).

cnf(f_2392_3,plain,
    c_Divides_Odivmod__int__rel(U_8315,U_8316) = 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_8315))),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_8316)))))),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_8316))),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_8316))))),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_8316)))),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_8316))),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_2392_2]) ).

fof(f_2393_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_2393_2,plain,
    ! [U_8321,U_8320,U_8319] :
      ( hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
      | ? [U_8318,U_8317] :
          ( ~ hBOOL(hAPP(hAPP(U_8321,U_8318),U_8317))
          & ( hBOOL(hAPP(hAPP(U_8321,U_8318),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_8317)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8318),U_8317)) )
          & 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_8318),U_8317))) )
      | ~ 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_8319),U_8320))) ),
    inference(variable_rename,[status(thm)],[f_2393_1]) ).

fof(f_2393_3,plain,
    ! [U_8321,U_8320,U_8319] :
      ( hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
      | ? [U_8317] :
          ( ~ hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),U_8317))
          & ( hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),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_8317)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK156(U_8321,U_8320,U_8319)),U_8317)) )
          & 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),sK156(U_8321,U_8320,U_8319)),U_8317))) )
      | ~ 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_8319),U_8320))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_8318,sK156(U_8321,U_8320,U_8319))],[f_2393_2]) ).

fof(f_2393_4,plain,
    ! [U_8321,U_8320,U_8319] :
      ( hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
      | ( ~ hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319)))
        & ( hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),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)))),sK157(U_8321,U_8320,U_8319))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK157(U_8321,U_8320,U_8319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319))) )
        & 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),sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319)))) )
      | ~ 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_8319),U_8320))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_8317,sK157(U_8321,U_8320,U_8319))],[f_2393_3]) ).

cnf(f_2393_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),sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319))))
    | hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
    | ~ 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_8319),U_8320))) ),
    inference(clausify,[status(thm)],[f_2393_4]) ).

cnf(f_2393_6,plain,
    ( hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),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)))),sK157(U_8321,U_8320,U_8319))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK157(U_8321,U_8320,U_8319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319)))
    | hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
    | ~ 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_8319),U_8320))) ),
    inference(clausify,[status(thm)],[f_2393_4]) ).

cnf(f_2393_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8321,sK156(U_8321,U_8320,U_8319)),sK157(U_8321,U_8320,U_8319)))
    | hBOOL(hAPP(hAPP(U_8321,U_8319),U_8320))
    | ~ 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_8319),U_8320))) ),
    inference(clausify,[status(thm)],[f_2393_4]) ).

fof(f_2394_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_2394_2,plain,
    ! [U_8323,U_8322] :
      ( ( ( c_Nitpick_Onat__gcd(U_8322,U_8323) = c_Nitpick_Onat__gcd(U_8323,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8322,U_8323))
          | U_8323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_8322,U_8323) = U_8322
          | U_8323 != 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_8322),U_8323))) ),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

cnf(f_2394_3,plain,
    ( c_Nitpick_Onat__gcd(U_8322,U_8323) = U_8322
    | U_8323 != 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_8322),U_8323))) ),
    inference(clausify,[status(thm)],[f_2394_2]) ).

cnf(f_2394_4,plain,
    ( c_Nitpick_Onat__gcd(U_8322,U_8323) = c_Nitpick_Onat__gcd(U_8323,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8322,U_8323))
    | U_8323 = 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_8322),U_8323))) ),
    inference(clausify,[status(thm)],[f_2394_2]) ).

fof(f_2395_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_2395_2,plain,
    ! [U_8327,U_8326,U_8325] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Int_Oint),U_8327),U_8326) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8325),c_Int_Onat),U_8327)),U_8326))
      | ? [U_8324] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8327,U_8324))
          & hBOOL(hAPP(hAPP(c_member(U_8325),U_8324),U_8326)) ) ),
    inference(variable_rename,[status(thm)],[f_2395_1]) ).

fof(f_2395_3,plain,
    ! [U_8327,U_8326,U_8325] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Int_Oint),U_8327),U_8326) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8325),c_Int_Onat),U_8327)),U_8326))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8327,sK158(U_8327,U_8326,U_8325)))
        & hBOOL(hAPP(hAPP(c_member(U_8325),sK158(U_8327,U_8326,U_8325)),U_8326)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_8324,sK158(U_8327,U_8326,U_8325))],[f_2395_2]) ).

cnf(f_2395_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8325),sK158(U_8327,U_8326,U_8325)),U_8326))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Int_Oint),U_8327),U_8326) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8325),c_Int_Onat),U_8327)),U_8326)) ),
    inference(clausify,[status(thm)],[f_2395_3]) ).

cnf(f_2395_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8327,sK158(U_8327,U_8326,U_8325)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Int_Oint),U_8327),U_8326) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8325,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8325),c_Int_Onat),U_8327)),U_8326)) ),
    inference(clausify,[status(thm)],[f_2395_3]) ).

fof(f_2396_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_2396_2,plain,
    ! [U_8328] :
      ( 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_8328)) = 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_8328)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8328)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2396_1]) ).

cnf(f_2396_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_8328)) = 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_8328)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8328)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2396_2]) ).

fof(f_2397_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_2397_2,plain,
    ! [U_8333,U_8332,U_8331,U_8330,U_8329] :
      ( U_8332 = U_8333
      | hAPP(c_Product__Type_Osnd(U_8329,U_8330),hAPP(hAPP(c_Product__Type_OPair(U_8329,U_8330),U_8331),U_8332)) != U_8333 ),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

fof(f_2397_3,plain,
    ! [U_8333,U_8332] :
      ( ! [U_8331,U_8330,U_8329] : hAPP(c_Product__Type_Osnd(U_8329,U_8330),hAPP(hAPP(c_Product__Type_OPair(U_8329,U_8330),U_8331),U_8332)) != U_8333
      | U_8332 = U_8333 ),
    inference(miniscope,[status(thm)],[f_2397_2]) ).

cnf(f_2397_4,plain,
    ( hAPP(c_Product__Type_Osnd(U_8329,U_8330),hAPP(hAPP(c_Product__Type_OPair(U_8329,U_8330),U_8331),U_8332)) != U_8333
    | U_8332 = U_8333 ),
    inference(clausify,[status(thm)],[f_2397_3]) ).

fof(f_2398_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_2398_2,plain,
    ! [U_8337,U_8336,U_8335,U_8334] : hAPP(c_Product__Type_Osnd(U_8334,U_8335),hAPP(hAPP(c_Product__Type_OPair(U_8334,U_8335),U_8336),U_8337)) = U_8337,
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

cnf(f_2398_3,plain,
    hAPP(c_Product__Type_Osnd(U_8334,U_8335),hAPP(hAPP(c_Product__Type_OPair(U_8334,U_8335),U_8336),U_8337)) = U_8337,
    inference(clausify,[status(thm)],[f_2398_2]) ).

fof(f_2399_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_2399_2,plain,
    ! [U_8343,U_8342,U_8341,U_8340,U_8339,U_8338] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_8338,U_8339,U_8340,U_8341),U_8342) = hAPP(c_Product__Type_Oapsnd(U_8338,U_8339,U_8340,U_8343),U_8342)
        | hAPP(U_8341,hAPP(c_Product__Type_Osnd(U_8340,U_8338),U_8342)) != hAPP(U_8343,hAPP(c_Product__Type_Osnd(U_8340,U_8338),U_8342)) )
      & ( hAPP(U_8341,hAPP(c_Product__Type_Osnd(U_8340,U_8338),U_8342)) = hAPP(U_8343,hAPP(c_Product__Type_Osnd(U_8340,U_8338),U_8342))
        | hAPP(c_Product__Type_Oapsnd(U_8338,U_8339,U_8340,U_8341),U_8342) != hAPP(c_Product__Type_Oapsnd(U_8338,U_8339,U_8340,U_8343),U_8342) ) ),
    inference(variable_rename,[status(thm)],[f_2399_1]) ).

fof(f_2399_3,plain,
    ( ! [U_8355,U_8353,U_8351,U_8349,U_8347,U_8345] :
        ( hAPP(c_Product__Type_Oapsnd(U_8345,U_8347,U_8349,U_8351),U_8353) = hAPP(c_Product__Type_Oapsnd(U_8345,U_8347,U_8349,U_8355),U_8353)
        | hAPP(U_8351,hAPP(c_Product__Type_Osnd(U_8349,U_8345),U_8353)) != hAPP(U_8355,hAPP(c_Product__Type_Osnd(U_8349,U_8345),U_8353)) )
    & ! [U_8354,U_8352,U_8350,U_8348,U_8346,U_8344] :
        ( hAPP(U_8350,hAPP(c_Product__Type_Osnd(U_8348,U_8344),U_8352)) = hAPP(U_8354,hAPP(c_Product__Type_Osnd(U_8348,U_8344),U_8352))
        | hAPP(c_Product__Type_Oapsnd(U_8344,U_8346,U_8348,U_8350),U_8352) != hAPP(c_Product__Type_Oapsnd(U_8344,U_8346,U_8348,U_8354),U_8352) ) ),
    inference(miniscope,[status(thm)],[f_2399_2]) ).

cnf(f_2399_4,plain,
    ( hAPP(U_8350,hAPP(c_Product__Type_Osnd(U_8348,U_8344),U_8352)) = hAPP(U_8354,hAPP(c_Product__Type_Osnd(U_8348,U_8344),U_8352))
    | hAPP(c_Product__Type_Oapsnd(U_8344,U_8346,U_8348,U_8350),U_8352) != hAPP(c_Product__Type_Oapsnd(U_8344,U_8346,U_8348,U_8354),U_8352) ),
    inference(clausify,[status(thm)],[f_2399_3]) ).

cnf(f_2399_5,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_8345,U_8347,U_8349,U_8351),U_8353) = hAPP(c_Product__Type_Oapsnd(U_8345,U_8347,U_8349,U_8355),U_8353)
    | hAPP(U_8351,hAPP(c_Product__Type_Osnd(U_8349,U_8345),U_8353)) != hAPP(U_8355,hAPP(c_Product__Type_Osnd(U_8349,U_8345),U_8353)) ),
    inference(clausify,[status(thm)],[f_2399_3]) ).

fof(f_2400_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_2400_2,plain,
    ! [U_8360,U_8359,U_8358,U_8357,U_8356] : hAPP(c_Product__Type_Osnd(U_8356,U_8357),hAPP(c_Product__Type_Oapsnd(U_8358,U_8357,U_8356,U_8359),U_8360)) = hAPP(U_8359,hAPP(c_Product__Type_Osnd(U_8356,U_8358),U_8360)),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

cnf(f_2400_3,plain,
    hAPP(c_Product__Type_Osnd(U_8356,U_8357),hAPP(c_Product__Type_Oapsnd(U_8358,U_8357,U_8356,U_8359),U_8360)) = hAPP(U_8359,hAPP(c_Product__Type_Osnd(U_8356,U_8358),U_8360)),
    inference(clausify,[status(thm)],[f_2400_2]) ).

fof(f_2401_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_2401_2,plain,
    ! [U_8363,U_8362,U_8361] : hAPP(c_Product__Type_Osnd(U_8361,U_8362),U_8363) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8361,U_8362,U_8362),hAPP(c_COMBK(tc_fun(U_8362,U_8362),U_8361),c_COMBI(U_8362))),U_8363),
    inference(variable_rename,[status(thm)],[f_2401_1]) ).

cnf(f_2401_3,plain,
    hAPP(c_Product__Type_Osnd(U_8361,U_8362),U_8363) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8361,U_8362,U_8362),hAPP(c_COMBK(tc_fun(U_8362,U_8362),U_8361),c_COMBI(U_8362))),U_8363),
    inference(clausify,[status(thm)],[f_2401_2]) ).

fof(f_2402_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_2402_2,plain,
    ! [U_8365,U_8364] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8364,U_8365) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_8364,U_8365)),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

cnf(f_2402_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8364,U_8365) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_8364,U_8365)),
    inference(clausify,[status(thm)],[f_2402_2]) ).

fof(f_2403_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_2403_2,plain,
    ! [U_8367,U_8366] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8366,U_8367) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_8366,U_8367))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8367))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8366),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

cnf(f_2403_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8366,U_8367) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_8366,U_8367))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8367))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8366),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2403_2]) ).

fof(f_2404_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_2404_2,plain,
    ! [U_8369,U_8368] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8368,U_8369) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_8368,U_8369))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8369))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8368)) ),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

cnf(f_2404_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8368,U_8369) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_8368,U_8369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8368)) ),
    inference(clausify,[status(thm)],[f_2404_2]) ).

fof(f_2405_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_2405_2,plain,
    ! [U_8370] :
      ( 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_8370)) = 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_8370)))
      | ~ 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_8370))) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

cnf(f_2405_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_8370)) = 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_8370)))
    | ~ 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_8370))) ),
    inference(clausify,[status(thm)],[f_2405_2]) ).

fof(f_2406_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_2406_2,plain,
    ! [U_8372,U_8371] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8371,U_8372) = 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_8371),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8372))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8372),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_8371)) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

cnf(f_2406_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8371,U_8372) = 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_8371),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8372))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8372),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_8371)) ),
    inference(clausify,[status(thm)],[f_2406_2]) ).

fof(f_2407_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_2407_2,plain,
    ! [U_8374,U_8373] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8373,U_8374) = 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_8373),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8374))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8374),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8373),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

cnf(f_2407_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8373,U_8374) = 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_8373),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8374))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8374),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8373),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2407_2]) ).

fof(f_2408_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_2408_2,plain,
    ! [U_8378,U_8377,U_8376,U_8375] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8375,U_8375)),hAPP(hAPP(c_Product__Type_OPair(U_8375,U_8375),U_8376),U_8377)),hAPP(c_Wellfounded_Omeasure(U_8375),U_8378)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8378,U_8376)),hAPP(U_8378,U_8377))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8378,U_8376)),hAPP(U_8378,U_8377)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8375,U_8375)),hAPP(hAPP(c_Product__Type_OPair(U_8375,U_8375),U_8376),U_8377)),hAPP(c_Wellfounded_Omeasure(U_8375),U_8378))) ) ),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

fof(f_2408_3,plain,
    ( ! [U_8386,U_8384,U_8382] :
        ( ! [U_8380] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8380,U_8380)),hAPP(hAPP(c_Product__Type_OPair(U_8380,U_8380),U_8382),U_8384)),hAPP(c_Wellfounded_Omeasure(U_8380),U_8386)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8386,U_8382)),hAPP(U_8386,U_8384))) )
    & ! [U_8385,U_8383,U_8381] :
        ( ! [U_8379] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8379,U_8379)),hAPP(hAPP(c_Product__Type_OPair(U_8379,U_8379),U_8381),U_8383)),hAPP(c_Wellfounded_Omeasure(U_8379),U_8385)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8385,U_8381)),hAPP(U_8385,U_8383))) ) ),
    inference(miniscope,[status(thm)],[f_2408_2]) ).

cnf(f_2408_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8379,U_8379)),hAPP(hAPP(c_Product__Type_OPair(U_8379,U_8379),U_8381),U_8383)),hAPP(c_Wellfounded_Omeasure(U_8379),U_8385)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8385,U_8381)),hAPP(U_8385,U_8383))) ),
    inference(clausify,[status(thm)],[f_2408_3]) ).

cnf(f_2408_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8380,U_8380)),hAPP(hAPP(c_Product__Type_OPair(U_8380,U_8380),U_8382),U_8384)),hAPP(c_Wellfounded_Omeasure(U_8380),U_8386)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8386,U_8382)),hAPP(U_8386,U_8384))) ),
    inference(clausify,[status(thm)],[f_2408_3]) ).

fof(f_2409_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_2409_2,plain,
    ! [U_8390,U_8389,U_8388] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Int_Oint),U_8390),U_8389) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8388),c_Int_Onat),U_8390)),U_8389))
      | ? [U_8387] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8390,U_8387))
          & hBOOL(hAPP(hAPP(c_member(U_8388),U_8387),U_8389)) ) ),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

fof(f_2409_3,plain,
    ! [U_8390,U_8389,U_8388] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Int_Oint),U_8390),U_8389) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8388),c_Int_Onat),U_8390)),U_8389))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8390,sK159(U_8390,U_8389,U_8388)))
        & hBOOL(hAPP(hAPP(c_member(U_8388),sK159(U_8390,U_8389,U_8388)),U_8389)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_8387,sK159(U_8390,U_8389,U_8388))],[f_2409_2]) ).

cnf(f_2409_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8388),sK159(U_8390,U_8389,U_8388)),U_8389))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Int_Oint),U_8390),U_8389) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8388),c_Int_Onat),U_8390)),U_8389)) ),
    inference(clausify,[status(thm)],[f_2409_3]) ).

cnf(f_2409_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8390,sK159(U_8390,U_8389,U_8388)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Int_Oint),U_8390),U_8389) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8388,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8388),c_Int_Onat),U_8390)),U_8389)) ),
    inference(clausify,[status(thm)],[f_2409_3]) ).

fof(f_2410_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_2410_2,plain,
    ! [U_8395,U_8394,U_8393] :
      ( hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
      | ? [U_8392,U_8391] :
          ( ~ hBOOL(hAPP(hAPP(U_8395,U_8392),U_8391))
          & ( hBOOL(hAPP(hAPP(U_8395,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8392)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8391)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8391),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_8392),U_8391))) )
      | ~ 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_8393),U_8394))) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

fof(f_2410_3,plain,
    ! [U_8395,U_8394,U_8393] :
      ( hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
      | ? [U_8391] :
          ( ~ hBOOL(hAPP(hAPP(U_8395,sK160(U_8395,U_8394,U_8393)),U_8391))
          & ( hBOOL(hAPP(hAPP(U_8395,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK160(U_8395,U_8394,U_8393))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8391)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8391),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),sK160(U_8395,U_8394,U_8393)),U_8391))) )
      | ~ 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_8393),U_8394))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_8392,sK160(U_8395,U_8394,U_8393))],[f_2410_2]) ).

fof(f_2410_4,plain,
    ! [U_8395,U_8394,U_8393] :
      ( hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
      | ( ~ hBOOL(hAPP(hAPP(U_8395,sK160(U_8395,U_8394,U_8393)),sK161(U_8395,U_8394,U_8393)))
        & ( hBOOL(hAPP(hAPP(U_8395,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK160(U_8395,U_8394,U_8393))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK161(U_8395,U_8394,U_8393))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK161(U_8395,U_8394,U_8393)),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),sK160(U_8395,U_8394,U_8393)),sK161(U_8395,U_8394,U_8393)))) )
      | ~ 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_8393),U_8394))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_8391,sK161(U_8395,U_8394,U_8393))],[f_2410_3]) ).

cnf(f_2410_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),sK160(U_8395,U_8394,U_8393)),sK161(U_8395,U_8394,U_8393))))
    | hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
    | ~ 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_8393),U_8394))) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_6,plain,
    ( hBOOL(hAPP(hAPP(U_8395,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK160(U_8395,U_8394,U_8393))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK161(U_8395,U_8394,U_8393))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK161(U_8395,U_8394,U_8393)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
    | ~ 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_8393),U_8394))) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8395,sK160(U_8395,U_8394,U_8393)),sK161(U_8395,U_8394,U_8393)))
    | hBOOL(hAPP(hAPP(U_8395,U_8393),U_8394))
    | ~ 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_8393),U_8394))) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

fof(f_2411_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_2411_2,plain,
    ! [U_8396] :
      ( 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_8396)) = 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_8396)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8396)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2411_1]) ).

cnf(f_2411_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_8396)) = 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_8396)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8396)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2411_2]) ).

fof(f_2412_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_2412_2,plain,
    ! [U_8400,U_8399,U_8398,U_8397] :
      ( U_8399 = U_8400
      | hAPP(c_Product__Type_Osnd(U_8397,U_8398),U_8399) != hAPP(c_Product__Type_Osnd(U_8397,U_8398),U_8400)
      | hAPP(c_Product__Type_Ofst(U_8397,U_8398),U_8399) != hAPP(c_Product__Type_Ofst(U_8397,U_8398),U_8400) ),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

cnf(f_2412_3,plain,
    ( U_8399 = U_8400
    | hAPP(c_Product__Type_Osnd(U_8397,U_8398),U_8399) != hAPP(c_Product__Type_Osnd(U_8397,U_8398),U_8400)
    | hAPP(c_Product__Type_Ofst(U_8397,U_8398),U_8399) != hAPP(c_Product__Type_Ofst(U_8397,U_8398),U_8400) ),
    inference(clausify,[status(thm)],[f_2412_2]) ).

fof(f_2413_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_2413_2,plain,
    ! [U_8404,U_8403,U_8402,U_8401] :
      ( ( U_8401 = U_8402
        | hAPP(c_Product__Type_Osnd(U_8403,U_8404),U_8401) != hAPP(c_Product__Type_Osnd(U_8403,U_8404),U_8402)
        | hAPP(c_Product__Type_Ofst(U_8403,U_8404),U_8401) != hAPP(c_Product__Type_Ofst(U_8403,U_8404),U_8402) )
      & ( ( hAPP(c_Product__Type_Osnd(U_8403,U_8404),U_8401) = hAPP(c_Product__Type_Osnd(U_8403,U_8404),U_8402)
          & hAPP(c_Product__Type_Ofst(U_8403,U_8404),U_8401) = hAPP(c_Product__Type_Ofst(U_8403,U_8404),U_8402) )
        | U_8401 != U_8402 ) ),
    inference(variable_rename,[status(thm)],[f_2413_1]) ).

fof(f_2413_3,plain,
    ( ! [U_8412,U_8410,U_8408,U_8406] :
        ( U_8406 = U_8408
        | hAPP(c_Product__Type_Osnd(U_8410,U_8412),U_8406) != hAPP(c_Product__Type_Osnd(U_8410,U_8412),U_8408)
        | hAPP(c_Product__Type_Ofst(U_8410,U_8412),U_8406) != hAPP(c_Product__Type_Ofst(U_8410,U_8412),U_8408) )
    & ! [U_8411,U_8409,U_8407,U_8405] :
        ( ( hAPP(c_Product__Type_Osnd(U_8409,U_8411),U_8405) = hAPP(c_Product__Type_Osnd(U_8409,U_8411),U_8407)
          & hAPP(c_Product__Type_Ofst(U_8409,U_8411),U_8405) = hAPP(c_Product__Type_Ofst(U_8409,U_8411),U_8407) )
        | U_8405 != U_8407 ) ),
    inference(miniscope,[status(thm)],[f_2413_2]) ).

cnf(f_2413_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_8409,U_8411),U_8405) = hAPP(c_Product__Type_Ofst(U_8409,U_8411),U_8407)
    | U_8405 != U_8407 ),
    inference(clausify,[status(thm)],[f_2413_3]) ).

cnf(f_2413_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_8409,U_8411),U_8405) = hAPP(c_Product__Type_Osnd(U_8409,U_8411),U_8407)
    | U_8405 != U_8407 ),
    inference(clausify,[status(thm)],[f_2413_3]) ).

cnf(f_2413_6,plain,
    ( U_8406 = U_8408
    | hAPP(c_Product__Type_Osnd(U_8410,U_8412),U_8406) != hAPP(c_Product__Type_Osnd(U_8410,U_8412),U_8408)
    | hAPP(c_Product__Type_Ofst(U_8410,U_8412),U_8406) != hAPP(c_Product__Type_Ofst(U_8410,U_8412),U_8408) ),
    inference(clausify,[status(thm)],[f_2413_3]) ).

fof(f_2414_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_2414_2,plain,
    ! [U_8416,U_8415,U_8414,U_8413] : hAPP(c_Product__Type_Ofst(U_8413,U_8414),hAPP(hAPP(c_Product__Type_OPair(U_8413,U_8414),U_8415),U_8416)) = U_8415,
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

cnf(f_2414_3,plain,
    hAPP(c_Product__Type_Ofst(U_8413,U_8414),hAPP(hAPP(c_Product__Type_OPair(U_8413,U_8414),U_8415),U_8416)) = U_8415,
    inference(clausify,[status(thm)],[f_2414_2]) ).

fof(f_2415_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_2415_2,plain,
    ! [U_8421,U_8420,U_8419,U_8418,U_8417] :
      ( U_8419 = U_8421
      | hAPP(c_Product__Type_Ofst(U_8417,U_8418),hAPP(hAPP(c_Product__Type_OPair(U_8417,U_8418),U_8419),U_8420)) != U_8421 ),
    inference(variable_rename,[status(thm)],[f_2415_1]) ).

fof(f_2415_3,plain,
    ! [U_8421,U_8420,U_8419] :
      ( ! [U_8418,U_8417] : hAPP(c_Product__Type_Ofst(U_8417,U_8418),hAPP(hAPP(c_Product__Type_OPair(U_8417,U_8418),U_8419),U_8420)) != U_8421
      | U_8419 = U_8421 ),
    inference(miniscope,[status(thm)],[f_2415_2]) ).

cnf(f_2415_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_8417,U_8418),hAPP(hAPP(c_Product__Type_OPair(U_8417,U_8418),U_8419),U_8420)) != U_8421
    | U_8419 = U_8421 ),
    inference(clausify,[status(thm)],[f_2415_3]) ).

fof(f_2416_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_2416_2,plain,
    ! [U_8426,U_8425,U_8424,U_8423,U_8422] : hAPP(c_Product__Type_Ofst(U_8422,U_8423),hAPP(c_Product__Type_Oapsnd(U_8424,U_8423,U_8422,U_8425),U_8426)) = hAPP(c_Product__Type_Ofst(U_8422,U_8424),U_8426),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

cnf(f_2416_3,plain,
    hAPP(c_Product__Type_Ofst(U_8422,U_8423),hAPP(c_Product__Type_Oapsnd(U_8424,U_8423,U_8422,U_8425),U_8426)) = hAPP(c_Product__Type_Ofst(U_8422,U_8424),U_8426),
    inference(clausify,[status(thm)],[f_2416_2]) ).

fof(f_2417_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_2417_2,plain,
    ! [U_8429,U_8428,U_8427] : hAPP(c_Product__Type_Ofst(U_8427,U_8428),U_8429) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8427,U_8428,U_8427),c_COMBK(U_8427,U_8428)),U_8429),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

cnf(f_2417_3,plain,
    hAPP(c_Product__Type_Ofst(U_8427,U_8428),U_8429) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8427,U_8428,U_8427),c_COMBK(U_8427,U_8428)),U_8429),
    inference(clausify,[status(thm)],[f_2417_2]) ).

fof(f_2418_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_2418_2,plain,
    ! [U_8432,U_8431,U_8430] : U_8430 = hAPP(hAPP(c_Product__Type_OPair(U_8431,U_8432),hAPP(c_Product__Type_Ofst(U_8431,U_8432),U_8430)),hAPP(c_Product__Type_Osnd(U_8431,U_8432),U_8430)),
    inference(variable_rename,[status(thm)],[f_2418_1]) ).

cnf(f_2418_3,plain,
    U_8430 = hAPP(hAPP(c_Product__Type_OPair(U_8431,U_8432),hAPP(c_Product__Type_Ofst(U_8431,U_8432),U_8430)),hAPP(c_Product__Type_Osnd(U_8431,U_8432),U_8430)),
    inference(clausify,[status(thm)],[f_2418_2]) ).

fof(f_2419_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_2419_2,plain,
    ! [U_8435,U_8434,U_8433] : hAPP(hAPP(c_Product__Type_OPair(U_8433,U_8434),hAPP(c_Product__Type_Ofst(U_8433,U_8434),U_8435)),hAPP(c_Product__Type_Osnd(U_8433,U_8434),U_8435)) = U_8435,
    inference(variable_rename,[status(thm)],[f_2419_1]) ).

cnf(f_2419_3,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_8433,U_8434),hAPP(c_Product__Type_Ofst(U_8433,U_8434),U_8435)),hAPP(c_Product__Type_Osnd(U_8433,U_8434),U_8435)) = U_8435,
    inference(clausify,[status(thm)],[f_2419_2]) ).

fof(f_2420_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_2420_2,plain,
    ! [U_8440,U_8439,U_8438,U_8437,U_8436] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8436,U_8437,U_8438),U_8439),U_8440) = hAPP(hAPP(U_8439,hAPP(c_Product__Type_Ofst(U_8436,U_8437),U_8440)),hAPP(c_Product__Type_Osnd(U_8436,U_8437),U_8440)),
    inference(variable_rename,[status(thm)],[f_2420_1]) ).

cnf(f_2420_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8436,U_8437,U_8438),U_8439),U_8440) = hAPP(hAPP(U_8439,hAPP(c_Product__Type_Ofst(U_8436,U_8437),U_8440)),hAPP(c_Product__Type_Osnd(U_8436,U_8437),U_8440)),
    inference(clausify,[status(thm)],[f_2420_2]) ).

fof(f_2421_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_2421_2,plain,
    ! [U_8442,U_8441] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8441),U_8442) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_8441,U_8442)),
    inference(variable_rename,[status(thm)],[f_2421_1]) ).

cnf(f_2421_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8441),U_8442) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_8441,U_8442)),
    inference(clausify,[status(thm)],[f_2421_2]) ).

fof(f_2422_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_2422_2,plain,
    ! [U_8444,U_8443] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8443,U_8444) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_8443,U_8444)),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

cnf(f_2422_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8443,U_8444) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_8443,U_8444)),
    inference(clausify,[status(thm)],[f_2422_2]) ).

fof(f_2423_1,plain,
    ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_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_2423_2,plain,
    ! [U_8449,U_8448,U_8447,U_8446,U_8445] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8445,U_8446,U_8447),U_8448),U_8449) = hAPP(hAPP(U_8448,hAPP(c_Product__Type_Ofst(U_8445,U_8446),U_8449)),hAPP(c_Product__Type_Osnd(U_8445,U_8446),U_8449)),
    inference(variable_rename,[status(thm)],[f_2423_1]) ).

cnf(f_2423_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8445,U_8446,U_8447),U_8448),U_8449) = hAPP(hAPP(U_8448,hAPP(c_Product__Type_Ofst(U_8445,U_8446),U_8449)),hAPP(c_Product__Type_Osnd(U_8445,U_8446),U_8449)),
    inference(clausify,[status(thm)],[f_2423_2]) ).

fof(f_2424_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_2424_2,plain,
    ! [U_8455,U_8454,U_8453,U_8452,U_8451,U_8450] : hAPP(hAPP(c_COMBS(tc_prod(U_8450,U_8451),U_8451,U_8452),hAPP(hAPP(c_COMBB(U_8453,tc_fun(U_8451,U_8452),tc_prod(U_8450,U_8451)),U_8454),hAPP(hAPP(c_COMBB(U_8450,U_8453,tc_prod(U_8450,U_8451)),U_8455),c_Product__Type_Ofst(U_8450,U_8451)))),c_Product__Type_Osnd(U_8450,U_8451)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_8450,U_8451,U_8452),hAPP(hAPP(c_COMBB(U_8453,tc_fun(U_8451,U_8452),U_8450),U_8454),U_8455)),
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

cnf(f_2424_3,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_8450,U_8451),U_8451,U_8452),hAPP(hAPP(c_COMBB(U_8453,tc_fun(U_8451,U_8452),tc_prod(U_8450,U_8451)),U_8454),hAPP(hAPP(c_COMBB(U_8450,U_8453,tc_prod(U_8450,U_8451)),U_8455),c_Product__Type_Ofst(U_8450,U_8451)))),c_Product__Type_Osnd(U_8450,U_8451)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_8450,U_8451,U_8452),hAPP(hAPP(c_COMBB(U_8453,tc_fun(U_8451,U_8452),U_8450),U_8454),U_8455)),
    inference(clausify,[status(thm)],[f_2424_2]) ).

fof(f_2425_1,plain,
    ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_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_2425_2,plain,
    ! [U_8460,U_8459,U_8458,U_8457,U_8456] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8456,U_8457,U_8458),U_8459),U_8460) = hAPP(hAPP(U_8459,hAPP(c_Product__Type_Ofst(U_8456,U_8457),U_8460)),hAPP(c_Product__Type_Osnd(U_8456,U_8457),U_8460)),
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

cnf(f_2425_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8456,U_8457,U_8458),U_8459),U_8460) = hAPP(hAPP(U_8459,hAPP(c_Product__Type_Ofst(U_8456,U_8457),U_8460)),hAPP(c_Product__Type_Osnd(U_8456,U_8457),U_8460)),
    inference(clausify,[status(thm)],[f_2425_2]) ).

fof(f_2426_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_2426_2,plain,
    ! [U_8462,U_8461] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8461),U_8462) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_8461,U_8462))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8462))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8461),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2426_1]) ).

cnf(f_2426_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8461),U_8462) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_8461,U_8462))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8462))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8461),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2426_2]) ).

fof(f_2427_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_2427_2,plain,
    ! [U_8464,U_8463] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8463),U_8464) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_8463,U_8464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8463)) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

cnf(f_2427_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8463),U_8464) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_8463,U_8464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8463)) ),
    inference(clausify,[status(thm)],[f_2427_2]) ).

fof(f_2428_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_2428_2,plain,
    ! [U_8465] :
      ( 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_8465)) = 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_8465)))
      | ~ 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_8465))) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

cnf(f_2428_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_8465)) = 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_8465)))
    | ~ 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_8465))) ),
    inference(clausify,[status(thm)],[f_2428_2]) ).

fof(f_2429_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_2429_2,plain,
    ! [U_8467,U_8466] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8466),U_8467) = 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_8466),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8467))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8467),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_8466)) ),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

cnf(f_2429_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8466),U_8467) = 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_8466),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8467))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8467),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_8466)) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

fof(f_2430_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_2430_2,plain,
    ! [U_8469,U_8468] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8468),U_8469) = 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_8468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8469))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8469),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

cnf(f_2430_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8468),U_8469) = 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_8468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8469))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8469),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

fof(f_2431_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_2431_2,plain,
    ! [U_8474,U_8473,U_8472,U_8471,U_8470] : c_Product__Type_Oprod_Oprod__size(U_8470,U_8471,U_8472,U_8473,U_8474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8472,hAPP(c_Product__Type_Ofst(U_8470,U_8471),U_8474))),hAPP(U_8473,hAPP(c_Product__Type_Osnd(U_8470,U_8471),U_8474)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

cnf(f_2431_3,plain,
    c_Product__Type_Oprod_Oprod__size(U_8470,U_8471,U_8472,U_8473,U_8474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8472,hAPP(c_Product__Type_Ofst(U_8470,U_8471),U_8474))),hAPP(U_8473,hAPP(c_Product__Type_Osnd(U_8470,U_8471),U_8474)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2431_2]) ).

fof(f_2432_1,plain,
    ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).

fof(f_2432_2,plain,
    ! [U_8479,U_8478,U_8477,U_8476,U_8475] :
      ( hBOOL(hAPP(hAPP(U_8475,hAPP(c_Product__Type_Osnd(U_8478,U_8479),hAPP(hAPP(c_Product__Type_OPair(U_8478,U_8479),U_8477),U_8476))),hAPP(c_Product__Type_Ofst(U_8478,U_8479),hAPP(hAPP(c_Product__Type_OPair(U_8478,U_8479),U_8477),U_8476))))
      | ~ hBOOL(hAPP(hAPP(U_8475,U_8476),U_8477)) ),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

cnf(f_2432_3,plain,
    ( hBOOL(hAPP(hAPP(U_8475,hAPP(c_Product__Type_Osnd(U_8478,U_8479),hAPP(hAPP(c_Product__Type_OPair(U_8478,U_8479),U_8477),U_8476))),hAPP(c_Product__Type_Ofst(U_8478,U_8479),hAPP(hAPP(c_Product__Type_OPair(U_8478,U_8479),U_8477),U_8476))))
    | ~ hBOOL(hAPP(hAPP(U_8475,U_8476),U_8477)) ),
    inference(clausify,[status(thm)],[f_2432_2]) ).

fof(f_2433_1,plain,
    ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Qa_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_Pa_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_Qa_2,V_q_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).

fof(f_2433_2,plain,
    ! [U_8485,U_8484,U_8483,U_8482,U_8481,U_8480] :
      ( ( hBOOL(hAPP(U_8482,hAPP(c_Product__Type_Osnd(U_8484,U_8485),hAPP(hAPP(c_Product__Type_OPair(U_8484,U_8485),U_8481),U_8483))))
        & hBOOL(hAPP(U_8480,hAPP(c_Product__Type_Ofst(U_8484,U_8485),hAPP(hAPP(c_Product__Type_OPair(U_8484,U_8485),U_8481),U_8483)))) )
      | ~ hBOOL(hAPP(U_8482,U_8483))
      | ~ hBOOL(hAPP(U_8480,U_8481)) ),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

cnf(f_2433_3,plain,
    ( hBOOL(hAPP(U_8480,hAPP(c_Product__Type_Ofst(U_8484,U_8485),hAPP(hAPP(c_Product__Type_OPair(U_8484,U_8485),U_8481),U_8483))))
    | ~ hBOOL(hAPP(U_8482,U_8483))
    | ~ hBOOL(hAPP(U_8480,U_8481)) ),
    inference(clausify,[status(thm)],[f_2433_2]) ).

cnf(f_2433_4,plain,
    ( hBOOL(hAPP(U_8482,hAPP(c_Product__Type_Osnd(U_8484,U_8485),hAPP(hAPP(c_Product__Type_OPair(U_8484,U_8485),U_8481),U_8483))))
    | ~ hBOOL(hAPP(U_8482,U_8483))
    | ~ hBOOL(hAPP(U_8480,U_8481)) ),
    inference(clausify,[status(thm)],[f_2433_2]) ).

fof(f_2434_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_2434_2,plain,
    ! [U_8490,U_8489,U_8488] :
      ( hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
      | ? [U_8487,U_8486] :
          ( ~ hBOOL(hAPP(hAPP(U_8490,U_8487),U_8486))
          & ( hBOOL(hAPP(hAPP(U_8490,U_8486),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8487,U_8486)))
            | U_8486 = 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_8487),U_8486))) )
      | ~ 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_8488),U_8489))) ),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

fof(f_2434_3,plain,
    ! [U_8490,U_8489,U_8488] :
      ( hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
      | ? [U_8486] :
          ( ~ hBOOL(hAPP(hAPP(U_8490,sK162(U_8490,U_8489,U_8488)),U_8486))
          & ( hBOOL(hAPP(hAPP(U_8490,U_8486),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK162(U_8490,U_8489,U_8488),U_8486)))
            | U_8486 = 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),sK162(U_8490,U_8489,U_8488)),U_8486))) )
      | ~ 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_8488),U_8489))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_8487,sK162(U_8490,U_8489,U_8488))],[f_2434_2]) ).

fof(f_2434_4,plain,
    ! [U_8490,U_8489,U_8488] :
      ( hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
      | ( ~ hBOOL(hAPP(hAPP(U_8490,sK162(U_8490,U_8489,U_8488)),sK163(U_8490,U_8489,U_8488)))
        & ( hBOOL(hAPP(hAPP(U_8490,sK163(U_8490,U_8489,U_8488)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK162(U_8490,U_8489,U_8488),sK163(U_8490,U_8489,U_8488))))
          | sK163(U_8490,U_8489,U_8488) = 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),sK162(U_8490,U_8489,U_8488)),sK163(U_8490,U_8489,U_8488)))) )
      | ~ 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_8488),U_8489))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_8486,sK163(U_8490,U_8489,U_8488))],[f_2434_3]) ).

cnf(f_2434_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),sK162(U_8490,U_8489,U_8488)),sK163(U_8490,U_8489,U_8488))))
    | hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
    | ~ 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_8488),U_8489))) ),
    inference(clausify,[status(thm)],[f_2434_4]) ).

cnf(f_2434_6,plain,
    ( hBOOL(hAPP(hAPP(U_8490,sK163(U_8490,U_8489,U_8488)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK162(U_8490,U_8489,U_8488),sK163(U_8490,U_8489,U_8488))))
    | sK163(U_8490,U_8489,U_8488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
    | ~ 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_8488),U_8489))) ),
    inference(clausify,[status(thm)],[f_2434_4]) ).

cnf(f_2434_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8490,sK162(U_8490,U_8489,U_8488)),sK163(U_8490,U_8489,U_8488)))
    | hBOOL(hAPP(hAPP(U_8490,U_8488),U_8489))
    | ~ 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_8488),U_8489))) ),
    inference(clausify,[status(thm)],[f_2434_4]) ).

fof(f_2435_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_2435_2,plain,
    ! [U_8492,U_8491] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8491),U_8492) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_8491,U_8492)),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

cnf(f_2435_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8491),U_8492) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_8491,U_8492)),
    inference(clausify,[status(thm)],[f_2435_2]) ).

fof(f_2436_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_2436_2,plain,
    ! [U_8495,U_8494,U_8493] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8493,U_8494),U_8495))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8494),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8494)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)),U_8494))
                | ~ 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_8495))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8494)) ) )
          & U_8494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8495) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_8494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_8493 != 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_8495)),U_8494)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8494),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8494)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)),U_8494))
                  & 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_8495))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8494)) ) )
            | U_8494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_8494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_8493 = 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_8495)),U_8494)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8495)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8493,U_8494),U_8495)) ) ),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

fof(f_2436_3,plain,
    ( ! [U_8501,U_8499,U_8497] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8499),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),U_8499))
                | ~ 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_8501))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499)) ) )
          & U_8499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)) )
    & ! [U_8500,U_8498,U_8496] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8498),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8498)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500)),U_8498))
                  & 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_8500))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8498)) ) )
            | U_8498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8500) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_8498 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_8496 = 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_8500)),U_8498)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ) ),
    inference(miniscope,[status(thm)],[f_2436_2]) ).

cnf(f_2436_4,plain,
    ( U_8496 = 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_8500)),U_8498)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_5,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8500) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8498 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8498))
    | U_8498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8500)),U_8498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8498))
    | U_8498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8498),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8500)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8498))
    | U_8498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8500)),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_8498))
    | U_8498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8496,U_8498),U_8500)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_10,plain,
    ( U_8499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8501)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8499),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),U_8499))
    | ~ 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_8501)))
    | U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8501)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8499),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),U_8499))
    | ~ 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_8501)))
    | U_8499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_15,plain,
    ( U_8499 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8501)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8499),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),U_8499))
    | ~ 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_8501)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_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_8501)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8499),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501)),U_8499))
    | ~ 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_8501)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_8501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8497 != 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_8501)),U_8499)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_8501))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_8497,U_8499),U_8501)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

fof(f_2437_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_2437_2,plain,
    ! [U_8503,U_8502] :
      ( 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_8502),U_8503))),U_8502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_8502)) ),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

cnf(f_2437_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_8502),U_8503))),U_8502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_8502)) ),
    inference(clausify,[status(thm)],[f_2437_2]) ).

fof(f_2438_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_2438_2,plain,
    ! [U_8506,U_8505,U_8504] : 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_8504)),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_8505))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8506))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8506)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8504),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8504),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_8506),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8505)))),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

cnf(f_2438_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_8504)),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_8505))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8506))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8506)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8504),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8504),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_8506),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8505)))),
    inference(clausify,[status(thm)],[f_2438_2]) ).

fof(f_2439_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_2439_2,plain,
    ! [U_8511,U_8510,U_8509,U_8508,U_8507] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8510,U_8510)),hAPP(hAPP(c_Product__Type_OPair(U_8510,U_8510),U_8508),U_8509)),c_Wellfounded_Omlex__prod(U_8510,U_8507,U_8511)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8510,U_8510)),hAPP(hAPP(c_Product__Type_OPair(U_8510,U_8510),U_8508),U_8509)),U_8511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8507,U_8508)),hAPP(U_8507,U_8509))) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

cnf(f_2439_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8510,U_8510)),hAPP(hAPP(c_Product__Type_OPair(U_8510,U_8510),U_8508),U_8509)),c_Wellfounded_Omlex__prod(U_8510,U_8507,U_8511)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8510,U_8510)),hAPP(hAPP(c_Product__Type_OPair(U_8510,U_8510),U_8508),U_8509)),U_8511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8507,U_8508)),hAPP(U_8507,U_8509))) ),
    inference(clausify,[status(thm)],[f_2439_2]) ).

fof(f_2440_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_2440_2,plain,
    ! [U_8516,U_8515,U_8514,U_8513,U_8512] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8515,U_8515)),hAPP(hAPP(c_Product__Type_OPair(U_8515,U_8515),U_8513),U_8514)),c_Wellfounded_Omlex__prod(U_8515,U_8512,U_8516)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8512,U_8513)),hAPP(U_8512,U_8514))) ),
    inference(variable_rename,[status(thm)],[f_2440_1]) ).

cnf(f_2440_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8515,U_8515)),hAPP(hAPP(c_Product__Type_OPair(U_8515,U_8515),U_8513),U_8514)),c_Wellfounded_Omlex__prod(U_8515,U_8512,U_8516)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8512,U_8513)),hAPP(U_8512,U_8514))) ),
    inference(clausify,[status(thm)],[f_2440_2]) ).

fof(f_2441_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_2441_2,plain,
    ! [U_8517] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8517))),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

cnf(f_2441_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8517))),
    inference(clausify,[status(thm)],[f_2441_2]) ).

fof(f_2442_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_2442_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_2442_1]) ).

fof(f_2443_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_2443_2,plain,
    ! [U_8518] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8518)) = U_8518,
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

cnf(f_2443_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8518)) = U_8518,
    inference(clausify,[status(thm)],[f_2443_2]) ).

fof(f_2444_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_2444_2,plain,
    ! [U_8521,U_8520,U_8519] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8520) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8521)
          | U_8520 != U_8521 )
        & ( U_8520 = U_8521
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8520) != hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8521) ) )
      | ~ class_Orderings_Olinorder(U_8519) ),
    inference(variable_rename,[status(thm)],[f_2444_1]) ).

cnf(f_2444_3,plain,
    ( U_8520 = U_8521
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8520) != hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8521)
    | ~ class_Orderings_Olinorder(U_8519) ),
    inference(clausify,[status(thm)],[f_2444_2]) ).

cnf(f_2444_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8520) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8519),U_8521)
    | U_8520 != U_8521
    | ~ class_Orderings_Olinorder(U_8519) ),
    inference(clausify,[status(thm)],[f_2444_2]) ).

fof(f_2445_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_2445_2,plain,
    ! [U_8522] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8522)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8522),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8522)),
    inference(variable_rename,[status(thm)],[f_2445_1]) ).

cnf(f_2445_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8522)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8522),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8522)),
    inference(clausify,[status(thm)],[f_2445_2]) ).

fof(f_2446_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_2446_2,plain,
    ! [U_8525,U_8524,U_8523] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_8523),U_8524),hAPP(c_SetInterval_Oord__class_OlessThan(U_8523),U_8525)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8523),U_8524),U_8525)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8523),U_8524),U_8525))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8523),U_8524),hAPP(c_SetInterval_Oord__class_OlessThan(U_8523),U_8525))) ) )
      | ~ class_Orderings_Oord(U_8523) ),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

cnf(f_2446_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8523),U_8524),U_8525))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8523),U_8524),hAPP(c_SetInterval_Oord__class_OlessThan(U_8523),U_8525)))
    | ~ class_Orderings_Oord(U_8523) ),
    inference(clausify,[status(thm)],[f_2446_2]) ).

cnf(f_2446_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8523),U_8524),hAPP(c_SetInterval_Oord__class_OlessThan(U_8523),U_8525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8523),U_8524),U_8525))
    | ~ class_Orderings_Oord(U_8523) ),
    inference(clausify,[status(thm)],[f_2446_2]) ).

fof(f_2447_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_2447_2,plain,
    ! [U_8528,U_8527,U_8526] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8526,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8527)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8528)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8526),U_8527),U_8528)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8526),U_8527),U_8528))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8526,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8527)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8528))) ) )
      | ~ class_Orderings_Olinorder(U_8526) ),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

cnf(f_2447_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8526),U_8527),U_8528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8526,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8527)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8528)))
    | ~ class_Orderings_Olinorder(U_8526) ),
    inference(clausify,[status(thm)],[f_2447_2]) ).

cnf(f_2447_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8526,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8527)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8526),U_8528)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8526),U_8527),U_8528))
    | ~ class_Orderings_Olinorder(U_8526) ),
    inference(clausify,[status(thm)],[f_2447_2]) ).

fof(f_2448_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_2448_2,plain,
    ! [U_8531,U_8530,U_8529] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8529),U_8530),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8531))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8529),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8529),U_8530),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8531))),hAPP(U_8530,U_8531))
      | ~ class_Groups_Ocomm__monoid__add(U_8529) ),
    inference(variable_rename,[status(thm)],[f_2448_1]) ).

cnf(f_2448_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8529),U_8530),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8531))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8529),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8529),U_8530),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8531))),hAPP(U_8530,U_8531))
    | ~ class_Groups_Ocomm__monoid__add(U_8529) ),
    inference(clausify,[status(thm)],[f_2448_2]) ).

fof(f_2449_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_2449_2,plain,
    ! [U_8534,U_8533,U_8532] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8533)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8534)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8532),U_8533),U_8534)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8532),U_8533),U_8534))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8533)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8534))) ) )
      | ~ class_Orderings_Olinorder(U_8532) ),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

cnf(f_2449_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8532),U_8533),U_8534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8533)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8534)))
    | ~ class_Orderings_Olinorder(U_8532) ),
    inference(clausify,[status(thm)],[f_2449_2]) ).

cnf(f_2449_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8533)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8532),U_8534)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8532),U_8533),U_8534))
    | ~ class_Orderings_Olinorder(U_8532) ),
    inference(clausify,[status(thm)],[f_2449_2]) ).

fof(f_2450_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_2450_2,plain,
    ! [U_8536,U_8535] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8535,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8535),U_8536),c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_8535),U_8536)) = hAPP(hAPP(c_Set_Oinsert(U_8535),U_8536),c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_8535) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

cnf(f_2450_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8535,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8535),U_8536),c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_8535),U_8536)) = hAPP(hAPP(c_Set_Oinsert(U_8535),U_8536),c_Orderings_Obot__class_Obot(tc_fun(U_8535,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_8535) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

fof(f_2451_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_2451_2,plain,
    ! [U_8541] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8541))
        | ! [U_8540] :
          ? [U_8539] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8539),U_8540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8539),U_8541)) ) )
      & ( ? [U_8538] :
          ! [U_8537] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8537),U_8538))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8537),U_8541)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8541)) ) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

fof(f_2451_3,plain,
    ( ! [U_8543] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8543))
        | ! [U_8540] :
          ? [U_8539] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8539),U_8540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8539),U_8543)) ) )
    & ! [U_8542] :
        ( ? [U_8538] :
          ! [U_8537] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8537),U_8538))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8537),U_8542)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8542)) ) ),
    inference(miniscope,[status(thm)],[f_2451_2]) ).

fof(f_2451_4,plain,
    ( ! [U_8543] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8543))
        | ! [U_8540] :
          ? [U_8539] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8539),U_8540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8539),U_8543)) ) )
    & ! [U_8542] :
        ( ! [U_8537] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8537),sK164(U_8542)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8537),U_8542)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8542)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_8538,sK164(U_8542))],[f_2451_3]) ).

fof(f_2451_5,plain,
    ( ! [U_8543] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8543))
        | ! [U_8540] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK165(U_8543,U_8540)),U_8540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK165(U_8543,U_8540)),U_8543)) ) )
    & ! [U_8542] :
        ( ! [U_8537] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8537),sK164(U_8542)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8537),U_8542)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8542)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_8539,sK165(U_8543,U_8540))],[f_2451_4]) ).

cnf(f_2451_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8537),sK164(U_8542)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8537),U_8542))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8542)) ),
    inference(clausify,[status(thm)],[f_2451_5]) ).

cnf(f_2451_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK165(U_8543,U_8540)),U_8543))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8543)) ),
    inference(clausify,[status(thm)],[f_2451_5]) ).

cnf(f_2451_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK165(U_8543,U_8540)),U_8540))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8543)) ),
    inference(clausify,[status(thm)],[f_2451_5]) ).

fof(f_2452_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_2452_2,plain,
    ! [U_8548] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8548))
        | ! [U_8547] :
          ? [U_8546] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8546),U_8547))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8546),U_8548)) ) )
      & ( ? [U_8545] :
          ! [U_8544] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8544),U_8545))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8544),U_8548)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8548)) ) ),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

fof(f_2452_3,plain,
    ( ! [U_8550] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8550))
        | ! [U_8547] :
          ? [U_8546] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8546),U_8547))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8546),U_8550)) ) )
    & ! [U_8549] :
        ( ? [U_8545] :
          ! [U_8544] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8544),U_8545))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8544),U_8549)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8549)) ) ),
    inference(miniscope,[status(thm)],[f_2452_2]) ).

fof(f_2452_4,plain,
    ( ! [U_8550] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8550))
        | ! [U_8547] :
          ? [U_8546] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8546),U_8547))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8546),U_8550)) ) )
    & ! [U_8549] :
        ( ! [U_8544] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8544),sK166(U_8549)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8544),U_8549)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8549)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_8545,sK166(U_8549))],[f_2452_3]) ).

fof(f_2452_5,plain,
    ( ! [U_8550] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8550))
        | ! [U_8547] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK167(U_8550,U_8547)),U_8547))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK167(U_8550,U_8547)),U_8550)) ) )
    & ! [U_8549] :
        ( ! [U_8544] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8544),sK166(U_8549)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8544),U_8549)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8549)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_8546,sK167(U_8550,U_8547))],[f_2452_4]) ).

cnf(f_2452_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8544),sK166(U_8549)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8544),U_8549))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8549)) ),
    inference(clausify,[status(thm)],[f_2452_5]) ).

cnf(f_2452_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK167(U_8550,U_8547)),U_8550))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8550)) ),
    inference(clausify,[status(thm)],[f_2452_5]) ).

cnf(f_2452_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK167(U_8550,U_8547)),U_8547))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_8550)) ),
    inference(clausify,[status(thm)],[f_2452_5]) ).

fof(f_2453_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_2453_2,plain,
    ! [U_8554,U_8553,U_8552,U_8551] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),c_Groups_Oone__class_Oone(U_8551)),c_Groups_Oone__class_Oone(U_8551))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8551),hAPP(hAPP(c_COMBB(U_8551,U_8551,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_8551,U_8551),hAPP(hAPP(c_COMBB(U_8551,tc_fun(U_8551,U_8551),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_8551)),c_Nat_Osemiring__1__class_Oof__nat(U_8551))),U_8553))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8554))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8551),U_8554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8551),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8554),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8553))))
      | ~ class_Rings_Ocomm__semiring__1(U_8551) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

cnf(f_2453_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),c_Groups_Oone__class_Oone(U_8551)),c_Groups_Oone__class_Oone(U_8551))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8551),hAPP(hAPP(c_COMBB(U_8551,U_8551,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_8551,U_8551),hAPP(hAPP(c_COMBB(U_8551,tc_fun(U_8551,U_8551),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_8551)),c_Nat_Osemiring__1__class_Oof__nat(U_8551))),U_8553))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8554))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8551),U_8554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8551),U_8552),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8551),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8551),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8554),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8553))))
    | ~ class_Rings_Ocomm__semiring__1(U_8551) ),
    inference(clausify,[status(thm)],[f_2453_2]) ).

fof(f_2454_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_2454_2,plain,
    ! [U_8557,U_8556,U_8555] : 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_8555)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_8556))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8557))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8557),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_8556)))),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

cnf(f_2454_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_8555)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_8556))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8557))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8557),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_8556)))),
    inference(clausify,[status(thm)],[f_2454_2]) ).

fof(f_2455_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_2455_2,plain,
    ! [U_8558] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_8558)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

cnf(f_2455_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_8558)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2455_2]) ).

fof(f_2456_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_2456_2,plain,
    ! [U_8564,U_8563,U_8562,U_8561,U_8560,U_8559] : c_Product__Type_Oprod_Oprod__rec(U_8559,U_8560,U_8561,U_8562,hAPP(hAPP(c_Product__Type_OPair(U_8559,U_8560),U_8563),U_8564)) = hAPP(hAPP(U_8562,U_8563),U_8564),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

cnf(f_2456_3,plain,
    c_Product__Type_Oprod_Oprod__rec(U_8559,U_8560,U_8561,U_8562,hAPP(hAPP(c_Product__Type_OPair(U_8559,U_8560),U_8563),U_8564)) = hAPP(hAPP(U_8562,U_8563),U_8564),
    inference(clausify,[status(thm)],[f_2456_2]) ).

fof(f_2457_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_2457_2,plain,
    ! [U_8570,U_8569,U_8568,U_8567,U_8566,U_8565] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8565),U_8566),c_SetInterval_Oord_OgreaterThanAtMost(U_8565,U_8567,U_8568,U_8569,U_8570)))
        | ~ hBOOL(hAPP(hAPP(U_8567,U_8566),U_8570))
        | ~ hBOOL(hAPP(hAPP(U_8568,U_8569),U_8566)) )
      & ( ( hBOOL(hAPP(hAPP(U_8567,U_8566),U_8570))
          & hBOOL(hAPP(hAPP(U_8568,U_8569),U_8566)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8565),U_8566),c_SetInterval_Oord_OgreaterThanAtMost(U_8565,U_8567,U_8568,U_8569,U_8570))) ) ),
    inference(variable_rename,[status(thm)],[f_2457_1]) ).

fof(f_2457_3,plain,
    ( ! [U_8582,U_8580,U_8578,U_8576,U_8574] :
        ( ! [U_8572] : hBOOL(hAPP(hAPP(c_member(U_8572),U_8574),c_SetInterval_Oord_OgreaterThanAtMost(U_8572,U_8576,U_8578,U_8580,U_8582)))
        | ~ hBOOL(hAPP(hAPP(U_8576,U_8574),U_8582))
        | ~ hBOOL(hAPP(hAPP(U_8578,U_8580),U_8574)) )
    & ! [U_8581,U_8579,U_8577,U_8575,U_8573] :
        ( ! [U_8571] : ~ hBOOL(hAPP(hAPP(c_member(U_8571),U_8573),c_SetInterval_Oord_OgreaterThanAtMost(U_8571,U_8575,U_8577,U_8579,U_8581)))
        | ( hBOOL(hAPP(hAPP(U_8575,U_8573),U_8581))
          & hBOOL(hAPP(hAPP(U_8577,U_8579),U_8573)) ) ) ),
    inference(miniscope,[status(thm)],[f_2457_2]) ).

cnf(f_2457_4,plain,
    ( hBOOL(hAPP(hAPP(U_8577,U_8579),U_8573))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8571),U_8573),c_SetInterval_Oord_OgreaterThanAtMost(U_8571,U_8575,U_8577,U_8579,U_8581))) ),
    inference(clausify,[status(thm)],[f_2457_3]) ).

cnf(f_2457_5,plain,
    ( hBOOL(hAPP(hAPP(U_8575,U_8573),U_8581))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8571),U_8573),c_SetInterval_Oord_OgreaterThanAtMost(U_8571,U_8575,U_8577,U_8579,U_8581))) ),
    inference(clausify,[status(thm)],[f_2457_3]) ).

cnf(f_2457_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8572),U_8574),c_SetInterval_Oord_OgreaterThanAtMost(U_8572,U_8576,U_8578,U_8580,U_8582)))
    | ~ hBOOL(hAPP(hAPP(U_8576,U_8574),U_8582))
    | ~ hBOOL(hAPP(hAPP(U_8578,U_8580),U_8574)) ),
    inference(clausify,[status(thm)],[f_2457_3]) ).

fof(f_2458_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_2458_2,plain,
    ! [U_8588,U_8587,U_8586,U_8585,U_8584,U_8583] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8583),U_8584),c_SetInterval_Oord_OatLeastLessThan(U_8583,U_8585,U_8586,U_8587,U_8588)))
        | ~ hBOOL(hAPP(hAPP(U_8586,U_8584),U_8588))
        | ~ hBOOL(hAPP(hAPP(U_8585,U_8587),U_8584)) )
      & ( ( hBOOL(hAPP(hAPP(U_8586,U_8584),U_8588))
          & hBOOL(hAPP(hAPP(U_8585,U_8587),U_8584)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8583),U_8584),c_SetInterval_Oord_OatLeastLessThan(U_8583,U_8585,U_8586,U_8587,U_8588))) ) ),
    inference(variable_rename,[status(thm)],[f_2458_1]) ).

fof(f_2458_3,plain,
    ( ! [U_8600,U_8598,U_8596,U_8594,U_8592] :
        ( ! [U_8590] : hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),c_SetInterval_Oord_OatLeastLessThan(U_8590,U_8594,U_8596,U_8598,U_8600)))
        | ~ hBOOL(hAPP(hAPP(U_8596,U_8592),U_8600))
        | ~ hBOOL(hAPP(hAPP(U_8594,U_8598),U_8592)) )
    & ! [U_8599,U_8597,U_8595,U_8593,U_8591] :
        ( ! [U_8589] : ~ hBOOL(hAPP(hAPP(c_member(U_8589),U_8591),c_SetInterval_Oord_OatLeastLessThan(U_8589,U_8593,U_8595,U_8597,U_8599)))
        | ( hBOOL(hAPP(hAPP(U_8595,U_8591),U_8599))
          & hBOOL(hAPP(hAPP(U_8593,U_8597),U_8591)) ) ) ),
    inference(miniscope,[status(thm)],[f_2458_2]) ).

cnf(f_2458_4,plain,
    ( hBOOL(hAPP(hAPP(U_8593,U_8597),U_8591))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8589),U_8591),c_SetInterval_Oord_OatLeastLessThan(U_8589,U_8593,U_8595,U_8597,U_8599))) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

cnf(f_2458_5,plain,
    ( hBOOL(hAPP(hAPP(U_8595,U_8591),U_8599))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8589),U_8591),c_SetInterval_Oord_OatLeastLessThan(U_8589,U_8593,U_8595,U_8597,U_8599))) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

cnf(f_2458_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8590),U_8592),c_SetInterval_Oord_OatLeastLessThan(U_8590,U_8594,U_8596,U_8598,U_8600)))
    | ~ hBOOL(hAPP(hAPP(U_8596,U_8592),U_8600))
    | ~ hBOOL(hAPP(hAPP(U_8594,U_8598),U_8592)) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

fof(f_2459_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_2459_2,plain,
    ! [U_8601] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_8601) = U_8601,
    inference(variable_rename,[status(thm)],[f_2459_1]) ).

cnf(f_2459_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_8601) = U_8601,
    inference(clausify,[status(thm)],[f_2459_2]) ).

fof(f_2460_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_2460_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_2460_1]) ).

fof(f_2461_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_2461_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_2461_1]) ).

fof(f_2462_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_2462_2,plain,
    ! [U_8605,U_8604,U_8603,U_8602] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8602),U_8603),c_SetInterval_Oord_OatMost(U_8602,U_8604,U_8605)))
        | ~ hBOOL(hAPP(hAPP(U_8604,U_8603),U_8605)) )
      & ( hBOOL(hAPP(hAPP(U_8604,U_8603),U_8605))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8602),U_8603),c_SetInterval_Oord_OatMost(U_8602,U_8604,U_8605))) ) ),
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

fof(f_2462_3,plain,
    ( ! [U_8613,U_8611,U_8609] :
        ( ! [U_8607] : hBOOL(hAPP(hAPP(c_member(U_8607),U_8609),c_SetInterval_Oord_OatMost(U_8607,U_8611,U_8613)))
        | ~ hBOOL(hAPP(hAPP(U_8611,U_8609),U_8613)) )
    & ! [U_8612,U_8610,U_8608] :
        ( ! [U_8606] : ~ hBOOL(hAPP(hAPP(c_member(U_8606),U_8608),c_SetInterval_Oord_OatMost(U_8606,U_8610,U_8612)))
        | hBOOL(hAPP(hAPP(U_8610,U_8608),U_8612)) ) ),
    inference(miniscope,[status(thm)],[f_2462_2]) ).

cnf(f_2462_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8606),U_8608),c_SetInterval_Oord_OatMost(U_8606,U_8610,U_8612)))
    | hBOOL(hAPP(hAPP(U_8610,U_8608),U_8612)) ),
    inference(clausify,[status(thm)],[f_2462_3]) ).

cnf(f_2462_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8607),U_8609),c_SetInterval_Oord_OatMost(U_8607,U_8611,U_8613)))
    | ~ hBOOL(hAPP(hAPP(U_8611,U_8609),U_8613)) ),
    inference(clausify,[status(thm)],[f_2462_3]) ).

fof(f_2463_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_2463_2,plain,
    ! [U_8617,U_8616,U_8615,U_8614] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8614),U_8615),c_SetInterval_Oord_OatLeast(U_8614,U_8616,U_8617)))
        | ~ hBOOL(hAPP(hAPP(U_8616,U_8617),U_8615)) )
      & ( hBOOL(hAPP(hAPP(U_8616,U_8617),U_8615))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8614),U_8615),c_SetInterval_Oord_OatLeast(U_8614,U_8616,U_8617))) ) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

fof(f_2463_3,plain,
    ( ! [U_8625,U_8623,U_8621] :
        ( ! [U_8619] : hBOOL(hAPP(hAPP(c_member(U_8619),U_8621),c_SetInterval_Oord_OatLeast(U_8619,U_8623,U_8625)))
        | ~ hBOOL(hAPP(hAPP(U_8623,U_8625),U_8621)) )
    & ! [U_8624,U_8622,U_8620] :
        ( ! [U_8618] : ~ hBOOL(hAPP(hAPP(c_member(U_8618),U_8620),c_SetInterval_Oord_OatLeast(U_8618,U_8622,U_8624)))
        | hBOOL(hAPP(hAPP(U_8622,U_8624),U_8620)) ) ),
    inference(miniscope,[status(thm)],[f_2463_2]) ).

cnf(f_2463_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8618),U_8620),c_SetInterval_Oord_OatLeast(U_8618,U_8622,U_8624)))
    | hBOOL(hAPP(hAPP(U_8622,U_8624),U_8620)) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

cnf(f_2463_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8619),U_8621),c_SetInterval_Oord_OatLeast(U_8619,U_8623,U_8625)))
    | ~ hBOOL(hAPP(hAPP(U_8623,U_8625),U_8621)) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

fof(f_2464_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_2464_2,plain,
    ! [U_8629,U_8628,U_8627,U_8626] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),c_SetInterval_Oord_OlessThan(U_8626,U_8628,U_8629)))
        | ~ hBOOL(hAPP(hAPP(U_8628,U_8627),U_8629)) )
      & ( hBOOL(hAPP(hAPP(U_8628,U_8627),U_8629))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),c_SetInterval_Oord_OlessThan(U_8626,U_8628,U_8629))) ) ),
    inference(variable_rename,[status(thm)],[f_2464_1]) ).

fof(f_2464_3,plain,
    ( ! [U_8637,U_8635,U_8633] :
        ( ! [U_8631] : hBOOL(hAPP(hAPP(c_member(U_8631),U_8633),c_SetInterval_Oord_OlessThan(U_8631,U_8635,U_8637)))
        | ~ hBOOL(hAPP(hAPP(U_8635,U_8633),U_8637)) )
    & ! [U_8636,U_8634,U_8632] :
        ( ! [U_8630] : ~ hBOOL(hAPP(hAPP(c_member(U_8630),U_8632),c_SetInterval_Oord_OlessThan(U_8630,U_8634,U_8636)))
        | hBOOL(hAPP(hAPP(U_8634,U_8632),U_8636)) ) ),
    inference(miniscope,[status(thm)],[f_2464_2]) ).

cnf(f_2464_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8630),U_8632),c_SetInterval_Oord_OlessThan(U_8630,U_8634,U_8636)))
    | hBOOL(hAPP(hAPP(U_8634,U_8632),U_8636)) ),
    inference(clausify,[status(thm)],[f_2464_3]) ).

cnf(f_2464_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8631),U_8633),c_SetInterval_Oord_OlessThan(U_8631,U_8635,U_8637)))
    | ~ hBOOL(hAPP(hAPP(U_8635,U_8633),U_8637)) ),
    inference(clausify,[status(thm)],[f_2464_3]) ).

fof(f_2465_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_2465_2,plain,
    ! [U_8641,U_8640,U_8639,U_8638] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8638),U_8639),c_SetInterval_Oord_OgreaterThan(U_8638,U_8640,U_8641)))
        | ~ hBOOL(hAPP(hAPP(U_8640,U_8641),U_8639)) )
      & ( hBOOL(hAPP(hAPP(U_8640,U_8641),U_8639))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8638),U_8639),c_SetInterval_Oord_OgreaterThan(U_8638,U_8640,U_8641))) ) ),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

fof(f_2465_3,plain,
    ( ! [U_8649,U_8647,U_8645] :
        ( ! [U_8643] : hBOOL(hAPP(hAPP(c_member(U_8643),U_8645),c_SetInterval_Oord_OgreaterThan(U_8643,U_8647,U_8649)))
        | ~ hBOOL(hAPP(hAPP(U_8647,U_8649),U_8645)) )
    & ! [U_8648,U_8646,U_8644] :
        ( ! [U_8642] : ~ hBOOL(hAPP(hAPP(c_member(U_8642),U_8644),c_SetInterval_Oord_OgreaterThan(U_8642,U_8646,U_8648)))
        | hBOOL(hAPP(hAPP(U_8646,U_8648),U_8644)) ) ),
    inference(miniscope,[status(thm)],[f_2465_2]) ).

cnf(f_2465_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8642),U_8644),c_SetInterval_Oord_OgreaterThan(U_8642,U_8646,U_8648)))
    | hBOOL(hAPP(hAPP(U_8646,U_8648),U_8644)) ),
    inference(clausify,[status(thm)],[f_2465_3]) ).

cnf(f_2465_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8643),U_8645),c_SetInterval_Oord_OgreaterThan(U_8643,U_8647,U_8649)))
    | ~ hBOOL(hAPP(hAPP(U_8647,U_8649),U_8645)) ),
    inference(clausify,[status(thm)],[f_2465_3]) ).

fof(f_2466_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_2466_2,plain,
    ! [U_8654,U_8653,U_8652,U_8651,U_8650] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8650),U_8651),c_SetInterval_Oord_OgreaterThanLessThan(U_8650,U_8652,U_8653,U_8654)))
        | ~ hBOOL(hAPP(hAPP(U_8652,U_8651),U_8654))
        | ~ hBOOL(hAPP(hAPP(U_8652,U_8653),U_8651)) )
      & ( ( hBOOL(hAPP(hAPP(U_8652,U_8651),U_8654))
          & hBOOL(hAPP(hAPP(U_8652,U_8653),U_8651)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8650),U_8651),c_SetInterval_Oord_OgreaterThanLessThan(U_8650,U_8652,U_8653,U_8654))) ) ),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

fof(f_2466_3,plain,
    ( ! [U_8664,U_8662,U_8660,U_8658] :
        ( ! [U_8656] : hBOOL(hAPP(hAPP(c_member(U_8656),U_8658),c_SetInterval_Oord_OgreaterThanLessThan(U_8656,U_8660,U_8662,U_8664)))
        | ~ hBOOL(hAPP(hAPP(U_8660,U_8658),U_8664))
        | ~ hBOOL(hAPP(hAPP(U_8660,U_8662),U_8658)) )
    & ! [U_8663,U_8661,U_8659,U_8657] :
        ( ! [U_8655] : ~ hBOOL(hAPP(hAPP(c_member(U_8655),U_8657),c_SetInterval_Oord_OgreaterThanLessThan(U_8655,U_8659,U_8661,U_8663)))
        | ( hBOOL(hAPP(hAPP(U_8659,U_8657),U_8663))
          & hBOOL(hAPP(hAPP(U_8659,U_8661),U_8657)) ) ) ),
    inference(miniscope,[status(thm)],[f_2466_2]) ).

cnf(f_2466_4,plain,
    ( hBOOL(hAPP(hAPP(U_8659,U_8661),U_8657))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8655),U_8657),c_SetInterval_Oord_OgreaterThanLessThan(U_8655,U_8659,U_8661,U_8663))) ),
    inference(clausify,[status(thm)],[f_2466_3]) ).

cnf(f_2466_5,plain,
    ( hBOOL(hAPP(hAPP(U_8659,U_8657),U_8663))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8655),U_8657),c_SetInterval_Oord_OgreaterThanLessThan(U_8655,U_8659,U_8661,U_8663))) ),
    inference(clausify,[status(thm)],[f_2466_3]) ).

cnf(f_2466_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8656),U_8658),c_SetInterval_Oord_OgreaterThanLessThan(U_8656,U_8660,U_8662,U_8664)))
    | ~ hBOOL(hAPP(hAPP(U_8660,U_8658),U_8664))
    | ~ hBOOL(hAPP(hAPP(U_8660,U_8662),U_8658)) ),
    inference(clausify,[status(thm)],[f_2466_3]) ).

fof(f_2467_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_2467_2,plain,
    ! [U_8669,U_8668,U_8667,U_8666,U_8665] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8665),U_8666),c_SetInterval_Oord_OatLeastAtMost(U_8665,U_8667,U_8668,U_8669)))
        | ~ hBOOL(hAPP(hAPP(U_8667,U_8666),U_8669))
        | ~ hBOOL(hAPP(hAPP(U_8667,U_8668),U_8666)) )
      & ( ( hBOOL(hAPP(hAPP(U_8667,U_8666),U_8669))
          & hBOOL(hAPP(hAPP(U_8667,U_8668),U_8666)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8665),U_8666),c_SetInterval_Oord_OatLeastAtMost(U_8665,U_8667,U_8668,U_8669))) ) ),
    inference(variable_rename,[status(thm)],[f_2467_1]) ).

fof(f_2467_3,plain,
    ( ! [U_8679,U_8677,U_8675,U_8673] :
        ( ! [U_8671] : hBOOL(hAPP(hAPP(c_member(U_8671),U_8673),c_SetInterval_Oord_OatLeastAtMost(U_8671,U_8675,U_8677,U_8679)))
        | ~ hBOOL(hAPP(hAPP(U_8675,U_8673),U_8679))
        | ~ hBOOL(hAPP(hAPP(U_8675,U_8677),U_8673)) )
    & ! [U_8678,U_8676,U_8674,U_8672] :
        ( ! [U_8670] : ~ hBOOL(hAPP(hAPP(c_member(U_8670),U_8672),c_SetInterval_Oord_OatLeastAtMost(U_8670,U_8674,U_8676,U_8678)))
        | ( hBOOL(hAPP(hAPP(U_8674,U_8672),U_8678))
          & hBOOL(hAPP(hAPP(U_8674,U_8676),U_8672)) ) ) ),
    inference(miniscope,[status(thm)],[f_2467_2]) ).

cnf(f_2467_4,plain,
    ( hBOOL(hAPP(hAPP(U_8674,U_8676),U_8672))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8670),U_8672),c_SetInterval_Oord_OatLeastAtMost(U_8670,U_8674,U_8676,U_8678))) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

cnf(f_2467_5,plain,
    ( hBOOL(hAPP(hAPP(U_8674,U_8672),U_8678))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8670),U_8672),c_SetInterval_Oord_OatLeastAtMost(U_8670,U_8674,U_8676,U_8678))) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

cnf(f_2467_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8671),U_8673),c_SetInterval_Oord_OatLeastAtMost(U_8671,U_8675,U_8677,U_8679)))
    | ~ hBOOL(hAPP(hAPP(U_8675,U_8673),U_8679))
    | ~ hBOOL(hAPP(hAPP(U_8675,U_8677),U_8673)) ),
    inference(clausify,[status(thm)],[f_2467_3]) ).

fof(f_2468_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_2468_2,plain,
    ! [U_8687,U_8686,U_8685,U_8684,U_8683,U_8682,U_8681,U_8680] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8680,U_8681),tc_prod(U_8680,U_8681))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8680,U_8681),tc_prod(U_8680,U_8681)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8681),U_8682),U_8683)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8681),U_8684),U_8685))),c_Wellfounded_Olex__prod(U_8680,U_8681,U_8686,U_8687)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8681,U_8681)),hAPP(hAPP(c_Product__Type_OPair(U_8681,U_8681),U_8683),U_8685)),U_8687))
            | U_8682 != U_8684 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8680,U_8680)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8680),U_8682),U_8684)),U_8686)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8681,U_8681)),hAPP(hAPP(c_Product__Type_OPair(U_8681,U_8681),U_8683),U_8685)),U_8687))
          & U_8682 = U_8684 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8680,U_8680)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8680),U_8682),U_8684)),U_8686))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8680,U_8681),tc_prod(U_8680,U_8681))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8680,U_8681),tc_prod(U_8680,U_8681)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8681),U_8682),U_8683)),hAPP(hAPP(c_Product__Type_OPair(U_8680,U_8681),U_8684),U_8685))),c_Wellfounded_Olex__prod(U_8680,U_8681,U_8686,U_8687))) ) ),
    inference(variable_rename,[status(thm)],[f_2468_1]) ).

fof(f_2468_3,plain,
    ( ! [U_8703,U_8701,U_8699,U_8697,U_8695,U_8693,U_8691,U_8689] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8693),U_8695)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8697),U_8699))),c_Wellfounded_Olex__prod(U_8689,U_8691,U_8701,U_8703)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8691,U_8691)),hAPP(hAPP(c_Product__Type_OPair(U_8691,U_8691),U_8695),U_8699)),U_8703))
            | U_8693 != U_8697 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8689,U_8689)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8689),U_8693),U_8697)),U_8701)) ) )
    & ! [U_8702,U_8700,U_8698,U_8696,U_8694,U_8692,U_8690,U_8688] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8690,U_8690)),hAPP(hAPP(c_Product__Type_OPair(U_8690,U_8690),U_8694),U_8698)),U_8702))
          & U_8692 = U_8696 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8688,U_8688)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8688),U_8692),U_8696)),U_8700))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8692),U_8694)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8696),U_8698))),c_Wellfounded_Olex__prod(U_8688,U_8690,U_8700,U_8702))) ) ),
    inference(miniscope,[status(thm)],[f_2468_2]) ).

cnf(f_2468_4,plain,
    ( U_8692 = U_8696
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8688,U_8688)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8688),U_8692),U_8696)),U_8700))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8692),U_8694)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8696),U_8698))),c_Wellfounded_Olex__prod(U_8688,U_8690,U_8700,U_8702))) ),
    inference(clausify,[status(thm)],[f_2468_3]) ).

cnf(f_2468_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8690,U_8690)),hAPP(hAPP(c_Product__Type_OPair(U_8690,U_8690),U_8694),U_8698)),U_8702))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8688,U_8688)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8688),U_8692),U_8696)),U_8700))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8688,U_8690),tc_prod(U_8688,U_8690)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8692),U_8694)),hAPP(hAPP(c_Product__Type_OPair(U_8688,U_8690),U_8696),U_8698))),c_Wellfounded_Olex__prod(U_8688,U_8690,U_8700,U_8702))) ),
    inference(clausify,[status(thm)],[f_2468_3]) ).

cnf(f_2468_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8689,U_8689)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8689),U_8693),U_8697)),U_8701))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8693),U_8695)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8697),U_8699))),c_Wellfounded_Olex__prod(U_8689,U_8691,U_8701,U_8703))) ),
    inference(clausify,[status(thm)],[f_2468_3]) ).

cnf(f_2468_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8691,U_8691)),hAPP(hAPP(c_Product__Type_OPair(U_8691,U_8691),U_8695),U_8699)),U_8703))
    | U_8693 != U_8697
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8689,U_8691),tc_prod(U_8689,U_8691)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8693),U_8695)),hAPP(hAPP(c_Product__Type_OPair(U_8689,U_8691),U_8697),U_8699))),c_Wellfounded_Olex__prod(U_8689,U_8691,U_8701,U_8703))) ),
    inference(clausify,[status(thm)],[f_2468_3]) ).

fof(f_2469_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_2469_2,plain,
    ! [U_8706,U_8705,U_8704] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8704,tc_HOL_Obool),tc_fun(U_8704,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8704,tc_HOL_Obool),tc_fun(U_8704,tc_HOL_Obool)),U_8705),U_8706)),c_Wellfounded_Ofinite__psubset(U_8704)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8704,tc_HOL_Obool)),U_8705),U_8706)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8706))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8704,tc_HOL_Obool)),U_8705),U_8706)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8704,tc_HOL_Obool),tc_fun(U_8704,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8704,tc_HOL_Obool),tc_fun(U_8704,tc_HOL_Obool)),U_8705),U_8706)),c_Wellfounded_Ofinite__psubset(U_8704))) ) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

fof(f_2469_3,plain,
    ( ! [U_8712,U_8710,U_8708] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8708,tc_HOL_Obool),tc_fun(U_8708,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8708,tc_HOL_Obool),tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8712)),c_Wellfounded_Ofinite__psubset(U_8708)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8708),U_8712))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8712)) )
    & ! [U_8711,U_8709,U_8707] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8707),U_8711))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8707,tc_HOL_Obool)),U_8709),U_8711)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool)),U_8709),U_8711)),c_Wellfounded_Ofinite__psubset(U_8707))) ) ),
    inference(miniscope,[status(thm)],[f_2469_2]) ).

cnf(f_2469_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8707,tc_HOL_Obool)),U_8709),U_8711))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool)),U_8709),U_8711)),c_Wellfounded_Ofinite__psubset(U_8707))) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

cnf(f_2469_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8707),U_8711))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8707,tc_HOL_Obool),tc_fun(U_8707,tc_HOL_Obool)),U_8709),U_8711)),c_Wellfounded_Ofinite__psubset(U_8707))) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

cnf(f_2469_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8708,tc_HOL_Obool),tc_fun(U_8708,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8708,tc_HOL_Obool),tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8712)),c_Wellfounded_Ofinite__psubset(U_8708)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8708),U_8712))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8712)) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

fof(f_2470_1,plain,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_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_Pa_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_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).

fof(f_2470_2,plain,
    ! [U_8719,U_8718,U_8717,U_8716,U_8715,U_8714,U_8713] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8719,U_8715),tc_prod(U_8719,U_8715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8719,U_8715),tc_prod(U_8719,U_8715)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8715),U_8714),U_8716)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8715),U_8714),U_8717))),c_Recdef_Osame__fst(U_8719,U_8715,U_8713,U_8718)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8715,U_8715)),hAPP(hAPP(c_Product__Type_OPair(U_8715,U_8715),U_8716),U_8717)),hAPP(U_8718,U_8714)))
      | ~ hBOOL(hAPP(U_8713,U_8714)) ),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

cnf(f_2470_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8719,U_8715),tc_prod(U_8719,U_8715))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8719,U_8715),tc_prod(U_8719,U_8715)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8715),U_8714),U_8716)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8715),U_8714),U_8717))),c_Recdef_Osame__fst(U_8719,U_8715,U_8713,U_8718)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8715,U_8715)),hAPP(hAPP(c_Product__Type_OPair(U_8715,U_8715),U_8716),U_8717)),hAPP(U_8718,U_8714)))
    | ~ hBOOL(hAPP(U_8713,U_8714)) ),
    inference(clausify,[status(thm)],[f_2470_2]) ).

fof(f_2471_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_2471_2,plain,
    ! [U_8726,U_8725,U_8724,U_8723,U_8722,U_8721] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),hAPP(U_8724,U_8726)),U_8725))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8722),U_8726),U_8723))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8722,U_8721),U_8724),U_8723) != U_8725
      | ? [U_8720] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),c_Groups_Ozero__class_Ozero(U_8721)),hAPP(U_8724,U_8720)))
          & hBOOL(hAPP(hAPP(c_member(U_8722),U_8720),U_8723)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8722),U_8723))
      | ~ class_Groups_Oordered__ab__group__add(U_8721) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

fof(f_2471_3,plain,
    ! [U_8726,U_8725,U_8724,U_8723,U_8722,U_8721] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),hAPP(U_8724,U_8726)),U_8725))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8722),U_8726),U_8723))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8722,U_8721),U_8724),U_8723) != U_8725
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),c_Groups_Ozero__class_Ozero(U_8721)),hAPP(U_8724,sK168(U_8726,U_8725,U_8724,U_8723,U_8722,U_8721))))
        & hBOOL(hAPP(hAPP(c_member(U_8722),sK168(U_8726,U_8725,U_8724,U_8723,U_8722,U_8721)),U_8723)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8722),U_8723))
      | ~ class_Groups_Oordered__ab__group__add(U_8721) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_8720,sK168(U_8726,U_8725,U_8724,U_8723,U_8722,U_8721))],[f_2471_2]) ).

cnf(f_2471_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8722),sK168(U_8726,U_8725,U_8724,U_8723,U_8722,U_8721)),U_8723))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),hAPP(U_8724,U_8726)),U_8725))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8722),U_8726),U_8723))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8722,U_8721),U_8724),U_8723) != U_8725
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8722),U_8723))
    | ~ class_Groups_Oordered__ab__group__add(U_8721) ),
    inference(clausify,[status(thm)],[f_2471_3]) ).

cnf(f_2471_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),c_Groups_Ozero__class_Ozero(U_8721)),hAPP(U_8724,sK168(U_8726,U_8725,U_8724,U_8723,U_8722,U_8721))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8721),hAPP(U_8724,U_8726)),U_8725))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8722),U_8726),U_8723))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8722,U_8721),U_8724),U_8723) != U_8725
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8722),U_8723))
    | ~ class_Groups_Oordered__ab__group__add(U_8721) ),
    inference(clausify,[status(thm)],[f_2471_3]) ).

fof(f_2472_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_2472_2,plain,
    ! [U_8732,U_8731,U_8730,U_8729,U_8728] :
      ( hAPP(U_8731,U_8732) = c_Groups_Ozero__class_Ozero(U_8728)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8729),U_8732),U_8730))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8729,U_8728),U_8731),U_8730) != c_Groups_Ozero__class_Ozero(U_8728)
      | ? [U_8727] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),c_Groups_Ozero__class_Ozero(U_8728)),hAPP(U_8731,U_8727)))
          & hBOOL(hAPP(hAPP(c_member(U_8729),U_8727),U_8730)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8729),U_8730))
      | ~ class_Groups_Oordered__ab__group__add(U_8728) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

fof(f_2472_3,plain,
    ! [U_8732,U_8731,U_8730,U_8729,U_8728] :
      ( hAPP(U_8731,U_8732) = c_Groups_Ozero__class_Ozero(U_8728)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8729),U_8732),U_8730))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8729,U_8728),U_8731),U_8730) != c_Groups_Ozero__class_Ozero(U_8728)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),c_Groups_Ozero__class_Ozero(U_8728)),hAPP(U_8731,sK169(U_8732,U_8731,U_8730,U_8729,U_8728))))
        & hBOOL(hAPP(hAPP(c_member(U_8729),sK169(U_8732,U_8731,U_8730,U_8729,U_8728)),U_8730)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8729),U_8730))
      | ~ class_Groups_Oordered__ab__group__add(U_8728) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_8727,sK169(U_8732,U_8731,U_8730,U_8729,U_8728))],[f_2472_2]) ).

cnf(f_2472_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8729),sK169(U_8732,U_8731,U_8730,U_8729,U_8728)),U_8730))
    | hAPP(U_8731,U_8732) = c_Groups_Ozero__class_Ozero(U_8728)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8729),U_8732),U_8730))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8729,U_8728),U_8731),U_8730) != c_Groups_Ozero__class_Ozero(U_8728)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8729),U_8730))
    | ~ class_Groups_Oordered__ab__group__add(U_8728) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

cnf(f_2472_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),c_Groups_Ozero__class_Ozero(U_8728)),hAPP(U_8731,sK169(U_8732,U_8731,U_8730,U_8729,U_8728))))
    | hAPP(U_8731,U_8732) = c_Groups_Ozero__class_Ozero(U_8728)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8729),U_8732),U_8730))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8729,U_8728),U_8731),U_8730) != c_Groups_Ozero__class_Ozero(U_8728)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8729),U_8730))
    | ~ class_Groups_Oordered__ab__group__add(U_8728) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

fof(f_2473_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_2473_2,plain,
    ! [U_8734,U_8733] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8733)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8734)) = 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_8734))),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_8733))),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_8733)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

cnf(f_2473_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8733)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8734)) = 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_8734))),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_8733))),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_8733)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2473_2]) ).

fof(f_2474_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_2474_2,plain,
    ! [U_8735] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8735) = c_Orderings_Oord__class_Omax(U_8735)
      | ~ class_Orderings_Olinorder(U_8735)
      | ~ class_Lattices_Osemilattice__sup(U_8735) ),
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

cnf(f_2474_3,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_8735) = c_Orderings_Oord__class_Omax(U_8735)
    | ~ class_Orderings_Olinorder(U_8735)
    | ~ class_Lattices_Osemilattice__sup(U_8735) ),
    inference(clausify,[status(thm)],[f_2474_2]) ).

fof(f_2475_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_2475_2,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2475_1]) ).

fof(f_2476_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_2476_2,plain,
    ! [U_8738,U_8737,U_8736] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8736),U_8737),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8736),U_8737),U_8738)))
      | ~ class_Orderings_Olinorder(U_8736) ),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

cnf(f_2476_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8736),U_8737),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8736),U_8737),U_8738)))
    | ~ class_Orderings_Olinorder(U_8736) ),
    inference(clausify,[status(thm)],[f_2476_2]) ).

fof(f_2477_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_2477_2,plain,
    ! [U_8741,U_8740,U_8739] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8740),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8739),U_8741),U_8740)))
      | ~ class_Orderings_Olinorder(U_8739) ),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

cnf(f_2477_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8740),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8739),U_8741),U_8740)))
    | ~ class_Orderings_Olinorder(U_8739) ),
    inference(clausify,[status(thm)],[f_2477_2]) ).

fof(f_2478_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_2478_2,plain,
    ! [U_8744,U_8743,U_8742] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),U_8743),U_8744))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744) != U_8744 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744) = U_8744
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),U_8743),U_8744)) ) )
      | ~ class_Orderings_Olinorder(U_8742) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

cnf(f_2478_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744) = U_8744
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),U_8743),U_8744))
    | ~ class_Orderings_Olinorder(U_8742) ),
    inference(clausify,[status(thm)],[f_2478_2]) ).

cnf(f_2478_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),U_8743),U_8744))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744) != U_8744
    | ~ class_Orderings_Olinorder(U_8742) ),
    inference(clausify,[status(thm)],[f_2478_2]) ).

fof(f_2479_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_2479_2,plain,
    ! [U_8748,U_8747,U_8746,U_8745] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8745),U_8746),U_8747)),U_8748))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8747),U_8748))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8746),U_8748)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8747),U_8748))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8746),U_8748)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8745),U_8746),U_8747)),U_8748)) ) )
      | ~ class_Orderings_Olinorder(U_8745) ),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

cnf(f_2479_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8746),U_8748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8745),U_8746),U_8747)),U_8748))
    | ~ class_Orderings_Olinorder(U_8745) ),
    inference(clausify,[status(thm)],[f_2479_2]) ).

cnf(f_2479_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8747),U_8748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8745),U_8746),U_8747)),U_8748))
    | ~ class_Orderings_Olinorder(U_8745) ),
    inference(clausify,[status(thm)],[f_2479_2]) ).

cnf(f_2479_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8745),U_8746),U_8747)),U_8748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8747),U_8748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),U_8746),U_8748))
    | ~ class_Orderings_Olinorder(U_8745) ),
    inference(clausify,[status(thm)],[f_2479_2]) ).

fof(f_2480_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_2480_2,plain,
    ! [U_8752,U_8751,U_8750,U_8749] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8749),U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8749),U_8751),U_8752)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8749),U_8750),U_8751))
      | ~ class_Orderings_Olinorder(U_8749) ),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

cnf(f_2480_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8749),U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8749),U_8751),U_8752)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8749),U_8750),U_8751))
    | ~ class_Orderings_Olinorder(U_8749) ),
    inference(clausify,[status(thm)],[f_2480_2]) ).

fof(f_2481_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_2481_2,plain,
    ! [U_8756,U_8755,U_8754,U_8753] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8753),U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8753),U_8756),U_8755)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8753),U_8754),U_8755))
      | ~ class_Orderings_Olinorder(U_8753) ),
    inference(variable_rename,[status(thm)],[f_2481_1]) ).

cnf(f_2481_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8753),U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8753),U_8756),U_8755)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8753),U_8754),U_8755))
    | ~ class_Orderings_Olinorder(U_8753) ),
    inference(clausify,[status(thm)],[f_2481_2]) ).

fof(f_2482_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_2482_2,plain,
    ! [U_8759,U_8758,U_8757] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8757),U_8758),U_8759) = U_8759
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8757),U_8758),U_8759))
      | ~ class_Orderings_Olinorder(U_8757) ),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

cnf(f_2482_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8757),U_8758),U_8759) = U_8759
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8757),U_8758),U_8759))
    | ~ class_Orderings_Olinorder(U_8757) ),
    inference(clausify,[status(thm)],[f_2482_2]) ).

fof(f_2483_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_2483_2,plain,
    ! [U_8762,U_8761,U_8760] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8760),U_8762),U_8761) = U_8762
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8760),U_8761),U_8762))
      | ~ class_Orderings_Olinorder(U_8760) ),
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

cnf(f_2483_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8760),U_8762),U_8761) = U_8762
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8760),U_8761),U_8762))
    | ~ class_Orderings_Olinorder(U_8760) ),
    inference(clausify,[status(thm)],[f_2483_2]) ).

fof(f_2484_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_2484_2,plain,
    ! [U_8766,U_8765,U_8764,U_8763] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8763),U_8764),U_8766)),U_8765))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),U_8766),U_8765))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),U_8764),U_8765))
      | ~ class_Orderings_Olinorder(U_8763) ),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

cnf(f_2484_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8763),U_8764),U_8766)),U_8765))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),U_8766),U_8765))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8763),U_8764),U_8765))
    | ~ class_Orderings_Olinorder(U_8763) ),
    inference(clausify,[status(thm)],[f_2484_2]) ).

fof(f_2485_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_2485_2,plain,
    ! [U_8770,U_8769,U_8768,U_8767] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8767),U_8768),U_8770)),U_8769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),U_8770),U_8769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),U_8768),U_8769))
      | ~ class_Orderings_Olinorder(U_8767) ),
    inference(variable_rename,[status(thm)],[f_2485_1]) ).

cnf(f_2485_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8767),U_8768),U_8770)),U_8769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),U_8770),U_8769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8767),U_8768),U_8769))
    | ~ class_Orderings_Olinorder(U_8767) ),
    inference(clausify,[status(thm)],[f_2485_2]) ).

fof(f_2486_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_2486_2,plain,
    ! [U_8775,U_8774,U_8773,U_8772,U_8771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8771),U_8772),U_8774)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8771),U_8773),U_8775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),U_8774),U_8775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),U_8772),U_8773))
      | ~ class_Orderings_Olinorder(U_8771) ),
    inference(variable_rename,[status(thm)],[f_2486_1]) ).

cnf(f_2486_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8771),U_8772),U_8774)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8771),U_8773),U_8775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),U_8774),U_8775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8771),U_8772),U_8773))
    | ~ class_Orderings_Olinorder(U_8771) ),
    inference(clausify,[status(thm)],[f_2486_2]) ).

fof(f_2487_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_2487_2,plain,
    ! [U_8779,U_8778,U_8777,U_8776] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),U_8778),U_8779))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),U_8777),U_8779)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8776),U_8777),U_8778)),U_8779))
      | ~ class_Orderings_Olinorder(U_8776) ),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

cnf(f_2487_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),U_8777),U_8779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8776),U_8777),U_8778)),U_8779))
    | ~ class_Orderings_Olinorder(U_8776) ),
    inference(clausify,[status(thm)],[f_2487_2]) ).

cnf(f_2487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),U_8778),U_8779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8776),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8776),U_8777),U_8778)),U_8779))
    | ~ class_Orderings_Olinorder(U_8776) ),
    inference(clausify,[status(thm)],[f_2487_2]) ).

fof(f_2488_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_2488_2,plain,
    ! [U_8783,U_8782,U_8781,U_8780] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8780),U_8782),U_8783)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8783))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8782)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8783))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8782))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8780),U_8782),U_8783))) ) )
      | ~ class_Orderings_Olinorder(U_8780) ),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

cnf(f_2488_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8783))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8782))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8780),U_8782),U_8783)))
    | ~ class_Orderings_Olinorder(U_8780) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

cnf(f_2488_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8782))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8780),U_8782),U_8783)))
    | ~ class_Orderings_Olinorder(U_8780) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

cnf(f_2488_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),U_8783))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8780),U_8781),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8780),U_8782),U_8783)))
    | ~ class_Orderings_Olinorder(U_8780) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

fof(f_2489_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_2489_2,plain,
    ! [U_8787,U_8786,U_8785,U_8784] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8784),U_8785),U_8786)),U_8787) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8784),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),U_8785),U_8787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),U_8786),U_8787))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8784) ),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

cnf(f_2489_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8784),U_8785),U_8786)),U_8787) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8784),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),U_8785),U_8787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8784),U_8786),U_8787))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8784) ),
    inference(clausify,[status(thm)],[f_2489_2]) ).

fof(f_2490_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_2490_2,plain,
    ! [U_8791,U_8790,U_8789,U_8788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8788),U_8789),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8788),U_8790),U_8791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8788),U_8789),U_8790))
      | ~ class_Orderings_Olinorder(U_8788) ),
    inference(variable_rename,[status(thm)],[f_2490_1]) ).

cnf(f_2490_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8788),U_8789),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8788),U_8790),U_8791)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8788),U_8789),U_8790))
    | ~ class_Orderings_Olinorder(U_8788) ),
    inference(clausify,[status(thm)],[f_2490_2]) ).

fof(f_2491_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_2491_2,plain,
    ! [U_8795,U_8794,U_8793,U_8792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8792),U_8793),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8792),U_8795),U_8794)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8792),U_8793),U_8794))
      | ~ class_Orderings_Olinorder(U_8792) ),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

cnf(f_2491_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8792),U_8793),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8792),U_8795),U_8794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8792),U_8793),U_8794))
    | ~ class_Orderings_Olinorder(U_8792) ),
    inference(clausify,[status(thm)],[f_2491_2]) ).

fof(f_2492_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_2492_2,plain,
    ! [U_8799,U_8798,U_8797,U_8796] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8796),U_8798),U_8799)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8799))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8798)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8799))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8798))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8796),U_8798),U_8799))) ) )
      | ~ class_Orderings_Olinorder(U_8796) ),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

cnf(f_2492_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8799))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8796),U_8798),U_8799)))
    | ~ class_Orderings_Olinorder(U_8796) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

cnf(f_2492_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8798))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8796),U_8798),U_8799)))
    | ~ class_Orderings_Olinorder(U_8796) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

cnf(f_2492_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),U_8799))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8796),U_8797),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8796),U_8798),U_8799)))
    | ~ class_Orderings_Olinorder(U_8796) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

fof(f_2493_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_2493_2,plain,
    ! [U_8803,U_8802,U_8801,U_8800] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8800),U_8801),U_8802)),U_8803))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8802),U_8803))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8801),U_8803)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8802),U_8803))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8801),U_8803)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8800),U_8801),U_8802)),U_8803)) ) )
      | ~ class_Orderings_Olinorder(U_8800) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

cnf(f_2493_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8801),U_8803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8800),U_8801),U_8802)),U_8803))
    | ~ class_Orderings_Olinorder(U_8800) ),
    inference(clausify,[status(thm)],[f_2493_2]) ).

cnf(f_2493_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8802),U_8803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8800),U_8801),U_8802)),U_8803))
    | ~ class_Orderings_Olinorder(U_8800) ),
    inference(clausify,[status(thm)],[f_2493_2]) ).

cnf(f_2493_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8800),U_8801),U_8802)),U_8803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8802),U_8803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8800),U_8801),U_8803))
    | ~ class_Orderings_Olinorder(U_8800) ),
    inference(clausify,[status(thm)],[f_2493_2]) ).

fof(f_2494_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_2494_2,plain,
    ! [U_8807,U_8806,U_8805,U_8804] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),U_8805),U_8806)),U_8807) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),U_8805),U_8807)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),U_8806),U_8807))
      | ~ class_Groups_Oordered__ab__group__add(U_8804) ),
    inference(variable_rename,[status(thm)],[f_2494_1]) ).

cnf(f_2494_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),U_8805),U_8806)),U_8807) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),U_8805),U_8807)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8804),U_8806),U_8807))
    | ~ class_Groups_Oordered__ab__group__add(U_8804) ),
    inference(clausify,[status(thm)],[f_2494_2]) ).

fof(f_2495_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_2495_2,plain,
    ! [U_8809,U_8808] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8808),U_8809),U_8809) = U_8809
      | ~ class_Orderings_Olinorder(U_8808) ),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

cnf(f_2495_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8808),U_8809),U_8809) = U_8809
    | ~ class_Orderings_Olinorder(U_8808) ),
    inference(clausify,[status(thm)],[f_2495_2]) ).

fof(f_2496_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_2496_2,plain,
    ! [U_8812,U_8811,U_8810] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8810),U_8811),U_8812) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8810),U_8812),U_8811)
      | ~ class_Orderings_Olinorder(U_8810) ),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

cnf(f_2496_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8810),U_8811),U_8812) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8810),U_8812),U_8811)
    | ~ class_Orderings_Olinorder(U_8810) ),
    inference(clausify,[status(thm)],[f_2496_2]) ).

fof(f_2497_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_2497_2,plain,
    ! [U_8815,U_8814,U_8813] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8813),U_8814),U_8815) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8813),U_8815),U_8814)
      | ~ class_Orderings_Olinorder(U_8813) ),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

cnf(f_2497_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8813),U_8814),U_8815) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8813),U_8815),U_8814)
    | ~ class_Orderings_Olinorder(U_8813) ),
    inference(clausify,[status(thm)],[f_2497_2]) ).

fof(f_2498_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_2498_2,plain,
    ! [U_8818,U_8817,U_8816] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),U_8818)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),U_8818)
      | ~ class_Orderings_Olinorder(U_8816) ),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

cnf(f_2498_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),U_8818)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8816),U_8817),U_8818)
    | ~ class_Orderings_Olinorder(U_8816) ),
    inference(clausify,[status(thm)],[f_2498_2]) ).

fof(f_2499_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_2499_2,plain,
    ! [U_8821,U_8820,U_8819] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),U_8821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),U_8821)
      | ~ class_Orderings_Olinorder(U_8819) ),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

cnf(f_2499_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),U_8821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8819),U_8820),U_8821)
    | ~ class_Orderings_Olinorder(U_8819) ),
    inference(clausify,[status(thm)],[f_2499_2]) ).

fof(f_2500_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_2500_2,plain,
    ! [U_8825,U_8824,U_8823,U_8822] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8823),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),U_8825)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8823),U_8825))
      | ~ class_Orderings_Olinorder(U_8822) ),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

cnf(f_2500_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8823),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),U_8825)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8823),U_8825))
    | ~ class_Orderings_Olinorder(U_8822) ),
    inference(clausify,[status(thm)],[f_2500_2]) ).

fof(f_2501_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_2501_2,plain,
    ! [U_8829,U_8828,U_8827,U_8826] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8827),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8828),U_8829)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8828),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8827),U_8829))
      | ~ class_Orderings_Olinorder(U_8826) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

cnf(f_2501_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8827),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8828),U_8829)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8828),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8827),U_8829))
    | ~ class_Orderings_Olinorder(U_8826) ),
    inference(clausify,[status(thm)],[f_2501_2]) ).

fof(f_2502_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_2502_2,plain,
    ! [U_8833,U_8832,U_8831,U_8830] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),U_8832)),U_8833) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8832),U_8833))
      | ~ class_Orderings_Olinorder(U_8830) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

cnf(f_2502_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),U_8832)),U_8833) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8832),U_8833))
    | ~ class_Orderings_Olinorder(U_8830) ),
    inference(clausify,[status(thm)],[f_2502_2]) ).

fof(f_2503_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_2503_2,plain,
    ! [U_8837,U_8836,U_8835,U_8834] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8835),U_8836)),U_8837) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8835),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8836),U_8837))
      | ~ class_Orderings_Olinorder(U_8834) ),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

cnf(f_2503_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8835),U_8836)),U_8837) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8835),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8834),U_8836),U_8837))
    | ~ class_Orderings_Olinorder(U_8834) ),
    inference(clausify,[status(thm)],[f_2503_2]) ).

fof(f_2504_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_2504_2,plain,
    ! [U_8839,U_8838] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8838),U_8839),U_8839) = U_8839
      | ~ class_Orderings_Olinorder(U_8838) ),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

cnf(f_2504_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8838),U_8839),U_8839) = U_8839
    | ~ class_Orderings_Olinorder(U_8838) ),
    inference(clausify,[status(thm)],[f_2504_2]) ).

fof(f_2505_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_2505_2,plain,
    ! [U_8843,U_8842,U_8841,U_8840] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),U_8841),U_8842)),U_8843) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),U_8841),U_8843)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),U_8842),U_8843))
      | ~ class_Orderings_Olinorder(U_8840) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

cnf(f_2505_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),U_8841),U_8842)),U_8843) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),U_8841),U_8843)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8840),U_8842),U_8843))
    | ~ class_Orderings_Olinorder(U_8840) ),
    inference(clausify,[status(thm)],[f_2505_2]) ).

fof(f_2506_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_2506_2,plain,
    ! [U_8847,U_8846,U_8845,U_8844] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8844),U_8845),U_8846)),U_8847) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8844),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),U_8845),U_8847)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),U_8846),U_8847))
      | ~ class_Orderings_Olinorder(U_8844) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

cnf(f_2506_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8844),U_8845),U_8846)),U_8847) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8844),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),U_8845),U_8847)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8844),U_8846),U_8847))
    | ~ class_Orderings_Olinorder(U_8844) ),
    inference(clausify,[status(thm)],[f_2506_2]) ).

fof(f_2507_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_2507_2,plain,
    ! [U_8851,U_8850,U_8849,U_8848] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8848),U_8850),U_8851)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8848),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),U_8850)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),U_8851))
      | ~ class_Orderings_Olinorder(U_8848) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

cnf(f_2507_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8848),U_8850),U_8851)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8848),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),U_8850)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8848),U_8849),U_8851))
    | ~ class_Orderings_Olinorder(U_8848) ),
    inference(clausify,[status(thm)],[f_2507_2]) ).

fof(f_2508_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_2508_2,plain,
    ! [U_8855,U_8854,U_8853,U_8852] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8852),U_8854),U_8855)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8852),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),U_8854)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),U_8855))
      | ~ class_Orderings_Olinorder(U_8852) ),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

cnf(f_2508_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8852),U_8854),U_8855)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8852),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),U_8854)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8852),U_8853),U_8855))
    | ~ class_Orderings_Olinorder(U_8852) ),
    inference(clausify,[status(thm)],[f_2508_2]) ).

fof(f_2509_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_2509_2,plain,
    ! [U_8858,U_8857,U_8856] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8856),U_8857),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8856),U_8857),U_8858)) = U_8857
      | ~ class_Orderings_Olinorder(U_8856) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

cnf(f_2509_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8856),U_8857),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8856),U_8857),U_8858)) = U_8857
    | ~ class_Orderings_Olinorder(U_8856) ),
    inference(clausify,[status(thm)],[f_2509_2]) ).

fof(f_2510_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_2510_2,plain,
    ! [U_8861,U_8860,U_8859] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8859),U_8860),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8859),U_8860),U_8861)) = U_8860
      | ~ class_Orderings_Olinorder(U_8859) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

cnf(f_2510_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8859),U_8860),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8859),U_8860),U_8861)) = U_8860
    | ~ class_Orderings_Olinorder(U_8859) ),
    inference(clausify,[status(thm)],[f_2510_2]) ).

fof(f_2511_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_2511_2,plain,
    ! [U_8863,U_8862] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8862)),hAPP(c_Nat_OSuc,U_8863)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8862),U_8863)),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

cnf(f_2511_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8862)),hAPP(c_Nat_OSuc,U_8863)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8862),U_8863)),
    inference(clausify,[status(thm)],[f_2511_2]) ).

fof(f_2512_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_2512_2,plain,
    ! [U_8864] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8864) = U_8864,
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

cnf(f_2512_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8864) = U_8864,
    inference(clausify,[status(thm)],[f_2512_2]) ).

fof(f_2513_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_2513_2,plain,
    ! [U_8865] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8865),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8865,
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

cnf(f_2513_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8865),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8865,
    inference(clausify,[status(thm)],[f_2513_2]) ).

fof(f_2514_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_2514_2,plain,
    ! [U_8866] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_8866,U_8866,c_Orderings_Oord__class_Omax(U_8866))
      | ~ class_Orderings_Olinorder(U_8866) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

cnf(f_2514_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_8866,U_8866,c_Orderings_Oord__class_Omax(U_8866))
    | ~ class_Orderings_Olinorder(U_8866) ),
    inference(clausify,[status(thm)],[f_2514_2]) ).

fof(f_2515_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_2515_2,plain,
    ! [U_8869,U_8868,U_8867] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869))) ) )
      | ~ class_Orderings_Oord(U_8867)
      | ~ class_Int_Onumber(U_8867) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

cnf(f_2515_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)))
    | ~ class_Orderings_Oord(U_8867)
    | ~ class_Int_Onumber(U_8867) ),
    inference(clausify,[status(thm)],[f_2515_2]) ).

cnf(f_2515_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8867),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8868)),hAPP(c_Int_Onumber__class_Onumber__of(U_8867),U_8869)))
    | ~ class_Orderings_Oord(U_8867)
    | ~ class_Int_Onumber(U_8867) ),
    inference(clausify,[status(thm)],[f_2515_2]) ).

fof(f_2516_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_2516_2,plain,
    ! [U_8873,U_8872,U_8871,U_8870] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8870),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8870),U_8872),U_8873))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8870),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),U_8872)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),U_8873))))
      | ~ class_Orderings_Olinorder(U_8870) ),
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

cnf(f_2516_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8870),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8870),U_8872),U_8873))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8870),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),U_8872)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8870),U_8871),U_8873))))
    | ~ class_Orderings_Olinorder(U_8870) ),
    inference(clausify,[status(thm)],[f_2516_2]) ).

fof(f_2517_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_2517_2,plain,
    ! [U_8877,U_8876,U_8875,U_8874] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8874),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8874),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),U_8876)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),U_8877))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8874),U_8876),U_8877))))
      | ~ class_Orderings_Olinorder(U_8874) ),
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

cnf(f_2517_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8874),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8874),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),U_8876)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),U_8877))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8874),U_8875),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8874),U_8876),U_8877))))
    | ~ class_Orderings_Olinorder(U_8874) ),
    inference(clausify,[status(thm)],[f_2517_2]) ).

fof(f_2518_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_2518_2,plain,
    ! [U_8880,U_8879,U_8878] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8878),U_8879),U_8880)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8878),hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),U_8879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),U_8880))
      | ~ class_Groups_Olinordered__ab__group__add(U_8878) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

cnf(f_2518_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8878),U_8879),U_8880)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8878),hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),U_8879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8878),U_8880))
    | ~ class_Groups_Olinordered__ab__group__add(U_8878) ),
    inference(clausify,[status(thm)],[f_2518_2]) ).

fof(f_2519_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_2519_2,plain,
    ! [U_8883,U_8882,U_8881] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8881),U_8882),U_8883)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8883))
      | ~ class_Groups_Olinordered__ab__group__add(U_8881) ),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

cnf(f_2519_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8881),U_8882),U_8883)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8881),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8882)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8881),U_8883))
    | ~ class_Groups_Olinordered__ab__group__add(U_8881) ),
    inference(clausify,[status(thm)],[f_2519_2]) ).

fof(f_2520_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_2520_2,plain,
    ! [U_8885,U_8884] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8884),U_8885)),U_8885) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8884),U_8885),
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

cnf(f_2520_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8884),U_8885)),U_8885) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8884),U_8885),
    inference(clausify,[status(thm)],[f_2520_2]) ).

fof(f_2521_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_2521_2,plain,
    ! [U_8887,U_8886] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8886),hAPP(c_Nat_OSuc,U_8887)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8887),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_8887)),U_8886),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

cnf(f_2521_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8886),hAPP(c_Nat_OSuc,U_8887)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8887),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_8887)),U_8886),
    inference(clausify,[status(thm)],[f_2521_2]) ).

fof(f_2522_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_2522_2,plain,
    ! [U_8889,U_8888] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8888)),U_8889) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8888),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_8888)),U_8889),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

cnf(f_2522_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8888)),U_8889) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8888),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_8888)),U_8889),
    inference(clausify,[status(thm)],[f_2522_2]) ).

fof(f_2523_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_2523_2,plain,
    ! [U_8890] :
      ( c_Orderings_Oord__class_Omax(U_8890) = c_Orderings_Oord_Omax(U_8890,c_Orderings_Oord__class_Oless__eq(U_8890))
      | ~ class_Orderings_Oord(U_8890) ),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

cnf(f_2523_3,plain,
    ( c_Orderings_Oord__class_Omax(U_8890) = c_Orderings_Oord_Omax(U_8890,c_Orderings_Oord__class_Oless__eq(U_8890))
    | ~ class_Orderings_Oord(U_8890) ),
    inference(clausify,[status(thm)],[f_2523_2]) ).

fof(f_2524_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_2524_2,plain,
    ! [U_8894,U_8893,U_8892,U_8891] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_8891,U_8891,c_Orderings_Oord__class_Omax(U_8891)),U_8893),hAPP(hAPP(c_Set_Oinsert(U_8891),U_8894),U_8892)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8891),U_8894),hAPP(hAPP(c_Finite__Set_Ofold(U_8891,U_8891,c_Orderings_Oord__class_Omax(U_8891)),U_8893),U_8892))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8891),U_8892))
      | ~ class_Orderings_Olinorder(U_8891) ),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

cnf(f_2524_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_8891,U_8891,c_Orderings_Oord__class_Omax(U_8891)),U_8893),hAPP(hAPP(c_Set_Oinsert(U_8891),U_8894),U_8892)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8891),U_8894),hAPP(hAPP(c_Finite__Set_Ofold(U_8891,U_8891,c_Orderings_Oord__class_Omax(U_8891)),U_8893),U_8892))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8891),U_8892))
    | ~ class_Orderings_Olinorder(U_8891) ),
    inference(clausify,[status(thm)],[f_2524_2]) ).

fof(f_2525_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_2525_2,plain,
    ! [U_8895] :
      ( c_Orderings_Oord_Omin(U_8895,hAPP(c_COMBC(U_8895,U_8895,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_8895))) = c_Orderings_Oord__class_Omax(U_8895)
      | ~ class_Orderings_Olinorder(U_8895) ),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

cnf(f_2525_3,plain,
    ( c_Orderings_Oord_Omin(U_8895,hAPP(c_COMBC(U_8895,U_8895,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_8895))) = c_Orderings_Oord__class_Omax(U_8895)
    | ~ class_Orderings_Olinorder(U_8895) ),
    inference(clausify,[status(thm)],[f_2525_2]) ).

fof(f_2526_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_2526_2,plain,
    ! [U_8899,U_8898,U_8897,U_8896] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8896),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8896),U_8898),U_8899)),hAPP(hAPP(c_Finite__Set_Ofold(U_8896,U_8896,c_Orderings_Oord__class_Omax(U_8896)),U_8899),U_8897)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8896),U_8898),U_8897))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8896),U_8897))
      | ~ class_Orderings_Olinorder(U_8896) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

cnf(f_2526_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8896),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8896),U_8898),U_8899)),hAPP(hAPP(c_Finite__Set_Ofold(U_8896,U_8896,c_Orderings_Oord__class_Omax(U_8896)),U_8899),U_8897)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8896),U_8898),U_8897))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8896),U_8897))
    | ~ class_Orderings_Olinorder(U_8896) ),
    inference(clausify,[status(thm)],[f_2526_2]) ).

fof(f_2527_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_2527_2,plain,
    ! [U_8902,U_8901,U_8900] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8900),U_8902),c_Big__Operators_Olattice_OInf__fin(U_8900,c_Orderings_Oord__class_Omin(U_8900),U_8901)) = U_8902
      | ~ hBOOL(hAPP(hAPP(c_member(U_8900),U_8902),U_8901))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8900),U_8901))
      | ~ class_Orderings_Olinorder(U_8900) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

cnf(f_2527_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8900),U_8902),c_Big__Operators_Olattice_OInf__fin(U_8900,c_Orderings_Oord__class_Omin(U_8900),U_8901)) = U_8902
    | ~ hBOOL(hAPP(hAPP(c_member(U_8900),U_8902),U_8901))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8900),U_8901))
    | ~ class_Orderings_Olinorder(U_8900) ),
    inference(clausify,[status(thm)],[f_2527_2]) ).

fof(f_2528_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_2528_2,plain,
    ! [U_8904,U_8903] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8903)),hAPP(c_Nat_OSuc,U_8904)) = 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_8903))),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_8904))),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_8904)))),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

cnf(f_2528_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8903)),hAPP(c_Nat_OSuc,U_8904)) = 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_8903))),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_8904))),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_8904)))),
    inference(clausify,[status(thm)],[f_2528_2]) ).

fof(f_2529_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_2529_2,plain,
    ! [U_8907,U_8906,U_8905] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_8905,U_8906) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8905),U_8907),c_Big__Operators_Olinorder__class_OMax(U_8905,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_8905,U_8906) = U_8907
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8907),U_8906))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8905),U_8906))
      | ~ class_Orderings_Olinorder(U_8905) ),
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

cnf(f_2529_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8905,U_8906) = U_8907
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8907),U_8906))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8905),U_8906))
    | ~ class_Orderings_Olinorder(U_8905) ),
    inference(clausify,[status(thm)],[f_2529_2]) ).

cnf(f_2529_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8905,U_8906) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8905),U_8907),c_Big__Operators_Olinorder__class_OMax(U_8905,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8905,tc_HOL_Obool)),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8905,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8907),U_8906))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8905),U_8906))
    | ~ class_Orderings_Olinorder(U_8905) ),
    inference(clausify,[status(thm)],[f_2529_2]) ).

fof(f_2530_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_2530_2,plain,
    ! [U_8909,U_8908] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8908),c_Big__Operators_Olattice_OInf__fin(U_8908,c_Orderings_Oord__class_Omin(U_8908),U_8909)),c_Big__Operators_Olattice_OSup__fin(U_8908,c_Orderings_Oord__class_Omax(U_8908),U_8909)))
      | U_8909 = c_Orderings_Obot__class_Obot(tc_fun(U_8908,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8908),U_8909))
      | ~ class_Orderings_Olinorder(U_8908) ),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

cnf(f_2530_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8908),c_Big__Operators_Olattice_OInf__fin(U_8908,c_Orderings_Oord__class_Omin(U_8908),U_8909)),c_Big__Operators_Olattice_OSup__fin(U_8908,c_Orderings_Oord__class_Omax(U_8908),U_8909)))
    | U_8909 = c_Orderings_Obot__class_Obot(tc_fun(U_8908,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8908),U_8909))
    | ~ class_Orderings_Olinorder(U_8908) ),
    inference(clausify,[status(thm)],[f_2530_2]) ).

fof(f_2531_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_2531_2,plain,
    ! [U_8912,U_8911,U_8910] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),U_8911) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8910),U_8912),c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),U_8911) = U_8912
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8910),U_8912),U_8911))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8911))
      | ~ class_Orderings_Olinorder(U_8910) ),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

cnf(f_2531_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),U_8911) = U_8912
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8910),U_8912),U_8911))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8911))
    | ~ class_Orderings_Olinorder(U_8910) ),
    inference(clausify,[status(thm)],[f_2531_2]) ).

cnf(f_2531_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),U_8911) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8910),U_8912),c_Big__Operators_Olattice_OSup__fin(U_8910,c_Orderings_Oord__class_Omax(U_8910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8910,tc_HOL_Obool)),U_8911),hAPP(hAPP(c_Set_Oinsert(U_8910),U_8912),c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8910,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8910),U_8912),U_8911))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8910),U_8911))
    | ~ class_Orderings_Olinorder(U_8910) ),
    inference(clausify,[status(thm)],[f_2531_2]) ).

fof(f_2532_1,plain,
    ! [V_n_2,V_Pa_2,V_Qa_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_Pa_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_Qa_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_Pa_2)),V_Qa_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_Qa_2,B_x)),hAPP(V_Pa_2,B_x))) ),
    inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).

fof(f_2532_2,plain,
    ! [U_8916,U_8915,U_8914] :
      ( 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_8915),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8914),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))) = 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_8915)),U_8914)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))
      | ? [U_8913] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8914,U_8913)),hAPP(U_8915,U_8913))) ),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

fof(f_2532_3,plain,
    ! [U_8916,U_8915,U_8914] :
      ( 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_8915),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8914),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))) = 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_8915)),U_8914)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8914,sK170(U_8916,U_8915,U_8914))),hAPP(U_8915,sK170(U_8916,U_8915,U_8914)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_8913,sK170(U_8916,U_8915,U_8914))],[f_2532_2]) ).

cnf(f_2532_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_8915),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8914),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))) = 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_8915)),U_8914)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8914,sK170(U_8916,U_8915,U_8914))),hAPP(U_8915,sK170(U_8916,U_8915,U_8914)))) ),
    inference(clausify,[status(thm)],[f_2532_3]) ).

fof(f_2533_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_2533_2,plain,
    ! [U_8918,U_8917] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8917,hAPP(hAPP(c_Set_Oinsert(U_8917),U_8918),c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool)))) = U_8918
      | ~ class_Orderings_Olinorder(U_8917) ),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

cnf(f_2533_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8917,hAPP(hAPP(c_Set_Oinsert(U_8917),U_8918),c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool)))) = U_8918
    | ~ class_Orderings_Olinorder(U_8917) ),
    inference(clausify,[status(thm)],[f_2533_2]) ).

fof(f_2534_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_2534_2,plain,
    ! [U_8921,U_8920,U_8919] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8919),U_8921),c_Big__Operators_Olattice_OSup__fin(U_8919,c_Orderings_Oord__class_Omax(U_8919),U_8920)) = c_Big__Operators_Olattice_OSup__fin(U_8919,c_Orderings_Oord__class_Omax(U_8919),U_8920)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8921),U_8920))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8919),U_8920))
      | ~ class_Orderings_Olinorder(U_8919) ),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

cnf(f_2534_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8919),U_8921),c_Big__Operators_Olattice_OSup__fin(U_8919,c_Orderings_Oord__class_Omax(U_8919),U_8920)) = c_Big__Operators_Olattice_OSup__fin(U_8919,c_Orderings_Oord__class_Omax(U_8919),U_8920)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8921),U_8920))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8919),U_8920))
    | ~ class_Orderings_Olinorder(U_8919) ),
    inference(clausify,[status(thm)],[f_2534_2]) ).

fof(f_2535_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_2535_2,plain,
    ! [U_8924,U_8923,U_8922] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8922),U_8924),c_Big__Operators_Olinorder__class_OMax(U_8922,U_8923)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8922),U_8924),U_8923))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8922),U_8923))
      | ~ class_Orderings_Olinorder(U_8922) ),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

cnf(f_2535_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8922),U_8924),c_Big__Operators_Olinorder__class_OMax(U_8922,U_8923)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8922),U_8924),U_8923))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8922),U_8923))
    | ~ class_Orderings_Olinorder(U_8922) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

fof(f_2536_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_2536_2,plain,
    ! [U_8926,U_8925] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8925,c_Orderings_Oord__class_Omax(U_8925),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8926),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) = U_8926
      | ~ class_Orderings_Olinorder(U_8925) ),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

cnf(f_2536_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8925,c_Orderings_Oord__class_Omax(U_8925),hAPP(hAPP(c_Set_Oinsert(U_8925),U_8926),c_Orderings_Obot__class_Obot(tc_fun(U_8925,tc_HOL_Obool)))) = U_8926
    | ~ class_Orderings_Olinorder(U_8925) ),
    inference(clausify,[status(thm)],[f_2536_2]) ).

fof(f_2537_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_2537_2,plain,
    ! [U_8928,U_8927] :
      ( hBOOL(hAPP(hAPP(c_member(U_8927),c_Big__Operators_Olinorder__class_OMax(U_8927,U_8928)),U_8928))
      | U_8928 = c_Orderings_Obot__class_Obot(tc_fun(U_8927,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8927),U_8928))
      | ~ class_Orderings_Olinorder(U_8927) ),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

cnf(f_2537_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8927),c_Big__Operators_Olinorder__class_OMax(U_8927,U_8928)),U_8928))
    | U_8928 = c_Orderings_Obot__class_Obot(tc_fun(U_8927,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8927),U_8928))
    | ~ class_Orderings_Olinorder(U_8927) ),
    inference(clausify,[status(thm)],[f_2537_2]) ).

fof(f_2538_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_2538_2,plain,
    ! [U_8931,U_8930,U_8929] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8929),U_8931),c_Big__Operators_Olinorder__class_OMax(U_8929,U_8930)) = c_Big__Operators_Olinorder__class_OMax(U_8929,U_8930)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8929),U_8931),U_8930))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8929),U_8930))
      | ~ class_Orderings_Olinorder(U_8929) ),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

cnf(f_2538_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8929),U_8931),c_Big__Operators_Olinorder__class_OMax(U_8929,U_8930)) = c_Big__Operators_Olinorder__class_OMax(U_8929,U_8930)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8929),U_8931),U_8930))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8929),U_8930))
    | ~ class_Orderings_Olinorder(U_8929) ),
    inference(clausify,[status(thm)],[f_2538_2]) ).

fof(f_2539_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_2539_2,plain,
    ! [U_8933,U_8932] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8932,c_Orderings_Oord__class_Omax(U_8932),U_8933) = hAPP(c_Finite__Set_Ofold1(U_8932,c_Orderings_Oord__class_Omax(U_8932)),U_8933)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8932),U_8933))
      | ~ class_Orderings_Olinorder(U_8932) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

cnf(f_2539_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8932,c_Orderings_Oord__class_Omax(U_8932),U_8933) = hAPP(c_Finite__Set_Ofold1(U_8932,c_Orderings_Oord__class_Omax(U_8932)),U_8933)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8932),U_8933))
    | ~ class_Orderings_Olinorder(U_8932) ),
    inference(clausify,[status(thm)],[f_2539_2]) ).

fof(f_2540_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_2540_2,plain,
    ! [U_8935,U_8934] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8934,U_8935) = hAPP(c_Finite__Set_Ofold1(U_8934,c_Orderings_Oord__class_Omax(U_8934)),U_8935)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8934),U_8935))
      | ~ class_Orderings_Olinorder(U_8934) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

cnf(f_2540_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8934,U_8935) = hAPP(c_Finite__Set_Ofold1(U_8934,c_Orderings_Oord__class_Omax(U_8934)),U_8935)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8934),U_8935))
    | ~ class_Orderings_Olinorder(U_8934) ),
    inference(clausify,[status(thm)],[f_2540_2]) ).

fof(f_2541_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_2541_2,plain,
    ! [U_8938,U_8937,U_8936] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8936,c_Orderings_Oord__class_Omax(U_8936),hAPP(hAPP(c_Set_Oinsert(U_8936),U_8938),U_8937)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8936),U_8938),c_Big__Operators_Olattice_OSup__fin(U_8936,c_Orderings_Oord__class_Omax(U_8936),U_8937))
      | U_8937 = c_Orderings_Obot__class_Obot(tc_fun(U_8936,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8936),U_8937))
      | ~ class_Orderings_Olinorder(U_8936) ),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

cnf(f_2541_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8936,c_Orderings_Oord__class_Omax(U_8936),hAPP(hAPP(c_Set_Oinsert(U_8936),U_8938),U_8937)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8936),U_8938),c_Big__Operators_Olattice_OSup__fin(U_8936,c_Orderings_Oord__class_Omax(U_8936),U_8937))
    | U_8937 = c_Orderings_Obot__class_Obot(tc_fun(U_8936,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8936),U_8937))
    | ~ class_Orderings_Olinorder(U_8936) ),
    inference(clausify,[status(thm)],[f_2541_2]) ).

fof(f_2542_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_2542_2,plain,
    ! [U_8941,U_8940,U_8939] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8939),c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8941)),c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8940)) = c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8940)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8939,tc_HOL_Obool)),U_8941),U_8940))
      | U_8941 = c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8939),U_8940))
      | ~ class_Orderings_Olinorder(U_8939) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

cnf(f_2542_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8939),c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8941)),c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8940)) = c_Big__Operators_Olattice_OSup__fin(U_8939,c_Orderings_Oord__class_Omax(U_8939),U_8940)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8939,tc_HOL_Obool)),U_8941),U_8940))
    | U_8941 = c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8939),U_8940))
    | ~ class_Orderings_Olinorder(U_8939) ),
    inference(clausify,[status(thm)],[f_2542_2]) ).

fof(f_2543_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_2543_2,plain,
    ! [U_8944,U_8943,U_8942] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8942),U_8944),c_Big__Operators_Olattice_OSup__fin(U_8942,c_Orderings_Oord__class_Omax(U_8942),U_8943)) = U_8944
      | ~ hBOOL(hAPP(hAPP(c_member(U_8942),U_8944),U_8943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8942),U_8943))
      | ~ class_Orderings_Olinorder(U_8942) ),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

cnf(f_2543_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8942),U_8944),c_Big__Operators_Olattice_OSup__fin(U_8942,c_Orderings_Oord__class_Omax(U_8942),U_8943)) = U_8944
    | ~ hBOOL(hAPP(hAPP(c_member(U_8942),U_8944),U_8943))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8942),U_8943))
    | ~ class_Orderings_Olinorder(U_8942) ),
    inference(clausify,[status(thm)],[f_2543_2]) ).

fof(f_2544_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_2544_2,plain,
    ! [U_8947,U_8946,U_8945] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8945,tc_HOL_Obool)),U_8946),U_8947)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8945),c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),U_8946)),c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),U_8947))
      | U_8947 = c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8947))
      | U_8946 = c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8946))
      | ~ class_Orderings_Olinorder(U_8945) ),
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

cnf(f_2544_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8945,tc_HOL_Obool)),U_8946),U_8947)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8945),c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),U_8946)),c_Big__Operators_Olattice_OSup__fin(U_8945,c_Orderings_Oord__class_Omax(U_8945),U_8947))
    | U_8947 = c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8947))
    | U_8946 = c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8946))
    | ~ class_Orderings_Olinorder(U_8945) ),
    inference(clausify,[status(thm)],[f_2544_2]) ).

fof(f_2545_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_2545_2,plain,
    ! [U_8950,U_8949,U_8948] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8948),c_Big__Operators_Olinorder__class_OMax(U_8948,U_8949)),c_Big__Operators_Olinorder__class_OMax(U_8948,U_8950)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8948),U_8950))
      | U_8949 = c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8948,tc_HOL_Obool)),U_8949),U_8950))
      | ~ class_Orderings_Olinorder(U_8948) ),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

cnf(f_2545_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8948),c_Big__Operators_Olinorder__class_OMax(U_8948,U_8949)),c_Big__Operators_Olinorder__class_OMax(U_8948,U_8950)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8948),U_8950))
    | U_8949 = c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8948,tc_HOL_Obool)),U_8949),U_8950))
    | ~ class_Orderings_Olinorder(U_8948) ),
    inference(clausify,[status(thm)],[f_2545_2]) ).

fof(f_2546_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_2546_2,plain,
    ! [U_8953,U_8952,U_8951] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8951,c_Orderings_Oord__class_Omax(U_8951),hAPP(hAPP(c_Set_Oinsert(U_8951),U_8953),U_8952)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8951,U_8951,c_Orderings_Oord__class_Omax(U_8951)),U_8953),U_8952)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8951),U_8952))
      | ~ class_Orderings_Olinorder(U_8951) ),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

cnf(f_2546_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8951,c_Orderings_Oord__class_Omax(U_8951),hAPP(hAPP(c_Set_Oinsert(U_8951),U_8953),U_8952)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8951,U_8951,c_Orderings_Oord__class_Omax(U_8951)),U_8953),U_8952)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8951),U_8952))
    | ~ class_Orderings_Olinorder(U_8951) ),
    inference(clausify,[status(thm)],[f_2546_2]) ).

fof(f_2547_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_2547_2,plain,
    ! [U_8956,U_8955,U_8954] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8954,hAPP(hAPP(c_Set_Oinsert(U_8954),U_8956),U_8955)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8954),U_8956),c_Big__Operators_Olinorder__class_OMax(U_8954,U_8955))
      | U_8955 = c_Orderings_Obot__class_Obot(tc_fun(U_8954,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8954),U_8955))
      | ~ class_Orderings_Olinorder(U_8954) ),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

cnf(f_2547_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8954,hAPP(hAPP(c_Set_Oinsert(U_8954),U_8956),U_8955)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8954),U_8956),c_Big__Operators_Olinorder__class_OMax(U_8954,U_8955))
    | U_8955 = c_Orderings_Obot__class_Obot(tc_fun(U_8954,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8954),U_8955))
    | ~ class_Orderings_Olinorder(U_8954) ),
    inference(clausify,[status(thm)],[f_2547_2]) ).

fof(f_2548_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_2548_2,plain,
    ! [U_8959,U_8958,U_8957] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8957),c_Big__Operators_Olinorder__class_OMax(U_8957,U_8959)),c_Big__Operators_Olinorder__class_OMax(U_8957,U_8958)) = c_Big__Operators_Olinorder__class_OMax(U_8957,U_8958)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8957,tc_HOL_Obool)),U_8959),U_8958))
      | U_8959 = c_Orderings_Obot__class_Obot(tc_fun(U_8957,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8957),U_8958))
      | ~ class_Orderings_Olinorder(U_8957) ),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

cnf(f_2548_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8957),c_Big__Operators_Olinorder__class_OMax(U_8957,U_8959)),c_Big__Operators_Olinorder__class_OMax(U_8957,U_8958)) = c_Big__Operators_Olinorder__class_OMax(U_8957,U_8958)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8957,tc_HOL_Obool)),U_8959),U_8958))
    | U_8959 = c_Orderings_Obot__class_Obot(tc_fun(U_8957,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8957),U_8958))
    | ~ class_Orderings_Olinorder(U_8957) ),
    inference(clausify,[status(thm)],[f_2548_2]) ).

fof(f_2549_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_2549_2,plain,
    ! [U_8962,U_8961,U_8960] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8960,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8960,tc_HOL_Obool)),U_8961),U_8962)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8960),c_Big__Operators_Olinorder__class_OMax(U_8960,U_8961)),c_Big__Operators_Olinorder__class_OMax(U_8960,U_8962))
      | U_8962 = c_Orderings_Obot__class_Obot(tc_fun(U_8960,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8960),U_8962))
      | U_8961 = c_Orderings_Obot__class_Obot(tc_fun(U_8960,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8960),U_8961))
      | ~ class_Orderings_Olinorder(U_8960) ),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

cnf(f_2549_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8960,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8960,tc_HOL_Obool)),U_8961),U_8962)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8960),c_Big__Operators_Olinorder__class_OMax(U_8960,U_8961)),c_Big__Operators_Olinorder__class_OMax(U_8960,U_8962))
    | U_8962 = c_Orderings_Obot__class_Obot(tc_fun(U_8960,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8960),U_8962))
    | U_8961 = c_Orderings_Obot__class_Obot(tc_fun(U_8960,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8960),U_8961))
    | ~ class_Orderings_Olinorder(U_8960) ),
    inference(clausify,[status(thm)],[f_2549_2]) ).

fof(f_2550_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_2550_2,plain,
    ! [U_8965,U_8964,U_8963] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8963),U_8965),U_8964)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8963,U_8963,c_Orderings_Oord__class_Omax(U_8963)),U_8965),U_8964)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8963),U_8964))
      | ~ class_Orderings_Olinorder(U_8963) ),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

cnf(f_2550_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8963,hAPP(hAPP(c_Set_Oinsert(U_8963),U_8965),U_8964)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8963,U_8963,c_Orderings_Oord__class_Omax(U_8963)),U_8965),U_8964)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8963),U_8964))
    | ~ class_Orderings_Olinorder(U_8963) ),
    inference(clausify,[status(thm)],[f_2550_2]) ).

fof(f_2551_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_2551_2,plain,
    ! [U_8968,U_8967,U_8966] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8966,c_Orderings_Oord__class_Omax(U_8966),hAPP(hAPP(c_Set_Oinsert(U_8966),U_8968),U_8967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8966),U_8968),c_Big__Operators_Olattice_OSup__fin(U_8966,c_Orderings_Oord__class_Omax(U_8966),U_8967))
      | U_8967 = c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_8966),U_8968),U_8967))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8966),U_8967))
      | ~ class_Orderings_Olinorder(U_8966) ),
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

cnf(f_2551_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8966,c_Orderings_Oord__class_Omax(U_8966),hAPP(hAPP(c_Set_Oinsert(U_8966),U_8968),U_8967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8966),U_8968),c_Big__Operators_Olattice_OSup__fin(U_8966,c_Orderings_Oord__class_Omax(U_8966),U_8967))
    | U_8967 = c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_8966),U_8968),U_8967))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8966),U_8967))
    | ~ class_Orderings_Olinorder(U_8966) ),
    inference(clausify,[status(thm)],[f_2551_2]) ).

fof(f_2552_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_2552_2,plain,
    ! [U_8971,U_8970,U_8969] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8969),U_8971),c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8970)) = U_8971
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8969),U_8970))
      | ~ class_Orderings_Olinorder(U_8969) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

cnf(f_2552_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8970)) = U_8971
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8969),U_8970))
    | ~ class_Orderings_Olinorder(U_8969) ),
    inference(clausify,[status(thm)],[f_2552_2]) ).

cnf(f_2552_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8969),U_8971),c_Big__Operators_Olattice_OSup__fin(U_8969,c_Orderings_Oord__class_Omax(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8969,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8969),U_8970))
    | ~ class_Orderings_Olinorder(U_8969) ),
    inference(clausify,[status(thm)],[f_2552_2]) ).

fof(f_2553_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_2553_2,plain,
    ! [U_8974,U_8973,U_8972] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8972,tc_HOL_Obool)),U_8973),U_8974)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8972),c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),U_8973)),c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),U_8974))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8972,tc_HOL_Obool)),U_8973),U_8974) != c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
      | U_8974 = c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8972),U_8974))
      | U_8973 = c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8972),U_8973))
      | ~ class_Orderings_Olinorder(U_8972) ),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

cnf(f_2553_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8972,tc_HOL_Obool)),U_8973),U_8974)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8972),c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),U_8973)),c_Big__Operators_Olattice_OSup__fin(U_8972,c_Orderings_Oord__class_Omax(U_8972),U_8974))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8972,tc_HOL_Obool)),U_8973),U_8974) != c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
    | U_8974 = c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8972),U_8974))
    | U_8973 = c_Orderings_Obot__class_Obot(tc_fun(U_8972,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8972),U_8973))
    | ~ class_Orderings_Olinorder(U_8972) ),
    inference(clausify,[status(thm)],[f_2553_2]) ).

fof(f_2554_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_2554_2,plain,
    ! [U_8977,U_8976,U_8975] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977))),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976)),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8977))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977) = c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8977))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8976))
      | ~ class_Orderings_Olinorder(U_8975) ),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

cnf(f_2554_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977))),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976)),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8977))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8975,tc_HOL_Obool)),U_8976),U_8977) = c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8977))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8976))
    | ~ class_Orderings_Olinorder(U_8975) ),
    inference(clausify,[status(thm)],[f_2554_2]) ).

fof(f_2555_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_2555_2,plain,
    ! [U_8980,U_8979,U_8978] :
      ( c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),hAPP(hAPP(c_Set_Oinsert(U_8978),U_8980),U_8979)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8978,U_8978,c_Orderings_Oord__class_Omax(U_8978)),U_8980),U_8979)
      | hBOOL(hAPP(hAPP(c_member(U_8978),U_8980),U_8979))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8978),U_8979))
      | ~ class_Orderings_Olinorder(U_8978) ),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

cnf(f_2555_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),hAPP(hAPP(c_Set_Oinsert(U_8978),U_8980),U_8979)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8978,U_8978,c_Orderings_Oord__class_Omax(U_8978)),U_8980),U_8979)
    | hBOOL(hAPP(hAPP(c_member(U_8978),U_8980),U_8979))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8978),U_8979))
    | ~ class_Orderings_Olinorder(U_8978) ),
    inference(clausify,[status(thm)],[f_2555_2]) ).

fof(f_2556_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_2556_2,plain,
    ! [U_8983,U_8982,U_8981] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8981,hAPP(hAPP(c_Set_Oinsert(U_8981),U_8983),U_8982)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8981),U_8983),c_Big__Operators_Olinorder__class_OMax(U_8981,U_8982))
      | U_8982 = c_Orderings_Obot__class_Obot(tc_fun(U_8981,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_8981),U_8983),U_8982))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8981),U_8982))
      | ~ class_Orderings_Olinorder(U_8981) ),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

cnf(f_2556_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8981,hAPP(hAPP(c_Set_Oinsert(U_8981),U_8983),U_8982)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8981),U_8983),c_Big__Operators_Olinorder__class_OMax(U_8981,U_8982))
    | U_8982 = c_Orderings_Obot__class_Obot(tc_fun(U_8981,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_8981),U_8983),U_8982))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8981),U_8982))
    | ~ class_Orderings_Olinorder(U_8981) ),
    inference(clausify,[status(thm)],[f_2556_2]) ).

fof(f_2557_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_2557_2,plain,
    ! [U_8986,U_8985,U_8984] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),U_8985)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8984),U_8986),c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),U_8985)) = U_8986
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8984),U_8985))
      | ~ class_Orderings_Olinorder(U_8984) ),
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

cnf(f_2557_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),U_8985)) = U_8986
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8984),U_8985))
    | ~ class_Orderings_Olinorder(U_8984) ),
    inference(clausify,[status(thm)],[f_2557_2]) ).

cnf(f_2557_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),U_8985)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8984),U_8986),c_Big__Operators_Olinorder__class_OMax(U_8984,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8984,tc_HOL_Obool)),U_8985),hAPP(hAPP(c_Set_Oinsert(U_8984),U_8986),c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8984,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8984),U_8985))
    | ~ class_Orderings_Olinorder(U_8984) ),
    inference(clausify,[status(thm)],[f_2557_2]) ).

fof(f_2558_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_2558_2,plain,
    ! [U_8989,U_8988,U_8987] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8987,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8987,tc_HOL_Obool)),U_8988),U_8989)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8987),c_Big__Operators_Olinorder__class_OMax(U_8987,U_8988)),c_Big__Operators_Olinorder__class_OMax(U_8987,U_8989))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8987,tc_HOL_Obool)),U_8988),U_8989) != c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
      | U_8989 = c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8987),U_8989))
      | U_8988 = c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8987),U_8988))
      | ~ class_Orderings_Olinorder(U_8987) ),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

cnf(f_2558_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8987,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8987,tc_HOL_Obool)),U_8988),U_8989)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8987),c_Big__Operators_Olinorder__class_OMax(U_8987,U_8988)),c_Big__Operators_Olinorder__class_OMax(U_8987,U_8989))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8987,tc_HOL_Obool)),U_8988),U_8989) != c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
    | U_8989 = c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8987),U_8989))
    | U_8988 = c_Orderings_Obot__class_Obot(tc_fun(U_8987,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8987),U_8988))
    | ~ class_Orderings_Olinorder(U_8987) ),
    inference(clausify,[status(thm)],[f_2558_2]) ).

fof(f_2559_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_2559_2,plain,
    ! [U_8992,U_8991,U_8990] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8990),c_Big__Operators_Olinorder__class_OMax(U_8990,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992))),c_Big__Operators_Olinorder__class_OMax(U_8990,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8990),c_Big__Operators_Olinorder__class_OMax(U_8990,U_8991)),c_Big__Operators_Olinorder__class_OMax(U_8990,U_8992))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992) = c_Orderings_Obot__class_Obot(tc_fun(U_8990,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8990),U_8992))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8990),U_8991))
      | ~ class_Orderings_Olinorder(U_8990) ),
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

cnf(f_2559_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8990),c_Big__Operators_Olinorder__class_OMax(U_8990,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992))),c_Big__Operators_Olinorder__class_OMax(U_8990,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8990),c_Big__Operators_Olinorder__class_OMax(U_8990,U_8991)),c_Big__Operators_Olinorder__class_OMax(U_8990,U_8992))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8990,tc_HOL_Obool)),U_8991),U_8992) = c_Orderings_Obot__class_Obot(tc_fun(U_8990,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8990),U_8992))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8990),U_8991))
    | ~ class_Orderings_Olinorder(U_8990) ),
    inference(clausify,[status(thm)],[f_2559_2]) ).

fof(f_2560_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_2560_2,plain,
    ! [U_8995,U_8994,U_8993] :
      ( c_Big__Operators_Olinorder__class_OMax(U_8993,hAPP(hAPP(c_Set_Oinsert(U_8993),U_8995),U_8994)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8993,U_8993,c_Orderings_Oord__class_Omax(U_8993)),U_8995),U_8994)
      | hBOOL(hAPP(hAPP(c_member(U_8993),U_8995),U_8994))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8993),U_8994))
      | ~ class_Orderings_Olinorder(U_8993) ),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

cnf(f_2560_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_8993,hAPP(hAPP(c_Set_Oinsert(U_8993),U_8995),U_8994)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8993,U_8993,c_Orderings_Oord__class_Omax(U_8993)),U_8995),U_8994)
    | hBOOL(hAPP(hAPP(c_member(U_8993),U_8995),U_8994))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8993),U_8994))
    | ~ class_Orderings_Olinorder(U_8993) ),
    inference(clausify,[status(thm)],[f_2560_2]) ).

fof(f_2561_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_2561_2,plain,
    ! [U_8999,U_8998] :
      ( hBOOL(hAPP(hAPP(c_member(U_8998),c_Big__Operators_Olattice_OSup__fin(U_8998,c_Orderings_Oord__class_Omax(U_8998),U_8999)),U_8999))
      | ? [U_8997,U_8996] : ~ hBOOL(hAPP(hAPP(c_member(U_8998),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8998),U_8997),U_8996)),hAPP(hAPP(c_Set_Oinsert(U_8998),U_8997),hAPP(hAPP(c_Set_Oinsert(U_8998),U_8996),c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))))))
      | U_8999 = c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8998),U_8999))
      | ~ class_Orderings_Olinorder(U_8998) ),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ! [U_8999,U_8998] :
      ( hBOOL(hAPP(hAPP(c_member(U_8998),c_Big__Operators_Olattice_OSup__fin(U_8998,c_Orderings_Oord__class_Omax(U_8998),U_8999)),U_8999))
      | ? [U_8996] : ~ hBOOL(hAPP(hAPP(c_member(U_8998),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8998),sK171(U_8999,U_8998)),U_8996)),hAPP(hAPP(c_Set_Oinsert(U_8998),sK171(U_8999,U_8998)),hAPP(hAPP(c_Set_Oinsert(U_8998),U_8996),c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))))))
      | U_8999 = c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8998),U_8999))
      | ~ class_Orderings_Olinorder(U_8998) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_8997,sK171(U_8999,U_8998))],[f_2561_2]) ).

fof(f_2561_4,plain,
    ! [U_8999,U_8998] :
      ( hBOOL(hAPP(hAPP(c_member(U_8998),c_Big__Operators_Olattice_OSup__fin(U_8998,c_Orderings_Oord__class_Omax(U_8998),U_8999)),U_8999))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8998),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8998),sK171(U_8999,U_8998)),sK172(U_8999,U_8998))),hAPP(hAPP(c_Set_Oinsert(U_8998),sK171(U_8999,U_8998)),hAPP(hAPP(c_Set_Oinsert(U_8998),sK172(U_8999,U_8998)),c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))))))
      | U_8999 = c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8998),U_8999))
      | ~ class_Orderings_Olinorder(U_8998) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_8996,sK172(U_8999,U_8998))],[f_2561_3]) ).

cnf(f_2561_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8998),c_Big__Operators_Olattice_OSup__fin(U_8998,c_Orderings_Oord__class_Omax(U_8998),U_8999)),U_8999))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8998),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8998),sK171(U_8999,U_8998)),sK172(U_8999,U_8998))),hAPP(hAPP(c_Set_Oinsert(U_8998),sK171(U_8999,U_8998)),hAPP(hAPP(c_Set_Oinsert(U_8998),sK172(U_8999,U_8998)),c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))))))
    | U_8999 = c_Orderings_Obot__class_Obot(tc_fun(U_8998,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8998),U_8999))
    | ~ class_Orderings_Olinorder(U_8998) ),
    inference(clausify,[status(thm)],[f_2561_4]) ).

fof(f_2562_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_2562_2,plain,
    ! [U_9003,U_9002] :
      ( hBOOL(hAPP(hAPP(c_member(U_9002),c_Big__Operators_Olinorder__class_OMax(U_9002,U_9003)),U_9003))
      | ? [U_9001,U_9000] : ~ hBOOL(hAPP(hAPP(c_member(U_9002),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9002),U_9001),U_9000)),hAPP(hAPP(c_Set_Oinsert(U_9002),U_9001),hAPP(hAPP(c_Set_Oinsert(U_9002),U_9000),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))))))
      | U_9003 = c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9002),U_9003))
      | ~ class_Orderings_Olinorder(U_9002) ),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

fof(f_2562_3,plain,
    ! [U_9003,U_9002] :
      ( hBOOL(hAPP(hAPP(c_member(U_9002),c_Big__Operators_Olinorder__class_OMax(U_9002,U_9003)),U_9003))
      | ? [U_9000] : ~ hBOOL(hAPP(hAPP(c_member(U_9002),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9002),sK173(U_9003,U_9002)),U_9000)),hAPP(hAPP(c_Set_Oinsert(U_9002),sK173(U_9003,U_9002)),hAPP(hAPP(c_Set_Oinsert(U_9002),U_9000),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))))))
      | U_9003 = c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9002),U_9003))
      | ~ class_Orderings_Olinorder(U_9002) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_9001,sK173(U_9003,U_9002))],[f_2562_2]) ).

fof(f_2562_4,plain,
    ! [U_9003,U_9002] :
      ( hBOOL(hAPP(hAPP(c_member(U_9002),c_Big__Operators_Olinorder__class_OMax(U_9002,U_9003)),U_9003))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9002),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9002),sK173(U_9003,U_9002)),sK174(U_9003,U_9002))),hAPP(hAPP(c_Set_Oinsert(U_9002),sK173(U_9003,U_9002)),hAPP(hAPP(c_Set_Oinsert(U_9002),sK174(U_9003,U_9002)),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))))))
      | U_9003 = c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9002),U_9003))
      | ~ class_Orderings_Olinorder(U_9002) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_9000,sK174(U_9003,U_9002))],[f_2562_3]) ).

cnf(f_2562_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9002),c_Big__Operators_Olinorder__class_OMax(U_9002,U_9003)),U_9003))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9002),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9002),sK173(U_9003,U_9002)),sK174(U_9003,U_9002))),hAPP(hAPP(c_Set_Oinsert(U_9002),sK173(U_9003,U_9002)),hAPP(hAPP(c_Set_Oinsert(U_9002),sK174(U_9003,U_9002)),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))))))
    | U_9003 = c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9002),U_9003))
    | ~ class_Orderings_Olinorder(U_9002) ),
    inference(clausify,[status(thm)],[f_2562_4]) ).

fof(f_2563_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_2563_2,plain,
    ! [U_9010,U_9009,U_9008,U_9007,U_9006,U_9005,U_9004] : hAPP(c_Product__Type_Oapsnd(U_9004,U_9005,U_9006,U_9007),hAPP(c_Product__Type_Oapfst(U_9008,U_9006,U_9004,U_9009),U_9010)) = hAPP(hAPP(c_Product__Type_OPair(U_9006,U_9005),hAPP(U_9009,hAPP(c_Product__Type_Ofst(U_9008,U_9004),U_9010))),hAPP(U_9007,hAPP(c_Product__Type_Osnd(U_9008,U_9004),U_9010))),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

cnf(f_2563_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_9004,U_9005,U_9006,U_9007),hAPP(c_Product__Type_Oapfst(U_9008,U_9006,U_9004,U_9009),U_9010)) = hAPP(hAPP(c_Product__Type_OPair(U_9006,U_9005),hAPP(U_9009,hAPP(c_Product__Type_Ofst(U_9008,U_9004),U_9010))),hAPP(U_9007,hAPP(c_Product__Type_Osnd(U_9008,U_9004),U_9010))),
    inference(clausify,[status(thm)],[f_2563_2]) ).

fof(f_2564_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_2564_2,plain,
    ! [U_9017,U_9016,U_9015,U_9014,U_9013,U_9012,U_9011] : hAPP(c_Product__Type_Oapfst(U_9011,U_9012,U_9013,U_9014),hAPP(c_Product__Type_Oapsnd(U_9015,U_9013,U_9011,U_9016),U_9017)) = hAPP(hAPP(c_Product__Type_OPair(U_9012,U_9013),hAPP(U_9014,hAPP(c_Product__Type_Ofst(U_9011,U_9015),U_9017))),hAPP(U_9016,hAPP(c_Product__Type_Osnd(U_9011,U_9015),U_9017))),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

cnf(f_2564_3,plain,
    hAPP(c_Product__Type_Oapfst(U_9011,U_9012,U_9013,U_9014),hAPP(c_Product__Type_Oapsnd(U_9015,U_9013,U_9011,U_9016),U_9017)) = hAPP(hAPP(c_Product__Type_OPair(U_9012,U_9013),hAPP(U_9014,hAPP(c_Product__Type_Ofst(U_9011,U_9015),U_9017))),hAPP(U_9016,hAPP(c_Product__Type_Osnd(U_9011,U_9015),U_9017))),
    inference(clausify,[status(thm)],[f_2564_2]) ).

fof(f_2565_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_2565_2,plain,
    ! [U_9023,U_9022,U_9021,U_9020,U_9019,U_9018] : hAPP(c_Product__Type_Oapfst(U_9018,U_9019,U_9020,U_9021),hAPP(hAPP(c_Product__Type_OPair(U_9018,U_9020),U_9022),U_9023)) = hAPP(hAPP(c_Product__Type_OPair(U_9019,U_9020),hAPP(U_9021,U_9022)),U_9023),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

cnf(f_2565_3,plain,
    hAPP(c_Product__Type_Oapfst(U_9018,U_9019,U_9020,U_9021),hAPP(hAPP(c_Product__Type_OPair(U_9018,U_9020),U_9022),U_9023)) = hAPP(hAPP(c_Product__Type_OPair(U_9019,U_9020),hAPP(U_9021,U_9022)),U_9023),
    inference(clausify,[status(thm)],[f_2565_2]) ).

fof(f_2566_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_2566_2,plain,
    ! [U_9028,U_9027,U_9026,U_9025,U_9024] : hAPP(c_Product__Type_Ofst(U_9024,U_9025),hAPP(c_Product__Type_Oapfst(U_9026,U_9024,U_9025,U_9027),U_9028)) = hAPP(U_9027,hAPP(c_Product__Type_Ofst(U_9026,U_9025),U_9028)),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

cnf(f_2566_3,plain,
    hAPP(c_Product__Type_Ofst(U_9024,U_9025),hAPP(c_Product__Type_Oapfst(U_9026,U_9024,U_9025,U_9027),U_9028)) = hAPP(U_9027,hAPP(c_Product__Type_Ofst(U_9026,U_9025),U_9028)),
    inference(clausify,[status(thm)],[f_2566_2]) ).

fof(f_2567_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_2567_2,plain,
    ! [U_9034,U_9033,U_9032,U_9031,U_9030,U_9029] :
      ( ( hAPP(c_Product__Type_Oapfst(U_9029,U_9030,U_9031,U_9032),U_9033) = hAPP(c_Product__Type_Oapfst(U_9029,U_9030,U_9031,U_9034),U_9033)
        | hAPP(U_9032,hAPP(c_Product__Type_Ofst(U_9029,U_9031),U_9033)) != hAPP(U_9034,hAPP(c_Product__Type_Ofst(U_9029,U_9031),U_9033)) )
      & ( hAPP(U_9032,hAPP(c_Product__Type_Ofst(U_9029,U_9031),U_9033)) = hAPP(U_9034,hAPP(c_Product__Type_Ofst(U_9029,U_9031),U_9033))
        | hAPP(c_Product__Type_Oapfst(U_9029,U_9030,U_9031,U_9032),U_9033) != hAPP(c_Product__Type_Oapfst(U_9029,U_9030,U_9031,U_9034),U_9033) ) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

fof(f_2567_3,plain,
    ( ! [U_9046,U_9044,U_9042,U_9040,U_9038,U_9036] :
        ( hAPP(c_Product__Type_Oapfst(U_9036,U_9038,U_9040,U_9042),U_9044) = hAPP(c_Product__Type_Oapfst(U_9036,U_9038,U_9040,U_9046),U_9044)
        | hAPP(U_9042,hAPP(c_Product__Type_Ofst(U_9036,U_9040),U_9044)) != hAPP(U_9046,hAPP(c_Product__Type_Ofst(U_9036,U_9040),U_9044)) )
    & ! [U_9045,U_9043,U_9041,U_9039,U_9037,U_9035] :
        ( hAPP(U_9041,hAPP(c_Product__Type_Ofst(U_9035,U_9039),U_9043)) = hAPP(U_9045,hAPP(c_Product__Type_Ofst(U_9035,U_9039),U_9043))
        | hAPP(c_Product__Type_Oapfst(U_9035,U_9037,U_9039,U_9041),U_9043) != hAPP(c_Product__Type_Oapfst(U_9035,U_9037,U_9039,U_9045),U_9043) ) ),
    inference(miniscope,[status(thm)],[f_2567_2]) ).

cnf(f_2567_4,plain,
    ( hAPP(U_9041,hAPP(c_Product__Type_Ofst(U_9035,U_9039),U_9043)) = hAPP(U_9045,hAPP(c_Product__Type_Ofst(U_9035,U_9039),U_9043))
    | hAPP(c_Product__Type_Oapfst(U_9035,U_9037,U_9039,U_9041),U_9043) != hAPP(c_Product__Type_Oapfst(U_9035,U_9037,U_9039,U_9045),U_9043) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

cnf(f_2567_5,plain,
    ( hAPP(c_Product__Type_Oapfst(U_9036,U_9038,U_9040,U_9042),U_9044) = hAPP(c_Product__Type_Oapfst(U_9036,U_9038,U_9040,U_9046),U_9044)
    | hAPP(U_9042,hAPP(c_Product__Type_Ofst(U_9036,U_9040),U_9044)) != hAPP(U_9046,hAPP(c_Product__Type_Ofst(U_9036,U_9040),U_9044)) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

fof(f_2568_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_2568_2,plain,
    ! [U_9051,U_9050,U_9049,U_9048,U_9047] : hAPP(c_Product__Type_Osnd(U_9047,U_9048),hAPP(c_Product__Type_Oapfst(U_9049,U_9047,U_9048,U_9050),U_9051)) = hAPP(c_Product__Type_Osnd(U_9049,U_9048),U_9051),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

cnf(f_2568_3,plain,
    hAPP(c_Product__Type_Osnd(U_9047,U_9048),hAPP(c_Product__Type_Oapfst(U_9049,U_9047,U_9048,U_9050),U_9051)) = hAPP(c_Product__Type_Osnd(U_9049,U_9048),U_9051),
    inference(clausify,[status(thm)],[f_2568_2]) ).

fof(f_2569_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_2569_2,plain,
    ! [U_9058,U_9057,U_9056,U_9055,U_9054,U_9053,U_9052] : hAPP(c_Product__Type_Oapsnd(U_9052,U_9053,U_9054,U_9055),hAPP(c_Product__Type_Oapfst(U_9056,U_9054,U_9052,U_9057),U_9058)) = hAPP(c_Product__Type_Oapfst(U_9056,U_9054,U_9053,U_9057),hAPP(c_Product__Type_Oapsnd(U_9052,U_9053,U_9056,U_9055),U_9058)),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

cnf(f_2569_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_9052,U_9053,U_9054,U_9055),hAPP(c_Product__Type_Oapfst(U_9056,U_9054,U_9052,U_9057),U_9058)) = hAPP(c_Product__Type_Oapfst(U_9056,U_9054,U_9053,U_9057),hAPP(c_Product__Type_Oapsnd(U_9052,U_9053,U_9056,U_9055),U_9058)),
    inference(clausify,[status(thm)],[f_2569_2]) ).

fof(f_2570_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_2570_2,plain,
    ! [U_9062,U_9061,U_9060,U_9059] :
      ( 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_9059),U_9061)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9060),U_9062))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9061),U_9062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9059),U_9060)) ),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

cnf(f_2570_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_9059),U_9061)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9060),U_9062))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9061),U_9062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9059),U_9060)) ),
    inference(clausify,[status(thm)],[f_2570_2]) ).

fof(f_2571_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_2571_2,plain,
    ! [U_9066,U_9065,U_9064,U_9063] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9063),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_9063,U_9063),hAPP(hAPP(c_COMBB(U_9063,tc_fun(U_9063,U_9063),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_9063)),U_9066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9063,tc_Nat_Onat),U_9066),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_9064,U_9065)) = c_Groups_Ozero__class_Ozero(U_9063)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9064),U_9065)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9063),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_9063,U_9063),hAPP(hAPP(c_COMBB(U_9063,tc_fun(U_9063,U_9063),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_9063)),U_9066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9063,tc_Nat_Onat),U_9066),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_9064,U_9065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9063),hAPP(U_9066,U_9064)),hAPP(U_9066,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9065),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9064),U_9065)) ) )
      | ~ class_Groups_Oab__group__add(U_9063) ),
    inference(variable_rename,[status(thm)],[f_2571_1]) ).

cnf(f_2571_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9063),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_9063,U_9063),hAPP(hAPP(c_COMBB(U_9063,tc_fun(U_9063,U_9063),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_9063)),U_9066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9063,tc_Nat_Onat),U_9066),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_9064,U_9065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9063),hAPP(U_9066,U_9064)),hAPP(U_9066,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9065),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9064),U_9065))
    | ~ class_Groups_Oab__group__add(U_9063) ),
    inference(clausify,[status(thm)],[f_2571_2]) ).

cnf(f_2571_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9063),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_9063,U_9063),hAPP(hAPP(c_COMBB(U_9063,tc_fun(U_9063,U_9063),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_9063)),U_9066)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9063,tc_Nat_Onat),U_9066),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_9064,U_9065)) = c_Groups_Ozero__class_Ozero(U_9063)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9064),U_9065))
    | ~ class_Groups_Oab__group__add(U_9063) ),
    inference(clausify,[status(thm)],[f_2571_2]) ).

fof(f_2572_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_2572_2,plain,
    ! [U_9068,U_9067] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9067),c_Groups_Oone__class_Oone(U_9067)),c_Groups_Oone__class_Oone(U_9067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9067),c_Nat_Osemiring__1__class_Oof__nat(U_9067)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_9068))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9067),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9067),U_9068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9067),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9067),U_9068)),c_Groups_Oone__class_Oone(U_9067)))
      | ~ class_Rings_Ocomm__semiring__1(U_9067) ),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

cnf(f_2572_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9067),c_Groups_Oone__class_Oone(U_9067)),c_Groups_Oone__class_Oone(U_9067))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9067),c_Nat_Osemiring__1__class_Oof__nat(U_9067)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_9068))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9067),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9067),U_9068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9067),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9067),U_9068)),c_Groups_Oone__class_Oone(U_9067)))
    | ~ class_Rings_Ocomm__semiring__1(U_9067) ),
    inference(clausify,[status(thm)],[f_2572_2]) ).

fof(f_2573_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_2573_2,plain,
    ! [U_9072,U_9071,U_9070,U_9069] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9070,U_9069),U_9071),U_9072) = hAPP(hAPP(c_Finite__Set_Ofold(U_9070,U_9069,hAPP(hAPP(c_COMBB(U_9069,tc_fun(U_9069,U_9069),U_9070),c_Lattices_Osemilattice__inf__class_Oinf(U_9069)),U_9072)),c_Orderings_Otop__class_Otop(U_9069)),U_9071)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9070),U_9071))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9069) ),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

cnf(f_2573_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9070,U_9069),U_9071),U_9072) = hAPP(hAPP(c_Finite__Set_Ofold(U_9070,U_9069,hAPP(hAPP(c_COMBB(U_9069,tc_fun(U_9069,U_9069),U_9070),c_Lattices_Osemilattice__inf__class_Oinf(U_9069)),U_9072)),c_Orderings_Otop__class_Otop(U_9069)),U_9071)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9070),U_9071))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9069) ),
    inference(clausify,[status(thm)],[f_2573_2]) ).

fof(f_2574_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_2574_2,plain,
    ! [U_9078,U_9077,U_9076,U_9075,U_9074,U_9073] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9078),U_9075))
      | hBOOL(hAPP(hAPP(U_9076,U_9078),U_9077))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9074,tc_HOL_Obool)),U_9075),U_9076),U_9077)) ),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

cnf(f_2574_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9078),U_9075))
    | hBOOL(hAPP(hAPP(U_9076,U_9078),U_9077))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9074,tc_HOL_Obool)),U_9075),U_9076),U_9077)) ),
    inference(clausify,[status(thm)],[f_2574_2]) ).

fof(f_2575_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_2575_2,plain,
    ! [U_9084,U_9083,U_9082,U_9081,U_9080,U_9079] :
      ( hBOOL(hAPP(hAPP(U_9082,U_9084),U_9083))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9084),U_9081))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9079,tc_fun(U_9080,tc_HOL_Obool)),U_9081),U_9082),U_9083)) ),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

cnf(f_2575_3,plain,
    ( hBOOL(hAPP(hAPP(U_9082,U_9084),U_9083))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9084),U_9081))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9079,tc_fun(U_9080,tc_HOL_Obool)),U_9081),U_9082),U_9083)) ),
    inference(clausify,[status(thm)],[f_2575_2]) ).

fof(f_2576_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_2576_2,plain,
    ! [U_9090,U_9089,U_9088,U_9087,U_9086,U_9085] :
      ( hBOOL(hAPP(hAPP(c_member(U_9085),U_9086),hAPP(U_9089,U_9090)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9087),U_9090),U_9088))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9085),U_9086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9087,tc_fun(U_9085,tc_HOL_Obool)),U_9088),U_9089))) ),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

cnf(f_2576_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9085),U_9086),hAPP(U_9089,U_9090)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9087),U_9090),U_9088))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9085),U_9086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9087,tc_fun(U_9085,tc_HOL_Obool)),U_9088),U_9089))) ),
    inference(clausify,[status(thm)],[f_2576_2]) ).

fof(f_2577_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_2577_2,plain,
    ! [U_9096,U_9095,U_9094,U_9093,U_9092,U_9091] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9093),U_9096),U_9094))
      | hBOOL(hAPP(hAPP(c_member(U_9091),U_9092),hAPP(U_9095,U_9096)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9091),U_9092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9093,tc_fun(U_9091,tc_HOL_Obool)),U_9094),U_9095))) ),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

cnf(f_2577_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9093),U_9096),U_9094))
    | hBOOL(hAPP(hAPP(c_member(U_9091),U_9092),hAPP(U_9095,U_9096)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9091),U_9092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9093,tc_fun(U_9091,tc_HOL_Obool)),U_9094),U_9095))) ),
    inference(clausify,[status(thm)],[f_2577_2]) ).

fof(f_2578_1,plain,
    ! [V_a_2,V_ca_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_ca_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_ca_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).

fof(f_2578_2,plain,
    ! [U_9104,U_9103,U_9102,U_9101,U_9100,U_9099,U_9098,U_9097] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9097),U_9104),U_9100))
      | hBOOL(hAPP(hAPP(hAPP(U_9101,U_9104),U_9102),U_9103))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9097,tc_fun(U_9098,tc_fun(U_9099,tc_HOL_Obool))),U_9100),U_9101),U_9102),U_9103)) ),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

cnf(f_2578_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9097),U_9104),U_9100))
    | hBOOL(hAPP(hAPP(hAPP(U_9101,U_9104),U_9102),U_9103))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9097,tc_fun(U_9098,tc_fun(U_9099,tc_HOL_Obool))),U_9100),U_9101),U_9102),U_9103)) ),
    inference(clausify,[status(thm)],[f_2578_2]) ).

fof(f_2579_1,plain,
    ! [V_a_2,V_ca_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_ca_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_ca_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).

fof(f_2579_2,plain,
    ! [U_9112,U_9111,U_9110,U_9109,U_9108,U_9107,U_9106,U_9105] :
      ( hBOOL(hAPP(hAPP(hAPP(U_9109,U_9112),U_9110),U_9111))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9105),U_9112),U_9108))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9105,tc_fun(U_9106,tc_fun(U_9107,tc_HOL_Obool))),U_9108),U_9109),U_9110),U_9111)) ),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

cnf(f_2579_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_9109,U_9112),U_9110),U_9111))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9105),U_9112),U_9108))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9105,tc_fun(U_9106,tc_fun(U_9107,tc_HOL_Obool))),U_9108),U_9109),U_9110),U_9111)) ),
    inference(clausify,[status(thm)],[f_2579_2]) ).

fof(f_2580_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_2580_2,plain,
    ! [U_9117,U_9116,U_9115,U_9114] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9114,tc_fun(U_9116,tc_HOL_Obool)),U_9115),U_9117)))
      | ! [U_9113] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9116),hAPP(U_9117,U_9113)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9114),U_9113),U_9115)) ) ),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

cnf(f_2580_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9114,tc_fun(U_9116,tc_HOL_Obool)),U_9115),U_9117)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9116),hAPP(U_9117,U_9113)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9114),U_9113),U_9115)) ),
    inference(clausify,[status(thm)],[f_2580_2]) ).

fof(f_2581_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_2581_2,plain,
    ! [U_9119,U_9118] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9118,U_9119))),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

cnf(f_2581_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9118,U_9119))),
    inference(clausify,[status(thm)],[f_2581_2]) ).

fof(f_2582_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_2582_2,plain,
    ! [U_9125,U_9124,U_9123,U_9122] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_9122,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9123,tc_fun(U_9122,tc_HOL_Obool)),U_9124),U_9125)
        | ? [U_9121] :
            ( hAPP(U_9125,U_9121) != c_Orderings_Otop__class_Otop(tc_fun(U_9122,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9123),U_9121),U_9124)) ) )
      & ( ! [U_9120] :
            ( hAPP(U_9125,U_9120) = c_Orderings_Otop__class_Otop(tc_fun(U_9122,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9123),U_9120),U_9124)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9122,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9123,tc_fun(U_9122,tc_HOL_Obool)),U_9124),U_9125) ) ),
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

fof(f_2582_3,plain,
    ( ! [U_9133,U_9131,U_9129,U_9127] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9129,tc_fun(U_9127,tc_HOL_Obool)),U_9131),U_9133)
        | ? [U_9121] :
            ( hAPP(U_9133,U_9121) != c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9129),U_9121),U_9131)) ) )
    & ! [U_9132,U_9130,U_9128,U_9126] :
        ( ! [U_9120] :
            ( hAPP(U_9132,U_9120) = c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9128),U_9120),U_9130)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9128,tc_fun(U_9126,tc_HOL_Obool)),U_9130),U_9132) ) ),
    inference(miniscope,[status(thm)],[f_2582_2]) ).

fof(f_2582_4,plain,
    ( ! [U_9133,U_9131,U_9129,U_9127] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9129,tc_fun(U_9127,tc_HOL_Obool)),U_9131),U_9133)
        | ( hAPP(U_9133,sK175(U_9133,U_9131,U_9129,U_9127)) != c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9129),sK175(U_9133,U_9131,U_9129,U_9127)),U_9131)) ) )
    & ! [U_9132,U_9130,U_9128,U_9126] :
        ( ! [U_9120] :
            ( hAPP(U_9132,U_9120) = c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9128),U_9120),U_9130)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9128,tc_fun(U_9126,tc_HOL_Obool)),U_9130),U_9132) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_9121,sK175(U_9133,U_9131,U_9129,U_9127))],[f_2582_3]) ).

cnf(f_2582_5,plain,
    ( hAPP(U_9132,U_9120) = c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9128),U_9120),U_9130))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9128,tc_fun(U_9126,tc_HOL_Obool)),U_9130),U_9132) ),
    inference(clausify,[status(thm)],[f_2582_4]) ).

cnf(f_2582_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9129),sK175(U_9133,U_9131,U_9129,U_9127)),U_9131))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9129,tc_fun(U_9127,tc_HOL_Obool)),U_9131),U_9133) ),
    inference(clausify,[status(thm)],[f_2582_4]) ).

cnf(f_2582_7,plain,
    ( hAPP(U_9133,sK175(U_9133,U_9131,U_9129,U_9127)) != c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9127,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9129,tc_fun(U_9127,tc_HOL_Obool)),U_9131),U_9133) ),
    inference(clausify,[status(thm)],[f_2582_4]) ).

fof(f_2583_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_2583_2,plain,
    ! [U_9139,U_9138,U_9137,U_9136] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9136,tc_fun(U_9137,tc_HOL_Obool)),U_9138),U_9139) = c_Orderings_Otop__class_Otop(tc_fun(U_9137,tc_HOL_Obool))
        | ? [U_9135] :
            ( hAPP(U_9139,U_9135) != c_Orderings_Otop__class_Otop(tc_fun(U_9137,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9136),U_9135),U_9138)) ) )
      & ( ! [U_9134] :
            ( hAPP(U_9139,U_9134) = c_Orderings_Otop__class_Otop(tc_fun(U_9137,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9136),U_9134),U_9138)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9136,tc_fun(U_9137,tc_HOL_Obool)),U_9138),U_9139) != c_Orderings_Otop__class_Otop(tc_fun(U_9137,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

fof(f_2583_3,plain,
    ( ! [U_9147,U_9145,U_9143,U_9141] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9141,tc_fun(U_9143,tc_HOL_Obool)),U_9145),U_9147) = c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool))
        | ? [U_9135] :
            ( hAPP(U_9147,U_9135) != c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9141),U_9135),U_9145)) ) )
    & ! [U_9146,U_9144,U_9142,U_9140] :
        ( ! [U_9134] :
            ( hAPP(U_9146,U_9134) = c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9140),U_9134),U_9144)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9142,tc_HOL_Obool)),U_9144),U_9146) != c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2583_2]) ).

fof(f_2583_4,plain,
    ( ! [U_9147,U_9145,U_9143,U_9141] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9141,tc_fun(U_9143,tc_HOL_Obool)),U_9145),U_9147) = c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool))
        | ( hAPP(U_9147,sK176(U_9147,U_9145,U_9143,U_9141)) != c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9141),sK176(U_9147,U_9145,U_9143,U_9141)),U_9145)) ) )
    & ! [U_9146,U_9144,U_9142,U_9140] :
        ( ! [U_9134] :
            ( hAPP(U_9146,U_9134) = c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9140),U_9134),U_9144)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9142,tc_HOL_Obool)),U_9144),U_9146) != c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_9135,sK176(U_9147,U_9145,U_9143,U_9141))],[f_2583_3]) ).

cnf(f_2583_5,plain,
    ( hAPP(U_9146,U_9134) = c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9140),U_9134),U_9144))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9142,tc_HOL_Obool)),U_9144),U_9146) != c_Orderings_Otop__class_Otop(tc_fun(U_9142,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2583_4]) ).

cnf(f_2583_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9141),sK176(U_9147,U_9145,U_9143,U_9141)),U_9145))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9141,tc_fun(U_9143,tc_HOL_Obool)),U_9145),U_9147) = c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2583_4]) ).

cnf(f_2583_7,plain,
    ( hAPP(U_9147,sK176(U_9147,U_9145,U_9143,U_9141)) != c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9141,tc_fun(U_9143,tc_HOL_Obool)),U_9145),U_9147) = c_Orderings_Otop__class_Otop(tc_fun(U_9143,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2583_4]) ).

fof(f_2584_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_2584_2,plain,
    ! [U_9154,U_9153,U_9152,U_9151,U_9150] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9150,tc_HOL_Obool)),U_9151),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9152,tc_fun(U_9150,tc_HOL_Obool)),U_9153),U_9154)))
        | ? [U_9149] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9150,tc_HOL_Obool)),U_9151),hAPP(U_9154,U_9149)))
            & hBOOL(hAPP(hAPP(c_member(U_9152),U_9149),U_9153)) ) )
      & ( ! [U_9148] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9150,tc_HOL_Obool)),U_9151),hAPP(U_9154,U_9148)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9152),U_9148),U_9153)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9150,tc_HOL_Obool)),U_9151),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9152,tc_fun(U_9150,tc_HOL_Obool)),U_9153),U_9154))) ) ),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

fof(f_2584_3,plain,
    ( ! [U_9164,U_9162,U_9160,U_9158,U_9156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9160,tc_fun(U_9156,tc_HOL_Obool)),U_9162),U_9164)))
        | ? [U_9149] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(U_9164,U_9149)))
            & hBOOL(hAPP(hAPP(c_member(U_9160),U_9149),U_9162)) ) )
    & ! [U_9163,U_9161,U_9159,U_9157,U_9155] :
        ( ! [U_9148] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(U_9163,U_9148)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9148),U_9161)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9159,tc_fun(U_9155,tc_HOL_Obool)),U_9161),U_9163))) ) ),
    inference(miniscope,[status(thm)],[f_2584_2]) ).

fof(f_2584_4,plain,
    ( ! [U_9164,U_9162,U_9160,U_9158,U_9156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9160,tc_fun(U_9156,tc_HOL_Obool)),U_9162),U_9164)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(U_9164,sK177(U_9164,U_9162,U_9160,U_9158,U_9156))))
          & hBOOL(hAPP(hAPP(c_member(U_9160),sK177(U_9164,U_9162,U_9160,U_9158,U_9156)),U_9162)) ) )
    & ! [U_9163,U_9161,U_9159,U_9157,U_9155] :
        ( ! [U_9148] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(U_9163,U_9148)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9148),U_9161)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9159,tc_fun(U_9155,tc_HOL_Obool)),U_9161),U_9163))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_9149,sK177(U_9164,U_9162,U_9160,U_9158,U_9156))],[f_2584_3]) ).

cnf(f_2584_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(U_9163,U_9148)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9159),U_9148),U_9161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9155,tc_HOL_Obool)),U_9157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9159,tc_fun(U_9155,tc_HOL_Obool)),U_9161),U_9163))) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

cnf(f_2584_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9160),sK177(U_9164,U_9162,U_9160,U_9158,U_9156)),U_9162))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9160,tc_fun(U_9156,tc_HOL_Obool)),U_9162),U_9164))) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

cnf(f_2584_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(U_9164,sK177(U_9164,U_9162,U_9160,U_9158,U_9156))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9156,tc_HOL_Obool)),U_9158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9160,tc_fun(U_9156,tc_HOL_Obool)),U_9162),U_9164))) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

fof(f_2585_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_2585_2,plain,
    ! [U_9169,U_9168,U_9167,U_9166,U_9165] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),hAPP(hAPP(c_COMBS(U_9165,tc_fun(U_9166,tc_HOL_Obool),tc_fun(U_9166,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9166,tc_HOL_Obool),tc_fun(tc_fun(U_9166,tc_HOL_Obool),tc_fun(U_9166,tc_HOL_Obool)),U_9165),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9166,tc_HOL_Obool))),U_9168)),U_9169)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9166,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),U_9168)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),U_9169)),
    inference(variable_rename,[status(thm)],[f_2585_1]) ).

cnf(f_2585_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),hAPP(hAPP(c_COMBS(U_9165,tc_fun(U_9166,tc_HOL_Obool),tc_fun(U_9166,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9166,tc_HOL_Obool),tc_fun(tc_fun(U_9166,tc_HOL_Obool),tc_fun(U_9166,tc_HOL_Obool)),U_9165),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9166,tc_HOL_Obool))),U_9168)),U_9169)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9166,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),U_9168)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9165,tc_fun(U_9166,tc_HOL_Obool)),U_9167),U_9169)),
    inference(clausify,[status(thm)],[f_2585_2]) ).

fof(f_2586_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_2586_2,plain,
    ! [U_9173,U_9172,U_9171,U_9170] : hAPP(c_Set_OPow(U_9170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9171,tc_fun(U_9170,tc_HOL_Obool)),U_9172),U_9173)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9171,tc_fun(tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool)),U_9172),hAPP(hAPP(c_COMBB(tc_fun(U_9170,tc_HOL_Obool),tc_fun(tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),U_9171),c_Set_OPow(U_9170)),U_9173)),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

cnf(f_2586_3,plain,
    hAPP(c_Set_OPow(U_9170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9171,tc_fun(U_9170,tc_HOL_Obool)),U_9172),U_9173)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9171,tc_fun(tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool)),U_9172),hAPP(hAPP(c_COMBB(tc_fun(U_9170,tc_HOL_Obool),tc_fun(tc_fun(U_9170,tc_HOL_Obool),tc_HOL_Obool),U_9171),c_Set_OPow(U_9170)),U_9173)),
    inference(clausify,[status(thm)],[f_2586_2]) ).

fof(f_2587_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_2587_2,plain,
    ! [U_9177,U_9176,U_9175,U_9174] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9174,tc_HOL_Obool),tc_fun(U_9175,tc_HOL_Obool)),U_9176),hAPP(hAPP(c_COMBC(tc_fun(U_9174,tc_HOL_Obool),tc_fun(U_9174,tc_fun(U_9175,tc_HOL_Obool)),tc_fun(U_9175,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9174,tc_fun(U_9175,tc_HOL_Obool))),U_9177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9174,tc_fun(U_9175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9174,tc_HOL_Obool),U_9176)),U_9177),
    inference(variable_rename,[status(thm)],[f_2587_1]) ).

cnf(f_2587_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9174,tc_HOL_Obool),tc_fun(U_9175,tc_HOL_Obool)),U_9176),hAPP(hAPP(c_COMBC(tc_fun(U_9174,tc_HOL_Obool),tc_fun(U_9174,tc_fun(U_9175,tc_HOL_Obool)),tc_fun(U_9175,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9174,tc_fun(U_9175,tc_HOL_Obool))),U_9177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9174,tc_fun(U_9175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9174,tc_HOL_Obool),U_9176)),U_9177),
    inference(clausify,[status(thm)],[f_2587_2]) ).

fof(f_2588_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_2588_2,plain,
    ! [U_9181,U_9180,U_9179,U_9178] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9178,tc_fun(U_9179,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9178,tc_HOL_Obool),U_9180)),U_9181) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9178,tc_HOL_Obool),tc_fun(U_9179,tc_HOL_Obool)),U_9180),hAPP(hAPP(c_COMBC(tc_fun(U_9178,tc_HOL_Obool),tc_fun(U_9178,tc_fun(U_9179,tc_HOL_Obool)),tc_fun(U_9179,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9178,tc_fun(U_9179,tc_HOL_Obool))),U_9181)),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

cnf(f_2588_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9178,tc_fun(U_9179,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9178,tc_HOL_Obool),U_9180)),U_9181) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9178,tc_HOL_Obool),tc_fun(U_9179,tc_HOL_Obool)),U_9180),hAPP(hAPP(c_COMBC(tc_fun(U_9178,tc_HOL_Obool),tc_fun(U_9178,tc_fun(U_9179,tc_HOL_Obool)),tc_fun(U_9179,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9178,tc_fun(U_9179,tc_HOL_Obool))),U_9181)),
    inference(clausify,[status(thm)],[f_2588_2]) ).

fof(f_2589_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_2589_2,plain,
    ! [U_9187,U_9186,U_9185,U_9184,U_9183,U_9182] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9183,tc_fun(U_9184,U_9182)),U_9185),U_9186),U_9187) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9183,U_9182),U_9185),hAPP(hAPP(c_COMBC(U_9183,U_9184,U_9182),U_9186),U_9187))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9182) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

cnf(f_2589_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9183,tc_fun(U_9184,U_9182)),U_9185),U_9186),U_9187) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9183,U_9182),U_9185),hAPP(hAPP(c_COMBC(U_9183,U_9184,U_9182),U_9186),U_9187))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9182) ),
    inference(clausify,[status(thm)],[f_2589_2]) ).

fof(f_2590_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_2590_2,plain,
    ! [U_9193,U_9192,U_9191,U_9190,U_9189,U_9188] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9189,U_9188),U_9190),hAPP(hAPP(c_COMBB(tc_fun(U_9191,U_9188),U_9188,U_9189),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9191,U_9188),U_9192)),U_9193)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9191,U_9188),U_9192),hAPP(hAPP(c_COMBB(tc_fun(U_9189,U_9188),U_9188,U_9191),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9189,U_9188),U_9190)),hAPP(c_COMBC(U_9189,U_9191,U_9188),U_9193)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9188) ),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

cnf(f_2590_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9189,U_9188),U_9190),hAPP(hAPP(c_COMBB(tc_fun(U_9191,U_9188),U_9188,U_9189),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9191,U_9188),U_9192)),U_9193)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9191,U_9188),U_9192),hAPP(hAPP(c_COMBB(tc_fun(U_9189,U_9188),U_9188,U_9191),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9189,U_9188),U_9190)),hAPP(c_COMBC(U_9189,U_9191,U_9188),U_9193)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9188) ),
    inference(clausify,[status(thm)],[f_2590_2]) ).

fof(f_2591_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_2591_2,plain,
    ! [U_9198,U_9197,U_9196,U_9195,U_9194] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9194,tc_fun(U_9195,tc_HOL_Obool)),U_9196),hAPP(hAPP(c_COMBB(tc_fun(U_9195,tc_HOL_Obool),tc_fun(U_9195,tc_HOL_Obool),U_9194),hAPP(c_Set_Oinsert(U_9195),U_9197)),U_9198)) = hAPP(hAPP(c_Set_Oinsert(U_9195),U_9197),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9194,tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9198)),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

cnf(f_2591_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9194,tc_fun(U_9195,tc_HOL_Obool)),U_9196),hAPP(hAPP(c_COMBB(tc_fun(U_9195,tc_HOL_Obool),tc_fun(U_9195,tc_HOL_Obool),U_9194),hAPP(c_Set_Oinsert(U_9195),U_9197)),U_9198)) = hAPP(hAPP(c_Set_Oinsert(U_9195),U_9197),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9194,tc_fun(U_9195,tc_HOL_Obool)),U_9196),U_9198)),
    inference(clausify,[status(thm)],[f_2591_2]) ).

fof(f_2592_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_2592_2,plain,
    ! [U_9203,U_9202,U_9201,U_9200,U_9199] : hAPP(hAPP(c_Set_Oinsert(U_9199),U_9200),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9201,tc_fun(U_9199,tc_HOL_Obool)),U_9202),U_9203)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9201,tc_fun(U_9199,tc_HOL_Obool)),U_9202),hAPP(hAPP(c_COMBB(tc_fun(U_9199,tc_HOL_Obool),tc_fun(U_9199,tc_HOL_Obool),U_9201),hAPP(c_Set_Oinsert(U_9199),U_9200)),U_9203)),
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

cnf(f_2592_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9199),U_9200),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9201,tc_fun(U_9199,tc_HOL_Obool)),U_9202),U_9203)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9201,tc_fun(U_9199,tc_HOL_Obool)),U_9202),hAPP(hAPP(c_COMBB(tc_fun(U_9199,tc_HOL_Obool),tc_fun(U_9199,tc_HOL_Obool),U_9201),hAPP(c_Set_Oinsert(U_9199),U_9200)),U_9203)),
    inference(clausify,[status(thm)],[f_2592_2]) ).

fof(f_2593_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_2593_2,plain,
    ! [U_9210,U_9209,U_9208,U_9207,U_9206] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9206),U_9207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9208,tc_fun(U_9206,tc_HOL_Obool)),U_9209),U_9210)))
        | ? [U_9205] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9206),U_9207),hAPP(U_9210,U_9205)))
            & hBOOL(hAPP(hAPP(c_member(U_9208),U_9205),U_9209)) ) )
      & ( ! [U_9204] :
            ( hBOOL(hAPP(hAPP(c_member(U_9206),U_9207),hAPP(U_9210,U_9204)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9208),U_9204),U_9209)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9206),U_9207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9208,tc_fun(U_9206,tc_HOL_Obool)),U_9209),U_9210))) ) ),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

fof(f_2593_3,plain,
    ( ! [U_9220,U_9218,U_9216,U_9214,U_9212] :
        ( hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9216,tc_fun(U_9212,tc_HOL_Obool)),U_9218),U_9220)))
        | ? [U_9205] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(U_9220,U_9205)))
            & hBOOL(hAPP(hAPP(c_member(U_9216),U_9205),U_9218)) ) )
    & ! [U_9219,U_9217,U_9215,U_9213,U_9211] :
        ( ! [U_9204] :
            ( hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(U_9219,U_9204)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9215),U_9204),U_9217)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9215,tc_fun(U_9211,tc_HOL_Obool)),U_9217),U_9219))) ) ),
    inference(miniscope,[status(thm)],[f_2593_2]) ).

fof(f_2593_4,plain,
    ( ! [U_9220,U_9218,U_9216,U_9214,U_9212] :
        ( hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9216,tc_fun(U_9212,tc_HOL_Obool)),U_9218),U_9220)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(U_9220,sK178(U_9220,U_9218,U_9216,U_9214,U_9212))))
          & hBOOL(hAPP(hAPP(c_member(U_9216),sK178(U_9220,U_9218,U_9216,U_9214,U_9212)),U_9218)) ) )
    & ! [U_9219,U_9217,U_9215,U_9213,U_9211] :
        ( ! [U_9204] :
            ( hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(U_9219,U_9204)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9215),U_9204),U_9217)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9215,tc_fun(U_9211,tc_HOL_Obool)),U_9217),U_9219))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_9205,sK178(U_9220,U_9218,U_9216,U_9214,U_9212))],[f_2593_3]) ).

cnf(f_2593_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(U_9219,U_9204)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9215),U_9204),U_9217))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9213),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9215,tc_fun(U_9211,tc_HOL_Obool)),U_9217),U_9219))) ),
    inference(clausify,[status(thm)],[f_2593_4]) ).

cnf(f_2593_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9216),sK178(U_9220,U_9218,U_9216,U_9214,U_9212)),U_9218))
    | hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9216,tc_fun(U_9212,tc_HOL_Obool)),U_9218),U_9220))) ),
    inference(clausify,[status(thm)],[f_2593_4]) ).

cnf(f_2593_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(U_9220,sK178(U_9220,U_9218,U_9216,U_9214,U_9212))))
    | hBOOL(hAPP(hAPP(c_member(U_9212),U_9214),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9216,tc_fun(U_9212,tc_HOL_Obool)),U_9218),U_9220))) ),
    inference(clausify,[status(thm)],[f_2593_4]) ).

fof(f_2594_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_2594_2,plain,
    ! [U_9222,U_9221] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9221,tc_HOL_Obool),U_9222) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9221,tc_HOL_Obool),tc_fun(U_9221,tc_HOL_Obool)),U_9222),c_COMBI(tc_fun(U_9221,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

cnf(f_2594_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9221,tc_HOL_Obool),U_9222) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9221,tc_HOL_Obool),tc_fun(U_9221,tc_HOL_Obool)),U_9222),c_COMBI(tc_fun(U_9221,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2594_2]) ).

fof(f_2595_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_2595_2,plain,
    ! [U_9229,U_9228,U_9227,U_9226,U_9225,U_9224,U_9223] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9224,tc_fun(U_9223,tc_HOL_Obool)),U_9225),U_9226)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9227,tc_fun(U_9223,tc_HOL_Obool)),U_9228),U_9229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9224,tc_fun(U_9223,tc_HOL_Obool)),U_9225),hAPP(hAPP(c_COMBB(tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9223,tc_HOL_Obool),U_9224),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9227,tc_fun(U_9223,tc_HOL_Obool)),U_9228)),hAPP(hAPP(c_COMBC(U_9224,tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),tc_fun(tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool))),U_9224),c_COMBB(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool),U_9227)),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_9224),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool))),U_9226))),U_9229))),
    inference(variable_rename,[status(thm)],[f_2595_1]) ).

cnf(f_2595_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9224,tc_fun(U_9223,tc_HOL_Obool)),U_9225),U_9226)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9227,tc_fun(U_9223,tc_HOL_Obool)),U_9228),U_9229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9224,tc_fun(U_9223,tc_HOL_Obool)),U_9225),hAPP(hAPP(c_COMBB(tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9223,tc_HOL_Obool),U_9224),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9227,tc_fun(U_9223,tc_HOL_Obool)),U_9228)),hAPP(hAPP(c_COMBC(U_9224,tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),tc_fun(tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool)),tc_fun(U_9227,tc_fun(U_9223,tc_HOL_Obool))),U_9224),c_COMBB(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool),U_9227)),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_9224),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool))),U_9226))),U_9229))),
    inference(clausify,[status(thm)],[f_2595_2]) ).

fof(f_2596_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_2596_2,plain,
    ! [U_9234,U_9233,U_9232,U_9231,U_9230] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9231,tc_fun(U_9230,tc_HOL_Obool)),U_9232),U_9233)),U_9234) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9231,tc_fun(U_9230,tc_HOL_Obool)),U_9232),hAPP(hAPP(c_COMBC(U_9231,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_9231),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool))),U_9233)),U_9234)),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

cnf(f_2596_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9231,tc_fun(U_9230,tc_HOL_Obool)),U_9232),U_9233)),U_9234) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9231,tc_fun(U_9230,tc_HOL_Obool)),U_9232),hAPP(hAPP(c_COMBC(U_9231,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_9231),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool))),U_9233)),U_9234)),
    inference(clausify,[status(thm)],[f_2596_2]) ).

fof(f_2597_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_2597_2,plain,
    ! [U_9239,U_9238,U_9237,U_9236,U_9235] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9235,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9237,tc_fun(U_9235,tc_HOL_Obool)),U_9238),U_9239)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9237,tc_fun(U_9235,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_COMBB(tc_fun(U_9235,tc_HOL_Obool),tc_fun(U_9235,tc_HOL_Obool),U_9237),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9235,tc_HOL_Obool)),U_9236)),U_9239)),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

cnf(f_2597_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9235,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9237,tc_fun(U_9235,tc_HOL_Obool)),U_9238),U_9239)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9237,tc_fun(U_9235,tc_HOL_Obool)),U_9238),hAPP(hAPP(c_COMBB(tc_fun(U_9235,tc_HOL_Obool),tc_fun(U_9235,tc_HOL_Obool),U_9237),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9235,tc_HOL_Obool)),U_9236)),U_9239)),
    inference(clausify,[status(thm)],[f_2597_2]) ).

fof(f_2598_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_2598_2,plain,
    ! [U_9244,U_9243,U_9242,U_9241,U_9240] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9240,tc_HOL_Obool)),U_9241),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9242,tc_fun(U_9240,tc_HOL_Obool)),U_9243),U_9244)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9242,tc_fun(U_9240,tc_HOL_Obool)),U_9243),hAPP(hAPP(c_COMBB(tc_fun(U_9240,tc_HOL_Obool),tc_fun(U_9240,tc_HOL_Obool),U_9242),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9240,tc_HOL_Obool)),U_9241)),U_9244)),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

cnf(f_2598_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9240,tc_HOL_Obool)),U_9241),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9242,tc_fun(U_9240,tc_HOL_Obool)),U_9243),U_9244)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9242,tc_fun(U_9240,tc_HOL_Obool)),U_9243),hAPP(hAPP(c_COMBB(tc_fun(U_9240,tc_HOL_Obool),tc_fun(U_9240,tc_HOL_Obool),U_9242),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9240,tc_HOL_Obool)),U_9241)),U_9244)),
    inference(clausify,[status(thm)],[f_2598_2]) ).

fof(f_2599_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_2599_2,plain,
    ! [U_9249,U_9248,U_9247,U_9246,U_9245] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9245,tc_fun(U_9246,tc_HOL_Obool)),U_9247),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9246,tc_HOL_Obool),tc_fun(tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool)),U_9245),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool))),U_9248)),U_9249)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9245,tc_fun(U_9246,tc_HOL_Obool)),U_9247),U_9248)),U_9249),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

cnf(f_2599_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9245,tc_fun(U_9246,tc_HOL_Obool)),U_9247),hAPP(hAPP(c_COMBC(U_9245,tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9246,tc_HOL_Obool),tc_fun(tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool)),U_9245),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool))),U_9248)),U_9249)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9245,tc_fun(U_9246,tc_HOL_Obool)),U_9247),U_9248)),U_9249),
    inference(clausify,[status(thm)],[f_2599_2]) ).

fof(f_2600_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_2600_2,plain,
    ! [U_9254,U_9253,U_9252,U_9251,U_9250] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9250,tc_fun(U_9251,tc_HOL_Obool)),U_9252),hAPP(hAPP(c_COMBB(tc_fun(U_9251,tc_HOL_Obool),tc_fun(U_9251,tc_HOL_Obool),U_9250),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9251,tc_HOL_Obool)),U_9253)),U_9254)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9251,tc_HOL_Obool)),U_9253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9250,tc_fun(U_9251,tc_HOL_Obool)),U_9252),U_9254)),
    inference(variable_rename,[status(thm)],[f_2600_1]) ).

cnf(f_2600_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9250,tc_fun(U_9251,tc_HOL_Obool)),U_9252),hAPP(hAPP(c_COMBB(tc_fun(U_9251,tc_HOL_Obool),tc_fun(U_9251,tc_HOL_Obool),U_9250),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9251,tc_HOL_Obool)),U_9253)),U_9254)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9251,tc_HOL_Obool)),U_9253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9250,tc_fun(U_9251,tc_HOL_Obool)),U_9252),U_9254)),
    inference(clausify,[status(thm)],[f_2600_2]) ).

fof(f_2601_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_2601_2,plain,
    ! [U_9260,U_9259,U_9258,U_9257,U_9256,U_9255] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9255,tc_fun(U_9256,tc_fun(U_9257,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9255,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9256,tc_fun(U_9257,tc_HOL_Obool)),U_9255),hAPP(c_COMBC(U_9256,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9257,tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9257,tc_HOL_Obool)),U_9256),c_COMBC(U_9257,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9257,tc_prod(U_9256,U_9257)),tc_fun(U_9257,tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),U_9256),hAPP(c_COMBB(tc_prod(U_9256,U_9257),tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool),U_9257),c_member(tc_prod(U_9256,U_9257)))),c_Product__Type_OPair(U_9256,U_9257))))),U_9258)),U_9259),U_9260))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9256,U_9257)),hAPP(hAPP(c_Product__Type_OPair(U_9256,U_9257),U_9259),U_9260)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9255,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9255,tc_HOL_Obool))),U_9258))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9256,U_9257)),hAPP(hAPP(c_Product__Type_OPair(U_9256,U_9257),U_9259),U_9260)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9255,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9255,tc_HOL_Obool))),U_9258)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9255,tc_fun(U_9256,tc_fun(U_9257,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9255,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9256,tc_fun(U_9257,tc_HOL_Obool)),U_9255),hAPP(c_COMBC(U_9256,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9257,tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_fun(U_9257,tc_HOL_Obool)),U_9256),c_COMBC(U_9257,tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9257,tc_prod(U_9256,U_9257)),tc_fun(U_9257,tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool)),U_9256),hAPP(c_COMBB(tc_prod(U_9256,U_9257),tc_fun(tc_fun(tc_prod(U_9256,U_9257),tc_HOL_Obool),tc_HOL_Obool),U_9257),c_member(tc_prod(U_9256,U_9257)))),c_Product__Type_OPair(U_9256,U_9257))))),U_9258)),U_9259),U_9260)) ) ),
    inference(variable_rename,[status(thm)],[f_2601_1]) ).

fof(f_2601_3,plain,
    ( ! [U_9272,U_9270,U_9268,U_9266,U_9264,U_9262] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9262,tc_fun(U_9264,tc_fun(U_9266,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9262,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9264,tc_fun(U_9266,tc_HOL_Obool)),U_9262),hAPP(c_COMBC(U_9264,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9266,tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9266,tc_HOL_Obool)),U_9264),c_COMBC(U_9266,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9266,tc_prod(U_9264,U_9266)),tc_fun(U_9266,tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),U_9264),hAPP(c_COMBB(tc_prod(U_9264,U_9266),tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool),U_9266),c_member(tc_prod(U_9264,U_9266)))),c_Product__Type_OPair(U_9264,U_9266))))),U_9268)),U_9270),U_9272))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9264,U_9266)),hAPP(hAPP(c_Product__Type_OPair(U_9264,U_9266),U_9270),U_9272)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9262,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9262,tc_HOL_Obool))),U_9268))) )
    & ! [U_9271,U_9269,U_9267,U_9265,U_9263,U_9261] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9263,U_9265)),hAPP(hAPP(c_Product__Type_OPair(U_9263,U_9265),U_9269),U_9271)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))),U_9267)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9263,tc_fun(U_9265,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9263,tc_fun(U_9265,tc_HOL_Obool)),U_9261),hAPP(c_COMBC(U_9263,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9265,tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9265,tc_HOL_Obool)),U_9263),c_COMBC(U_9265,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9265,tc_prod(U_9263,U_9265)),tc_fun(U_9265,tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),U_9263),hAPP(c_COMBB(tc_prod(U_9263,U_9265),tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool),U_9265),c_member(tc_prod(U_9263,U_9265)))),c_Product__Type_OPair(U_9263,U_9265))))),U_9267)),U_9269),U_9271)) ) ),
    inference(miniscope,[status(thm)],[f_2601_2]) ).

cnf(f_2601_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9263,U_9265)),hAPP(hAPP(c_Product__Type_OPair(U_9263,U_9265),U_9269),U_9271)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))),U_9267)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9263,tc_fun(U_9265,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9263,tc_fun(U_9265,tc_HOL_Obool)),U_9261),hAPP(c_COMBC(U_9263,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9265,tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_fun(U_9265,tc_HOL_Obool)),U_9263),c_COMBC(U_9265,tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9265,tc_prod(U_9263,U_9265)),tc_fun(U_9265,tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool)),U_9263),hAPP(c_COMBB(tc_prod(U_9263,U_9265),tc_fun(tc_fun(tc_prod(U_9263,U_9265),tc_HOL_Obool),tc_HOL_Obool),U_9265),c_member(tc_prod(U_9263,U_9265)))),c_Product__Type_OPair(U_9263,U_9265))))),U_9267)),U_9269),U_9271)) ),
    inference(clausify,[status(thm)],[f_2601_3]) ).

cnf(f_2601_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9262,tc_fun(U_9264,tc_fun(U_9266,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9262,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9264,tc_fun(U_9266,tc_HOL_Obool)),U_9262),hAPP(c_COMBC(U_9264,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9266,tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_fun(U_9266,tc_HOL_Obool)),U_9264),c_COMBC(U_9266,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9266,tc_prod(U_9264,U_9266)),tc_fun(U_9266,tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool)),U_9264),hAPP(c_COMBB(tc_prod(U_9264,U_9266),tc_fun(tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool),tc_HOL_Obool),U_9266),c_member(tc_prod(U_9264,U_9266)))),c_Product__Type_OPair(U_9264,U_9266))))),U_9268)),U_9270),U_9272))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9264,U_9266)),hAPP(hAPP(c_Product__Type_OPair(U_9264,U_9266),U_9270),U_9272)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9262,tc_fun(tc_prod(U_9264,U_9266),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9262,tc_HOL_Obool))),U_9268))) ),
    inference(clausify,[status(thm)],[f_2601_3]) ).

fof(f_2602_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_2602_2,plain,
    ! [U_9279,U_9278,U_9277,U_9276,U_9275] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279)))
          | ? [U_9274] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,U_9274)))
              & hBOOL(hAPP(hAPP(c_member(U_9277),U_9274),U_9278)) ) )
        & ( ! [U_9273] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,U_9273)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9277),U_9273),U_9278)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9275) ),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

fof(f_2602_3,plain,
    ! [U_9279,U_9278,U_9277,U_9276,U_9275] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,sK179(U_9279,U_9278,U_9277,U_9276,U_9275))))
            & hBOOL(hAPP(hAPP(c_member(U_9277),sK179(U_9279,U_9278,U_9277,U_9276,U_9275)),U_9278)) ) )
        & ( ! [U_9273] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,U_9273)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9277),U_9273),U_9278)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9275) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_9274,sK179(U_9279,U_9278,U_9277,U_9276,U_9275))],[f_2602_2]) ).

cnf(f_2602_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,U_9273)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9277),U_9273),U_9278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9275) ),
    inference(clausify,[status(thm)],[f_2602_3]) ).

cnf(f_2602_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9277),sK179(U_9279,U_9278,U_9277,U_9276,U_9275)),U_9278))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9275) ),
    inference(clausify,[status(thm)],[f_2602_3]) ).

cnf(f_2602_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(U_9279,sK179(U_9279,U_9278,U_9277,U_9276,U_9275))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9275),U_9276),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9277,U_9275),U_9278),U_9279)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9275) ),
    inference(clausify,[status(thm)],[f_2602_3]) ).

fof(f_2603_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_2603_2,plain,
    ! [U_9286,U_9285,U_9284,U_9283,U_9282] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286))
          | ! [U_9281] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,U_9281)),U_9286))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9284)) ) )
        & ( ? [U_9280] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,U_9280)),U_9286))
              & hBOOL(hAPP(hAPP(c_member(U_9283),U_9280),U_9284)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286)) ) )
      | ~ class_Orderings_Olinorder(U_9282)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9282) ),
    inference(variable_rename,[status(thm)],[f_2603_1]) ).

fof(f_2603_3,plain,
    ! [U_9286,U_9285,U_9284,U_9283,U_9282] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286))
          | ! [U_9281] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,U_9281)),U_9286))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9284)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,sK180(U_9286,U_9285,U_9284,U_9283,U_9282))),U_9286))
            & hBOOL(hAPP(hAPP(c_member(U_9283),sK180(U_9286,U_9285,U_9284,U_9283,U_9282)),U_9284)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286)) ) )
      | ~ class_Orderings_Olinorder(U_9282)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9282) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_9280,sK180(U_9286,U_9285,U_9284,U_9283,U_9282))],[f_2603_2]) ).

cnf(f_2603_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9283),sK180(U_9286,U_9285,U_9284,U_9283,U_9282)),U_9284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286))
    | ~ class_Orderings_Olinorder(U_9282)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9282) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

cnf(f_2603_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,sK180(U_9286,U_9285,U_9284,U_9283,U_9282))),U_9286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286))
    | ~ class_Orderings_Olinorder(U_9282)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9282) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

cnf(f_2603_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9283,U_9282),U_9284),U_9285)),U_9286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9282),hAPP(U_9285,U_9281)),U_9286))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9284))
    | ~ class_Orderings_Olinorder(U_9282)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9282) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

fof(f_2604_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_2604_2,plain,
    ! [U_9292,U_9291,U_9290,U_9289,U_9288,U_9287] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9287,tc_fun(U_9290,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_COMBB(tc_fun(U_9290,tc_HOL_Obool),tc_fun(U_9290,tc_HOL_Obool),U_9287),hAPP(c_Set_Oinsert(U_9290),U_9291)),U_9292)) = hAPP(hAPP(c_Set_Oinsert(U_9290),U_9291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9287,tc_fun(U_9290,tc_HOL_Obool)),U_9289),U_9292))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9287),U_9288),U_9289)) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

cnf(f_2604_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9287,tc_fun(U_9290,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_COMBB(tc_fun(U_9290,tc_HOL_Obool),tc_fun(U_9290,tc_HOL_Obool),U_9287),hAPP(c_Set_Oinsert(U_9290),U_9291)),U_9292)) = hAPP(hAPP(c_Set_Oinsert(U_9290),U_9291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9287,tc_fun(U_9290,tc_HOL_Obool)),U_9289),U_9292))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9287),U_9288),U_9289)) ),
    inference(clausify,[status(thm)],[f_2604_2]) ).

fof(f_2605_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_2605_2,plain,
    ! [U_9297,U_9296,U_9295,U_9294,U_9293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9296,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9293,tc_fun(U_9296,tc_HOL_Obool)),U_9295),U_9297)),hAPP(U_9297,U_9294)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9293),U_9294),U_9295)) ),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

cnf(f_2605_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9296,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9293,tc_fun(U_9296,tc_HOL_Obool)),U_9295),U_9297)),hAPP(U_9297,U_9294)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9293),U_9294),U_9295)) ),
    inference(clausify,[status(thm)],[f_2605_2]) ).

fof(f_2606_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_2606_2,plain,
    ! [U_9301,U_9300,U_9299,U_9298] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9298,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool),U_9298),hAPP(c_COMBC(U_9299,tc_fun(U_9299,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9299))),U_9300)),U_9301))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9299),U_9301),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9298,tc_HOL_Obool))),U_9300))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9299),U_9301),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9298,tc_HOL_Obool))),U_9300)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9298,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool),U_9298),hAPP(c_COMBC(U_9299,tc_fun(U_9299,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9299))),U_9300)),U_9301)) ) ),
    inference(variable_rename,[status(thm)],[f_2606_1]) ).

fof(f_2606_3,plain,
    ( ! [U_9309,U_9307,U_9305,U_9303] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9303,tc_fun(U_9305,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9303,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool),U_9303),hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305))),U_9307)),U_9309))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9305),U_9309),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9303,tc_fun(U_9305,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9303,tc_HOL_Obool))),U_9307))) )
    & ! [U_9308,U_9306,U_9304,U_9302] :
        ( hBOOL(hAPP(hAPP(c_member(U_9304),U_9308),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9302,tc_fun(U_9304,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9302,tc_HOL_Obool))),U_9306)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9302,tc_fun(U_9304,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9302,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9304,tc_HOL_Obool),tc_fun(U_9304,tc_HOL_Obool),U_9302),hAPP(c_COMBC(U_9304,tc_fun(U_9304,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9304))),U_9306)),U_9308)) ) ),
    inference(miniscope,[status(thm)],[f_2606_2]) ).

cnf(f_2606_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9304),U_9308),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9302,tc_fun(U_9304,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9302,tc_HOL_Obool))),U_9306)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9302,tc_fun(U_9304,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9302,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9304,tc_HOL_Obool),tc_fun(U_9304,tc_HOL_Obool),U_9302),hAPP(c_COMBC(U_9304,tc_fun(U_9304,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9304))),U_9306)),U_9308)) ),
    inference(clausify,[status(thm)],[f_2606_3]) ).

cnf(f_2606_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9303,tc_fun(U_9305,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9303,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9305,tc_HOL_Obool),tc_fun(U_9305,tc_HOL_Obool),U_9303),hAPP(c_COMBC(U_9305,tc_fun(U_9305,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9305))),U_9307)),U_9309))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9305),U_9309),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9303,tc_fun(U_9305,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9303,tc_HOL_Obool))),U_9307))) ),
    inference(clausify,[status(thm)],[f_2606_3]) ).

fof(f_2607_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_2607_2,plain,
    ! [U_9314,U_9313,U_9312,U_9311,U_9310] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9313,tc_HOL_Obool)),hAPP(U_9314,U_9311)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9310,tc_fun(U_9313,tc_HOL_Obool)),U_9312),U_9314)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9310,tc_fun(U_9313,tc_HOL_Obool)),U_9312),U_9314)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9310),U_9311),U_9312)) ),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

cnf(f_2607_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9313,tc_HOL_Obool)),hAPP(U_9314,U_9311)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9310,tc_fun(U_9313,tc_HOL_Obool)),U_9312),U_9314)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9310,tc_fun(U_9313,tc_HOL_Obool)),U_9312),U_9314)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9310),U_9311),U_9312)) ),
    inference(clausify,[status(thm)],[f_2607_2]) ).

fof(f_2608_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_2608_2,plain,
    ! [U_9318,U_9317,U_9316,U_9315] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9317,U_9315),U_9316),hAPP(c_COMBK(U_9315,U_9317),U_9318)) = U_9318
      | U_9316 = c_Orderings_Obot__class_Obot(tc_fun(U_9317,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9315) ),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

cnf(f_2608_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9317,U_9315),U_9316),hAPP(c_COMBK(U_9315,U_9317),U_9318)) = U_9318
    | U_9316 = c_Orderings_Obot__class_Obot(tc_fun(U_9317,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9315) ),
    inference(clausify,[status(thm)],[f_2608_2]) ).

fof(f_2609_1,plain,
    ! [V_ca_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_ca_2)) = V_ca_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_ca_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_2609_2,plain,
    ! [U_9322,U_9321,U_9320,U_9319] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9321,tc_HOL_Obool)),U_9319),hAPP(c_COMBK(tc_fun(U_9321,tc_HOL_Obool),U_9320),U_9322)) = U_9322
        | U_9319 = c_Orderings_Obot__class_Obot(tc_fun(U_9320,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9321,tc_HOL_Obool)),U_9319),hAPP(c_COMBK(tc_fun(U_9321,tc_HOL_Obool),U_9320),U_9322)) = c_Orderings_Otop__class_Otop(tc_fun(U_9321,tc_HOL_Obool))
        | U_9319 != c_Orderings_Obot__class_Obot(tc_fun(U_9320,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

fof(f_2609_3,plain,
    ( ! [U_9330,U_9328,U_9326,U_9324] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),hAPP(c_COMBK(tc_fun(U_9328,tc_HOL_Obool),U_9326),U_9330)) = U_9330
        | U_9324 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool)) )
    & ! [U_9329,U_9327,U_9325,U_9323] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9325,tc_fun(U_9327,tc_HOL_Obool)),U_9323),hAPP(c_COMBK(tc_fun(U_9327,tc_HOL_Obool),U_9325),U_9329)) = c_Orderings_Otop__class_Otop(tc_fun(U_9327,tc_HOL_Obool))
        | U_9323 != c_Orderings_Obot__class_Obot(tc_fun(U_9325,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2609_2]) ).

cnf(f_2609_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9325,tc_fun(U_9327,tc_HOL_Obool)),U_9323),hAPP(c_COMBK(tc_fun(U_9327,tc_HOL_Obool),U_9325),U_9329)) = c_Orderings_Otop__class_Otop(tc_fun(U_9327,tc_HOL_Obool))
    | U_9323 != c_Orderings_Obot__class_Obot(tc_fun(U_9325,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2609_3]) ).

cnf(f_2609_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9326,tc_fun(U_9328,tc_HOL_Obool)),U_9324),hAPP(c_COMBK(tc_fun(U_9328,tc_HOL_Obool),U_9326),U_9330)) = U_9330
    | U_9324 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2609_3]) ).

fof(f_2610_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_2610_2,plain,
    ! [U_9333,U_9332,U_9331] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9331,tc_fun(U_9332,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))),U_9333) = c_Orderings_Otop__class_Otop(tc_fun(U_9332,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

cnf(f_2610_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9331,tc_fun(U_9332,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))),U_9333) = c_Orderings_Otop__class_Otop(tc_fun(U_9332,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2610_2]) ).

fof(f_2611_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_2611_2,plain,
    ! [U_9338,U_9337,U_9336,U_9335,U_9334] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9336,tc_HOL_Obool)),U_9337),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9335,tc_fun(U_9336,tc_HOL_Obool)),U_9334),U_9338)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9335,tc_fun(U_9336,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_COMBB(tc_fun(U_9336,tc_HOL_Obool),tc_fun(U_9336,tc_HOL_Obool),U_9335),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9336,tc_HOL_Obool)),U_9337)),U_9338))
        | U_9334 = c_Orderings_Obot__class_Obot(tc_fun(U_9335,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9336,tc_HOL_Obool)),U_9337),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9335,tc_fun(U_9336,tc_HOL_Obool)),U_9334),U_9338)) = U_9337
        | U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9335,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

fof(f_2611_3,plain,
    ( ! [U_9348,U_9346,U_9344,U_9342,U_9340] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9344,tc_HOL_Obool)),U_9346),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9342,tc_fun(U_9344,tc_HOL_Obool)),U_9340),U_9348)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9342,tc_fun(U_9344,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_COMBB(tc_fun(U_9344,tc_HOL_Obool),tc_fun(U_9344,tc_HOL_Obool),U_9342),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9344,tc_HOL_Obool)),U_9346)),U_9348))
        | U_9340 = c_Orderings_Obot__class_Obot(tc_fun(U_9342,tc_HOL_Obool)) )
    & ! [U_9347,U_9345,U_9343,U_9341,U_9339] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),U_9345),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),U_9347)) = U_9345
        | U_9339 != c_Orderings_Obot__class_Obot(tc_fun(U_9341,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2611_2]) ).

cnf(f_2611_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9343,tc_HOL_Obool)),U_9345),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9341,tc_fun(U_9343,tc_HOL_Obool)),U_9339),U_9347)) = U_9345
    | U_9339 != c_Orderings_Obot__class_Obot(tc_fun(U_9341,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

cnf(f_2611_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9344,tc_HOL_Obool)),U_9346),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9342,tc_fun(U_9344,tc_HOL_Obool)),U_9340),U_9348)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9342,tc_fun(U_9344,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_COMBB(tc_fun(U_9344,tc_HOL_Obool),tc_fun(U_9344,tc_HOL_Obool),U_9342),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9344,tc_HOL_Obool)),U_9346)),U_9348))
    | U_9340 = c_Orderings_Obot__class_Obot(tc_fun(U_9342,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

fof(f_2612_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_2612_2,plain,
    ! [U_9353,U_9352,U_9351,U_9350,U_9349] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9350,tc_fun(U_9351,tc_HOL_Obool)),U_9349),U_9352)),U_9353) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9350,tc_fun(U_9351,tc_HOL_Obool)),U_9349),hAPP(hAPP(c_COMBC(U_9350,tc_fun(U_9351,tc_HOL_Obool),tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9351,tc_HOL_Obool),tc_fun(tc_fun(U_9351,tc_HOL_Obool),tc_fun(U_9351,tc_HOL_Obool)),U_9350),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool))),U_9352)),U_9353))
        | U_9349 = c_Orderings_Obot__class_Obot(tc_fun(U_9350,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9351,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9350,tc_fun(U_9351,tc_HOL_Obool)),U_9349),U_9352)),U_9353) = U_9353
        | U_9349 != c_Orderings_Obot__class_Obot(tc_fun(U_9350,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

fof(f_2612_3,plain,
    ( ! [U_9363,U_9361,U_9359,U_9357,U_9355] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9357,tc_fun(U_9359,tc_HOL_Obool)),U_9355),U_9361)),U_9363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9357,tc_fun(U_9359,tc_HOL_Obool)),U_9355),hAPP(hAPP(c_COMBC(U_9357,tc_fun(U_9359,tc_HOL_Obool),tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9359,tc_HOL_Obool),tc_fun(tc_fun(U_9359,tc_HOL_Obool),tc_fun(U_9359,tc_HOL_Obool)),U_9357),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool))),U_9361)),U_9363))
        | U_9355 = c_Orderings_Obot__class_Obot(tc_fun(U_9357,tc_HOL_Obool)) )
    & ! [U_9362,U_9360,U_9358,U_9356,U_9354] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9358,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),U_9360)),U_9362) = U_9362
        | U_9354 != c_Orderings_Obot__class_Obot(tc_fun(U_9356,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2612_2]) ).

cnf(f_2612_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9358,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9356,tc_fun(U_9358,tc_HOL_Obool)),U_9354),U_9360)),U_9362) = U_9362
    | U_9354 != c_Orderings_Obot__class_Obot(tc_fun(U_9356,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2612_3]) ).

cnf(f_2612_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9357,tc_fun(U_9359,tc_HOL_Obool)),U_9355),U_9361)),U_9363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9357,tc_fun(U_9359,tc_HOL_Obool)),U_9355),hAPP(hAPP(c_COMBC(U_9357,tc_fun(U_9359,tc_HOL_Obool),tc_fun(U_9359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9359,tc_HOL_Obool),tc_fun(tc_fun(U_9359,tc_HOL_Obool),tc_fun(U_9359,tc_HOL_Obool)),U_9357),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9359,tc_HOL_Obool))),U_9361)),U_9363))
    | U_9355 = c_Orderings_Obot__class_Obot(tc_fun(U_9357,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2612_3]) ).

fof(f_2613_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_2613_2,plain,
    ! [U_9368,U_9367,U_9366,U_9365,U_9364] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9364,tc_fun(U_9365,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9364),U_9366),U_9367)),U_9368) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9365,tc_HOL_Obool)),hAPP(U_9368,U_9366)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9364,tc_fun(U_9365,tc_HOL_Obool)),U_9367),U_9368)),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

cnf(f_2613_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9364,tc_fun(U_9365,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9364),U_9366),U_9367)),U_9368) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9365,tc_HOL_Obool)),hAPP(U_9368,U_9366)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9364,tc_fun(U_9365,tc_HOL_Obool)),U_9367),U_9368)),
    inference(clausify,[status(thm)],[f_2613_2]) ).

fof(f_2614_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_2614_2,plain,
    ! [U_9373,U_9372,U_9371,U_9370,U_9369] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9369,tc_HOL_Obool)),U_9371),U_9372)),U_9373) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9370,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),U_9371),U_9373)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),U_9372),U_9373)),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

cnf(f_2614_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9369,tc_HOL_Obool)),U_9371),U_9372)),U_9373) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9370,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),U_9371),U_9373)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9369,tc_fun(U_9370,tc_HOL_Obool)),U_9372),U_9373)),
    inference(clausify,[status(thm)],[f_2614_2]) ).

fof(f_2615_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_2615_2,plain,
    ! [U_9376,U_9375,U_9374] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9374,tc_HOL_Obool)),U_9375),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9374,tc_HOL_Obool),U_9376)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9374,tc_HOL_Obool),tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9374,tc_HOL_Obool)),U_9375)),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

cnf(f_2615_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9374,tc_HOL_Obool)),U_9375),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9374,tc_HOL_Obool),U_9376)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9374,tc_HOL_Obool),tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9374,tc_HOL_Obool)),U_9375)),
    inference(clausify,[status(thm)],[f_2615_2]) ).

fof(f_2616_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_2616_2,plain,
    ! [U_9379,U_9378,U_9377] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_9377,U_9378,U_9379) = c_Orderings_Obot__class_Obot(tc_fun(U_9377,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9377),U_9378),U_9379)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9377),U_9378),U_9379))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_9377,U_9378,U_9379) != c_Orderings_Obot__class_Obot(tc_fun(U_9377,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_9377) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

cnf(f_2616_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9377),U_9378),U_9379))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_9377,U_9378,U_9379) != c_Orderings_Obot__class_Obot(tc_fun(U_9377,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9377) ),
    inference(clausify,[status(thm)],[f_2616_2]) ).

cnf(f_2616_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_9377,U_9378,U_9379) = c_Orderings_Obot__class_Obot(tc_fun(U_9377,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9377),U_9378),U_9379))
    | ~ class_Orderings_Oorder(U_9377) ),
    inference(clausify,[status(thm)],[f_2616_2]) ).

fof(f_2617_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_2617_2,plain,
    ! [U_9382,U_9381,U_9380] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_9380,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9380,U_9381,U_9382)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9380),U_9381),U_9382)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9380),U_9381),U_9382))
          | c_Orderings_Obot__class_Obot(tc_fun(U_9380,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_9380,U_9381,U_9382) ) )
      | ~ class_Orderings_Oorder(U_9380) ),
    inference(variable_rename,[status(thm)],[f_2617_1]) ).

cnf(f_2617_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9380),U_9381),U_9382))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9380,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_9380,U_9381,U_9382)
    | ~ class_Orderings_Oorder(U_9380) ),
    inference(clausify,[status(thm)],[f_2617_2]) ).

cnf(f_2617_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_9380,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9380,U_9381,U_9382)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9380),U_9381),U_9382))
    | ~ class_Orderings_Oorder(U_9380) ),
    inference(clausify,[status(thm)],[f_2617_2]) ).

fof(f_2618_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_2618_2,plain,
    ! [U_9385,U_9384,U_9383] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_9383,U_9385,U_9384) = c_Orderings_Obot__class_Obot(tc_fun(U_9383,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9383),U_9384),U_9385))
      | ~ class_Orderings_Oorder(U_9383) ),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

cnf(f_2618_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_9383,U_9385,U_9384) = c_Orderings_Obot__class_Obot(tc_fun(U_9383,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9383),U_9384),U_9385))
    | ~ class_Orderings_Oorder(U_9383) ),
    inference(clausify,[status(thm)],[f_2618_2]) ).

fof(f_2619_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_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_ca_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_ca_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(f_2619_2,plain,
    ! [U_9390,U_9389,U_9388,U_9387,U_9386] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9388),U_9390))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9389),U_9387)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9387),U_9388)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9388),U_9390))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9389),U_9387)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9387),U_9388))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390))) ) )
      | ~ class_Orderings_Oorder(U_9386) ),
    inference(variable_rename,[status(thm)],[f_2619_1]) ).

cnf(f_2619_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9389),U_9387))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9387),U_9388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390)))
    | ~ class_Orderings_Oorder(U_9386) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

cnf(f_2619_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9388),U_9390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9387),U_9388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390)))
    | ~ class_Orderings_Oorder(U_9386) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

cnf(f_2619_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9387),U_9388))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390)))
    | ~ class_Orderings_Oorder(U_9386) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

cnf(f_2619_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9388),U_9390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9386),U_9389),U_9387))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9386,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9387,U_9388)),c_SetInterval_Oord__class_OatLeastAtMost(U_9386,U_9389,U_9390)))
    | ~ class_Orderings_Oorder(U_9386) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

fof(f_2620_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_2620_2,plain,
    ! [U_9393,U_9392,U_9391] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_9391,U_9392,U_9393) = hAPP(hAPP(c_Set_Oinsert(U_9391),U_9392),c_Orderings_Obot__class_Obot(tc_fun(U_9391,tc_HOL_Obool)))
      | U_9392 != U_9393
      | ~ class_Orderings_Oorder(U_9391) ),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

cnf(f_2620_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_9391,U_9392,U_9393) = hAPP(hAPP(c_Set_Oinsert(U_9391),U_9392),c_Orderings_Obot__class_Obot(tc_fun(U_9391,tc_HOL_Obool)))
    | U_9392 != U_9393
    | ~ class_Orderings_Oorder(U_9391) ),
    inference(clausify,[status(thm)],[f_2620_2]) ).

fof(f_2621_1,plain,
    ! [V_ca_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_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
          | V_b_2 != V_ca_2
          | V_a_2 != V_b_2 )
        & ( ( V_b_2 = V_ca_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_ca_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_2621_2,plain,
    ! [U_9397,U_9396,U_9395,U_9394] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_9394,U_9395,U_9396) = hAPP(hAPP(c_Set_Oinsert(U_9394),U_9397),c_Orderings_Obot__class_Obot(tc_fun(U_9394,tc_HOL_Obool)))
          | U_9396 != U_9397
          | U_9395 != U_9396 )
        & ( ( U_9396 = U_9397
            & U_9395 = U_9396 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_9394,U_9395,U_9396) != hAPP(hAPP(c_Set_Oinsert(U_9394),U_9397),c_Orderings_Obot__class_Obot(tc_fun(U_9394,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_9394) ),
    inference(variable_rename,[status(thm)],[f_2621_1]) ).

cnf(f_2621_3,plain,
    ( U_9395 = U_9396
    | c_SetInterval_Oord__class_OatLeastAtMost(U_9394,U_9395,U_9396) != hAPP(hAPP(c_Set_Oinsert(U_9394),U_9397),c_Orderings_Obot__class_Obot(tc_fun(U_9394,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_9394) ),
    inference(clausify,[status(thm)],[f_2621_2]) ).

cnf(f_2621_4,plain,
    ( U_9396 = U_9397
    | c_SetInterval_Oord__class_OatLeastAtMost(U_9394,U_9395,U_9396) != hAPP(hAPP(c_Set_Oinsert(U_9394),U_9397),c_Orderings_Obot__class_Obot(tc_fun(U_9394,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_9394) ),
    inference(clausify,[status(thm)],[f_2621_2]) ).

cnf(f_2621_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_9394,U_9395,U_9396) = hAPP(hAPP(c_Set_Oinsert(U_9394),U_9397),c_Orderings_Obot__class_Obot(tc_fun(U_9394,tc_HOL_Obool)))
    | U_9396 != U_9397
    | U_9395 != U_9396
    | ~ class_Orderings_Oorder(U_9394) ),
    inference(clausify,[status(thm)],[f_2621_2]) ).

fof(f_2622_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_2622_2,plain,
    ! [U_9399,U_9398] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_9398,U_9399,U_9399) = hAPP(hAPP(c_Set_Oinsert(U_9398),U_9399),c_Orderings_Obot__class_Obot(tc_fun(U_9398,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_9398) ),
    inference(variable_rename,[status(thm)],[f_2622_1]) ).

cnf(f_2622_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_9398,U_9399,U_9399) = hAPP(hAPP(c_Set_Oinsert(U_9398),U_9399),c_Orderings_Obot__class_Obot(tc_fun(U_9398,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_9398) ),
    inference(clausify,[status(thm)],[f_2622_2]) ).

fof(f_2623_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_2623_2,plain,
    ! [U_9403,U_9402,U_9401,U_9400] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9400),U_9401),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9402),hAPP(c_Nat_OSuc,U_9403))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9400),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9400,tc_Nat_Onat),U_9401),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9402,U_9403))
      | ~ class_Groups_Ocomm__monoid__add(U_9400) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

cnf(f_2623_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9400),U_9401),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9402),hAPP(c_Nat_OSuc,U_9403))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9400),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9400,tc_Nat_Onat),U_9401),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9402,U_9403))
    | ~ class_Groups_Ocomm__monoid__add(U_9400) ),
    inference(clausify,[status(thm)],[f_2623_2]) ).

fof(f_2624_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_2624_2,plain,
    ! [U_9408,U_9407,U_9406,U_9405,U_9404] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9404),U_9405),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9406),U_9407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9408),U_9407))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9404),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9404,tc_Nat_Onat),U_9405),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9407))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9406,U_9408))
      | ~ class_Groups_Ocomm__monoid__add(U_9404) ),
    inference(variable_rename,[status(thm)],[f_2624_1]) ).

cnf(f_2624_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9404),U_9405),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9406),U_9407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9408),U_9407))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9404),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9404,tc_Nat_Onat),U_9405),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9407))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9406,U_9408))
    | ~ class_Groups_Ocomm__monoid__add(U_9404) ),
    inference(clausify,[status(thm)],[f_2624_2]) ).

fof(f_2625_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_2625_2,plain,
    ! [U_9413,U_9412,U_9411,U_9410,U_9409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9409),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9410,U_9409),U_9412),U_9413)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9410,U_9409),U_9411),U_9413)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9410,tc_HOL_Obool)),U_9411),U_9412))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9409) ),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

cnf(f_2625_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9409),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9410,U_9409),U_9412),U_9413)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9410,U_9409),U_9411),U_9413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9410,tc_HOL_Obool)),U_9411),U_9412))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9409) ),
    inference(clausify,[status(thm)],[f_2625_2]) ).

fof(f_2626_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_2626_2,plain,
    ! [U_9418,U_9417,U_9416,U_9415,U_9414] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9415,tc_fun(U_9416,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_COMBB(tc_fun(U_9416,tc_HOL_Obool),tc_fun(U_9416,tc_HOL_Obool),U_9415),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9416,tc_HOL_Obool)),U_9417)),U_9418)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9415,tc_fun(U_9416,tc_HOL_Obool)),U_9414),U_9418))
        | U_9414 = c_Orderings_Obot__class_Obot(tc_fun(U_9415,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9415,tc_fun(U_9416,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_COMBB(tc_fun(U_9416,tc_HOL_Obool),tc_fun(U_9416,tc_HOL_Obool),U_9415),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9416,tc_HOL_Obool)),U_9417)),U_9418)) = c_Orderings_Otop__class_Otop(tc_fun(U_9416,tc_HOL_Obool))
        | U_9414 != c_Orderings_Obot__class_Obot(tc_fun(U_9415,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

fof(f_2626_3,plain,
    ( ! [U_9428,U_9426,U_9424,U_9422,U_9420] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_HOL_Obool)),U_9420),hAPP(hAPP(c_COMBB(tc_fun(U_9424,tc_HOL_Obool),tc_fun(U_9424,tc_HOL_Obool),U_9422),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426)),U_9428)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_HOL_Obool)),U_9420),U_9428))
        | U_9420 = c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool)) )
    & ! [U_9427,U_9425,U_9423,U_9421,U_9419] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9421,tc_fun(U_9423,tc_HOL_Obool)),U_9419),hAPP(hAPP(c_COMBB(tc_fun(U_9423,tc_HOL_Obool),tc_fun(U_9423,tc_HOL_Obool),U_9421),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9423,tc_HOL_Obool)),U_9425)),U_9427)) = c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))
        | U_9419 != c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2626_2]) ).

cnf(f_2626_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9421,tc_fun(U_9423,tc_HOL_Obool)),U_9419),hAPP(hAPP(c_COMBB(tc_fun(U_9423,tc_HOL_Obool),tc_fun(U_9423,tc_HOL_Obool),U_9421),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9423,tc_HOL_Obool)),U_9425)),U_9427)) = c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))
    | U_9419 != c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2626_3]) ).

cnf(f_2626_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_HOL_Obool)),U_9420),hAPP(hAPP(c_COMBB(tc_fun(U_9424,tc_HOL_Obool),tc_fun(U_9424,tc_HOL_Obool),U_9422),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426)),U_9428)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9424,tc_HOL_Obool)),U_9426),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_HOL_Obool)),U_9420),U_9428))
    | U_9420 = c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2626_3]) ).

fof(f_2627_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_2627_2,plain,
    ! [U_9433,U_9432,U_9431,U_9430,U_9429] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9430,tc_fun(U_9431,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_COMBC(U_9430,tc_fun(U_9431,tc_HOL_Obool),tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9431,tc_HOL_Obool),tc_fun(tc_fun(U_9431,tc_HOL_Obool),tc_fun(U_9431,tc_HOL_Obool)),U_9430),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool))),U_9432)),U_9433)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9430,tc_fun(U_9431,tc_HOL_Obool)),U_9429),U_9432)),U_9433)
        | U_9429 = c_Orderings_Obot__class_Obot(tc_fun(U_9430,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9430,tc_fun(U_9431,tc_HOL_Obool)),U_9429),hAPP(hAPP(c_COMBC(U_9430,tc_fun(U_9431,tc_HOL_Obool),tc_fun(U_9431,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9431,tc_HOL_Obool),tc_fun(tc_fun(U_9431,tc_HOL_Obool),tc_fun(U_9431,tc_HOL_Obool)),U_9430),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9431,tc_HOL_Obool))),U_9432)),U_9433)) = c_Orderings_Otop__class_Otop(tc_fun(U_9431,tc_HOL_Obool))
        | U_9429 != c_Orderings_Obot__class_Obot(tc_fun(U_9430,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

fof(f_2627_3,plain,
    ( ! [U_9443,U_9441,U_9439,U_9437,U_9435] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9437,tc_fun(U_9439,tc_HOL_Obool)),U_9435),hAPP(hAPP(c_COMBC(U_9437,tc_fun(U_9439,tc_HOL_Obool),tc_fun(U_9439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9439,tc_HOL_Obool),tc_fun(tc_fun(U_9439,tc_HOL_Obool),tc_fun(U_9439,tc_HOL_Obool)),U_9437),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9439,tc_HOL_Obool))),U_9441)),U_9443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9439,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9437,tc_fun(U_9439,tc_HOL_Obool)),U_9435),U_9441)),U_9443)
        | U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9437,tc_HOL_Obool)) )
    & ! [U_9442,U_9440,U_9438,U_9436,U_9434] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9436,tc_fun(U_9438,tc_HOL_Obool)),U_9434),hAPP(hAPP(c_COMBC(U_9436,tc_fun(U_9438,tc_HOL_Obool),tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9438,tc_HOL_Obool),tc_fun(tc_fun(U_9438,tc_HOL_Obool),tc_fun(U_9438,tc_HOL_Obool)),U_9436),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9438,tc_HOL_Obool))),U_9440)),U_9442)) = c_Orderings_Otop__class_Otop(tc_fun(U_9438,tc_HOL_Obool))
        | U_9434 != c_Orderings_Obot__class_Obot(tc_fun(U_9436,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2627_2]) ).

cnf(f_2627_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9436,tc_fun(U_9438,tc_HOL_Obool)),U_9434),hAPP(hAPP(c_COMBC(U_9436,tc_fun(U_9438,tc_HOL_Obool),tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9438,tc_HOL_Obool),tc_fun(tc_fun(U_9438,tc_HOL_Obool),tc_fun(U_9438,tc_HOL_Obool)),U_9436),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9438,tc_HOL_Obool))),U_9440)),U_9442)) = c_Orderings_Otop__class_Otop(tc_fun(U_9438,tc_HOL_Obool))
    | U_9434 != c_Orderings_Obot__class_Obot(tc_fun(U_9436,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2627_3]) ).

cnf(f_2627_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9437,tc_fun(U_9439,tc_HOL_Obool)),U_9435),hAPP(hAPP(c_COMBC(U_9437,tc_fun(U_9439,tc_HOL_Obool),tc_fun(U_9439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9439,tc_HOL_Obool),tc_fun(tc_fun(U_9439,tc_HOL_Obool),tc_fun(U_9439,tc_HOL_Obool)),U_9437),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9439,tc_HOL_Obool))),U_9441)),U_9443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9439,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9437,tc_fun(U_9439,tc_HOL_Obool)),U_9435),U_9441)),U_9443)
    | U_9435 = c_Orderings_Obot__class_Obot(tc_fun(U_9437,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2627_3]) ).

fof(f_2628_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_2628_2,plain,
    ! [U_9448,U_9447,U_9446,U_9445,U_9444] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9445,tc_fun(U_9446,tc_HOL_Obool)),U_9444),hAPP(hAPP(c_COMBC(U_9445,tc_fun(U_9446,tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_HOL_Obool),tc_fun(tc_fun(U_9446,tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),U_9445),c_Groups_Ominus__class_Ominus(tc_fun(U_9446,tc_HOL_Obool))),U_9447)),U_9448)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9445,tc_fun(U_9446,tc_HOL_Obool)),U_9444),U_9447)),U_9448)
        | U_9444 = c_Orderings_Obot__class_Obot(tc_fun(U_9445,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9445,tc_fun(U_9446,tc_HOL_Obool)),U_9444),hAPP(hAPP(c_COMBC(U_9445,tc_fun(U_9446,tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_HOL_Obool),tc_fun(tc_fun(U_9446,tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),U_9445),c_Groups_Ominus__class_Ominus(tc_fun(U_9446,tc_HOL_Obool))),U_9447)),U_9448)) = c_Orderings_Otop__class_Otop(tc_fun(U_9446,tc_HOL_Obool))
        | U_9444 != c_Orderings_Obot__class_Obot(tc_fun(U_9445,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

fof(f_2628_3,plain,
    ( ! [U_9458,U_9456,U_9454,U_9452,U_9450] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9454,tc_HOL_Obool)),U_9450),hAPP(hAPP(c_COMBC(U_9452,tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9454,tc_HOL_Obool),tc_fun(tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),U_9452),c_Groups_Ominus__class_Ominus(tc_fun(U_9454,tc_HOL_Obool))),U_9456)),U_9458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9454,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9454,tc_HOL_Obool)),U_9450),U_9456)),U_9458)
        | U_9450 = c_Orderings_Obot__class_Obot(tc_fun(U_9452,tc_HOL_Obool)) )
    & ! [U_9457,U_9455,U_9453,U_9451,U_9449] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9451,tc_fun(U_9453,tc_HOL_Obool)),U_9449),hAPP(hAPP(c_COMBC(U_9451,tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9453,tc_HOL_Obool),tc_fun(tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool)),U_9451),c_Groups_Ominus__class_Ominus(tc_fun(U_9453,tc_HOL_Obool))),U_9455)),U_9457)) = c_Orderings_Otop__class_Otop(tc_fun(U_9453,tc_HOL_Obool))
        | U_9449 != c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2628_2]) ).

cnf(f_2628_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9451,tc_fun(U_9453,tc_HOL_Obool)),U_9449),hAPP(hAPP(c_COMBC(U_9451,tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9453,tc_HOL_Obool),tc_fun(tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool)),U_9451),c_Groups_Ominus__class_Ominus(tc_fun(U_9453,tc_HOL_Obool))),U_9455)),U_9457)) = c_Orderings_Otop__class_Otop(tc_fun(U_9453,tc_HOL_Obool))
    | U_9449 != c_Orderings_Obot__class_Obot(tc_fun(U_9451,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2628_3]) ).

cnf(f_2628_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9454,tc_HOL_Obool)),U_9450),hAPP(hAPP(c_COMBC(U_9452,tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9454,tc_HOL_Obool),tc_fun(tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),U_9452),c_Groups_Ominus__class_Ominus(tc_fun(U_9454,tc_HOL_Obool))),U_9456)),U_9458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9454,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9454,tc_HOL_Obool)),U_9450),U_9456)),U_9458)
    | U_9450 = c_Orderings_Obot__class_Obot(tc_fun(U_9452,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2628_3]) ).

fof(f_2629_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_2629_2,plain,
    ! [U_9463,U_9462,U_9461,U_9460,U_9459] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9461,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9460,tc_fun(U_9461,tc_HOL_Obool)),U_9459),U_9462)),U_9463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9460,tc_fun(U_9461,tc_HOL_Obool)),U_9459),hAPP(hAPP(c_COMBC(U_9460,tc_fun(U_9461,tc_HOL_Obool),tc_fun(U_9461,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9461,tc_HOL_Obool),tc_fun(tc_fun(U_9461,tc_HOL_Obool),tc_fun(U_9461,tc_HOL_Obool)),U_9460),c_Groups_Ominus__class_Ominus(tc_fun(U_9461,tc_HOL_Obool))),U_9462)),U_9463))
        | U_9459 = c_Orderings_Obot__class_Obot(tc_fun(U_9460,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9461,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9460,tc_fun(U_9461,tc_HOL_Obool)),U_9459),U_9462)),U_9463) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9461,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9461,tc_HOL_Obool))),U_9463)
        | U_9459 != c_Orderings_Obot__class_Obot(tc_fun(U_9460,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2629_1]) ).

fof(f_2629_3,plain,
    ( ! [U_9473,U_9471,U_9469,U_9467,U_9465] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9469,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9467,tc_fun(U_9469,tc_HOL_Obool)),U_9465),U_9471)),U_9473) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9467,tc_fun(U_9469,tc_HOL_Obool)),U_9465),hAPP(hAPP(c_COMBC(U_9467,tc_fun(U_9469,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9469,tc_HOL_Obool),tc_fun(tc_fun(U_9469,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool)),U_9467),c_Groups_Ominus__class_Ominus(tc_fun(U_9469,tc_HOL_Obool))),U_9471)),U_9473))
        | U_9465 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool)) )
    & ! [U_9472,U_9470,U_9468,U_9466,U_9464] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9468,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9468,tc_HOL_Obool)),U_9464),U_9470)),U_9472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9468,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9468,tc_HOL_Obool))),U_9472)
        | U_9464 != c_Orderings_Obot__class_Obot(tc_fun(U_9466,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2629_2]) ).

cnf(f_2629_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9468,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9468,tc_HOL_Obool)),U_9464),U_9470)),U_9472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9468,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9468,tc_HOL_Obool))),U_9472)
    | U_9464 != c_Orderings_Obot__class_Obot(tc_fun(U_9466,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2629_3]) ).

cnf(f_2629_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9469,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9467,tc_fun(U_9469,tc_HOL_Obool)),U_9465),U_9471)),U_9473) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9467,tc_fun(U_9469,tc_HOL_Obool)),U_9465),hAPP(hAPP(c_COMBC(U_9467,tc_fun(U_9469,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9469,tc_HOL_Obool),tc_fun(tc_fun(U_9469,tc_HOL_Obool),tc_fun(U_9469,tc_HOL_Obool)),U_9467),c_Groups_Ominus__class_Ominus(tc_fun(U_9469,tc_HOL_Obool))),U_9471)),U_9473))
    | U_9465 = c_Orderings_Obot__class_Obot(tc_fun(U_9467,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2629_3]) ).

fof(f_2630_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_2630_2,plain,
    ! [U_9475,U_9474] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9474,U_9475)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9475)),U_9474),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

cnf(f_2630_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9474,U_9475)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9475)),U_9474),
    inference(clausify,[status(thm)],[f_2630_2]) ).

fof(f_2631_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_2631_2,plain,
    ! [U_9477,U_9476] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9476,hAPP(c_Nat_OSuc,U_9477)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9477)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9476,U_9477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9476),hAPP(c_Nat_OSuc,U_9477))) ),
    inference(variable_rename,[status(thm)],[f_2631_1]) ).

cnf(f_2631_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9476,hAPP(c_Nat_OSuc,U_9477)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9477)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9476,U_9477))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9476),hAPP(c_Nat_OSuc,U_9477))) ),
    inference(clausify,[status(thm)],[f_2631_2]) ).

fof(f_2632_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_2632_2,plain,
    ! [U_9482,U_9481,U_9480,U_9479,U_9478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9478),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9478),U_9481),U_9482)),hAPP(U_9482,U_9480)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9479),U_9480),U_9481))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9478) ),
    inference(variable_rename,[status(thm)],[f_2632_1]) ).

cnf(f_2632_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9478),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9478),U_9481),U_9482)),hAPP(U_9482,U_9480)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9479),U_9480),U_9481))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9478) ),
    inference(clausify,[status(thm)],[f_2632_2]) ).

fof(f_2633_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_2633_2,plain,
    ! [U_9484,U_9483] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_9483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9484)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_9483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9484))
      | hAPP(U_9483,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

cnf(f_2633_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_9483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9484)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_9483),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9484))
    | hAPP(U_9483,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2633_2]) ).

fof(f_2634_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_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_2634_2,plain,
    ! [U_9489,U_9488,U_9487,U_9486,U_9485] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9485,U_9486,U_9487)),c_SetInterval_Oord__class_OatLeastAtMost(U_9485,U_9488,U_9489)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9485,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9485),U_9486),U_9488),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9485),U_9487),U_9489))
      | ~ class_Orderings_Olinorder(U_9485) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

cnf(f_2634_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9485,U_9486,U_9487)),c_SetInterval_Oord__class_OatLeastAtMost(U_9485,U_9488,U_9489)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9485,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9485),U_9486),U_9488),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9485),U_9487),U_9489))
    | ~ class_Orderings_Olinorder(U_9485) ),
    inference(clausify,[status(thm)],[f_2634_2]) ).

fof(f_2635_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(f_2635_2,plain,
    ! [U_9494,U_9493,U_9492,U_9491,U_9490] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9492),U_9494))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9493),U_9491)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9492),U_9494))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9491)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9492),U_9494))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9493),U_9491)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9492),U_9494))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9491)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494))) ) )
      | ~ class_Orderings_Oorder(U_9490) ),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

cnf(f_2635_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9492),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9492),U_9494))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9493),U_9491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9491),U_9492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9493),U_9491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9492),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

cnf(f_2635_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9490),U_9492),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9492),U_9494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9490),U_9493),U_9494))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9490,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9491,U_9492)),c_SetInterval_Oord__class_OatLeastAtMost(U_9490,U_9493,U_9494)))
    | ~ class_Orderings_Oorder(U_9490) ),
    inference(clausify,[status(thm)],[f_2635_2]) ).

fof(f_2636_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_2636_2,plain,
    ! [U_9497,U_9496,U_9495] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9495,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9495),U_9496)),c_SetInterval_Oord__class_OatLeastAtMost(U_9495,U_9496,U_9497)) = c_Orderings_Obot__class_Obot(tc_fun(U_9495,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9495) ),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

cnf(f_2636_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9495,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_9495),U_9496)),c_SetInterval_Oord__class_OatLeastAtMost(U_9495,U_9496,U_9497)) = c_Orderings_Obot__class_Obot(tc_fun(U_9495,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9495) ),
    inference(clausify,[status(thm)],[f_2636_2]) ).

fof(f_2637_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_2637_2,plain,
    ! [U_9501,U_9500,U_9499,U_9498] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9498),U_9501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9499,U_9500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9498),hAPP(U_9501,U_9499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9498),U_9501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9499),U_9500)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9499),U_9500))
      | ~ class_Groups_Ocomm__monoid__add(U_9498) ),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

cnf(f_2637_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9498),U_9501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9499,U_9500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9498),hAPP(U_9501,U_9499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9498),U_9501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9499),U_9500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9499),U_9500))
    | ~ class_Groups_Ocomm__monoid__add(U_9498) ),
    inference(clausify,[status(thm)],[f_2637_2]) ).

fof(f_2638_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_2638_2,plain,
    ! [U_9505,U_9504,U_9503,U_9502] :
      ( 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_9502),U_9504)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9503),U_9505))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9502),U_9503)) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

cnf(f_2638_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_9502),U_9504)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9503),U_9505))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9502),U_9503)) ),
    inference(clausify,[status(thm)],[f_2638_2]) ).

fof(f_2639_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_2639_2,plain,
    ! [U_9509,U_9508,U_9507,U_9506] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,hAPP(c_Nat_OSuc,U_9507))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9506),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,U_9507))),hAPP(U_9509,hAPP(c_Nat_OSuc,U_9507)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9507)),U_9508)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,hAPP(c_Nat_OSuc,U_9507))) = c_Groups_Ozero__class_Ozero(U_9506)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9507)),U_9508)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_9506) ),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

cnf(f_2639_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,hAPP(c_Nat_OSuc,U_9507))) = c_Groups_Ozero__class_Ozero(U_9506)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9507)),U_9508))
    | ~ class_Groups_Ocomm__monoid__add(U_9506) ),
    inference(clausify,[status(thm)],[f_2639_2]) ).

cnf(f_2639_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,hAPP(c_Nat_OSuc,U_9507))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9506),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9506),U_9509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9508,U_9507))),hAPP(U_9509,hAPP(c_Nat_OSuc,U_9507)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9507)),U_9508))
    | ~ class_Groups_Ocomm__monoid__add(U_9506) ),
    inference(clausify,[status(thm)],[f_2639_2]) ).

fof(f_2640_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_2640_2,plain,
    ! [U_9514,U_9513,U_9512,U_9511,U_9510] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9510),U_9513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9511,U_9510),U_9512),U_9514)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9511,U_9510,hAPP(hAPP(c_COMBB(U_9510,tc_fun(U_9510,U_9510),U_9511),c_Lattices_Osemilattice__inf__class_Oinf(U_9510)),U_9514)),U_9513),U_9512)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9511),U_9512))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9510) ),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

cnf(f_2640_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9510),U_9513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9511,U_9510),U_9512),U_9514)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9511,U_9510,hAPP(hAPP(c_COMBB(U_9510,tc_fun(U_9510,U_9510),U_9511),c_Lattices_Osemilattice__inf__class_Oinf(U_9510)),U_9514)),U_9513),U_9512)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9511),U_9512))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9510) ),
    inference(clausify,[status(thm)],[f_2640_2]) ).

fof(f_2641_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_2641_2,plain,
    ! [U_9519,U_9518,U_9517,U_9516,U_9515] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9516,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),U_9519))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9515),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9516,U_9517))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),U_9519))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_9515) ),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

cnf(f_2641_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9516,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),U_9519))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9515),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9516,U_9517))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9515),U_9518),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),U_9519))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9517),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_9515) ),
    inference(clausify,[status(thm)],[f_2641_2]) ).

fof(f_2642_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_2642_2,plain,
    ! [U_9525,U_9524] :
      ( ( ? [U_9523] :
            ( hBOOL(hAPP(U_9525,U_9523))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9523),U_9524)) )
        | ! [U_9522] :
            ( ~ hBOOL(hAPP(U_9525,U_9522))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9524))) ) )
      & ( ? [U_9521] :
            ( hBOOL(hAPP(U_9525,U_9521))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9521),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9524))) )
        | ! [U_9520] :
            ( ~ hBOOL(hAPP(U_9525,U_9520))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9524)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

fof(f_2642_3,plain,
    ( ! [U_9529,U_9527] :
        ( ? [U_9523] :
            ( hBOOL(hAPP(U_9529,U_9523))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9523),U_9527)) )
        | ! [U_9522] :
            ( ~ hBOOL(hAPP(U_9529,U_9522))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9527))) ) )
    & ! [U_9528,U_9526] :
        ( ? [U_9521] :
            ( hBOOL(hAPP(U_9528,U_9521))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9521),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9526))) )
        | ! [U_9520] :
            ( ~ hBOOL(hAPP(U_9528,U_9520))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9526)) ) ) ),
    inference(miniscope,[status(thm)],[f_2642_2]) ).

fof(f_2642_4,plain,
    ( ! [U_9529,U_9527] :
        ( ? [U_9523] :
            ( hBOOL(hAPP(U_9529,U_9523))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9523),U_9527)) )
        | ! [U_9522] :
            ( ~ hBOOL(hAPP(U_9529,U_9522))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9527))) ) )
    & ! [U_9528,U_9526] :
        ( ( hBOOL(hAPP(U_9528,sK181(U_9528,U_9526)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK181(U_9528,U_9526)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9526))) )
        | ! [U_9520] :
            ( ~ hBOOL(hAPP(U_9528,U_9520))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9526)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_9521,sK181(U_9528,U_9526))],[f_2642_3]) ).

fof(f_2642_5,plain,
    ( ! [U_9529,U_9527] :
        ( ( hBOOL(hAPP(U_9529,sK182(U_9529,U_9527)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK182(U_9529,U_9527)),U_9527)) )
        | ! [U_9522] :
            ( ~ hBOOL(hAPP(U_9529,U_9522))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9527))) ) )
    & ! [U_9528,U_9526] :
        ( ( hBOOL(hAPP(U_9528,sK181(U_9528,U_9526)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK181(U_9528,U_9526)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9526))) )
        | ! [U_9520] :
            ( ~ hBOOL(hAPP(U_9528,U_9520))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9526)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_9523,sK182(U_9529,U_9527))],[f_2642_4]) ).

cnf(f_2642_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK181(U_9528,U_9526)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9526)))
    | ~ hBOOL(hAPP(U_9528,U_9520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9526)) ),
    inference(clausify,[status(thm)],[f_2642_5]) ).

cnf(f_2642_7,plain,
    ( hBOOL(hAPP(U_9528,sK181(U_9528,U_9526)))
    | ~ hBOOL(hAPP(U_9528,U_9520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9520),U_9526)) ),
    inference(clausify,[status(thm)],[f_2642_5]) ).

cnf(f_2642_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK182(U_9529,U_9527)),U_9527))
    | ~ hBOOL(hAPP(U_9529,U_9522))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9527))) ),
    inference(clausify,[status(thm)],[f_2642_5]) ).

cnf(f_2642_9,plain,
    ( hBOOL(hAPP(U_9529,sK182(U_9529,U_9527)))
    | ~ hBOOL(hAPP(U_9529,U_9522))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9522),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9527))) ),
    inference(clausify,[status(thm)],[f_2642_5]) ).

fof(f_2643_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_2643_2,plain,
    ! [U_9535,U_9534] :
      ( ( ! [U_9533] :
            ( hBOOL(hAPP(U_9535,U_9533))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9534)) )
        | ? [U_9532] :
            ( ~ hBOOL(hAPP(U_9535,U_9532))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9532),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9534))) ) )
      & ( ! [U_9531] :
            ( hBOOL(hAPP(U_9535,U_9531))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9534))) )
        | ? [U_9530] :
            ( ~ hBOOL(hAPP(U_9535,U_9530))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9530),U_9534)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

fof(f_2643_3,plain,
    ( ! [U_9539,U_9537] :
        ( ! [U_9533] :
            ( hBOOL(hAPP(U_9539,U_9533))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9537)) )
        | ? [U_9532] :
            ( ~ hBOOL(hAPP(U_9539,U_9532))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9532),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9537))) ) )
    & ! [U_9538,U_9536] :
        ( ! [U_9531] :
            ( hBOOL(hAPP(U_9538,U_9531))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9536))) )
        | ? [U_9530] :
            ( ~ hBOOL(hAPP(U_9538,U_9530))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9530),U_9536)) ) ) ),
    inference(miniscope,[status(thm)],[f_2643_2]) ).

fof(f_2643_4,plain,
    ( ! [U_9539,U_9537] :
        ( ! [U_9533] :
            ( hBOOL(hAPP(U_9539,U_9533))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9537)) )
        | ? [U_9532] :
            ( ~ hBOOL(hAPP(U_9539,U_9532))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9532),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9537))) ) )
    & ! [U_9538,U_9536] :
        ( ! [U_9531] :
            ( hBOOL(hAPP(U_9538,U_9531))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9536))) )
        | ( ~ hBOOL(hAPP(U_9538,sK183(U_9538,U_9536)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK183(U_9538,U_9536)),U_9536)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_9530,sK183(U_9538,U_9536))],[f_2643_3]) ).

fof(f_2643_5,plain,
    ( ! [U_9539,U_9537] :
        ( ! [U_9533] :
            ( hBOOL(hAPP(U_9539,U_9533))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9537)) )
        | ( ~ hBOOL(hAPP(U_9539,sK184(U_9539,U_9537)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK184(U_9539,U_9537)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9537))) ) )
    & ! [U_9538,U_9536] :
        ( ! [U_9531] :
            ( hBOOL(hAPP(U_9538,U_9531))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9536))) )
        | ( ~ hBOOL(hAPP(U_9538,sK183(U_9538,U_9536)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK183(U_9538,U_9536)),U_9536)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_9532,sK184(U_9539,U_9537))],[f_2643_4]) ).

cnf(f_2643_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK183(U_9538,U_9536)),U_9536))
    | hBOOL(hAPP(U_9538,U_9531))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9536))) ),
    inference(clausify,[status(thm)],[f_2643_5]) ).

cnf(f_2643_7,plain,
    ( ~ hBOOL(hAPP(U_9538,sK183(U_9538,U_9536)))
    | hBOOL(hAPP(U_9538,U_9531))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9531),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9536))) ),
    inference(clausify,[status(thm)],[f_2643_5]) ).

cnf(f_2643_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK184(U_9539,U_9537)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_9537)))
    | hBOOL(hAPP(U_9539,U_9533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9537)) ),
    inference(clausify,[status(thm)],[f_2643_5]) ).

cnf(f_2643_9,plain,
    ( ~ hBOOL(hAPP(U_9539,sK184(U_9539,U_9537)))
    | hBOOL(hAPP(U_9539,U_9533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9533),U_9537)) ),
    inference(clausify,[status(thm)],[f_2643_5]) ).

fof(f_2644_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_2644_2,plain,
    ! [U_9543,U_9542,U_9541,U_9540] :
      ( 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_9540),U_9542)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9541),U_9543))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9542),U_9543))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9540),U_9541)) ),
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

cnf(f_2644_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_9540),U_9542)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9541),U_9543))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9542),U_9543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9540),U_9541)) ),
    inference(clausify,[status(thm)],[f_2644_2]) ).

fof(f_2645_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_2645_2,plain,
    ! [U_9547,U_9546,U_9545,U_9544] :
      ( 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_9546),U_9547)),U_9545)),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_9547),U_9545)),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_9546),U_9544)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9544),U_9545)) ),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

cnf(f_2645_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_9546),U_9547)),U_9545)),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_9547),U_9545)),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_9546),U_9544)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9544),U_9545)) ),
    inference(clausify,[status(thm)],[f_2645_2]) ).

fof(f_2646_1,plain,
    ! [V_ca_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_ca_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_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_ca_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_ca_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).

fof(f_2646_2,plain,
    ! [U_9556,U_9555,U_9554,U_9553,U_9552,U_9551,U_9550] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9550,tc_fun(U_9551,tc_fun(U_9552,tc_HOL_Obool))),U_9553),U_9554),U_9555),U_9556))
        | ? [U_9549] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_9554,U_9549),U_9555),U_9556))
            & hBOOL(hAPP(hAPP(c_member(U_9550),U_9549),U_9553)) ) )
      & ( ! [U_9548] :
            ( hBOOL(hAPP(hAPP(hAPP(U_9554,U_9548),U_9555),U_9556))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9550),U_9548),U_9553)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9550,tc_fun(U_9551,tc_fun(U_9552,tc_HOL_Obool))),U_9553),U_9554),U_9555),U_9556)) ) ),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

fof(f_2646_3,plain,
    ( ! [U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9558,tc_fun(U_9560,tc_fun(U_9562,tc_HOL_Obool))),U_9564),U_9566),U_9568),U_9570))
        | ? [U_9549] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_9566,U_9549),U_9568),U_9570))
            & hBOOL(hAPP(hAPP(c_member(U_9558),U_9549),U_9564)) ) )
    & ! [U_9569,U_9567,U_9565,U_9563,U_9561,U_9559,U_9557] :
        ( ! [U_9548] :
            ( hBOOL(hAPP(hAPP(hAPP(U_9565,U_9548),U_9567),U_9569))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9557),U_9548),U_9563)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9557,tc_fun(U_9559,tc_fun(U_9561,tc_HOL_Obool))),U_9563),U_9565),U_9567),U_9569)) ) ),
    inference(miniscope,[status(thm)],[f_2646_2]) ).

fof(f_2646_4,plain,
    ( ! [U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9558,tc_fun(U_9560,tc_fun(U_9562,tc_HOL_Obool))),U_9564),U_9566),U_9568),U_9570))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_9566,sK185(U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558)),U_9568),U_9570))
          & hBOOL(hAPP(hAPP(c_member(U_9558),sK185(U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558)),U_9564)) ) )
    & ! [U_9569,U_9567,U_9565,U_9563,U_9561,U_9559,U_9557] :
        ( ! [U_9548] :
            ( hBOOL(hAPP(hAPP(hAPP(U_9565,U_9548),U_9567),U_9569))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9557),U_9548),U_9563)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9557,tc_fun(U_9559,tc_fun(U_9561,tc_HOL_Obool))),U_9563),U_9565),U_9567),U_9569)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_9549,sK185(U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558))],[f_2646_3]) ).

cnf(f_2646_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_9565,U_9548),U_9567),U_9569))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9557),U_9548),U_9563))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9557,tc_fun(U_9559,tc_fun(U_9561,tc_HOL_Obool))),U_9563),U_9565),U_9567),U_9569)) ),
    inference(clausify,[status(thm)],[f_2646_4]) ).

cnf(f_2646_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9558),sK185(U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558)),U_9564))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9558,tc_fun(U_9560,tc_fun(U_9562,tc_HOL_Obool))),U_9564),U_9566),U_9568),U_9570)) ),
    inference(clausify,[status(thm)],[f_2646_4]) ).

cnf(f_2646_7,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_9566,sK185(U_9570,U_9568,U_9566,U_9564,U_9562,U_9560,U_9558)),U_9568),U_9570))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9558,tc_fun(U_9560,tc_fun(U_9562,tc_HOL_Obool))),U_9564),U_9566),U_9568),U_9570)) ),
    inference(clausify,[status(thm)],[f_2646_4]) ).

fof(f_2647_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_2647_2,plain,
    ! [U_9577,U_9576,U_9575,U_9574,U_9573] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9573,tc_fun(U_9574,tc_HOL_Obool)),U_9575),U_9576),U_9577))
        | ? [U_9572] :
            ( ~ hBOOL(hAPP(hAPP(U_9576,U_9572),U_9577))
            & hBOOL(hAPP(hAPP(c_member(U_9573),U_9572),U_9575)) ) )
      & ( ! [U_9571] :
            ( hBOOL(hAPP(hAPP(U_9576,U_9571),U_9577))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9573),U_9571),U_9575)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9573,tc_fun(U_9574,tc_HOL_Obool)),U_9575),U_9576),U_9577)) ) ),
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

fof(f_2647_3,plain,
    ( ! [U_9587,U_9585,U_9583,U_9581,U_9579] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9579,tc_fun(U_9581,tc_HOL_Obool)),U_9583),U_9585),U_9587))
        | ? [U_9572] :
            ( ~ hBOOL(hAPP(hAPP(U_9585,U_9572),U_9587))
            & hBOOL(hAPP(hAPP(c_member(U_9579),U_9572),U_9583)) ) )
    & ! [U_9586,U_9584,U_9582,U_9580,U_9578] :
        ( ! [U_9571] :
            ( hBOOL(hAPP(hAPP(U_9584,U_9571),U_9586))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9578),U_9571),U_9582)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(U_9580,tc_HOL_Obool)),U_9582),U_9584),U_9586)) ) ),
    inference(miniscope,[status(thm)],[f_2647_2]) ).

fof(f_2647_4,plain,
    ( ! [U_9587,U_9585,U_9583,U_9581,U_9579] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9579,tc_fun(U_9581,tc_HOL_Obool)),U_9583),U_9585),U_9587))
        | ( ~ hBOOL(hAPP(hAPP(U_9585,sK186(U_9587,U_9585,U_9583,U_9581,U_9579)),U_9587))
          & hBOOL(hAPP(hAPP(c_member(U_9579),sK186(U_9587,U_9585,U_9583,U_9581,U_9579)),U_9583)) ) )
    & ! [U_9586,U_9584,U_9582,U_9580,U_9578] :
        ( ! [U_9571] :
            ( hBOOL(hAPP(hAPP(U_9584,U_9571),U_9586))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9578),U_9571),U_9582)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(U_9580,tc_HOL_Obool)),U_9582),U_9584),U_9586)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_9572,sK186(U_9587,U_9585,U_9583,U_9581,U_9579))],[f_2647_3]) ).

cnf(f_2647_5,plain,
    ( hBOOL(hAPP(hAPP(U_9584,U_9571),U_9586))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9578),U_9571),U_9582))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(U_9580,tc_HOL_Obool)),U_9582),U_9584),U_9586)) ),
    inference(clausify,[status(thm)],[f_2647_4]) ).

cnf(f_2647_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9579),sK186(U_9587,U_9585,U_9583,U_9581,U_9579)),U_9583))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9579,tc_fun(U_9581,tc_HOL_Obool)),U_9583),U_9585),U_9587)) ),
    inference(clausify,[status(thm)],[f_2647_4]) ).

cnf(f_2647_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_9585,sK186(U_9587,U_9585,U_9583,U_9581,U_9579)),U_9587))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9579,tc_fun(U_9581,tc_HOL_Obool)),U_9583),U_9585),U_9587)) ),
    inference(clausify,[status(thm)],[f_2647_4]) ).

fof(f_2648_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_2648_2,plain,
    ! [U_9588] :
      ( 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_9588)),c_FunDef_Omax__strict))
      | U_9588 = 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_9588)) ),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

cnf(f_2648_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_9588)),c_FunDef_Omax__strict))
    | U_9588 = 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_9588)) ),
    inference(clausify,[status(thm)],[f_2648_2]) ).

fof(f_2649_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_2649_2,plain,
    ! [U_9590,U_9589] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9590,U_9589) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_9590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9590),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_9589))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9589),U_9590)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9590,U_9589) = 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_9589),U_9590)) ) ),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

fof(f_2649_3,plain,
    ( ! [U_9594,U_9592] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9594,U_9592) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_9594),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9594),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_9592))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9592),U_9594)) )
    & ! [U_9593,U_9591] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9593,U_9591) = 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_9591),U_9593)) ) ),
    inference(miniscope,[status(thm)],[f_2649_2]) ).

cnf(f_2649_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9593,U_9591) = 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_9591),U_9593)) ),
    inference(clausify,[status(thm)],[f_2649_3]) ).

cnf(f_2649_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9594,U_9592) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_9594),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9594),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_9592))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9592),U_9594)) ),
    inference(clausify,[status(thm)],[f_2649_3]) ).

fof(f_2650_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_2650_2,plain,
    ! [U_9596,U_9595] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9595,U_9596)) = 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_9596),U_9595)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

cnf(f_2650_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9595,U_9596)) = 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_9596),U_9595)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2650_2]) ).

fof(f_2651_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_2651_2,plain,
    ! [U_9600,U_9599,U_9598,U_9597] :
      ( 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_9597),U_9599)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9598),U_9600))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9597),U_9598)) ),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

cnf(f_2651_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_9597),U_9599)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9598),U_9600))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9597),U_9598)) ),
    inference(clausify,[status(thm)],[f_2651_2]) ).

fof(f_2652_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_2652_2,plain,
    ! [U_9604,U_9603,U_9602,U_9601] :
      ( 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_9602),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9603),U_9604))),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_9602),U_9604)),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_9601),U_9603)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9601),U_9602)) ),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

cnf(f_2652_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_9602),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9603),U_9604))),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_9602),U_9604)),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_9601),U_9603)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9601),U_9602)) ),
    inference(clausify,[status(thm)],[f_2652_2]) ).

fof(f_2653_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_2653_2,plain,
    ! [U_9608,U_9607,U_9606,U_9605] :
      ( 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_9607),U_9608)),U_9606)),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_9608),U_9606)),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_9607),U_9605)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9605),U_9606)) ),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

cnf(f_2653_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_9607),U_9608)),U_9606)),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_9608),U_9606)),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_9607),U_9605)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9605),U_9606)) ),
    inference(clausify,[status(thm)],[f_2653_2]) ).

fof(f_2654_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_2654_2,plain,
    ! [U_9612,U_9611,U_9610,U_9609] :
      ( 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_9610),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9611),U_9612))),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_9610),U_9612)),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_9609),U_9611)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9609),U_9610)) ),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

cnf(f_2654_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_9610),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9611),U_9612))),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_9610),U_9612)),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_9609),U_9611)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9609),U_9610)) ),
    inference(clausify,[status(thm)],[f_2654_2]) ).

fof(f_2655_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_2655_2,plain,
    ! [U_9618,U_9617,U_9616] :
      ( ! [U_9615] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
          | ? [U_9614] :
              ( ? [U_9613] :
                  ( U_9615 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9613),U_9614)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9613),U_9617)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9614),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9616))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

fof(f_2655_3,plain,
    ! [U_9618,U_9617,U_9616] :
      ( ! [U_9615] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
          | ( ? [U_9613] :
                ( U_9615 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9613),sK187(U_9618,U_9617,U_9616,U_9615))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9613),U_9617)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_9618,U_9617,U_9616,U_9615)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9616))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_9614,sK187(U_9618,U_9617,U_9616,U_9615))],[f_2655_2]) ).

fof(f_2655_4,plain,
    ! [U_9618,U_9617,U_9616] :
      ( ! [U_9615] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
          | ( U_9615 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK188(U_9618,U_9617,U_9616,U_9615)),sK187(U_9618,U_9617,U_9616,U_9615))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK188(U_9618,U_9617,U_9616,U_9615)),U_9617))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_9618,U_9617,U_9616,U_9615)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9616))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_9613,sK188(U_9618,U_9617,U_9616,U_9615))],[f_2655_3]) ).

cnf(f_2655_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_9618,U_9617,U_9616,U_9615)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(clausify,[status(thm)],[f_2655_4]) ).

cnf(f_2655_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK188(U_9618,U_9617,U_9616,U_9615)),U_9617))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(clausify,[status(thm)],[f_2655_4]) ).

cnf(f_2655_7,plain,
    ( U_9615 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK188(U_9618,U_9617,U_9616,U_9615)),sK187(U_9618,U_9617,U_9616,U_9615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9615),U_9616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9618),U_9615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9616)) ),
    inference(clausify,[status(thm)],[f_2655_4]) ).

fof(f_2656_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_2656_2,plain,
    ! [U_9620,U_9619] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9619,U_9620))),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

cnf(f_2656_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_9619,U_9620))),
    inference(clausify,[status(thm)],[f_2656_2]) ).

fof(f_2657_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_2657_2,plain,
    ! [U_9621] :
      ( 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_9621)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9621)) ),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

cnf(f_2657_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_9621)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9621)) ),
    inference(clausify,[status(thm)],[f_2657_2]) ).

fof(f_2658_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_2658_2,plain,
    ! [U_9622] : 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_9622),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_2658_1]) ).

cnf(f_2658_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_9622),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_2658_2]) ).

fof(f_2659_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_2659_2,plain,
    ! [U_9623] :
      ( 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_9623),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_9623 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

cnf(f_2659_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_9623),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_9623 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2659_2]) ).

fof(f_2660_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_2660_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_2660_1]) ).

fof(f_2661_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_2661_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_2661_1]) ).

fof(f_2662_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_2662_2,plain,
    ! [U_9629,U_9628,U_9627] :
      ( ! [U_9626] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
          | ? [U_9625] :
              ( ? [U_9624] :
                  ( U_9626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9624),U_9625)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9624),U_9629)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9625),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9627))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

fof(f_2662_3,plain,
    ! [U_9629,U_9628,U_9627] :
      ( ! [U_9626] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
          | ( ? [U_9624] :
                ( U_9626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9624),sK189(U_9629,U_9628,U_9627,U_9626))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9624),U_9629)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_9629,U_9628,U_9627,U_9626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9627))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_9625,sK189(U_9629,U_9628,U_9627,U_9626))],[f_2662_2]) ).

fof(f_2662_4,plain,
    ! [U_9629,U_9628,U_9627] :
      ( ! [U_9626] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
          | ( U_9626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK190(U_9629,U_9628,U_9627,U_9626)),sK189(U_9629,U_9628,U_9627,U_9626))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK190(U_9629,U_9628,U_9627,U_9626)),U_9629))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_9629,U_9628,U_9627,U_9626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9627))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_9624,sK190(U_9629,U_9628,U_9627,U_9626))],[f_2662_3]) ).

cnf(f_2662_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_9629,U_9628,U_9627,U_9626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9627)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

cnf(f_2662_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK190(U_9629,U_9628,U_9627,U_9626)),U_9629))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

cnf(f_2662_7,plain,
    ( U_9626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK190(U_9629,U_9628,U_9627,U_9626)),sK189(U_9629,U_9628,U_9627,U_9626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9626),U_9627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9628),U_9626))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9628),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9627)) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

fof(f_2663_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_2663_2,plain,
    ! [U_9635,U_9634,U_9633] :
      ( ! [U_9632] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
          | ? [U_9631] :
              ( ? [U_9630] :
                  ( U_9632 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9630),U_9631)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9630),U_9635)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9631),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9633))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

fof(f_2663_3,plain,
    ! [U_9635,U_9634,U_9633] :
      ( ! [U_9632] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
          | ( ? [U_9630] :
                ( U_9632 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9630),sK191(U_9635,U_9634,U_9633,U_9632))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9630),U_9635)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_9635,U_9634,U_9633,U_9632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9633))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_9631,sK191(U_9635,U_9634,U_9633,U_9632))],[f_2663_2]) ).

fof(f_2663_4,plain,
    ! [U_9635,U_9634,U_9633] :
      ( ! [U_9632] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
          | ( U_9632 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK192(U_9635,U_9634,U_9633,U_9632)),sK191(U_9635,U_9634,U_9633,U_9632))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK192(U_9635,U_9634,U_9633,U_9632)),U_9635))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_9635,U_9634,U_9633,U_9632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9633))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_9630,sK192(U_9635,U_9634,U_9633,U_9632))],[f_2663_3]) ).

cnf(f_2663_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_9635,U_9634,U_9633,U_9632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9633)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(clausify,[status(thm)],[f_2663_4]) ).

cnf(f_2663_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK192(U_9635,U_9634,U_9633,U_9632)),U_9635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(clausify,[status(thm)],[f_2663_4]) ).

cnf(f_2663_7,plain,
    ( U_9632 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK192(U_9635,U_9634,U_9633,U_9632)),sK191(U_9635,U_9634,U_9633,U_9632))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9632),U_9633)),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9632),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9634),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9633)) ),
    inference(clausify,[status(thm)],[f_2663_4]) ).

fof(f_2664_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_2664_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_2664_1]) ).

fof(f_2665_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_2665_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_2665_1]) ).

fof(f_2666_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_2666_2,plain,
    ! [U_9641,U_9640,U_9639,U_9638,U_9637,U_9636] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9636,tc_HOL_Obool)),U_9637),U_9640)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9636,tc_HOL_Obool)),U_9638),U_9641))),c_Wellfounded_Omax__ext(U_9636,U_9639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9641)),c_Wellfounded_Omax__ext(U_9636,U_9639)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),U_9637),U_9638)),c_Wellfounded_Omax__ext(U_9636,U_9639))) ),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

cnf(f_2666_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9636,tc_HOL_Obool)),U_9637),U_9640)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9636,tc_HOL_Obool)),U_9638),U_9641))),c_Wellfounded_Omax__ext(U_9636,U_9639)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),U_9640),U_9641)),c_Wellfounded_Omax__ext(U_9636,U_9639)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_HOL_Obool)),U_9637),U_9638)),c_Wellfounded_Omax__ext(U_9636,U_9639))) ),
    inference(clausify,[status(thm)],[f_2666_2]) ).

fof(f_2667_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_2667_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_2667_1]) ).

fof(f_2668_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_2668_2,plain,
    ! [U_9645,U_9644,U_9643,U_9642] :
      ( ( c_Wellfounded_Omax__extp(U_9642,hAPP(hAPP(c_COMBC(U_9642,tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9642,tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),U_9642),c_COMBC(U_9642,tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9642,tc_prod(U_9642,U_9642)),tc_fun(U_9642,tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),U_9642),hAPP(c_COMBB(tc_prod(U_9642,U_9642),tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool),U_9642),c_member(tc_prod(U_9642,U_9642)))),c_Product__Type_OPair(U_9642,U_9642)))),U_9643),U_9644,U_9645)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9642,tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9642,tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),U_9644),U_9645)),c_Wellfounded_Omax__ext(U_9642,U_9643))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9642,tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9642,tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),U_9644),U_9645)),c_Wellfounded_Omax__ext(U_9642,U_9643)))
        | ~ c_Wellfounded_Omax__extp(U_9642,hAPP(hAPP(c_COMBC(U_9642,tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9642,tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_fun(U_9642,tc_HOL_Obool)),U_9642),c_COMBC(U_9642,tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9642,tc_prod(U_9642,U_9642)),tc_fun(U_9642,tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool)),U_9642),hAPP(c_COMBB(tc_prod(U_9642,U_9642),tc_fun(tc_fun(tc_prod(U_9642,U_9642),tc_HOL_Obool),tc_HOL_Obool),U_9642),c_member(tc_prod(U_9642,U_9642)))),c_Product__Type_OPair(U_9642,U_9642)))),U_9643),U_9644,U_9645) ) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

fof(f_2668_3,plain,
    ( ! [U_9653,U_9651,U_9649,U_9647] :
        ( c_Wellfounded_Omax__extp(U_9647,hAPP(hAPP(c_COMBC(U_9647,tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9647,tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),U_9647),c_COMBC(U_9647,tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9647,tc_prod(U_9647,U_9647)),tc_fun(U_9647,tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),U_9647),hAPP(c_COMBB(tc_prod(U_9647,U_9647),tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool),U_9647),c_member(tc_prod(U_9647,U_9647)))),c_Product__Type_OPair(U_9647,U_9647)))),U_9649),U_9651,U_9653)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9647,tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9647,tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),U_9651),U_9653)),c_Wellfounded_Omax__ext(U_9647,U_9649))) )
    & ! [U_9652,U_9650,U_9648,U_9646] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9646,tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9646,tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),U_9650),U_9652)),c_Wellfounded_Omax__ext(U_9646,U_9648)))
        | ~ c_Wellfounded_Omax__extp(U_9646,hAPP(hAPP(c_COMBC(U_9646,tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9646,tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),U_9646),c_COMBC(U_9646,tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9646,tc_prod(U_9646,U_9646)),tc_fun(U_9646,tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),U_9646),hAPP(c_COMBB(tc_prod(U_9646,U_9646),tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool),U_9646),c_member(tc_prod(U_9646,U_9646)))),c_Product__Type_OPair(U_9646,U_9646)))),U_9648),U_9650,U_9652) ) ),
    inference(miniscope,[status(thm)],[f_2668_2]) ).

cnf(f_2668_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9646,tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9646,tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),U_9650),U_9652)),c_Wellfounded_Omax__ext(U_9646,U_9648)))
    | ~ c_Wellfounded_Omax__extp(U_9646,hAPP(hAPP(c_COMBC(U_9646,tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9646,tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_fun(U_9646,tc_HOL_Obool)),U_9646),c_COMBC(U_9646,tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9646,tc_prod(U_9646,U_9646)),tc_fun(U_9646,tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool)),U_9646),hAPP(c_COMBB(tc_prod(U_9646,U_9646),tc_fun(tc_fun(tc_prod(U_9646,U_9646),tc_HOL_Obool),tc_HOL_Obool),U_9646),c_member(tc_prod(U_9646,U_9646)))),c_Product__Type_OPair(U_9646,U_9646)))),U_9648),U_9650,U_9652) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

cnf(f_2668_5,plain,
    ( c_Wellfounded_Omax__extp(U_9647,hAPP(hAPP(c_COMBC(U_9647,tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9647,tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),U_9647),c_COMBC(U_9647,tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9647,tc_prod(U_9647,U_9647)),tc_fun(U_9647,tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool)),U_9647),hAPP(c_COMBB(tc_prod(U_9647,U_9647),tc_fun(tc_fun(tc_prod(U_9647,U_9647),tc_HOL_Obool),tc_HOL_Obool),U_9647),c_member(tc_prod(U_9647,U_9647)))),c_Product__Type_OPair(U_9647,U_9647)))),U_9649),U_9651,U_9653)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9647,tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9647,tc_HOL_Obool),tc_fun(U_9647,tc_HOL_Obool)),U_9651),U_9653)),c_Wellfounded_Omax__ext(U_9647,U_9649))) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

fof(f_2669_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_2669_2,plain,
    ! [U_9658,U_9657,U_9656] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
      | ? [U_9655] :
          ( ? [U_9654] :
              ( U_9657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9654),U_9655)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9654),U_9658)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9655),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9656))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(variable_rename,[status(thm)],[f_2669_1]) ).

fof(f_2669_3,plain,
    ! [U_9658,U_9657,U_9656] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
      | ( ? [U_9654] :
            ( U_9657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9654),sK193(U_9658,U_9657,U_9656))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9654),U_9658)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_9658,U_9657,U_9656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9656))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_9655,sK193(U_9658,U_9657,U_9656))],[f_2669_2]) ).

fof(f_2669_4,plain,
    ! [U_9658,U_9657,U_9656] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
      | ( U_9657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK194(U_9658,U_9657,U_9656)),sK193(U_9658,U_9657,U_9656))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK194(U_9658,U_9657,U_9656)),U_9658))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_9658,U_9657,U_9656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9656))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_9654,sK194(U_9658,U_9657,U_9656))],[f_2669_3]) ).

cnf(f_2669_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_9658,U_9657,U_9656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9656)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK194(U_9658,U_9657,U_9656)),U_9658))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_7,plain,
    ( U_9657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK194(U_9658,U_9657,U_9656)),sK193(U_9658,U_9657,U_9656))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),U_9656) = U_9657
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9657),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9656)) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

fof(f_2670_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_2670_2,plain,
    ! [U_9663,U_9662,U_9661] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
      | ? [U_9660] :
          ( ? [U_9659] :
              ( U_9662 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9659),U_9660)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9659),U_9663)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9660),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9661))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

fof(f_2670_3,plain,
    ! [U_9663,U_9662,U_9661] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
      | ( ? [U_9659] :
            ( U_9662 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9659),sK195(U_9663,U_9662,U_9661))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9659),U_9663)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_9663,U_9662,U_9661)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9661))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_9660,sK195(U_9663,U_9662,U_9661))],[f_2670_2]) ).

fof(f_2670_4,plain,
    ! [U_9663,U_9662,U_9661] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
      | ( U_9662 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK196(U_9663,U_9662,U_9661)),sK195(U_9663,U_9662,U_9661))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK196(U_9663,U_9662,U_9661)),U_9663))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_9663,U_9662,U_9661)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9661))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_9659,sK196(U_9663,U_9662,U_9661))],[f_2670_3]) ).

cnf(f_2670_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_9663,U_9662,U_9661)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9661)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK196(U_9663,U_9662,U_9661)),U_9663))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_7,plain,
    ( U_9662 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK196(U_9663,U_9662,U_9661)),sK195(U_9663,U_9662,U_9661))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),U_9661) = U_9662
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9662),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9661)) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

fof(f_2671_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_2671_2,plain,
    ! [U_9669,U_9668,U_9667] :
      ( ! [U_9666] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
          | ? [U_9665] :
              ( ? [U_9664] :
                  ( U_9666 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9664),U_9665)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9664),U_9669)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9667))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

fof(f_2671_3,plain,
    ! [U_9669,U_9668,U_9667] :
      ( ! [U_9666] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
          | ( ? [U_9664] :
                ( U_9666 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9664),sK197(U_9669,U_9668,U_9667,U_9666))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9664),U_9669)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_9669,U_9668,U_9667,U_9666)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9667))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_9665,sK197(U_9669,U_9668,U_9667,U_9666))],[f_2671_2]) ).

fof(f_2671_4,plain,
    ! [U_9669,U_9668,U_9667] :
      ( ! [U_9666] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
          | ( U_9666 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK198(U_9669,U_9668,U_9667,U_9666)),sK197(U_9669,U_9668,U_9667,U_9666))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK198(U_9669,U_9668,U_9667,U_9666)),U_9669))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_9669,U_9668,U_9667,U_9666)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9667))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_9664,sK198(U_9669,U_9668,U_9667,U_9666))],[f_2671_3]) ).

cnf(f_2671_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_9669,U_9668,U_9667,U_9666)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9667)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

cnf(f_2671_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK198(U_9669,U_9668,U_9667,U_9666)),U_9669))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

cnf(f_2671_7,plain,
    ( U_9666 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK198(U_9669,U_9668,U_9667,U_9666)),sK197(U_9669,U_9668,U_9667,U_9666))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9666),U_9667)),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9666),U_9668))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9668),U_9669))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9667)) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

fof(f_2672_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_2672_2,plain,
    ! [U_9675,U_9674,U_9673] :
      ( ! [U_9672] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
          | U_9672 = U_9674
          | ? [U_9671] :
              ( ? [U_9670] :
                  ( U_9672 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9670),U_9671)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9670),U_9675)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9671),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9673))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

fof(f_2672_3,plain,
    ! [U_9675,U_9674,U_9673] :
      ( ! [U_9672] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
          | U_9672 = U_9674
          | ( ? [U_9670] :
                ( U_9672 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9670),sK199(U_9675,U_9674,U_9673,U_9672))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9670),U_9675)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK199(U_9675,U_9674,U_9673,U_9672)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9673))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_9671,sK199(U_9675,U_9674,U_9673,U_9672))],[f_2672_2]) ).

fof(f_2672_4,plain,
    ! [U_9675,U_9674,U_9673] :
      ( ! [U_9672] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
          | U_9672 = U_9674
          | ( U_9672 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK200(U_9675,U_9674,U_9673,U_9672)),sK199(U_9675,U_9674,U_9673,U_9672))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK200(U_9675,U_9674,U_9673,U_9672)),U_9675))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK199(U_9675,U_9674,U_9673,U_9672)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9673))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_9670,sK200(U_9675,U_9674,U_9673,U_9672))],[f_2672_3]) ).

cnf(f_2672_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK199(U_9675,U_9674,U_9673,U_9672)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9673)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
    | U_9672 = U_9674
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK200(U_9675,U_9674,U_9673,U_9672)),U_9675))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
    | U_9672 = U_9674
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_7,plain,
    ( U_9672 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK200(U_9675,U_9674,U_9673,U_9672)),sK199(U_9675,U_9674,U_9673,U_9672))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9672),U_9673) != U_9674
    | U_9672 = U_9674
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9674),U_9675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9673)) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

fof(f_2673_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_2673_2,plain,
    ! [U_9681,U_9680,U_9679] :
      ( ! [U_9678] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
          | U_9678 = U_9680
          | ? [U_9677] :
              ( ? [U_9676] :
                  ( U_9678 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9676),U_9677)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9676),U_9681)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9677),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9679))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

fof(f_2673_3,plain,
    ! [U_9681,U_9680,U_9679] :
      ( ! [U_9678] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
          | U_9678 = U_9680
          | ( ? [U_9676] :
                ( U_9678 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9676),sK201(U_9681,U_9680,U_9679,U_9678))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9676),U_9681)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK201(U_9681,U_9680,U_9679,U_9678)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9679))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_9677,sK201(U_9681,U_9680,U_9679,U_9678))],[f_2673_2]) ).

fof(f_2673_4,plain,
    ! [U_9681,U_9680,U_9679] :
      ( ! [U_9678] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
          | U_9678 = U_9680
          | ( U_9678 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK202(U_9681,U_9680,U_9679,U_9678)),sK201(U_9681,U_9680,U_9679,U_9678))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK202(U_9681,U_9680,U_9679,U_9678)),U_9681))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK201(U_9681,U_9680,U_9679,U_9678)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9679))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_9676,sK202(U_9681,U_9680,U_9679,U_9678))],[f_2673_3]) ).

cnf(f_2673_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK201(U_9681,U_9680,U_9679,U_9678)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9679)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
    | U_9678 = U_9680
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(clausify,[status(thm)],[f_2673_4]) ).

cnf(f_2673_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK202(U_9681,U_9680,U_9679,U_9678)),U_9681))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
    | U_9678 = U_9680
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(clausify,[status(thm)],[f_2673_4]) ).

cnf(f_2673_7,plain,
    ( U_9678 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK202(U_9681,U_9680,U_9679,U_9678)),sK201(U_9681,U_9680,U_9679,U_9678))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9678),U_9679) != U_9680
    | U_9678 = U_9680
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9680),U_9681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9679)) ),
    inference(clausify,[status(thm)],[f_2673_4]) ).

fof(f_2674_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_2674_2,plain,
    ! [U_9687,U_9686,U_9685] :
      ( ! [U_9684] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
          | ? [U_9683] :
              ( ? [U_9682] :
                  ( U_9684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9682),U_9683)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9682),U_9687)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9683),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9685))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

fof(f_2674_3,plain,
    ! [U_9687,U_9686,U_9685] :
      ( ! [U_9684] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
          | ( ? [U_9682] :
                ( U_9684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9682),sK203(U_9687,U_9686,U_9685,U_9684))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9682),U_9687)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_9687,U_9686,U_9685,U_9684)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9685))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_9683,sK203(U_9687,U_9686,U_9685,U_9684))],[f_2674_2]) ).

fof(f_2674_4,plain,
    ! [U_9687,U_9686,U_9685] :
      ( ! [U_9684] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
          | ( U_9684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK204(U_9687,U_9686,U_9685,U_9684)),sK203(U_9687,U_9686,U_9685,U_9684))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK204(U_9687,U_9686,U_9685,U_9684)),U_9687))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_9687,U_9686,U_9685,U_9684)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9685))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_9682,sK204(U_9687,U_9686,U_9685,U_9684))],[f_2674_3]) ).

cnf(f_2674_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_9687,U_9686,U_9685,U_9684)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9685)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(clausify,[status(thm)],[f_2674_4]) ).

cnf(f_2674_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK204(U_9687,U_9686,U_9685,U_9684)),U_9687))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(clausify,[status(thm)],[f_2674_4]) ).

cnf(f_2674_7,plain,
    ( U_9684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK204(U_9687,U_9686,U_9685,U_9684)),sK203(U_9687,U_9686,U_9685,U_9684))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9684),U_9685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9686),U_9684))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9686),U_9687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9685)) ),
    inference(clausify,[status(thm)],[f_2674_4]) ).

fof(f_2675_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_2675_2,plain,
    ! [U_9693,U_9692,U_9691] :
      ( ! [U_9690] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
          | ? [U_9689] :
              ( ? [U_9688] :
                  ( U_9690 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9688),U_9689)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9688),U_9692)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9689),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9691))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

fof(f_2675_3,plain,
    ! [U_9693,U_9692,U_9691] :
      ( ! [U_9690] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
          | ( ? [U_9688] :
                ( U_9690 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9688),sK205(U_9693,U_9692,U_9691,U_9690))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9688),U_9692)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_9693,U_9692,U_9691,U_9690)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9691))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_9689,sK205(U_9693,U_9692,U_9691,U_9690))],[f_2675_2]) ).

fof(f_2675_4,plain,
    ! [U_9693,U_9692,U_9691] :
      ( ! [U_9690] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
          | ( U_9690 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK206(U_9693,U_9692,U_9691,U_9690)),sK205(U_9693,U_9692,U_9691,U_9690))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_9693,U_9692,U_9691,U_9690)),U_9692))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_9693,U_9692,U_9691,U_9690)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9691))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_9688,sK206(U_9693,U_9692,U_9691,U_9690))],[f_2675_3]) ).

cnf(f_2675_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_9693,U_9692,U_9691,U_9690)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9691)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(clausify,[status(thm)],[f_2675_4]) ).

cnf(f_2675_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_9693,U_9692,U_9691,U_9690)),U_9692))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(clausify,[status(thm)],[f_2675_4]) ).

cnf(f_2675_7,plain,
    ( U_9690 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK206(U_9693,U_9692,U_9691,U_9690)),sK205(U_9693,U_9692,U_9691,U_9690))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9690),U_9691)),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9690),U_9693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9691)) ),
    inference(clausify,[status(thm)],[f_2675_4]) ).

fof(f_2676_1,plain,
    ! [V_Pa_2,V_d_2] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) )
      | ? [B_x,B_k] :
          ( ( ~ hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_2676_2,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ? [U_9695,U_9694] :
          ( ( ~ hBOOL(hAPP(U_9701,U_9695))
            & hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9694),U_9700)))) )
          | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9694),U_9700))))
            & hBOOL(hAPP(U_9701,U_9695)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

fof(f_2676_3,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ? [U_9705] :
          ( ? [U_9703] : hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9703),U_9700))))
          & ~ hBOOL(hAPP(U_9701,U_9705)) )
      | ? [U_9704] :
          ( ? [U_9702] : ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9702),U_9700))))
          & hBOOL(hAPP(U_9701,U_9704)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(miniscope,[status(thm)],[f_2676_2]) ).

fof(f_2676_4,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ? [U_9705] :
          ( ? [U_9703] : hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9703),U_9700))))
          & ~ hBOOL(hAPP(U_9701,U_9705)) )
      | ( ? [U_9702] : ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9702),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_9704,sK207(U_9701,U_9700))],[f_2676_3]) ).

fof(f_2676_5,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ? [U_9705] :
          ( ? [U_9703] : hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9703),U_9700))))
          & ~ hBOOL(hAPP(U_9701,U_9705)) )
      | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_9702,sK208(U_9701,U_9700))],[f_2676_4]) ).

fof(f_2676_6,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ( ? [U_9703] : hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9703),U_9700))))
        & ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700))) )
      | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_9705,sK209(U_9701,U_9700))],[f_2676_5]) ).

fof(f_2676_7,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ? [U_9697] :
              ( hBOOL(hAPP(U_9701,U_9697))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9697),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
        & ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700))) )
      | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_9703,sK210(U_9701,U_9700))],[f_2676_6]) ).

fof(f_2676_8,plain,
    ! [U_9701,U_9700] :
      ( ( ( ? [U_9699] : hBOOL(hAPP(U_9701,U_9699))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ( hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
        & ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700))) )
      | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_9697,sK211(U_9701,U_9700))],[f_2676_7]) ).

fof(f_2676_9,plain,
    ! [U_9701,U_9700] :
      ( ( ( hBOOL(hAPP(U_9701,sK212(U_9701,U_9700)))
          | ! [U_9698] :
              ( ~ hBOOL(hAPP(U_9701,U_9698))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) ) )
        & ( ( hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700))) )
          | ! [U_9696] : ~ hBOOL(hAPP(U_9701,U_9696)) ) )
      | ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
        & ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700))) )
      | ( ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
        & hBOOL(hAPP(U_9701,sK207(U_9701,U_9700))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_9699,sK212(U_9701,U_9700))],[f_2676_8]) ).

cnf(f_2676_10,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_11,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_12,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_13,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_14,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_15,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_9701,U_9700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_16,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_17,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK211(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9696))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_18,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK212(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9698))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_19,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK207(U_9701,U_9700)))
    | hBOOL(hAPP(U_9701,sK212(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9698))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_20,plain,
    ( ~ hBOOL(hAPP(U_9701,sK209(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK212(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9698))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

cnf(f_2676_21,plain,
    ( hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK210(U_9701,U_9700)),U_9700))))
    | ~ hBOOL(hAPP(U_9701,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK207(U_9701,U_9700)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK208(U_9701,U_9700)),U_9700))))
    | hBOOL(hAPP(U_9701,sK212(U_9701,U_9700)))
    | ~ hBOOL(hAPP(U_9701,U_9698))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9698),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9700)) ),
    inference(clausify,[status(thm)],[f_2676_9]) ).

fof(f_2677_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_2677_2,plain,
    ! [U_9711,U_9710,U_9709] :
      ( ! [U_9708] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
          | ? [U_9707] :
              ( ? [U_9706] :
                  ( U_9708 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9706),U_9707)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9706),U_9710)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9707),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9709))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

fof(f_2677_3,plain,
    ! [U_9711,U_9710,U_9709] :
      ( ! [U_9708] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
          | ( ? [U_9706] :
                ( U_9708 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9706),sK213(U_9711,U_9710,U_9709,U_9708))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9706),U_9710)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_9711,U_9710,U_9709,U_9708)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9709))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_9707,sK213(U_9711,U_9710,U_9709,U_9708))],[f_2677_2]) ).

fof(f_2677_4,plain,
    ! [U_9711,U_9710,U_9709] :
      ( ! [U_9708] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
          | ( U_9708 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK214(U_9711,U_9710,U_9709,U_9708)),sK213(U_9711,U_9710,U_9709,U_9708))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK214(U_9711,U_9710,U_9709,U_9708)),U_9710))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_9711,U_9710,U_9709,U_9708)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9709))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_9706,sK214(U_9711,U_9710,U_9709,U_9708))],[f_2677_3]) ).

cnf(f_2677_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK213(U_9711,U_9710,U_9709,U_9708)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9709)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

cnf(f_2677_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK214(U_9711,U_9710,U_9709,U_9708)),U_9710))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

cnf(f_2677_7,plain,
    ( U_9708 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK214(U_9711,U_9710,U_9709,U_9708)),sK213(U_9711,U_9710,U_9709,U_9708))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9708),U_9709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9711),U_9708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9709)) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

fof(f_2678_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_2678_2,plain,
    ! [U_9717,U_9716,U_9715] :
      ( ! [U_9714] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
          | ? [U_9713] :
              ( ? [U_9712] :
                  ( U_9714 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9712),U_9713)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9712),U_9716)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9713),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9715))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ! [U_9717,U_9716,U_9715] :
      ( ! [U_9714] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
          | ( ? [U_9712] :
                ( U_9714 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9712),sK215(U_9717,U_9716,U_9715,U_9714))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9712),U_9716)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_9717,U_9716,U_9715,U_9714)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9715))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_9713,sK215(U_9717,U_9716,U_9715,U_9714))],[f_2678_2]) ).

fof(f_2678_4,plain,
    ! [U_9717,U_9716,U_9715] :
      ( ! [U_9714] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
          | ( U_9714 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK216(U_9717,U_9716,U_9715,U_9714)),sK215(U_9717,U_9716,U_9715,U_9714))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_9717,U_9716,U_9715,U_9714)),U_9716))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_9717,U_9716,U_9715,U_9714)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9715))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_9712,sK216(U_9717,U_9716,U_9715,U_9714))],[f_2678_3]) ).

cnf(f_2678_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK215(U_9717,U_9716,U_9715,U_9714)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9715)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

cnf(f_2678_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_9717,U_9716,U_9715,U_9714)),U_9716))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

cnf(f_2678_7,plain,
    ( U_9714 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK216(U_9717,U_9716,U_9715,U_9714)),sK215(U_9717,U_9716,U_9715,U_9714))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9714),U_9715)),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9714),U_9717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9715)) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

fof(f_2679_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_2679_2,plain,
    ! [U_9719,U_9718] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_9718,U_9719)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9719),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9718),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

cnf(f_2679_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_9718,U_9719)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9719),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9718),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2679_2]) ).

fof(f_2680_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_2680_2,plain,
    ! [U_9721,U_9720] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_9720,U_9721))),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

cnf(f_2680_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_9720,U_9721))),
    inference(clausify,[status(thm)],[f_2680_2]) ).

fof(f_2681_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_2681_2,plain,
    ! [U_9724,U_9723,U_9722] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_9722,U_9724,U_9723) = c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),U_9723),U_9724))
      | ~ class_Orderings_Oorder(U_9722) ),
    inference(variable_rename,[status(thm)],[f_2681_1]) ).

cnf(f_2681_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_9722,U_9724,U_9723) = c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9722),U_9723),U_9724))
    | ~ class_Orderings_Oorder(U_9722) ),
    inference(clausify,[status(thm)],[f_2681_2]) ).

fof(f_2682_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_2682_2,plain,
    ! [U_9728,U_9727,U_9726,U_9725] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9725,U_9726,U_9727)),c_SetInterval_Oord__class_OatLeastAtMost(U_9725,U_9727,U_9728)) = c_Orderings_Obot__class_Obot(tc_fun(U_9725,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9725) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

cnf(f_2682_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9725,U_9726,U_9727)),c_SetInterval_Oord__class_OatLeastAtMost(U_9725,U_9727,U_9728)) = c_Orderings_Obot__class_Obot(tc_fun(U_9725,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9725) ),
    inference(clausify,[status(thm)],[f_2682_2]) ).

fof(f_2683_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_2683_2,plain,
    ! [U_9732,U_9731,U_9730,U_9729] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9729,U_9730,U_9731)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9729,U_9731,U_9732)) = c_Orderings_Obot__class_Obot(tc_fun(U_9729,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9729) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

cnf(f_2683_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9729,U_9730,U_9731)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9729,U_9731,U_9732)) = c_Orderings_Obot__class_Obot(tc_fun(U_9729,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9729) ),
    inference(clausify,[status(thm)],[f_2683_2]) ).

fof(f_2684_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_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_2684_2,plain,
    ! [U_9737,U_9736,U_9735,U_9734,U_9733] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,U_9734,U_9735)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,U_9736,U_9737)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9733),U_9734),U_9736),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9733),U_9735),U_9737))
      | ~ class_Orderings_Olinorder(U_9733) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

cnf(f_2684_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,U_9734,U_9735)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,U_9736,U_9737)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9733,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9733),U_9734),U_9736),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9733),U_9735),U_9737))
    | ~ class_Orderings_Olinorder(U_9733) ),
    inference(clausify,[status(thm)],[f_2684_2]) ).

fof(f_2685_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_2685_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_2685_1]) ).

fof(f_2686_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_2686_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_2686_1]) ).

fof(f_2687_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_2687_2,plain,
    ! [U_9741,U_9740,U_9739,U_9738] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9738,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9738,U_9739,U_9740)),c_SetInterval_Oord__class_OatLeastAtMost(U_9738,U_9740,U_9741)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9738,U_9739,U_9741)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9738),U_9740),U_9741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9738),U_9739),U_9740))
      | ~ class_Orderings_Olinorder(U_9738) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

cnf(f_2687_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9738,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9738,U_9739,U_9740)),c_SetInterval_Oord__class_OatLeastAtMost(U_9738,U_9740,U_9741)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9738,U_9739,U_9741)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9738),U_9740),U_9741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9738),U_9739),U_9740))
    | ~ class_Orderings_Olinorder(U_9738) ),
    inference(clausify,[status(thm)],[f_2687_2]) ).

fof(f_2688_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_2688_2,plain,
    ! [U_9744,U_9743,U_9742] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9742,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9742,U_9743,U_9744)),hAPP(hAPP(c_Set_Oinsert(U_9742),U_9744),c_Orderings_Obot__class_Obot(tc_fun(U_9742,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9742,U_9743,U_9744)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9742),U_9743),U_9744))
      | ~ class_Orderings_Olinorder(U_9742) ),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

cnf(f_2688_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9742,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9742,U_9743,U_9744)),hAPP(hAPP(c_Set_Oinsert(U_9742),U_9744),c_Orderings_Obot__class_Obot(tc_fun(U_9742,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9742,U_9743,U_9744)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9742),U_9743),U_9744))
    | ~ class_Orderings_Olinorder(U_9742) ),
    inference(clausify,[status(thm)],[f_2688_2]) ).

fof(f_2689_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_2689_2,plain,
    ! [U_9746,U_9745] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9745,U_9746))),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

cnf(f_2689_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9745,U_9746))),
    inference(clausify,[status(thm)],[f_2689_2]) ).

fof(f_2690_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_2690_2,plain,
    ! [U_9748,U_9747] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_9747,U_9748))),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

cnf(f_2690_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_9747,U_9748))),
    inference(clausify,[status(thm)],[f_2690_2]) ).

fof(f_2691_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_2691_2,plain,
    ! [U_9750,U_9749] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9749,U_9750))),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

cnf(f_2691_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9749,U_9750))),
    inference(clausify,[status(thm)],[f_2691_2]) ).

fof(f_2692_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_2692_2,plain,
    ! [U_9753,U_9752,U_9751] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_9751,U_9753,U_9752) = c_Orderings_Obot__class_Obot(tc_fun(U_9751,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9751),U_9752),U_9753))
      | ~ class_Orderings_Oorder(U_9751) ),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

cnf(f_2692_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_9751,U_9753,U_9752) = c_Orderings_Obot__class_Obot(tc_fun(U_9751,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9751),U_9752),U_9753))
    | ~ class_Orderings_Oorder(U_9751) ),
    inference(clausify,[status(thm)],[f_2692_2]) ).

fof(f_2693_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_2693_2,plain,
    ! [U_9756,U_9755,U_9754] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_9754,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9754,U_9755,U_9756)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9754),U_9755),U_9756)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9754),U_9755),U_9756))
          | c_Orderings_Obot__class_Obot(tc_fun(U_9754,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_9754,U_9755,U_9756) ) )
      | ~ class_Orderings_Oorder(U_9754) ),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

cnf(f_2693_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9754),U_9755),U_9756))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9754,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_9754,U_9755,U_9756)
    | ~ class_Orderings_Oorder(U_9754) ),
    inference(clausify,[status(thm)],[f_2693_2]) ).

cnf(f_2693_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_9754,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9754,U_9755,U_9756)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9754),U_9755),U_9756))
    | ~ class_Orderings_Oorder(U_9754) ),
    inference(clausify,[status(thm)],[f_2693_2]) ).

fof(f_2694_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_2694_2,plain,
    ! [U_9759,U_9758,U_9757] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_9757,U_9758,U_9759) = c_Orderings_Obot__class_Obot(tc_fun(U_9757,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9757),U_9758),U_9759)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9757),U_9758),U_9759))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_9757,U_9758,U_9759) != c_Orderings_Obot__class_Obot(tc_fun(U_9757,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_9757) ),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

cnf(f_2694_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9757),U_9758),U_9759))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_9757,U_9758,U_9759) != c_Orderings_Obot__class_Obot(tc_fun(U_9757,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9757) ),
    inference(clausify,[status(thm)],[f_2694_2]) ).

cnf(f_2694_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_9757,U_9758,U_9759) = c_Orderings_Obot__class_Obot(tc_fun(U_9757,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9757),U_9758),U_9759))
    | ~ class_Orderings_Oorder(U_9757) ),
    inference(clausify,[status(thm)],[f_2694_2]) ).

fof(f_2695_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_2695_2,plain,
    ! [U_9763,U_9762,U_9761,U_9760] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9760,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9761,U_9762)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9762,U_9763)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9761,U_9763)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9760),U_9762),U_9763))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9760),U_9761),U_9762))
      | ~ class_Orderings_Olinorder(U_9760) ),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

cnf(f_2695_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9760,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9761,U_9762)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9762,U_9763)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9760,U_9761,U_9763)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9760),U_9762),U_9763))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9760),U_9761),U_9762))
    | ~ class_Orderings_Olinorder(U_9760) ),
    inference(clausify,[status(thm)],[f_2695_2]) ).

fof(f_2696_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_2696_2,plain,
    ! [U_9767,U_9766,U_9765,U_9764] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9764,U_9765,U_9766)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9764,U_9766,U_9767)) = c_Orderings_Obot__class_Obot(tc_fun(U_9764,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9764) ),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

cnf(f_2696_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9764,U_9765,U_9766)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9764,U_9766,U_9767)) = c_Orderings_Obot__class_Obot(tc_fun(U_9764,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9764) ),
    inference(clausify,[status(thm)],[f_2696_2]) ).

fof(f_2697_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_2697_2,plain,
    ! [U_9769,U_9768] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9768),U_9769) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9768,U_9769),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

cnf(f_2697_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9768),U_9769) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9768,U_9769),
    inference(clausify,[status(thm)],[f_2697_2]) ).

fof(f_2698_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_2698_2,plain,
    ! [U_9771,U_9770] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9770,U_9771)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9771),U_9770),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

cnf(f_2698_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9770,U_9771)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9771),U_9770),
    inference(clausify,[status(thm)],[f_2698_2]) ).

fof(f_2699_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_2699_2,plain,
    ! [U_9775,U_9774,U_9773,U_9772] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9772,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9772,U_9773,U_9774)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9772,U_9774,U_9775)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9772,U_9773,U_9775)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),U_9774),U_9775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),U_9773),U_9774))
      | ~ class_Orderings_Olinorder(U_9772) ),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

cnf(f_2699_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9772,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9772,U_9773,U_9774)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9772,U_9774,U_9775)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9772,U_9773,U_9775)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),U_9774),U_9775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9772),U_9773),U_9774))
    | ~ class_Orderings_Olinorder(U_9772) ),
    inference(clausify,[status(thm)],[f_2699_2]) ).

fof(f_2700_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_2700_2,plain,
    ! [U_9777,U_9776] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9776),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_9777) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9776,U_9777),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

cnf(f_2700_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9776),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_9777) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9776,U_9777),
    inference(clausify,[status(thm)],[f_2700_2]) ).

fof(f_2701_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_2701_2,plain,
    ! [U_9781,U_9780,U_9779,U_9778] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9778,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9778,U_9779,U_9780)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9778,U_9780,U_9781)) = c_Orderings_Obot__class_Obot(tc_fun(U_9778,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9778) ),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

cnf(f_2701_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9778,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_9778,U_9779,U_9780)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9778,U_9780,U_9781)) = c_Orderings_Obot__class_Obot(tc_fun(U_9778,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9778) ),
    inference(clausify,[status(thm)],[f_2701_2]) ).

fof(f_2702_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_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_2702_2,plain,
    ! [U_9786,U_9785,U_9784,U_9783,U_9782] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9782,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,U_9783,U_9784)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,U_9785,U_9786)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9782),U_9783),U_9785),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9782),U_9784),U_9786))
      | ~ class_Orderings_Olinorder(U_9782) ),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

cnf(f_2702_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9782,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,U_9783,U_9784)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,U_9785,U_9786)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_9782,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9782),U_9783),U_9785),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9782),U_9784),U_9786))
    | ~ class_Orderings_Olinorder(U_9782) ),
    inference(clausify,[status(thm)],[f_2702_2]) ).

fof(f_2703_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_2703_2,plain,
    ! [U_9790,U_9789,U_9788,U_9787] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9787,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9787,U_9788,U_9789)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9787,U_9789,U_9790)) = c_Orderings_Obot__class_Obot(tc_fun(U_9787,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_9787) ),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

cnf(f_2703_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9787,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9787,U_9788,U_9789)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9787,U_9789,U_9790)) = c_Orderings_Obot__class_Obot(tc_fun(U_9787,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_9787) ),
    inference(clausify,[status(thm)],[f_2703_2]) ).

fof(f_2704_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_2704_2,plain,
    ! [U_9792,U_9791] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_9791,U_9792)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9792),hAPP(c_Nat_OSuc,U_9791)),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

cnf(f_2704_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_9791,U_9792)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9792),hAPP(c_Nat_OSuc,U_9791)),
    inference(clausify,[status(thm)],[f_2704_2]) ).

fof(f_2705_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_2705_2,plain,
    ! [U_9794,U_9793] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9793,U_9794)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9794),U_9793)),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

cnf(f_2705_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_9793,U_9794)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9794),U_9793)),
    inference(clausify,[status(thm)],[f_2705_2]) ).

fof(f_2706_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_2706_2,plain,
    ! [U_9798,U_9797,U_9796,U_9795] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9795,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9795,U_9796,U_9797)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9795,U_9797,U_9798)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9795,U_9796,U_9798)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),U_9797),U_9798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9795),U_9796),U_9797))
      | ~ class_Orderings_Olinorder(U_9795) ),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

cnf(f_2706_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9795,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9795,U_9796,U_9797)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_9795,U_9797,U_9798)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_9795,U_9796,U_9798)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9795),U_9797),U_9798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9795),U_9796),U_9797))
    | ~ class_Orderings_Olinorder(U_9795) ),
    inference(clausify,[status(thm)],[f_2706_2]) ).

fof(f_2707_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_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_2707_2,plain,
    ! [U_9802,U_9801,U_9800,U_9799] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9799),U_9802),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9800,U_9801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9799),hAPP(U_9802,U_9800)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9799),U_9802),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9800,U_9801)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9800),U_9801))
      | ~ class_Groups_Ocomm__monoid__add(U_9799) ),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

cnf(f_2707_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9799),U_9802),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9800,U_9801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9799),hAPP(U_9802,U_9800)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9799),U_9802),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_9800,U_9801)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9800),U_9801))
    | ~ class_Groups_Ocomm__monoid__add(U_9799) ),
    inference(clausify,[status(thm)],[f_2707_2]) ).

fof(f_2708_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_2708_2,plain,
    ! [U_9805,U_9804,U_9803] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9803,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9804),c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9803,U_9804,U_9805)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9803,U_9804,U_9805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9803),U_9804),U_9805))
      | ~ class_Orderings_Olinorder(U_9803) ),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

cnf(f_2708_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9803,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9804),c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_9803,U_9804,U_9805)) = c_SetInterval_Oord__class_OatLeastAtMost(U_9803,U_9804,U_9805)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9803),U_9804),U_9805))
    | ~ class_Orderings_Olinorder(U_9803) ),
    inference(clausify,[status(thm)],[f_2708_2]) ).

fof(f_2709_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_2709_2,plain,
    ! [U_9807,U_9806] :
      ( ( 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_9806),U_9807)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9806),U_9807)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9806),U_9807))
        | ~ 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_9806),U_9807)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

fof(f_2709_3,plain,
    ( ! [U_9811,U_9809] :
        ( 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_9809),U_9811)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9809),U_9811)) )
    & ! [U_9810,U_9808] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9808),U_9810))
        | ~ 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_9808),U_9810)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_2709_2]) ).

cnf(f_2709_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9808),U_9810))
    | ~ 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_9808),U_9810)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_2709_3]) ).

cnf(f_2709_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_9809),U_9811)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9809),U_9811)) ),
    inference(clausify,[status(thm)],[f_2709_3]) ).

fof(f_2710_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_2710_2,plain,
    ! [U_9815,U_9814,U_9813,U_9812] :
      ( ( 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_9812),U_9813)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9814),U_9815))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9812),U_9815) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9814),U_9813) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9812),U_9815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9814),U_9813)
        | ~ 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_9812),U_9813)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9814),U_9815))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

fof(f_2710_3,plain,
    ( ! [U_9823,U_9821,U_9819,U_9817] :
        ( 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_9817),U_9819)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9821),U_9823))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9817),U_9823) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9821),U_9819) )
    & ! [U_9822,U_9820,U_9818,U_9816] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9816),U_9822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9820),U_9818)
        | ~ 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_9816),U_9818)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9820),U_9822))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_2710_2]) ).

cnf(f_2710_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9816),U_9822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9820),U_9818)
    | ~ 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_9816),U_9818)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9820),U_9822))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_2710_3]) ).

cnf(f_2710_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_9817),U_9819)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9821),U_9823))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9817),U_9823) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9821),U_9819) ),
    inference(clausify,[status(thm)],[f_2710_3]) ).

fof(f_2711_1,plain,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2))
      | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).

fof(f_2711_2,plain,
    ! [U_9827,U_9826,U_9825,U_9824] :
      ( c_FunDef_Oreduction__pair(U_9826,hAPP(hAPP(c_FunDef_Orp__inv__image(U_9824,U_9826),U_9825),U_9827))
      | ~ c_FunDef_Oreduction__pair(U_9824,U_9825) ),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

cnf(f_2711_3,plain,
    ( c_FunDef_Oreduction__pair(U_9826,hAPP(hAPP(c_FunDef_Orp__inv__image(U_9824,U_9826),U_9825),U_9827))
    | ~ c_FunDef_Oreduction__pair(U_9824,U_9825) ),
    inference(clausify,[status(thm)],[f_2711_2]) ).

fof(f_2712_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_2712_2,plain,
    ! [U_9831,U_9830,U_9829,U_9828] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9829,U_9828),U_9830),U_9831) = hAPP(hAPP(c_Finite__Set_Ofold(U_9829,U_9828,hAPP(hAPP(c_COMBB(U_9828,tc_fun(U_9828,U_9828),U_9829),c_Lattices_Osemilattice__sup__class_Osup(U_9828)),U_9831)),c_Orderings_Obot__class_Obot(U_9828)),U_9830)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9829),U_9830))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9828) ),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

cnf(f_2712_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9829,U_9828),U_9830),U_9831) = hAPP(hAPP(c_Finite__Set_Ofold(U_9829,U_9828,hAPP(hAPP(c_COMBB(U_9828,tc_fun(U_9828,U_9828),U_9829),c_Lattices_Osemilattice__sup__class_Osup(U_9828)),U_9831)),c_Orderings_Obot__class_Obot(U_9828)),U_9830)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9829),U_9830))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9828) ),
    inference(clausify,[status(thm)],[f_2712_2]) ).

fof(f_2713_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_2713_2,plain,
    ! [U_9837,U_9836,U_9835,U_9834,U_9833,U_9832] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9832,tc_fun(U_9837,tc_HOL_Obool)),U_9834),U_9835),U_9836))
      | ~ hBOOL(hAPP(hAPP(U_9835,U_9833),U_9836))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9832),U_9833),U_9834)) ),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

cnf(f_2713_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9832,tc_fun(U_9837,tc_HOL_Obool)),U_9834),U_9835),U_9836))
    | ~ hBOOL(hAPP(hAPP(U_9835,U_9833),U_9836))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9832),U_9833),U_9834)) ),
    inference(clausify,[status(thm)],[f_2713_2]) ).

fof(f_2714_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_2714_2,plain,
    ! [U_9843,U_9842,U_9841,U_9840,U_9839,U_9838] :
      ( hBOOL(hAPP(hAPP(c_member(U_9841),U_9842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9838,tc_fun(U_9841,tc_HOL_Obool)),U_9840),U_9843)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9841),U_9842),hAPP(U_9843,U_9839)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9839),U_9840)) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

cnf(f_2714_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9841),U_9842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9838,tc_fun(U_9841,tc_HOL_Obool)),U_9840),U_9843)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9841),U_9842),hAPP(U_9843,U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9839),U_9840)) ),
    inference(clausify,[status(thm)],[f_2714_2]) ).

fof(f_2715_1,plain,
    ! [T_d,T_c,V_ca_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_ca_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).

fof(f_2715_2,plain,
    ! [U_9851,U_9850,U_9849,U_9848,U_9847,U_9846,U_9845,U_9844] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9844,tc_fun(U_9850,tc_fun(U_9851,tc_HOL_Obool))),U_9846),U_9847),U_9848),U_9849))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_9847,U_9845),U_9848),U_9849))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9844),U_9845),U_9846)) ),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

cnf(f_2715_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9844,tc_fun(U_9850,tc_fun(U_9851,tc_HOL_Obool))),U_9846),U_9847),U_9848),U_9849))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_9847,U_9845),U_9848),U_9849))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9844),U_9845),U_9846)) ),
    inference(clausify,[status(thm)],[f_2715_2]) ).

fof(f_2716_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_2716_2,plain,
    ! [U_9857,U_9856,U_9855,U_9854] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9855,tc_fun(U_9854,tc_HOL_Obool)),U_9856),U_9857)
        | ? [U_9853] :
            ( hAPP(U_9857,U_9853) != c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9855),U_9853),U_9856)) ) )
      & ( ! [U_9852] :
            ( hAPP(U_9857,U_9852) = c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9855),U_9852),U_9856)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9854,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9855,tc_fun(U_9854,tc_HOL_Obool)),U_9856),U_9857) ) ),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

fof(f_2716_3,plain,
    ( ! [U_9865,U_9863,U_9861,U_9859] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9861,tc_fun(U_9859,tc_HOL_Obool)),U_9863),U_9865)
        | ? [U_9853] :
            ( hAPP(U_9865,U_9853) != c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9861),U_9853),U_9863)) ) )
    & ! [U_9864,U_9862,U_9860,U_9858] :
        ( ! [U_9852] :
            ( hAPP(U_9864,U_9852) = c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9860),U_9852),U_9862)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9860,tc_fun(U_9858,tc_HOL_Obool)),U_9862),U_9864) ) ),
    inference(miniscope,[status(thm)],[f_2716_2]) ).

fof(f_2716_4,plain,
    ( ! [U_9865,U_9863,U_9861,U_9859] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9861,tc_fun(U_9859,tc_HOL_Obool)),U_9863),U_9865)
        | ( hAPP(U_9865,sK217(U_9865,U_9863,U_9861,U_9859)) != c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9861),sK217(U_9865,U_9863,U_9861,U_9859)),U_9863)) ) )
    & ! [U_9864,U_9862,U_9860,U_9858] :
        ( ! [U_9852] :
            ( hAPP(U_9864,U_9852) = c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9860),U_9852),U_9862)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9860,tc_fun(U_9858,tc_HOL_Obool)),U_9862),U_9864) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_9853,sK217(U_9865,U_9863,U_9861,U_9859))],[f_2716_3]) ).

cnf(f_2716_5,plain,
    ( hAPP(U_9864,U_9852) = c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9860),U_9852),U_9862))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9860,tc_fun(U_9858,tc_HOL_Obool)),U_9862),U_9864) ),
    inference(clausify,[status(thm)],[f_2716_4]) ).

cnf(f_2716_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9861),sK217(U_9865,U_9863,U_9861,U_9859)),U_9863))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9861,tc_fun(U_9859,tc_HOL_Obool)),U_9863),U_9865) ),
    inference(clausify,[status(thm)],[f_2716_4]) ).

cnf(f_2716_7,plain,
    ( hAPP(U_9865,sK217(U_9865,U_9863,U_9861,U_9859)) != c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9861,tc_fun(U_9859,tc_HOL_Obool)),U_9863),U_9865) ),
    inference(clausify,[status(thm)],[f_2716_4]) ).

fof(f_2717_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_2717_2,plain,
    ! [U_9868,U_9867,U_9866] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9866,tc_fun(U_9867,tc_HOL_Obool)),U_9868),hAPP(c_COMBK(tc_fun(U_9867,tc_HOL_Obool),U_9866),c_Orderings_Obot__class_Obot(tc_fun(U_9867,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9867,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

cnf(f_2717_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9866,tc_fun(U_9867,tc_HOL_Obool)),U_9868),hAPP(c_COMBK(tc_fun(U_9867,tc_HOL_Obool),U_9866),c_Orderings_Obot__class_Obot(tc_fun(U_9867,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9867,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2717_2]) ).

fof(f_2718_1,plain,
    ! [V_ca_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_ca_2)) = V_ca_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_ca_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_2718_2,plain,
    ! [U_9872,U_9871,U_9870,U_9869] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9870,tc_fun(U_9871,tc_HOL_Obool)),U_9869),hAPP(c_COMBK(tc_fun(U_9871,tc_HOL_Obool),U_9870),U_9872)) = U_9872
        | U_9869 = c_Orderings_Obot__class_Obot(tc_fun(U_9870,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9870,tc_fun(U_9871,tc_HOL_Obool)),U_9869),hAPP(c_COMBK(tc_fun(U_9871,tc_HOL_Obool),U_9870),U_9872)) = c_Orderings_Obot__class_Obot(tc_fun(U_9871,tc_HOL_Obool))
        | U_9869 != c_Orderings_Obot__class_Obot(tc_fun(U_9870,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

fof(f_2718_3,plain,
    ( ! [U_9880,U_9878,U_9876,U_9874] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9876,tc_fun(U_9878,tc_HOL_Obool)),U_9874),hAPP(c_COMBK(tc_fun(U_9878,tc_HOL_Obool),U_9876),U_9880)) = U_9880
        | U_9874 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool)) )
    & ! [U_9879,U_9877,U_9875,U_9873] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9875,tc_fun(U_9877,tc_HOL_Obool)),U_9873),hAPP(c_COMBK(tc_fun(U_9877,tc_HOL_Obool),U_9875),U_9879)) = c_Orderings_Obot__class_Obot(tc_fun(U_9877,tc_HOL_Obool))
        | U_9873 != c_Orderings_Obot__class_Obot(tc_fun(U_9875,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2718_2]) ).

cnf(f_2718_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9875,tc_fun(U_9877,tc_HOL_Obool)),U_9873),hAPP(c_COMBK(tc_fun(U_9877,tc_HOL_Obool),U_9875),U_9879)) = c_Orderings_Obot__class_Obot(tc_fun(U_9877,tc_HOL_Obool))
    | U_9873 != c_Orderings_Obot__class_Obot(tc_fun(U_9875,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

cnf(f_2718_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9876,tc_fun(U_9878,tc_HOL_Obool)),U_9874),hAPP(c_COMBK(tc_fun(U_9878,tc_HOL_Obool),U_9876),U_9880)) = U_9880
    | U_9874 = c_Orderings_Obot__class_Obot(tc_fun(U_9876,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

fof(f_2719_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_2719_2,plain,
    ! [U_9886,U_9885,U_9884,U_9883] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9883,tc_fun(U_9884,tc_HOL_Obool)),U_9885),U_9886) = c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
        | ? [U_9882] :
            ( hAPP(U_9886,U_9882) != c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9883),U_9882),U_9885)) ) )
      & ( ! [U_9881] :
            ( hAPP(U_9886,U_9881) = c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9881),U_9885)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9883,tc_fun(U_9884,tc_HOL_Obool)),U_9885),U_9886) != c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

fof(f_2719_3,plain,
    ( ! [U_9894,U_9892,U_9890,U_9888] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9888,tc_fun(U_9890,tc_HOL_Obool)),U_9892),U_9894) = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
        | ? [U_9882] :
            ( hAPP(U_9894,U_9882) != c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9888),U_9882),U_9892)) ) )
    & ! [U_9893,U_9891,U_9889,U_9887] :
        ( ! [U_9881] :
            ( hAPP(U_9893,U_9881) = c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9887),U_9881),U_9891)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9887,tc_fun(U_9889,tc_HOL_Obool)),U_9891),U_9893) != c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2719_2]) ).

fof(f_2719_4,plain,
    ( ! [U_9894,U_9892,U_9890,U_9888] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9888,tc_fun(U_9890,tc_HOL_Obool)),U_9892),U_9894) = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
        | ( hAPP(U_9894,sK218(U_9894,U_9892,U_9890,U_9888)) != c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9888),sK218(U_9894,U_9892,U_9890,U_9888)),U_9892)) ) )
    & ! [U_9893,U_9891,U_9889,U_9887] :
        ( ! [U_9881] :
            ( hAPP(U_9893,U_9881) = c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9887),U_9881),U_9891)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9887,tc_fun(U_9889,tc_HOL_Obool)),U_9891),U_9893) != c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_9882,sK218(U_9894,U_9892,U_9890,U_9888))],[f_2719_3]) ).

cnf(f_2719_5,plain,
    ( hAPP(U_9893,U_9881) = c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9887),U_9881),U_9891))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9887,tc_fun(U_9889,tc_HOL_Obool)),U_9891),U_9893) != c_Orderings_Obot__class_Obot(tc_fun(U_9889,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2719_4]) ).

cnf(f_2719_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9888),sK218(U_9894,U_9892,U_9890,U_9888)),U_9892))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9888,tc_fun(U_9890,tc_HOL_Obool)),U_9892),U_9894) = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2719_4]) ).

cnf(f_2719_7,plain,
    ( hAPP(U_9894,sK218(U_9894,U_9892,U_9890,U_9888)) != c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9888,tc_fun(U_9890,tc_HOL_Obool)),U_9892),U_9894) = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2719_4]) ).

fof(f_2720_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_2720_2,plain,
    ! [U_9900,U_9899,U_9898,U_9897] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900)))
          | ? [U_9896] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,U_9896)))
              & hBOOL(hAPP(hAPP(c_member(U_9897),U_9896),U_9898)) ) )
        & ( ! [U_9895] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,U_9895)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9897),U_9895),U_9898)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898)) ),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

fof(f_2720_3,plain,
    ! [U_9900,U_9899,U_9898,U_9897] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,sK219(U_9900,U_9899,U_9898,U_9897))))
            & hBOOL(hAPP(hAPP(c_member(U_9897),sK219(U_9900,U_9899,U_9898,U_9897)),U_9898)) ) )
        & ( ! [U_9895] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,U_9895)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_9897),U_9895),U_9898)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_9896,sK219(U_9900,U_9899,U_9898,U_9897))],[f_2720_2]) ).

cnf(f_2720_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,U_9895)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9897),U_9895),U_9898))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898)) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

cnf(f_2720_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9897),sK219(U_9900,U_9899,U_9898,U_9897)),U_9898))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898)) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

cnf(f_2720_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(U_9900,sK219(U_9900,U_9899,U_9898,U_9897))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9897,tc_fun(U_9899,tc_HOL_Obool)),U_9898),U_9900)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9897),U_9898)) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

fof(f_2721_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_2721_2,plain,
    ! [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_COMBS(U_9901,tc_fun(U_9902,tc_HOL_Obool),tc_fun(U_9902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9902,tc_HOL_Obool),tc_fun(tc_fun(U_9902,tc_HOL_Obool),tc_fun(U_9902,tc_HOL_Obool)),U_9901),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9902,tc_HOL_Obool))),U_9904)),U_9905)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9902,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),U_9904)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),U_9905)),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

cnf(f_2721_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_COMBS(U_9901,tc_fun(U_9902,tc_HOL_Obool),tc_fun(U_9902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9902,tc_HOL_Obool),tc_fun(tc_fun(U_9902,tc_HOL_Obool),tc_fun(U_9902,tc_HOL_Obool)),U_9901),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9902,tc_HOL_Obool))),U_9904)),U_9905)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9902,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),U_9904)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),U_9905)),
    inference(clausify,[status(thm)],[f_2721_2]) ).

fof(f_2722_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_2722_2,plain,
    ! [U_9910,U_9909,U_9908,U_9907,U_9906] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9906,tc_HOL_Obool)),U_9908),U_9909)),U_9910) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9907,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),U_9908),U_9910)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),U_9909),U_9910)),
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

cnf(f_2722_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9906,tc_HOL_Obool)),U_9908),U_9909)),U_9910) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9907,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),U_9908),U_9910)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9906,tc_fun(U_9907,tc_HOL_Obool)),U_9909),U_9910)),
    inference(clausify,[status(thm)],[f_2722_2]) ).

fof(f_2723_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_2723_2,plain,
    ! [U_9917,U_9916,U_9915,U_9914,U_9913] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9913),U_9914),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9915,tc_fun(U_9913,tc_HOL_Obool)),U_9916),U_9917)))
        | ! [U_9912] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9913),U_9914),hAPP(U_9917,U_9912)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9915),U_9912),U_9916)) ) )
      & ( ? [U_9911] :
            ( hBOOL(hAPP(hAPP(c_member(U_9913),U_9914),hAPP(U_9917,U_9911)))
            & hBOOL(hAPP(hAPP(c_member(U_9915),U_9911),U_9916)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9913),U_9914),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9915,tc_fun(U_9913,tc_HOL_Obool)),U_9916),U_9917))) ) ),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

fof(f_2723_3,plain,
    ( ! [U_9927,U_9925,U_9923,U_9921,U_9919] :
        ( hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9923,tc_fun(U_9919,tc_HOL_Obool)),U_9925),U_9927)))
        | ! [U_9912] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(U_9927,U_9912)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9912),U_9925)) ) )
    & ! [U_9926,U_9924,U_9922,U_9920,U_9918] :
        ( ? [U_9911] :
            ( hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(U_9926,U_9911)))
            & hBOOL(hAPP(hAPP(c_member(U_9922),U_9911),U_9924)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9922,tc_fun(U_9918,tc_HOL_Obool)),U_9924),U_9926))) ) ),
    inference(miniscope,[status(thm)],[f_2723_2]) ).

fof(f_2723_4,plain,
    ( ! [U_9927,U_9925,U_9923,U_9921,U_9919] :
        ( hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9923,tc_fun(U_9919,tc_HOL_Obool)),U_9925),U_9927)))
        | ! [U_9912] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(U_9927,U_9912)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9912),U_9925)) ) )
    & ! [U_9926,U_9924,U_9922,U_9920,U_9918] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(U_9926,sK220(U_9926,U_9924,U_9922,U_9920,U_9918))))
          & hBOOL(hAPP(hAPP(c_member(U_9922),sK220(U_9926,U_9924,U_9922,U_9920,U_9918)),U_9924)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9922,tc_fun(U_9918,tc_HOL_Obool)),U_9924),U_9926))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_9911,sK220(U_9926,U_9924,U_9922,U_9920,U_9918))],[f_2723_3]) ).

cnf(f_2723_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9922),sK220(U_9926,U_9924,U_9922,U_9920,U_9918)),U_9924))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9922,tc_fun(U_9918,tc_HOL_Obool)),U_9924),U_9926))) ),
    inference(clausify,[status(thm)],[f_2723_4]) ).

cnf(f_2723_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(U_9926,sK220(U_9926,U_9924,U_9922,U_9920,U_9918))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9918),U_9920),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9922,tc_fun(U_9918,tc_HOL_Obool)),U_9924),U_9926))) ),
    inference(clausify,[status(thm)],[f_2723_4]) ).

cnf(f_2723_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9923,tc_fun(U_9919,tc_HOL_Obool)),U_9925),U_9927)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9921),hAPP(U_9927,U_9912)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9923),U_9912),U_9925)) ),
    inference(clausify,[status(thm)],[f_2723_4]) ).

fof(f_2724_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_2724_2,plain,
    ! [U_9933,U_9932,U_9931,U_9930,U_9929,U_9928] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9930,tc_fun(U_9928,tc_HOL_Obool)),U_9931),U_9932)),U_9933) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9930,tc_fun(U_9929,tc_HOL_Obool)),U_9931),hAPP(hAPP(c_COMBC(U_9930,tc_fun(U_9928,tc_fun(U_9929,tc_HOL_Obool)),tc_fun(U_9929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(tc_fun(U_9928,tc_fun(U_9929,tc_HOL_Obool)),tc_fun(U_9929,tc_HOL_Obool)),U_9930),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool))),U_9932)),U_9933)),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

cnf(f_2724_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9930,tc_fun(U_9928,tc_HOL_Obool)),U_9931),U_9932)),U_9933) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9930,tc_fun(U_9929,tc_HOL_Obool)),U_9931),hAPP(hAPP(c_COMBC(U_9930,tc_fun(U_9928,tc_fun(U_9929,tc_HOL_Obool)),tc_fun(U_9929,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(tc_fun(U_9928,tc_fun(U_9929,tc_HOL_Obool)),tc_fun(U_9929,tc_HOL_Obool)),U_9930),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9928,tc_fun(U_9929,tc_HOL_Obool))),U_9932)),U_9933)),
    inference(clausify,[status(thm)],[f_2724_2]) ).

fof(f_2725_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_2725_2,plain,
    ! [U_9939,U_9938,U_9937,U_9936,U_9935,U_9934] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9935,tc_HOL_Obool)),U_9936),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9937,tc_fun(U_9935,tc_HOL_Obool)),tc_fun(U_9935,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9937,tc_HOL_Obool),tc_fun(tc_fun(U_9937,tc_fun(U_9935,tc_HOL_Obool)),tc_fun(U_9935,tc_HOL_Obool)),U_9934),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9935,tc_HOL_Obool))),U_9938)),U_9939)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9935,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9934,tc_fun(U_9937,tc_HOL_Obool)),U_9936),U_9938)),U_9939),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

cnf(f_2725_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9935,tc_HOL_Obool)),U_9936),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9937,tc_fun(U_9935,tc_HOL_Obool)),tc_fun(U_9935,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9937,tc_HOL_Obool),tc_fun(tc_fun(U_9937,tc_fun(U_9935,tc_HOL_Obool)),tc_fun(U_9935,tc_HOL_Obool)),U_9934),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9935,tc_HOL_Obool))),U_9938)),U_9939)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9935,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9934,tc_fun(U_9937,tc_HOL_Obool)),U_9936),U_9938)),U_9939),
    inference(clausify,[status(thm)],[f_2725_2]) ).

fof(f_2726_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_2726_2,plain,
    ! [U_9943,U_9942,U_9941,U_9940] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9941,tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)),U_9942),hAPP(hAPP(c_COMBB(tc_fun(U_9940,tc_HOL_Obool),tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool),U_9941),c_Set_OPow(U_9940)),U_9943))),hAPP(c_Set_OPow(U_9940),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9941,tc_fun(U_9940,tc_HOL_Obool)),U_9942),U_9943)))),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

cnf(f_2726_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9941,tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)),U_9942),hAPP(hAPP(c_COMBB(tc_fun(U_9940,tc_HOL_Obool),tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool),U_9941),c_Set_OPow(U_9940)),U_9943))),hAPP(c_Set_OPow(U_9940),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9941,tc_fun(U_9940,tc_HOL_Obool)),U_9942),U_9943)))),
    inference(clausify,[status(thm)],[f_2726_2]) ).

fof(f_2727_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_2727_2,plain,
    ! [U_9950,U_9949,U_9948,U_9947,U_9946] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9947,tc_fun(U_9946,tc_HOL_Obool)),U_9948),U_9949)),U_9950))
        | ? [U_9945] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9946,tc_HOL_Obool)),hAPP(U_9949,U_9945)),U_9950))
            & hBOOL(hAPP(hAPP(c_member(U_9947),U_9945),U_9948)) ) )
      & ( ! [U_9944] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9946,tc_HOL_Obool)),hAPP(U_9949,U_9944)),U_9950))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9947),U_9944),U_9948)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9947,tc_fun(U_9946,tc_HOL_Obool)),U_9948),U_9949)),U_9950)) ) ),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

fof(f_2727_3,plain,
    ( ! [U_9960,U_9958,U_9956,U_9954,U_9952] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9954,tc_fun(U_9952,tc_HOL_Obool)),U_9956),U_9958)),U_9960))
        | ? [U_9945] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(U_9958,U_9945)),U_9960))
            & hBOOL(hAPP(hAPP(c_member(U_9954),U_9945),U_9956)) ) )
    & ! [U_9959,U_9957,U_9955,U_9953,U_9951] :
        ( ! [U_9944] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(U_9957,U_9944)),U_9959))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9953),U_9944),U_9955)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9953,tc_fun(U_9951,tc_HOL_Obool)),U_9955),U_9957)),U_9959)) ) ),
    inference(miniscope,[status(thm)],[f_2727_2]) ).

fof(f_2727_4,plain,
    ( ! [U_9960,U_9958,U_9956,U_9954,U_9952] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9954,tc_fun(U_9952,tc_HOL_Obool)),U_9956),U_9958)),U_9960))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(U_9958,sK221(U_9960,U_9958,U_9956,U_9954,U_9952))),U_9960))
          & hBOOL(hAPP(hAPP(c_member(U_9954),sK221(U_9960,U_9958,U_9956,U_9954,U_9952)),U_9956)) ) )
    & ! [U_9959,U_9957,U_9955,U_9953,U_9951] :
        ( ! [U_9944] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(U_9957,U_9944)),U_9959))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9953),U_9944),U_9955)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9953,tc_fun(U_9951,tc_HOL_Obool)),U_9955),U_9957)),U_9959)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_9945,sK221(U_9960,U_9958,U_9956,U_9954,U_9952))],[f_2727_3]) ).

cnf(f_2727_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(U_9957,U_9944)),U_9959))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9953),U_9944),U_9955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9953,tc_fun(U_9951,tc_HOL_Obool)),U_9955),U_9957)),U_9959)) ),
    inference(clausify,[status(thm)],[f_2727_4]) ).

cnf(f_2727_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9954),sK221(U_9960,U_9958,U_9956,U_9954,U_9952)),U_9956))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9954,tc_fun(U_9952,tc_HOL_Obool)),U_9956),U_9958)),U_9960)) ),
    inference(clausify,[status(thm)],[f_2727_4]) ).

cnf(f_2727_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(U_9958,sK221(U_9960,U_9958,U_9956,U_9954,U_9952))),U_9960))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9952,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9954,tc_fun(U_9952,tc_HOL_Obool)),U_9956),U_9958)),U_9960)) ),
    inference(clausify,[status(thm)],[f_2727_4]) ).

fof(f_2728_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_2728_2,plain,
    ! [U_9967,U_9966,U_9965,U_9964,U_9963,U_9962,U_9961] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9962,tc_fun(U_9961,tc_HOL_Obool)),U_9963),U_9964)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9965,tc_fun(U_9961,tc_HOL_Obool)),U_9966),U_9967)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9962,tc_fun(U_9961,tc_HOL_Obool)),U_9963),hAPP(hAPP(c_COMBB(tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9961,tc_HOL_Obool),U_9962),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9965,tc_fun(U_9961,tc_HOL_Obool)),U_9966)),hAPP(hAPP(c_COMBC(U_9962,tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool)),tc_fun(tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool))),U_9962),c_COMBB(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool),U_9965)),hAPP(hAPP(c_COMBB(tc_fun(U_9961,tc_HOL_Obool),tc_fun(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool)),U_9962),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9961,tc_HOL_Obool))),U_9964))),U_9967))),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

cnf(f_2728_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9961,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9962,tc_fun(U_9961,tc_HOL_Obool)),U_9963),U_9964)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9965,tc_fun(U_9961,tc_HOL_Obool)),U_9966),U_9967)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9962,tc_fun(U_9961,tc_HOL_Obool)),U_9963),hAPP(hAPP(c_COMBB(tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9961,tc_HOL_Obool),U_9962),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9965,tc_fun(U_9961,tc_HOL_Obool)),U_9966)),hAPP(hAPP(c_COMBC(U_9962,tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool)),tc_fun(tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool)),tc_fun(U_9965,tc_fun(U_9961,tc_HOL_Obool))),U_9962),c_COMBB(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool),U_9965)),hAPP(hAPP(c_COMBB(tc_fun(U_9961,tc_HOL_Obool),tc_fun(tc_fun(U_9961,tc_HOL_Obool),tc_fun(U_9961,tc_HOL_Obool)),U_9962),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9961,tc_HOL_Obool))),U_9964))),U_9967))),
    inference(clausify,[status(thm)],[f_2728_2]) ).

fof(f_2729_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_2729_2,plain,
    ! [U_9972,U_9971,U_9970,U_9969,U_9968] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9968,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9968,tc_HOL_Obool)),U_9970),U_9971)),U_9972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9968,tc_HOL_Obool)),U_9970),hAPP(hAPP(c_COMBC(U_9969,tc_fun(U_9968,tc_HOL_Obool),tc_fun(U_9968,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9968,tc_HOL_Obool),tc_fun(tc_fun(U_9968,tc_HOL_Obool),tc_fun(U_9968,tc_HOL_Obool)),U_9969),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9968,tc_HOL_Obool))),U_9971)),U_9972)),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

cnf(f_2729_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9968,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9968,tc_HOL_Obool)),U_9970),U_9971)),U_9972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9968,tc_HOL_Obool)),U_9970),hAPP(hAPP(c_COMBC(U_9969,tc_fun(U_9968,tc_HOL_Obool),tc_fun(U_9968,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9968,tc_HOL_Obool),tc_fun(tc_fun(U_9968,tc_HOL_Obool),tc_fun(U_9968,tc_HOL_Obool)),U_9969),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9968,tc_HOL_Obool))),U_9971)),U_9972)),
    inference(clausify,[status(thm)],[f_2729_2]) ).

fof(f_2730_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_2730_2,plain,
    ! [U_9977,U_9976,U_9975,U_9974,U_9973] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9973,tc_HOL_Obool)),U_9974),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9975,tc_fun(U_9973,tc_HOL_Obool)),U_9976),U_9977)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9975,tc_fun(U_9973,tc_HOL_Obool)),U_9976),hAPP(hAPP(c_COMBB(tc_fun(U_9973,tc_HOL_Obool),tc_fun(U_9973,tc_HOL_Obool),U_9975),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9973,tc_HOL_Obool)),U_9974)),U_9977)),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

cnf(f_2730_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9973,tc_HOL_Obool)),U_9974),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9975,tc_fun(U_9973,tc_HOL_Obool)),U_9976),U_9977)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9975,tc_fun(U_9973,tc_HOL_Obool)),U_9976),hAPP(hAPP(c_COMBB(tc_fun(U_9973,tc_HOL_Obool),tc_fun(U_9973,tc_HOL_Obool),U_9975),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9973,tc_HOL_Obool)),U_9974)),U_9977)),
    inference(clausify,[status(thm)],[f_2730_2]) ).

fof(f_2731_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_2731_2,plain,
    ! [U_9982,U_9981,U_9980,U_9979,U_9978] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9978,tc_HOL_Obool)),U_9979),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9980,tc_fun(U_9978,tc_HOL_Obool)),U_9981),U_9982)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9980,tc_fun(U_9978,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_COMBB(tc_fun(U_9978,tc_HOL_Obool),tc_fun(U_9978,tc_HOL_Obool),U_9980),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9978,tc_HOL_Obool)),U_9979)),U_9982)),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

cnf(f_2731_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9978,tc_HOL_Obool)),U_9979),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9980,tc_fun(U_9978,tc_HOL_Obool)),U_9981),U_9982)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9980,tc_fun(U_9978,tc_HOL_Obool)),U_9981),hAPP(hAPP(c_COMBB(tc_fun(U_9978,tc_HOL_Obool),tc_fun(U_9978,tc_HOL_Obool),U_9980),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9978,tc_HOL_Obool)),U_9979)),U_9982)),
    inference(clausify,[status(thm)],[f_2731_2]) ).

fof(f_2732_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_2732_2,plain,
    ! [U_9987,U_9986,U_9985,U_9984,U_9983] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9983,tc_fun(U_9984,tc_HOL_Obool)),U_9985),hAPP(hAPP(c_COMBC(U_9983,tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool)),U_9983),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9984,tc_HOL_Obool))),U_9986)),U_9987)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9984,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9983,tc_fun(U_9984,tc_HOL_Obool)),U_9985),U_9986)),U_9987),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

cnf(f_2732_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9983,tc_fun(U_9984,tc_HOL_Obool)),U_9985),hAPP(hAPP(c_COMBC(U_9983,tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9984,tc_HOL_Obool)),U_9983),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9984,tc_HOL_Obool))),U_9986)),U_9987)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9984,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9983,tc_fun(U_9984,tc_HOL_Obool)),U_9985),U_9986)),U_9987),
    inference(clausify,[status(thm)],[f_2732_2]) ).

fof(f_2733_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_2733_2,plain,
    ! [U_9992,U_9991,U_9990,U_9989,U_9988] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9988,tc_fun(U_9989,tc_HOL_Obool)),U_9990),hAPP(hAPP(c_COMBB(tc_fun(U_9989,tc_HOL_Obool),tc_fun(U_9989,tc_HOL_Obool),U_9988),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9991)),U_9992)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9988,tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9992)),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

cnf(f_2733_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9988,tc_fun(U_9989,tc_HOL_Obool)),U_9990),hAPP(hAPP(c_COMBB(tc_fun(U_9989,tc_HOL_Obool),tc_fun(U_9989,tc_HOL_Obool),U_9988),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9991)),U_9992)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9989,tc_HOL_Obool)),U_9991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9988,tc_fun(U_9989,tc_HOL_Obool)),U_9990),U_9992)),
    inference(clausify,[status(thm)],[f_2733_2]) ).

fof(f_2734_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_2734_2,plain,
    ! [U_9996,U_9995,U_9994,U_9993] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9993,tc_HOL_Obool),tc_fun(U_9994,tc_HOL_Obool)),U_9995),hAPP(hAPP(c_COMBC(tc_fun(U_9993,tc_HOL_Obool),tc_fun(U_9993,tc_fun(U_9994,tc_HOL_Obool)),tc_fun(U_9994,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9993,tc_fun(U_9994,tc_HOL_Obool))),U_9996)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9993,tc_fun(U_9994,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9993,tc_HOL_Obool),U_9995)),U_9996),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

cnf(f_2734_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9993,tc_HOL_Obool),tc_fun(U_9994,tc_HOL_Obool)),U_9995),hAPP(hAPP(c_COMBC(tc_fun(U_9993,tc_HOL_Obool),tc_fun(U_9993,tc_fun(U_9994,tc_HOL_Obool)),tc_fun(U_9994,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9993,tc_fun(U_9994,tc_HOL_Obool))),U_9996)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9993,tc_fun(U_9994,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9993,tc_HOL_Obool),U_9995)),U_9996),
    inference(clausify,[status(thm)],[f_2734_2]) ).

fof(f_2735_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_2735_2,plain,
    ! [U_10000,U_9999,U_9998,U_9997] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9997,tc_fun(U_9998,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9997,tc_HOL_Obool),U_9999)),U_10000) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9997,tc_HOL_Obool),tc_fun(U_9998,tc_HOL_Obool)),U_9999),hAPP(hAPP(c_COMBC(tc_fun(U_9997,tc_HOL_Obool),tc_fun(U_9997,tc_fun(U_9998,tc_HOL_Obool)),tc_fun(U_9998,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9997,tc_fun(U_9998,tc_HOL_Obool))),U_10000)),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

cnf(f_2735_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9997,tc_fun(U_9998,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9997,tc_HOL_Obool),U_9999)),U_10000) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9997,tc_HOL_Obool),tc_fun(U_9998,tc_HOL_Obool)),U_9999),hAPP(hAPP(c_COMBC(tc_fun(U_9997,tc_HOL_Obool),tc_fun(U_9997,tc_fun(U_9998,tc_HOL_Obool)),tc_fun(U_9998,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9997,tc_fun(U_9998,tc_HOL_Obool))),U_10000)),
    inference(clausify,[status(thm)],[f_2735_2]) ).

fof(f_2736_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_2736_2,plain,
    ! [U_10006,U_10005,U_10004,U_10003,U_10002,U_10001] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10003,U_10001)),U_10004),U_10005),U_10006) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,U_10001),U_10004),hAPP(hAPP(c_COMBC(U_10002,U_10003,U_10001),U_10005),U_10006))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10001) ),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

cnf(f_2736_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10003,U_10001)),U_10004),U_10005),U_10006) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,U_10001),U_10004),hAPP(hAPP(c_COMBC(U_10002,U_10003,U_10001),U_10005),U_10006))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10001) ),
    inference(clausify,[status(thm)],[f_2736_2]) ).

fof(f_2737_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_2737_2,plain,
    ! [U_10012,U_10011,U_10010,U_10009,U_10008,U_10007] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10008,U_10007),U_10009),hAPP(hAPP(c_COMBB(tc_fun(U_10010,U_10007),U_10007,U_10008),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10010,U_10007),U_10011)),U_10012)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10010,U_10007),U_10011),hAPP(hAPP(c_COMBB(tc_fun(U_10008,U_10007),U_10007,U_10010),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10008,U_10007),U_10009)),hAPP(c_COMBC(U_10008,U_10010,U_10007),U_10012)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10007) ),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

cnf(f_2737_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10008,U_10007),U_10009),hAPP(hAPP(c_COMBB(tc_fun(U_10010,U_10007),U_10007,U_10008),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10010,U_10007),U_10011)),U_10012)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10010,U_10007),U_10011),hAPP(hAPP(c_COMBB(tc_fun(U_10008,U_10007),U_10007,U_10010),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10008,U_10007),U_10009)),hAPP(c_COMBC(U_10008,U_10010,U_10007),U_10012)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10007) ),
    inference(clausify,[status(thm)],[f_2737_2]) ).

fof(f_2738_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_2738_2,plain,
    ! [U_10017,U_10016,U_10015,U_10014,U_10013] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10014,tc_HOL_Obool)),U_10015),hAPP(hAPP(c_COMBC(U_10013,tc_fun(U_10014,tc_HOL_Obool),tc_fun(U_10014,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10014,tc_HOL_Obool),tc_fun(tc_fun(U_10014,tc_HOL_Obool),tc_fun(U_10014,tc_HOL_Obool)),U_10013),c_Groups_Ominus__class_Ominus(tc_fun(U_10014,tc_HOL_Obool))),U_10016)),U_10017)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10014,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10014,tc_HOL_Obool)),U_10015),U_10016)),U_10017),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

cnf(f_2738_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10014,tc_HOL_Obool)),U_10015),hAPP(hAPP(c_COMBC(U_10013,tc_fun(U_10014,tc_HOL_Obool),tc_fun(U_10014,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10014,tc_HOL_Obool),tc_fun(tc_fun(U_10014,tc_HOL_Obool),tc_fun(U_10014,tc_HOL_Obool)),U_10013),c_Groups_Ominus__class_Ominus(tc_fun(U_10014,tc_HOL_Obool))),U_10016)),U_10017)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10014,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10014,tc_HOL_Obool)),U_10015),U_10016)),U_10017),
    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_10022,U_10021,U_10020,U_10019,U_10018] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10019,tc_fun(U_10018,tc_HOL_Obool)),U_10020),U_10021)),U_10022) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10019,tc_fun(U_10018,tc_HOL_Obool)),U_10020),hAPP(hAPP(c_COMBC(U_10019,tc_fun(U_10018,tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_HOL_Obool),tc_fun(tc_fun(U_10018,tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),U_10019),c_Groups_Ominus__class_Ominus(tc_fun(U_10018,tc_HOL_Obool))),U_10021)),U_10022)),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

cnf(f_2739_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10019,tc_fun(U_10018,tc_HOL_Obool)),U_10020),U_10021)),U_10022) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10019,tc_fun(U_10018,tc_HOL_Obool)),U_10020),hAPP(hAPP(c_COMBC(U_10019,tc_fun(U_10018,tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10018,tc_HOL_Obool),tc_fun(tc_fun(U_10018,tc_HOL_Obool),tc_fun(U_10018,tc_HOL_Obool)),U_10019),c_Groups_Ominus__class_Ominus(tc_fun(U_10018,tc_HOL_Obool))),U_10021)),U_10022)),
    inference(clausify,[status(thm)],[f_2739_2]) ).

fof(f_2740_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_2740_2,plain,
    ! [U_10024,U_10023] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10023,tc_HOL_Obool),U_10024) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10023,tc_HOL_Obool),tc_fun(U_10023,tc_HOL_Obool)),U_10024),c_COMBI(tc_fun(U_10023,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

cnf(f_2740_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10023,tc_HOL_Obool),U_10024) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10023,tc_HOL_Obool),tc_fun(U_10023,tc_HOL_Obool)),U_10024),c_COMBI(tc_fun(U_10023,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2740_2]) ).

fof(f_2741_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_2741_2,plain,
    ! [U_10030,U_10029,U_10028,U_10027,U_10026,U_10025] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10025,tc_fun(U_10026,tc_fun(U_10027,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10026,tc_fun(U_10027,tc_HOL_Obool)),U_10025),hAPP(c_COMBC(U_10026,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10027,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10027,tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10027,tc_HOL_Obool)),U_10026),c_COMBC(U_10027,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10027,tc_prod(U_10026,U_10027)),tc_fun(U_10027,tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),U_10026),hAPP(c_COMBB(tc_prod(U_10026,U_10027),tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool),U_10027),c_member(tc_prod(U_10026,U_10027)))),c_Product__Type_OPair(U_10026,U_10027))))),U_10028)),U_10029),U_10030))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10026,U_10027)),hAPP(hAPP(c_Product__Type_OPair(U_10026,U_10027),U_10029),U_10030)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10025,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))),U_10028))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10026,U_10027)),hAPP(hAPP(c_Product__Type_OPair(U_10026,U_10027),U_10029),U_10030)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10025,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))),U_10028)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10025,tc_fun(U_10026,tc_fun(U_10027,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10025,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10026,tc_fun(U_10027,tc_HOL_Obool)),U_10025),hAPP(c_COMBC(U_10026,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10027,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10027,tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_fun(U_10027,tc_HOL_Obool)),U_10026),c_COMBC(U_10027,tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10027,tc_prod(U_10026,U_10027)),tc_fun(U_10027,tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool)),U_10026),hAPP(c_COMBB(tc_prod(U_10026,U_10027),tc_fun(tc_fun(tc_prod(U_10026,U_10027),tc_HOL_Obool),tc_HOL_Obool),U_10027),c_member(tc_prod(U_10026,U_10027)))),c_Product__Type_OPair(U_10026,U_10027))))),U_10028)),U_10029),U_10030)) ) ),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

fof(f_2741_3,plain,
    ( ! [U_10042,U_10040,U_10038,U_10036,U_10034,U_10032] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10032,tc_fun(U_10034,tc_fun(U_10036,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10032,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10034,tc_fun(U_10036,tc_HOL_Obool)),U_10032),hAPP(c_COMBC(U_10034,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool)),U_10034),c_COMBC(U_10036,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_prod(U_10034,U_10036)),tc_fun(U_10036,tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),U_10034),hAPP(c_COMBB(tc_prod(U_10034,U_10036),tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool),U_10036),c_member(tc_prod(U_10034,U_10036)))),c_Product__Type_OPair(U_10034,U_10036))))),U_10038)),U_10040),U_10042))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10034,U_10036)),hAPP(hAPP(c_Product__Type_OPair(U_10034,U_10036),U_10040),U_10042)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10032,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10032,tc_HOL_Obool))),U_10038))) )
    & ! [U_10041,U_10039,U_10037,U_10035,U_10033,U_10031] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10033,U_10035)),hAPP(hAPP(c_Product__Type_OPair(U_10033,U_10035),U_10039),U_10041)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10031,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))),U_10037)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10031,tc_fun(U_10033,tc_fun(U_10035,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10033,tc_fun(U_10035,tc_HOL_Obool)),U_10031),hAPP(c_COMBC(U_10033,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10035,tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10035,tc_HOL_Obool)),U_10033),c_COMBC(U_10035,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10035,tc_prod(U_10033,U_10035)),tc_fun(U_10035,tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),U_10033),hAPP(c_COMBB(tc_prod(U_10033,U_10035),tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool),U_10035),c_member(tc_prod(U_10033,U_10035)))),c_Product__Type_OPair(U_10033,U_10035))))),U_10037)),U_10039),U_10041)) ) ),
    inference(miniscope,[status(thm)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10033,U_10035)),hAPP(hAPP(c_Product__Type_OPair(U_10033,U_10035),U_10039),U_10041)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10031,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))),U_10037)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10031,tc_fun(U_10033,tc_fun(U_10035,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10031,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10033,tc_fun(U_10035,tc_HOL_Obool)),U_10031),hAPP(c_COMBC(U_10033,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10035,tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_fun(U_10035,tc_HOL_Obool)),U_10033),c_COMBC(U_10035,tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10035,tc_prod(U_10033,U_10035)),tc_fun(U_10035,tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool)),U_10033),hAPP(c_COMBB(tc_prod(U_10033,U_10035),tc_fun(tc_fun(tc_prod(U_10033,U_10035),tc_HOL_Obool),tc_HOL_Obool),U_10035),c_member(tc_prod(U_10033,U_10035)))),c_Product__Type_OPair(U_10033,U_10035))))),U_10037)),U_10039),U_10041)) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

cnf(f_2741_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10032,tc_fun(U_10034,tc_fun(U_10036,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_10032,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10034,tc_fun(U_10036,tc_HOL_Obool)),U_10032),hAPP(c_COMBC(U_10034,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_fun(U_10036,tc_HOL_Obool)),U_10034),c_COMBC(U_10036,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10036,tc_prod(U_10034,U_10036)),tc_fun(U_10036,tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool)),U_10034),hAPP(c_COMBB(tc_prod(U_10034,U_10036),tc_fun(tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool),tc_HOL_Obool),U_10036),c_member(tc_prod(U_10034,U_10036)))),c_Product__Type_OPair(U_10034,U_10036))))),U_10038)),U_10040),U_10042))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10034,U_10036)),hAPP(hAPP(c_Product__Type_OPair(U_10034,U_10036),U_10040),U_10042)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10032,tc_fun(tc_prod(U_10034,U_10036),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10032,tc_HOL_Obool))),U_10038))) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

fof(f_2742_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_2742_2,plain,
    ! [U_10049,U_10048,U_10047,U_10046,U_10045] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049))
          | ? [U_10044] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,U_10044)),U_10049))
              & hBOOL(hAPP(hAPP(c_member(U_10046),U_10044),U_10047)) ) )
        & ( ! [U_10043] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,U_10043)),U_10049))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10046),U_10043),U_10047)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10045) ),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

fof(f_2742_3,plain,
    ! [U_10049,U_10048,U_10047,U_10046,U_10045] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,sK222(U_10049,U_10048,U_10047,U_10046,U_10045))),U_10049))
            & hBOOL(hAPP(hAPP(c_member(U_10046),sK222(U_10049,U_10048,U_10047,U_10046,U_10045)),U_10047)) ) )
        & ( ! [U_10043] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,U_10043)),U_10049))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10046),U_10043),U_10047)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10045) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_10044,sK222(U_10049,U_10048,U_10047,U_10046,U_10045))],[f_2742_2]) ).

cnf(f_2742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,U_10043)),U_10049))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10046),U_10043),U_10047))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10045) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

cnf(f_2742_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10046),sK222(U_10049,U_10048,U_10047,U_10046,U_10045)),U_10047))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10045) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

cnf(f_2742_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(U_10048,sK222(U_10049,U_10048,U_10047,U_10046,U_10045))),U_10049))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10046,U_10045),U_10047),U_10048)),U_10049))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10045) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

fof(f_2743_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_2743_2,plain,
    ! [U_10056,U_10055,U_10054,U_10053,U_10052] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056)))
          | ! [U_10051] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,U_10051)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10054),U_10051),U_10055)) ) )
        & ( ? [U_10050] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,U_10050)))
              & hBOOL(hAPP(hAPP(c_member(U_10054),U_10050),U_10055)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056))) ) )
      | ~ class_Orderings_Olinorder(U_10052)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10052) ),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

fof(f_2743_3,plain,
    ! [U_10056,U_10055,U_10054,U_10053,U_10052] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056)))
          | ! [U_10051] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,U_10051)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10054),U_10051),U_10055)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,sK223(U_10056,U_10055,U_10054,U_10053,U_10052))))
            & hBOOL(hAPP(hAPP(c_member(U_10054),sK223(U_10056,U_10055,U_10054,U_10053,U_10052)),U_10055)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056))) ) )
      | ~ class_Orderings_Olinorder(U_10052)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10052) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_10050,sK223(U_10056,U_10055,U_10054,U_10053,U_10052))],[f_2743_2]) ).

cnf(f_2743_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10054),sK223(U_10056,U_10055,U_10054,U_10053,U_10052)),U_10055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056)))
    | ~ class_Orderings_Olinorder(U_10052)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10052) ),
    inference(clausify,[status(thm)],[f_2743_3]) ).

cnf(f_2743_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,sK223(U_10056,U_10055,U_10054,U_10053,U_10052))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056)))
    | ~ class_Orderings_Olinorder(U_10052)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10052) ),
    inference(clausify,[status(thm)],[f_2743_3]) ).

cnf(f_2743_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10054,U_10052),U_10055),U_10056)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10052),U_10053),hAPP(U_10056,U_10051)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10054),U_10051),U_10055))
    | ~ class_Orderings_Olinorder(U_10052)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10052) ),
    inference(clausify,[status(thm)],[f_2743_3]) ).

fof(f_2744_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_2744_2,plain,
    ! [U_10060,U_10059,U_10058,U_10057] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10059,U_10057),U_10058),hAPP(c_COMBK(U_10057,U_10059),U_10060)) = U_10060
      | U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10059,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(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_10059,U_10057),U_10058),hAPP(c_COMBK(U_10057,U_10059),U_10060)) = U_10060
    | U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10059,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10057) ),
    inference(clausify,[status(thm)],[f_2744_2]) ).

fof(f_2745_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_2745_2,plain,
    ! [U_10066,U_10065,U_10064,U_10063,U_10062,U_10061] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10061,tc_fun(U_10064,tc_HOL_Obool)),U_10063),hAPP(hAPP(c_COMBB(tc_fun(U_10064,tc_HOL_Obool),tc_fun(U_10064,tc_HOL_Obool),U_10061),hAPP(c_Set_Oinsert(U_10064),U_10065)),U_10066)) = hAPP(hAPP(c_Set_Oinsert(U_10064),U_10065),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10061,tc_fun(U_10064,tc_HOL_Obool)),U_10063),U_10066))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10061),U_10062),U_10063)) ),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

cnf(f_2745_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10061,tc_fun(U_10064,tc_HOL_Obool)),U_10063),hAPP(hAPP(c_COMBB(tc_fun(U_10064,tc_HOL_Obool),tc_fun(U_10064,tc_HOL_Obool),U_10061),hAPP(c_Set_Oinsert(U_10064),U_10065)),U_10066)) = hAPP(hAPP(c_Set_Oinsert(U_10064),U_10065),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10061,tc_fun(U_10064,tc_HOL_Obool)),U_10063),U_10066))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10061),U_10062),U_10063)) ),
    inference(clausify,[status(thm)],[f_2745_2]) ).

fof(f_2746_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_2746_2,plain,
    ! [U_10071,U_10070,U_10069,U_10068,U_10067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10070,tc_HOL_Obool)),hAPP(U_10071,U_10068)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10067,tc_fun(U_10070,tc_HOL_Obool)),U_10069),U_10071)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10067),U_10068),U_10069)) ),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

cnf(f_2746_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10070,tc_HOL_Obool)),hAPP(U_10071,U_10068)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10067,tc_fun(U_10070,tc_HOL_Obool)),U_10069),U_10071)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10067),U_10068),U_10069)) ),
    inference(clausify,[status(thm)],[f_2746_2]) ).

fof(f_2747_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_2747_2,plain,
    ! [U_10075,U_10074,U_10073,U_10072] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10073,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10072,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10073,tc_HOL_Obool),tc_fun(U_10073,tc_HOL_Obool),U_10072),hAPP(c_COMBC(U_10073,tc_fun(U_10073,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10073))),U_10074)),U_10075))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10073),U_10075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10073,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10072,tc_HOL_Obool))),U_10074))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_10073),U_10075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10073,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10072,tc_HOL_Obool))),U_10074)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10073,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10072,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10073,tc_HOL_Obool),tc_fun(U_10073,tc_HOL_Obool),U_10072),hAPP(c_COMBC(U_10073,tc_fun(U_10073,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10073))),U_10074)),U_10075)) ) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

fof(f_2747_3,plain,
    ( ! [U_10083,U_10081,U_10079,U_10077] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10077,tc_fun(U_10079,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10077,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10079,tc_HOL_Obool),tc_fun(U_10079,tc_HOL_Obool),U_10077),hAPP(c_COMBC(U_10079,tc_fun(U_10079,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10079))),U_10081)),U_10083))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10079),U_10083),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10077,tc_fun(U_10079,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10077,tc_HOL_Obool))),U_10081))) )
    & ! [U_10082,U_10080,U_10078,U_10076] :
        ( hBOOL(hAPP(hAPP(c_member(U_10078),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10076,tc_fun(U_10078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10076,tc_HOL_Obool))),U_10080)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10076,tc_fun(U_10078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10076,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10078,tc_HOL_Obool),tc_fun(U_10078,tc_HOL_Obool),U_10076),hAPP(c_COMBC(U_10078,tc_fun(U_10078,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10078))),U_10080)),U_10082)) ) ),
    inference(miniscope,[status(thm)],[f_2747_2]) ).

cnf(f_2747_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10078),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10076,tc_fun(U_10078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10076,tc_HOL_Obool))),U_10080)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10076,tc_fun(U_10078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10076,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10078,tc_HOL_Obool),tc_fun(U_10078,tc_HOL_Obool),U_10076),hAPP(c_COMBC(U_10078,tc_fun(U_10078,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10078))),U_10080)),U_10082)) ),
    inference(clausify,[status(thm)],[f_2747_3]) ).

cnf(f_2747_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10077,tc_fun(U_10079,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10077,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10079,tc_HOL_Obool),tc_fun(U_10079,tc_HOL_Obool),U_10077),hAPP(c_COMBC(U_10079,tc_fun(U_10079,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10079))),U_10081)),U_10083))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10079),U_10083),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10077,tc_fun(U_10079,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10077,tc_HOL_Obool))),U_10081))) ),
    inference(clausify,[status(thm)],[f_2747_3]) ).

fof(f_2748_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_2748_2,plain,
    ! [U_10088,U_10087,U_10086,U_10085,U_10084] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10087,tc_HOL_Obool)),hAPP(U_10088,U_10085)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10084,tc_fun(U_10087,tc_HOL_Obool)),U_10086),U_10088)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10084,tc_fun(U_10087,tc_HOL_Obool)),U_10086),U_10088)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10084),U_10085),U_10086)) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

cnf(f_2748_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10087,tc_HOL_Obool)),hAPP(U_10088,U_10085)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10084,tc_fun(U_10087,tc_HOL_Obool)),U_10086),U_10088)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10084,tc_fun(U_10087,tc_HOL_Obool)),U_10086),U_10088)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10084),U_10085),U_10086)) ),
    inference(clausify,[status(thm)],[f_2748_2]) ).

fof(f_2749_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_2749_2,plain,
    ! [U_10093,U_10092,U_10091,U_10090,U_10089] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_10091),U_10092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10090,tc_fun(U_10091,tc_HOL_Obool)),U_10089),U_10093)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10090,tc_fun(U_10091,tc_HOL_Obool)),U_10089),hAPP(hAPP(c_COMBB(tc_fun(U_10091,tc_HOL_Obool),tc_fun(U_10091,tc_HOL_Obool),U_10090),hAPP(c_Set_Oinsert(U_10091),U_10092)),U_10093))
        | U_10089 = c_Orderings_Obot__class_Obot(tc_fun(U_10090,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_10091),U_10092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10090,tc_fun(U_10091,tc_HOL_Obool)),U_10089),U_10093)) = hAPP(hAPP(c_Set_Oinsert(U_10091),U_10092),c_Orderings_Obot__class_Obot(tc_fun(U_10091,tc_HOL_Obool)))
        | U_10089 != c_Orderings_Obot__class_Obot(tc_fun(U_10090,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

fof(f_2749_3,plain,
    ( ! [U_10103,U_10101,U_10099,U_10097,U_10095] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10099),U_10101),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10097,tc_fun(U_10099,tc_HOL_Obool)),U_10095),U_10103)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10097,tc_fun(U_10099,tc_HOL_Obool)),U_10095),hAPP(hAPP(c_COMBB(tc_fun(U_10099,tc_HOL_Obool),tc_fun(U_10099,tc_HOL_Obool),U_10097),hAPP(c_Set_Oinsert(U_10099),U_10101)),U_10103))
        | U_10095 = c_Orderings_Obot__class_Obot(tc_fun(U_10097,tc_HOL_Obool)) )
    & ! [U_10102,U_10100,U_10098,U_10096,U_10094] :
        ( hAPP(hAPP(c_Set_Oinsert(U_10098),U_10100),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10096,tc_fun(U_10098,tc_HOL_Obool)),U_10094),U_10102)) = hAPP(hAPP(c_Set_Oinsert(U_10098),U_10100),c_Orderings_Obot__class_Obot(tc_fun(U_10098,tc_HOL_Obool)))
        | U_10094 != c_Orderings_Obot__class_Obot(tc_fun(U_10096,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2749_2]) ).

cnf(f_2749_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_10098),U_10100),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10096,tc_fun(U_10098,tc_HOL_Obool)),U_10094),U_10102)) = hAPP(hAPP(c_Set_Oinsert(U_10098),U_10100),c_Orderings_Obot__class_Obot(tc_fun(U_10098,tc_HOL_Obool)))
    | U_10094 != c_Orderings_Obot__class_Obot(tc_fun(U_10096,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2749_3]) ).

cnf(f_2749_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_10099),U_10101),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10097,tc_fun(U_10099,tc_HOL_Obool)),U_10095),U_10103)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10097,tc_fun(U_10099,tc_HOL_Obool)),U_10095),hAPP(hAPP(c_COMBB(tc_fun(U_10099,tc_HOL_Obool),tc_fun(U_10099,tc_HOL_Obool),U_10097),hAPP(c_Set_Oinsert(U_10099),U_10101)),U_10103))
    | U_10095 = c_Orderings_Obot__class_Obot(tc_fun(U_10097,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2749_3]) ).

fof(f_2750_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_2750_2,plain,
    ! [U_10105,U_10104] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10104,tc_fun(U_10104,tc_HOL_Obool)),U_10105),hAPP(hAPP(c_COMBC(U_10104,tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool)),c_Set_Oinsert(U_10104)),c_Orderings_Obot__class_Obot(tc_fun(U_10104,tc_HOL_Obool)))) = U_10105,
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

cnf(f_2750_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10104,tc_fun(U_10104,tc_HOL_Obool)),U_10105),hAPP(hAPP(c_COMBC(U_10104,tc_fun(U_10104,tc_HOL_Obool),tc_fun(U_10104,tc_HOL_Obool)),c_Set_Oinsert(U_10104)),c_Orderings_Obot__class_Obot(tc_fun(U_10104,tc_HOL_Obool)))) = U_10105,
    inference(clausify,[status(thm)],[f_2750_2]) ).

fof(f_2751_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_2751_2,plain,
    ! [U_10110,U_10109,U_10108,U_10107,U_10106] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10107,tc_fun(U_10108,tc_HOL_Obool)),U_10106),hAPP(hAPP(c_COMBB(tc_fun(U_10108,tc_HOL_Obool),tc_fun(U_10108,tc_HOL_Obool),U_10107),hAPP(c_Set_Oinsert(U_10108),U_10109)),U_10110)) = hAPP(hAPP(c_Set_Oinsert(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10107,tc_fun(U_10108,tc_HOL_Obool)),U_10106),U_10110))
        | U_10106 = c_Orderings_Obot__class_Obot(tc_fun(U_10107,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10107,tc_fun(U_10108,tc_HOL_Obool)),U_10106),hAPP(hAPP(c_COMBB(tc_fun(U_10108,tc_HOL_Obool),tc_fun(U_10108,tc_HOL_Obool),U_10107),hAPP(c_Set_Oinsert(U_10108),U_10109)),U_10110)) = c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))
        | U_10106 != c_Orderings_Obot__class_Obot(tc_fun(U_10107,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

fof(f_2751_3,plain,
    ( ! [U_10120,U_10118,U_10116,U_10114,U_10112] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10114,tc_fun(U_10116,tc_HOL_Obool)),U_10112),hAPP(hAPP(c_COMBB(tc_fun(U_10116,tc_HOL_Obool),tc_fun(U_10116,tc_HOL_Obool),U_10114),hAPP(c_Set_Oinsert(U_10116),U_10118)),U_10120)) = hAPP(hAPP(c_Set_Oinsert(U_10116),U_10118),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10114,tc_fun(U_10116,tc_HOL_Obool)),U_10112),U_10120))
        | U_10112 = c_Orderings_Obot__class_Obot(tc_fun(U_10114,tc_HOL_Obool)) )
    & ! [U_10119,U_10117,U_10115,U_10113,U_10111] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10113,tc_fun(U_10115,tc_HOL_Obool)),U_10111),hAPP(hAPP(c_COMBB(tc_fun(U_10115,tc_HOL_Obool),tc_fun(U_10115,tc_HOL_Obool),U_10113),hAPP(c_Set_Oinsert(U_10115),U_10117)),U_10119)) = c_Orderings_Obot__class_Obot(tc_fun(U_10115,tc_HOL_Obool))
        | U_10111 != c_Orderings_Obot__class_Obot(tc_fun(U_10113,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2751_2]) ).

cnf(f_2751_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10113,tc_fun(U_10115,tc_HOL_Obool)),U_10111),hAPP(hAPP(c_COMBB(tc_fun(U_10115,tc_HOL_Obool),tc_fun(U_10115,tc_HOL_Obool),U_10113),hAPP(c_Set_Oinsert(U_10115),U_10117)),U_10119)) = c_Orderings_Obot__class_Obot(tc_fun(U_10115,tc_HOL_Obool))
    | U_10111 != c_Orderings_Obot__class_Obot(tc_fun(U_10113,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

cnf(f_2751_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10114,tc_fun(U_10116,tc_HOL_Obool)),U_10112),hAPP(hAPP(c_COMBB(tc_fun(U_10116,tc_HOL_Obool),tc_fun(U_10116,tc_HOL_Obool),U_10114),hAPP(c_Set_Oinsert(U_10116),U_10118)),U_10120)) = hAPP(hAPP(c_Set_Oinsert(U_10116),U_10118),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10114,tc_fun(U_10116,tc_HOL_Obool)),U_10112),U_10120))
    | U_10112 = c_Orderings_Obot__class_Obot(tc_fun(U_10114,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

fof(f_2752_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_2752_2,plain,
    ! [U_10125,U_10124,U_10123,U_10122,U_10121] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10122,tc_fun(U_10123,tc_HOL_Obool)),U_10121),U_10124)),U_10125) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10122,tc_fun(U_10123,tc_HOL_Obool)),U_10121),hAPP(hAPP(c_COMBC(U_10122,tc_fun(U_10123,tc_HOL_Obool),tc_fun(U_10123,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10123,tc_HOL_Obool),tc_fun(tc_fun(U_10123,tc_HOL_Obool),tc_fun(U_10123,tc_HOL_Obool)),U_10122),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool))),U_10124)),U_10125))
        | U_10121 = c_Orderings_Obot__class_Obot(tc_fun(U_10122,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10122,tc_fun(U_10123,tc_HOL_Obool)),U_10121),U_10124)),U_10125) = U_10125
        | U_10121 != c_Orderings_Obot__class_Obot(tc_fun(U_10122,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

fof(f_2752_3,plain,
    ( ! [U_10135,U_10133,U_10131,U_10129,U_10127] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10131,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10129,tc_fun(U_10131,tc_HOL_Obool)),U_10127),U_10133)),U_10135) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10129,tc_fun(U_10131,tc_HOL_Obool)),U_10127),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10131,tc_HOL_Obool),tc_fun(U_10131,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10131,tc_HOL_Obool),tc_fun(tc_fun(U_10131,tc_HOL_Obool),tc_fun(U_10131,tc_HOL_Obool)),U_10129),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10131,tc_HOL_Obool))),U_10133)),U_10135))
        | U_10127 = c_Orderings_Obot__class_Obot(tc_fun(U_10129,tc_HOL_Obool)) )
    & ! [U_10134,U_10132,U_10130,U_10128,U_10126] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10130,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10128,tc_fun(U_10130,tc_HOL_Obool)),U_10126),U_10132)),U_10134) = U_10134
        | U_10126 != c_Orderings_Obot__class_Obot(tc_fun(U_10128,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2752_2]) ).

cnf(f_2752_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10130,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10128,tc_fun(U_10130,tc_HOL_Obool)),U_10126),U_10132)),U_10134) = U_10134
    | U_10126 != c_Orderings_Obot__class_Obot(tc_fun(U_10128,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2752_3]) ).

cnf(f_2752_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10131,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10129,tc_fun(U_10131,tc_HOL_Obool)),U_10127),U_10133)),U_10135) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10129,tc_fun(U_10131,tc_HOL_Obool)),U_10127),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10131,tc_HOL_Obool),tc_fun(U_10131,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10131,tc_HOL_Obool),tc_fun(tc_fun(U_10131,tc_HOL_Obool),tc_fun(U_10131,tc_HOL_Obool)),U_10129),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10131,tc_HOL_Obool))),U_10133)),U_10135))
    | U_10127 = c_Orderings_Obot__class_Obot(tc_fun(U_10129,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2752_3]) ).

fof(f_2753_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_2753_2,plain,
    ! [U_10140,U_10139,U_10138,U_10137,U_10136] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10138,tc_HOL_Obool)),U_10139),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10137,tc_fun(U_10138,tc_HOL_Obool)),U_10136),U_10140)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10137,tc_fun(U_10138,tc_HOL_Obool)),U_10136),hAPP(hAPP(c_COMBB(tc_fun(U_10138,tc_HOL_Obool),tc_fun(U_10138,tc_HOL_Obool),U_10137),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10138,tc_HOL_Obool)),U_10139)),U_10140))
        | U_10136 = c_Orderings_Obot__class_Obot(tc_fun(U_10137,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10138,tc_HOL_Obool)),U_10139),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10137,tc_fun(U_10138,tc_HOL_Obool)),U_10136),U_10140)) = U_10139
        | U_10136 != c_Orderings_Obot__class_Obot(tc_fun(U_10137,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

fof(f_2753_3,plain,
    ( ! [U_10150,U_10148,U_10146,U_10144,U_10142] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10146,tc_HOL_Obool)),U_10148),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10144,tc_fun(U_10146,tc_HOL_Obool)),U_10142),U_10150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10144,tc_fun(U_10146,tc_HOL_Obool)),U_10142),hAPP(hAPP(c_COMBB(tc_fun(U_10146,tc_HOL_Obool),tc_fun(U_10146,tc_HOL_Obool),U_10144),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10146,tc_HOL_Obool)),U_10148)),U_10150))
        | U_10142 = c_Orderings_Obot__class_Obot(tc_fun(U_10144,tc_HOL_Obool)) )
    & ! [U_10149,U_10147,U_10145,U_10143,U_10141] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10145,tc_HOL_Obool)),U_10147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10143,tc_fun(U_10145,tc_HOL_Obool)),U_10141),U_10149)) = U_10147
        | U_10141 != c_Orderings_Obot__class_Obot(tc_fun(U_10143,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2753_2]) ).

cnf(f_2753_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10145,tc_HOL_Obool)),U_10147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10143,tc_fun(U_10145,tc_HOL_Obool)),U_10141),U_10149)) = U_10147
    | U_10141 != c_Orderings_Obot__class_Obot(tc_fun(U_10143,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

cnf(f_2753_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10146,tc_HOL_Obool)),U_10148),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10144,tc_fun(U_10146,tc_HOL_Obool)),U_10142),U_10150)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10144,tc_fun(U_10146,tc_HOL_Obool)),U_10142),hAPP(hAPP(c_COMBB(tc_fun(U_10146,tc_HOL_Obool),tc_fun(U_10146,tc_HOL_Obool),U_10144),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10146,tc_HOL_Obool)),U_10148)),U_10150))
    | U_10142 = c_Orderings_Obot__class_Obot(tc_fun(U_10144,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

fof(f_2754_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_2754_2,plain,
    ! [U_10155,U_10154,U_10153,U_10152,U_10151] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10152,tc_fun(U_10153,tc_HOL_Obool)),U_10151),hAPP(hAPP(c_COMBC(U_10152,tc_fun(U_10153,tc_HOL_Obool),tc_fun(U_10153,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10153,tc_HOL_Obool),tc_fun(tc_fun(U_10153,tc_HOL_Obool),tc_fun(U_10153,tc_HOL_Obool)),U_10152),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10153,tc_HOL_Obool))),U_10154)),U_10155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10153,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10152,tc_fun(U_10153,tc_HOL_Obool)),U_10151),U_10154)),U_10155)
        | U_10151 = c_Orderings_Obot__class_Obot(tc_fun(U_10152,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10152,tc_fun(U_10153,tc_HOL_Obool)),U_10151),hAPP(hAPP(c_COMBC(U_10152,tc_fun(U_10153,tc_HOL_Obool),tc_fun(U_10153,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10153,tc_HOL_Obool),tc_fun(tc_fun(U_10153,tc_HOL_Obool),tc_fun(U_10153,tc_HOL_Obool)),U_10152),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10153,tc_HOL_Obool))),U_10154)),U_10155)) = c_Orderings_Obot__class_Obot(tc_fun(U_10153,tc_HOL_Obool))
        | U_10151 != c_Orderings_Obot__class_Obot(tc_fun(U_10152,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

fof(f_2754_3,plain,
    ( ! [U_10165,U_10163,U_10161,U_10159,U_10157] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10161,tc_HOL_Obool)),U_10157),hAPP(hAPP(c_COMBC(U_10159,tc_fun(U_10161,tc_HOL_Obool),tc_fun(U_10161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10161,tc_HOL_Obool),tc_fun(tc_fun(U_10161,tc_HOL_Obool),tc_fun(U_10161,tc_HOL_Obool)),U_10159),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10161,tc_HOL_Obool))),U_10163)),U_10165)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10161,tc_HOL_Obool)),U_10157),U_10163)),U_10165)
        | U_10157 = c_Orderings_Obot__class_Obot(tc_fun(U_10159,tc_HOL_Obool)) )
    & ! [U_10164,U_10162,U_10160,U_10158,U_10156] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10158,tc_fun(U_10160,tc_HOL_Obool)),U_10156),hAPP(hAPP(c_COMBC(U_10158,tc_fun(U_10160,tc_HOL_Obool),tc_fun(U_10160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10160,tc_HOL_Obool),tc_fun(tc_fun(U_10160,tc_HOL_Obool),tc_fun(U_10160,tc_HOL_Obool)),U_10158),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10160,tc_HOL_Obool))),U_10162)),U_10164)) = c_Orderings_Obot__class_Obot(tc_fun(U_10160,tc_HOL_Obool))
        | U_10156 != c_Orderings_Obot__class_Obot(tc_fun(U_10158,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2754_2]) ).

cnf(f_2754_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10158,tc_fun(U_10160,tc_HOL_Obool)),U_10156),hAPP(hAPP(c_COMBC(U_10158,tc_fun(U_10160,tc_HOL_Obool),tc_fun(U_10160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10160,tc_HOL_Obool),tc_fun(tc_fun(U_10160,tc_HOL_Obool),tc_fun(U_10160,tc_HOL_Obool)),U_10158),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10160,tc_HOL_Obool))),U_10162)),U_10164)) = c_Orderings_Obot__class_Obot(tc_fun(U_10160,tc_HOL_Obool))
    | U_10156 != c_Orderings_Obot__class_Obot(tc_fun(U_10158,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

cnf(f_2754_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10161,tc_HOL_Obool)),U_10157),hAPP(hAPP(c_COMBC(U_10159,tc_fun(U_10161,tc_HOL_Obool),tc_fun(U_10161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10161,tc_HOL_Obool),tc_fun(tc_fun(U_10161,tc_HOL_Obool),tc_fun(U_10161,tc_HOL_Obool)),U_10159),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10161,tc_HOL_Obool))),U_10163)),U_10165)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10161,tc_HOL_Obool)),U_10157),U_10163)),U_10165)
    | U_10157 = c_Orderings_Obot__class_Obot(tc_fun(U_10159,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

fof(f_2755_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_2755_2,plain,
    ! [U_10170,U_10169,U_10168,U_10167,U_10166] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10167,tc_fun(U_10168,tc_HOL_Obool)),U_10166),hAPP(hAPP(c_COMBB(tc_fun(U_10168,tc_HOL_Obool),tc_fun(U_10168,tc_HOL_Obool),U_10167),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10168,tc_HOL_Obool)),U_10169)),U_10170)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10168,tc_HOL_Obool)),U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10167,tc_fun(U_10168,tc_HOL_Obool)),U_10166),U_10170))
        | U_10166 = c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10167,tc_fun(U_10168,tc_HOL_Obool)),U_10166),hAPP(hAPP(c_COMBB(tc_fun(U_10168,tc_HOL_Obool),tc_fun(U_10168,tc_HOL_Obool),U_10167),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10168,tc_HOL_Obool)),U_10169)),U_10170)) = c_Orderings_Obot__class_Obot(tc_fun(U_10168,tc_HOL_Obool))
        | U_10166 != c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

fof(f_2755_3,plain,
    ( ! [U_10180,U_10178,U_10176,U_10174,U_10172] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10174,tc_fun(U_10176,tc_HOL_Obool)),U_10172),hAPP(hAPP(c_COMBB(tc_fun(U_10176,tc_HOL_Obool),tc_fun(U_10176,tc_HOL_Obool),U_10174),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10176,tc_HOL_Obool)),U_10178)),U_10180)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10176,tc_HOL_Obool)),U_10178),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10174,tc_fun(U_10176,tc_HOL_Obool)),U_10172),U_10180))
        | U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10174,tc_HOL_Obool)) )
    & ! [U_10179,U_10177,U_10175,U_10173,U_10171] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10175,tc_HOL_Obool)),U_10171),hAPP(hAPP(c_COMBB(tc_fun(U_10175,tc_HOL_Obool),tc_fun(U_10175,tc_HOL_Obool),U_10173),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10175,tc_HOL_Obool)),U_10177)),U_10179)) = c_Orderings_Obot__class_Obot(tc_fun(U_10175,tc_HOL_Obool))
        | U_10171 != c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2755_2]) ).

cnf(f_2755_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10175,tc_HOL_Obool)),U_10171),hAPP(hAPP(c_COMBB(tc_fun(U_10175,tc_HOL_Obool),tc_fun(U_10175,tc_HOL_Obool),U_10173),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10175,tc_HOL_Obool)),U_10177)),U_10179)) = c_Orderings_Obot__class_Obot(tc_fun(U_10175,tc_HOL_Obool))
    | U_10171 != c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

cnf(f_2755_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10174,tc_fun(U_10176,tc_HOL_Obool)),U_10172),hAPP(hAPP(c_COMBB(tc_fun(U_10176,tc_HOL_Obool),tc_fun(U_10176,tc_HOL_Obool),U_10174),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10176,tc_HOL_Obool)),U_10178)),U_10180)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10176,tc_HOL_Obool)),U_10178),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10174,tc_fun(U_10176,tc_HOL_Obool)),U_10172),U_10180))
    | U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10174,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

fof(f_2756_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_2756_2,plain,
    ! [U_10185,U_10184,U_10183,U_10182,U_10181] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10181,tc_fun(U_10182,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10181),U_10183),U_10184)),U_10185) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10182,tc_HOL_Obool)),hAPP(U_10185,U_10183)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10181,tc_fun(U_10182,tc_HOL_Obool)),U_10184),U_10185)),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

cnf(f_2756_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10181,tc_fun(U_10182,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10181),U_10183),U_10184)),U_10185) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10182,tc_HOL_Obool)),hAPP(U_10185,U_10183)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10181,tc_fun(U_10182,tc_HOL_Obool)),U_10184),U_10185)),
    inference(clausify,[status(thm)],[f_2756_2]) ).

fof(f_2757_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_2757_2,plain,
    ! [U_10190,U_10189,U_10188,U_10187,U_10186] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10186,tc_HOL_Obool)),U_10187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10188,tc_fun(U_10186,tc_HOL_Obool)),U_10189),U_10190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10188,tc_fun(U_10186,tc_HOL_Obool)),U_10189),hAPP(hAPP(c_COMBB(tc_fun(U_10186,tc_HOL_Obool),tc_fun(U_10186,tc_HOL_Obool),U_10188),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10186,tc_HOL_Obool)),U_10187)),U_10190)),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

cnf(f_2757_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10186,tc_HOL_Obool)),U_10187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10188,tc_fun(U_10186,tc_HOL_Obool)),U_10189),U_10190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10188,tc_fun(U_10186,tc_HOL_Obool)),U_10189),hAPP(hAPP(c_COMBB(tc_fun(U_10186,tc_HOL_Obool),tc_fun(U_10186,tc_HOL_Obool),U_10188),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10186,tc_HOL_Obool)),U_10187)),U_10190)),
    inference(clausify,[status(thm)],[f_2757_2]) ).

fof(f_2758_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_2758_2,plain,
    ! [U_10195,U_10194,U_10193,U_10192,U_10191] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10191,tc_fun(U_10192,tc_HOL_Obool)),U_10193),hAPP(hAPP(c_COMBB(tc_fun(U_10192,tc_HOL_Obool),tc_fun(U_10192,tc_HOL_Obool),U_10191),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10192,tc_HOL_Obool)),U_10194)),U_10195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10192,tc_HOL_Obool)),U_10194),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10191,tc_fun(U_10192,tc_HOL_Obool)),U_10193),U_10195)),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

cnf(f_2758_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10191,tc_fun(U_10192,tc_HOL_Obool)),U_10193),hAPP(hAPP(c_COMBB(tc_fun(U_10192,tc_HOL_Obool),tc_fun(U_10192,tc_HOL_Obool),U_10191),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10192,tc_HOL_Obool)),U_10194)),U_10195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10192,tc_HOL_Obool)),U_10194),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10191,tc_fun(U_10192,tc_HOL_Obool)),U_10193),U_10195)),
    inference(clausify,[status(thm)],[f_2758_2]) ).

fof(f_2759_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_2759_2,plain,
    ! [U_10198,U_10197,U_10196] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_HOL_Obool)),U_10197),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10196,tc_HOL_Obool),U_10198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10196,tc_HOL_Obool),tc_fun(U_10196,tc_HOL_Obool)),U_10198),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_HOL_Obool)),U_10197)),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

cnf(f_2759_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_HOL_Obool)),U_10197),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10196,tc_HOL_Obool),U_10198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10196,tc_HOL_Obool),tc_fun(U_10196,tc_HOL_Obool)),U_10198),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_HOL_Obool)),U_10197)),
    inference(clausify,[status(thm)],[f_2759_2]) ).

fof(f_2760_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_2760_2,plain,
    ! [U_10201,U_10200,U_10199] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10199,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10199,tc_HOL_Obool),U_10200)),U_10201) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),U_10200),hAPP(hAPP(c_COMBC(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10199,tc_HOL_Obool))),U_10201)),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

cnf(f_2760_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10199,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10199,tc_HOL_Obool),U_10200)),U_10201) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),U_10200),hAPP(hAPP(c_COMBC(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10199,tc_HOL_Obool))),U_10201)),
    inference(clausify,[status(thm)],[f_2760_2]) ).

fof(f_2761_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_2761_2,plain,
    ! [U_10205,U_10204,U_10203,U_10202] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10203,tc_fun(U_10202,tc_HOL_Obool)),U_10204),U_10205)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10203,tc_fun(U_10202,tc_HOL_Obool)),U_10204),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool),U_10203),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10202,tc_HOL_Obool))),U_10205)),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

cnf(f_2761_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10203,tc_fun(U_10202,tc_HOL_Obool)),U_10204),U_10205)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10203,tc_fun(U_10202,tc_HOL_Obool)),U_10204),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool),U_10203),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10202,tc_HOL_Obool))),U_10205)),
    inference(clausify,[status(thm)],[f_2761_2]) ).

fof(f_2762_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_2762_2,plain,
    ! [U_10209,U_10208,U_10207,U_10206] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10206,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10206,tc_HOL_Obool)),U_10208),U_10209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10207,tc_fun(U_10206,tc_HOL_Obool)),U_10208),hAPP(hAPP(c_COMBB(tc_fun(U_10206,tc_HOL_Obool),tc_fun(U_10206,tc_HOL_Obool),U_10207),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10206,tc_HOL_Obool))),U_10209)),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

cnf(f_2762_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10206,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10206,tc_HOL_Obool)),U_10208),U_10209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10207,tc_fun(U_10206,tc_HOL_Obool)),U_10208),hAPP(hAPP(c_COMBB(tc_fun(U_10206,tc_HOL_Obool),tc_fun(U_10206,tc_HOL_Obool),U_10207),c_Groups_Ouminus__class_Ouminus(tc_fun(U_10206,tc_HOL_Obool))),U_10209)),
    inference(clausify,[status(thm)],[f_2762_2]) ).

fof(f_2763_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_2763_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_2763_1]) ).

fof(f_2764_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_2764_2,plain,
    ! [U_10214,U_10213,U_10212,U_10211,U_10210] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10210),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10211,U_10210),U_10212),U_10214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10211,U_10210),U_10213),U_10214)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10211,tc_HOL_Obool)),U_10212),U_10213))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10210) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

cnf(f_2764_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10210),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10211,U_10210),U_10212),U_10214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10211,U_10210),U_10213),U_10214)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10211,tc_HOL_Obool)),U_10212),U_10213))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10210) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

fof(f_2765_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_2765_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_2765_1]) ).

fof(f_2766_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_2766_2,plain,
    ! [U_10219,U_10218,U_10217,U_10216,U_10215] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10217,tc_HOL_Obool)),U_10218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10216,tc_fun(U_10217,tc_HOL_Obool)),U_10215),U_10219)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10216,tc_fun(U_10217,tc_HOL_Obool)),U_10215),hAPP(hAPP(c_COMBB(tc_fun(U_10217,tc_HOL_Obool),tc_fun(U_10217,tc_HOL_Obool),U_10216),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10217,tc_HOL_Obool)),U_10218)),U_10219))
        | U_10215 = c_Orderings_Obot__class_Obot(tc_fun(U_10216,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10217,tc_HOL_Obool)),U_10218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10216,tc_fun(U_10217,tc_HOL_Obool)),U_10215),U_10219)) = U_10218
        | U_10215 != c_Orderings_Obot__class_Obot(tc_fun(U_10216,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

fof(f_2766_3,plain,
    ( ! [U_10229,U_10227,U_10225,U_10223,U_10221] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10225,tc_HOL_Obool)),U_10227),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10225,tc_HOL_Obool)),U_10221),U_10229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10223,tc_fun(U_10225,tc_HOL_Obool)),U_10221),hAPP(hAPP(c_COMBB(tc_fun(U_10225,tc_HOL_Obool),tc_fun(U_10225,tc_HOL_Obool),U_10223),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10225,tc_HOL_Obool)),U_10227)),U_10229))
        | U_10221 = c_Orderings_Obot__class_Obot(tc_fun(U_10223,tc_HOL_Obool)) )
    & ! [U_10228,U_10226,U_10224,U_10222,U_10220] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10224,tc_HOL_Obool)),U_10226),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10222,tc_fun(U_10224,tc_HOL_Obool)),U_10220),U_10228)) = U_10226
        | U_10220 != c_Orderings_Obot__class_Obot(tc_fun(U_10222,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2766_2]) ).

cnf(f_2766_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10224,tc_HOL_Obool)),U_10226),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10222,tc_fun(U_10224,tc_HOL_Obool)),U_10220),U_10228)) = U_10226
    | U_10220 != c_Orderings_Obot__class_Obot(tc_fun(U_10222,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2766_3]) ).

cnf(f_2766_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10225,tc_HOL_Obool)),U_10227),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10225,tc_HOL_Obool)),U_10221),U_10229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10223,tc_fun(U_10225,tc_HOL_Obool)),U_10221),hAPP(hAPP(c_COMBB(tc_fun(U_10225,tc_HOL_Obool),tc_fun(U_10225,tc_HOL_Obool),U_10223),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10225,tc_HOL_Obool)),U_10227)),U_10229))
    | U_10221 = c_Orderings_Obot__class_Obot(tc_fun(U_10223,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2766_3]) ).

fof(f_2767_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_2767_2,plain,
    ! [U_10234,U_10233,U_10232,U_10231,U_10230] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10230),hAPP(U_10234,U_10232)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,U_10230),U_10233),U_10234)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10231),U_10232),U_10233))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10230) ),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

cnf(f_2767_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10230),hAPP(U_10234,U_10232)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10231,U_10230),U_10233),U_10234)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10231),U_10232),U_10233))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10230) ),
    inference(clausify,[status(thm)],[f_2767_2]) ).

fof(f_2768_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_2768_2,plain,
    ! [U_10239,U_10238,U_10237,U_10236,U_10235] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10236,tc_fun(U_10237,tc_HOL_Obool)),U_10235),hAPP(hAPP(c_COMBB(tc_fun(U_10237,tc_HOL_Obool),tc_fun(U_10237,tc_HOL_Obool),U_10236),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10237,tc_HOL_Obool)),U_10238)),U_10239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10237,tc_HOL_Obool)),U_10238),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10236,tc_fun(U_10237,tc_HOL_Obool)),U_10235),U_10239))
        | U_10235 = c_Orderings_Obot__class_Obot(tc_fun(U_10236,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10236,tc_fun(U_10237,tc_HOL_Obool)),U_10235),hAPP(hAPP(c_COMBB(tc_fun(U_10237,tc_HOL_Obool),tc_fun(U_10237,tc_HOL_Obool),U_10236),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10237,tc_HOL_Obool)),U_10238)),U_10239)) = c_Orderings_Otop__class_Otop(tc_fun(U_10237,tc_HOL_Obool))
        | U_10235 != c_Orderings_Obot__class_Obot(tc_fun(U_10236,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

fof(f_2768_3,plain,
    ( ! [U_10249,U_10247,U_10245,U_10243,U_10241] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10243,tc_fun(U_10245,tc_HOL_Obool)),U_10241),hAPP(hAPP(c_COMBB(tc_fun(U_10245,tc_HOL_Obool),tc_fun(U_10245,tc_HOL_Obool),U_10243),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10245,tc_HOL_Obool)),U_10247)),U_10249)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10245,tc_HOL_Obool)),U_10247),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10243,tc_fun(U_10245,tc_HOL_Obool)),U_10241),U_10249))
        | U_10241 = c_Orderings_Obot__class_Obot(tc_fun(U_10243,tc_HOL_Obool)) )
    & ! [U_10248,U_10246,U_10244,U_10242,U_10240] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10242,tc_fun(U_10244,tc_HOL_Obool)),U_10240),hAPP(hAPP(c_COMBB(tc_fun(U_10244,tc_HOL_Obool),tc_fun(U_10244,tc_HOL_Obool),U_10242),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10244,tc_HOL_Obool)),U_10246)),U_10248)) = c_Orderings_Otop__class_Otop(tc_fun(U_10244,tc_HOL_Obool))
        | U_10240 != c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2768_2]) ).

cnf(f_2768_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10242,tc_fun(U_10244,tc_HOL_Obool)),U_10240),hAPP(hAPP(c_COMBB(tc_fun(U_10244,tc_HOL_Obool),tc_fun(U_10244,tc_HOL_Obool),U_10242),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10244,tc_HOL_Obool)),U_10246)),U_10248)) = c_Orderings_Otop__class_Otop(tc_fun(U_10244,tc_HOL_Obool))
    | U_10240 != c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2768_3]) ).

cnf(f_2768_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10243,tc_fun(U_10245,tc_HOL_Obool)),U_10241),hAPP(hAPP(c_COMBB(tc_fun(U_10245,tc_HOL_Obool),tc_fun(U_10245,tc_HOL_Obool),U_10243),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10245,tc_HOL_Obool)),U_10247)),U_10249)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10245,tc_HOL_Obool)),U_10247),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10243,tc_fun(U_10245,tc_HOL_Obool)),U_10241),U_10249))
    | U_10241 = c_Orderings_Obot__class_Obot(tc_fun(U_10243,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2768_3]) ).

fof(f_2769_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_2769_2,plain,
    ! [U_10254,U_10253,U_10252,U_10251,U_10250] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10250),U_10253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10251,U_10250),U_10252),U_10254)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10251,U_10250,hAPP(hAPP(c_COMBB(U_10250,tc_fun(U_10250,U_10250),U_10251),c_Lattices_Osemilattice__sup__class_Osup(U_10250)),U_10254)),U_10253),U_10252)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10251),U_10252))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10250) ),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

cnf(f_2769_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10250),U_10253),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10251,U_10250),U_10252),U_10254)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10251,U_10250,hAPP(hAPP(c_COMBB(U_10250,tc_fun(U_10250,U_10250),U_10251),c_Lattices_Osemilattice__sup__class_Osup(U_10250)),U_10254)),U_10253),U_10252)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10251),U_10252))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10250) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

fof(f_2770_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_2770_2,plain,
    ! [U_10255] : hAPP(c_Int_Onat,U_10255) = 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_10255)),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_2770_1]) ).

cnf(f_2770_3,plain,
    hAPP(c_Int_Onat,U_10255) = 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_10255)),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_2770_2]) ).

fof(f_2771_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_2771_2,plain,
    ! [U_10258,U_10257,U_10256] : c_Wellfounded_Omlex__prod(U_10256,U_10257,U_10258) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_10256),U_10256),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_10256,c_Wellfounded_Oless__than,U_10258)),hAPP(hAPP(c_COMBS(U_10256,U_10256,tc_prod(tc_Nat_Onat,U_10256)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10256,tc_prod(tc_Nat_Onat,U_10256)),U_10256),c_Product__Type_OPair(tc_Nat_Onat,U_10256)),U_10257)),c_COMBI(U_10256))),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

cnf(f_2771_3,plain,
    c_Wellfounded_Omlex__prod(U_10256,U_10257,U_10258) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_10256),U_10256),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_10256,c_Wellfounded_Oless__than,U_10258)),hAPP(hAPP(c_COMBS(U_10256,U_10256,tc_prod(tc_Nat_Onat,U_10256)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10256,tc_prod(tc_Nat_Onat,U_10256)),U_10256),c_Product__Type_OPair(tc_Nat_Onat,U_10256)),U_10257)),c_COMBI(U_10256))),
    inference(clausify,[status(thm)],[f_2771_2]) ).

fof(f_2772_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_2772_2,plain,
    ! [U_10260,U_10259] : c_FunDef_Orp__inv__image(U_10259,U_10260) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),c_COMBS(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(U_10260,U_10259)),c_Product__Type_OPair(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),c_Relation_Oinv__image(U_10259,U_10260))))),c_Relation_Oinv__image(U_10259,U_10260))),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

cnf(f_2772_3,plain,
    c_FunDef_Orp__inv__image(U_10259,U_10260) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),c_COMBS(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)),tc_fun(tc_fun(U_10260,U_10259),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),tc_fun(tc_prod(U_10259,U_10259),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool))),tc_fun(U_10260,U_10259)),c_Product__Type_OPair(tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool),tc_fun(tc_prod(U_10260,U_10260),tc_HOL_Obool)))),c_Relation_Oinv__image(U_10259,U_10260))))),c_Relation_Oinv__image(U_10259,U_10260))),
    inference(clausify,[status(thm)],[f_2772_2]) ).

fof(f_2773_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_2773_2,plain,
    ! [U_10263,U_10262,U_10261] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10261,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10261),U_10262)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10261,U_10262,U_10263)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_10261),U_10263)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10261),U_10262),U_10263))
      | ~ class_Orderings_Olinorder(U_10261) ),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

cnf(f_2773_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10261,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10261),U_10262)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10261,U_10262,U_10263)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_10261),U_10263)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10261),U_10262),U_10263))
    | ~ class_Orderings_Olinorder(U_10261) ),
    inference(clausify,[status(thm)],[f_2773_2]) ).

fof(f_2774_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_2774_2,plain,
    ! [U_10264] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10264))),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

cnf(f_2774_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10264))),
    inference(clausify,[status(thm)],[f_2774_2]) ).

fof(f_2775_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_2775_2,plain,
    ! [U_10275,U_10274,U_10273,U_10272,U_10271] :
      ( ( ! [U_10270] :
            ( hBOOL(hAPP(U_10275,U_10270))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10271),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10272,tc_fun(U_10271,tc_HOL_Obool)),U_10273),U_10274))) )
        | ? [U_10269] :
            ( ? [U_10268] :
                ( ~ hBOOL(hAPP(U_10275,U_10268))
                & hBOOL(hAPP(hAPP(c_member(U_10271),U_10268),hAPP(U_10274,U_10269))) )
            & hBOOL(hAPP(hAPP(c_member(U_10272),U_10269),U_10273)) ) )
      & ( ! [U_10267] :
            ( ! [U_10266] :
                ( hBOOL(hAPP(U_10275,U_10266))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10271),U_10266),hAPP(U_10274,U_10267))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10272),U_10267),U_10273)) )
        | ? [U_10265] :
            ( ~ hBOOL(hAPP(U_10275,U_10265))
            & hBOOL(hAPP(hAPP(c_member(U_10271),U_10265),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10272,tc_fun(U_10271,tc_HOL_Obool)),U_10273),U_10274))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

fof(f_2775_3,plain,
    ( ! [U_10285,U_10283,U_10281,U_10279,U_10277] :
        ( ! [U_10270] :
            ( hBOOL(hAPP(U_10285,U_10270))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) )
        | ? [U_10269] :
            ( ? [U_10268] :
                ( ~ hBOOL(hAPP(U_10285,U_10268))
                & hBOOL(hAPP(hAPP(c_member(U_10277),U_10268),hAPP(U_10283,U_10269))) )
            & hBOOL(hAPP(hAPP(c_member(U_10279),U_10269),U_10281)) ) )
    & ! [U_10284,U_10282,U_10280,U_10278,U_10276] :
        ( ! [U_10267] :
            ( ! [U_10266] :
                ( hBOOL(hAPP(U_10284,U_10266))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) )
        | ? [U_10265] :
            ( ~ hBOOL(hAPP(U_10284,U_10265))
            & hBOOL(hAPP(hAPP(c_member(U_10276),U_10265),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10278,tc_fun(U_10276,tc_HOL_Obool)),U_10280),U_10282))) ) ) ),
    inference(miniscope,[status(thm)],[f_2775_2]) ).

fof(f_2775_4,plain,
    ( ! [U_10285,U_10283,U_10281,U_10279,U_10277] :
        ( ! [U_10270] :
            ( hBOOL(hAPP(U_10285,U_10270))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) )
        | ? [U_10269] :
            ( ? [U_10268] :
                ( ~ hBOOL(hAPP(U_10285,U_10268))
                & hBOOL(hAPP(hAPP(c_member(U_10277),U_10268),hAPP(U_10283,U_10269))) )
            & hBOOL(hAPP(hAPP(c_member(U_10279),U_10269),U_10281)) ) )
    & ! [U_10284,U_10282,U_10280,U_10278,U_10276] :
        ( ! [U_10267] :
            ( ! [U_10266] :
                ( hBOOL(hAPP(U_10284,U_10266))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) )
        | ( ~ hBOOL(hAPP(U_10284,sK224(U_10284,U_10282,U_10280,U_10278,U_10276)))
          & hBOOL(hAPP(hAPP(c_member(U_10276),sK224(U_10284,U_10282,U_10280,U_10278,U_10276)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10278,tc_fun(U_10276,tc_HOL_Obool)),U_10280),U_10282))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_10265,sK224(U_10284,U_10282,U_10280,U_10278,U_10276))],[f_2775_3]) ).

fof(f_2775_5,plain,
    ( ! [U_10285,U_10283,U_10281,U_10279,U_10277] :
        ( ! [U_10270] :
            ( hBOOL(hAPP(U_10285,U_10270))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) )
        | ( ? [U_10268] :
              ( ~ hBOOL(hAPP(U_10285,U_10268))
              & hBOOL(hAPP(hAPP(c_member(U_10277),U_10268),hAPP(U_10283,sK225(U_10285,U_10283,U_10281,U_10279,U_10277)))) )
          & hBOOL(hAPP(hAPP(c_member(U_10279),sK225(U_10285,U_10283,U_10281,U_10279,U_10277)),U_10281)) ) )
    & ! [U_10284,U_10282,U_10280,U_10278,U_10276] :
        ( ! [U_10267] :
            ( ! [U_10266] :
                ( hBOOL(hAPP(U_10284,U_10266))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) )
        | ( ~ hBOOL(hAPP(U_10284,sK224(U_10284,U_10282,U_10280,U_10278,U_10276)))
          & hBOOL(hAPP(hAPP(c_member(U_10276),sK224(U_10284,U_10282,U_10280,U_10278,U_10276)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10278,tc_fun(U_10276,tc_HOL_Obool)),U_10280),U_10282))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_10269,sK225(U_10285,U_10283,U_10281,U_10279,U_10277))],[f_2775_4]) ).

fof(f_2775_6,plain,
    ( ! [U_10285,U_10283,U_10281,U_10279,U_10277] :
        ( ! [U_10270] :
            ( hBOOL(hAPP(U_10285,U_10270))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) )
        | ( ~ hBOOL(hAPP(U_10285,sK226(U_10285,U_10283,U_10281,U_10279,U_10277)))
          & hBOOL(hAPP(hAPP(c_member(U_10277),sK226(U_10285,U_10283,U_10281,U_10279,U_10277)),hAPP(U_10283,sK225(U_10285,U_10283,U_10281,U_10279,U_10277))))
          & hBOOL(hAPP(hAPP(c_member(U_10279),sK225(U_10285,U_10283,U_10281,U_10279,U_10277)),U_10281)) ) )
    & ! [U_10284,U_10282,U_10280,U_10278,U_10276] :
        ( ! [U_10267] :
            ( ! [U_10266] :
                ( hBOOL(hAPP(U_10284,U_10266))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) )
        | ( ~ hBOOL(hAPP(U_10284,sK224(U_10284,U_10282,U_10280,U_10278,U_10276)))
          & hBOOL(hAPP(hAPP(c_member(U_10276),sK224(U_10284,U_10282,U_10280,U_10278,U_10276)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10278,tc_fun(U_10276,tc_HOL_Obool)),U_10280),U_10282))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_10268,sK226(U_10285,U_10283,U_10281,U_10279,U_10277))],[f_2775_5]) ).

cnf(f_2775_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10276),sK224(U_10284,U_10282,U_10280,U_10278,U_10276)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10278,tc_fun(U_10276,tc_HOL_Obool)),U_10280),U_10282)))
    | hBOOL(hAPP(U_10284,U_10266))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) ),
    inference(clausify,[status(thm)],[f_2775_6]) ).

cnf(f_2775_8,plain,
    ( ~ hBOOL(hAPP(U_10284,sK224(U_10284,U_10282,U_10280,U_10278,U_10276)))
    | hBOOL(hAPP(U_10284,U_10266))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10276),U_10266),hAPP(U_10282,U_10267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10267),U_10280)) ),
    inference(clausify,[status(thm)],[f_2775_6]) ).

cnf(f_2775_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10279),sK225(U_10285,U_10283,U_10281,U_10279,U_10277)),U_10281))
    | hBOOL(hAPP(U_10285,U_10270))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) ),
    inference(clausify,[status(thm)],[f_2775_6]) ).

cnf(f_2775_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10277),sK226(U_10285,U_10283,U_10281,U_10279,U_10277)),hAPP(U_10283,sK225(U_10285,U_10283,U_10281,U_10279,U_10277))))
    | hBOOL(hAPP(U_10285,U_10270))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) ),
    inference(clausify,[status(thm)],[f_2775_6]) ).

cnf(f_2775_11,plain,
    ( ~ hBOOL(hAPP(U_10285,sK226(U_10285,U_10283,U_10281,U_10279,U_10277)))
    | hBOOL(hAPP(U_10285,U_10270))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10277),U_10270),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10279,tc_fun(U_10277,tc_HOL_Obool)),U_10281),U_10283))) ),
    inference(clausify,[status(thm)],[f_2775_6]) ).

fof(f_2776_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_2776_2,plain,
    ! [U_10291,U_10290,U_10289,U_10288,U_10287,U_10286] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10286,tc_fun(U_10287,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10288,tc_fun(U_10286,tc_HOL_Obool)),U_10289),U_10290)),U_10291) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10288,tc_fun(U_10287,tc_HOL_Obool)),U_10289),hAPP(hAPP(c_COMBC(U_10288,tc_fun(U_10286,tc_fun(U_10287,tc_HOL_Obool)),tc_fun(U_10287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10286,tc_HOL_Obool),tc_fun(tc_fun(U_10286,tc_fun(U_10287,tc_HOL_Obool)),tc_fun(U_10287,tc_HOL_Obool)),U_10288),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10286,tc_fun(U_10287,tc_HOL_Obool))),U_10290)),U_10291)),
    inference(variable_rename,[status(thm)],[f_2776_1]) ).

cnf(f_2776_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10286,tc_fun(U_10287,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10288,tc_fun(U_10286,tc_HOL_Obool)),U_10289),U_10290)),U_10291) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10288,tc_fun(U_10287,tc_HOL_Obool)),U_10289),hAPP(hAPP(c_COMBC(U_10288,tc_fun(U_10286,tc_fun(U_10287,tc_HOL_Obool)),tc_fun(U_10287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10286,tc_HOL_Obool),tc_fun(tc_fun(U_10286,tc_fun(U_10287,tc_HOL_Obool)),tc_fun(U_10287,tc_HOL_Obool)),U_10288),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10286,tc_fun(U_10287,tc_HOL_Obool))),U_10290)),U_10291)),
    inference(clausify,[status(thm)],[f_2776_2]) ).

fof(f_2777_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_2777_2,plain,
    ! [U_10297,U_10296,U_10295,U_10294,U_10293,U_10292] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10292,tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10294,tc_fun(U_10292,tc_HOL_Obool)),U_10295),U_10296)),U_10297) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10294,tc_fun(U_10293,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_COMBC(U_10294,tc_fun(U_10292,tc_fun(U_10293,tc_HOL_Obool)),tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10292,tc_HOL_Obool),tc_fun(tc_fun(U_10292,tc_fun(U_10293,tc_HOL_Obool)),tc_fun(U_10293,tc_HOL_Obool)),U_10294),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10292,tc_fun(U_10293,tc_HOL_Obool))),U_10296)),U_10297)),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

cnf(f_2777_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10292,tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10294,tc_fun(U_10292,tc_HOL_Obool)),U_10295),U_10296)),U_10297) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10294,tc_fun(U_10293,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_COMBC(U_10294,tc_fun(U_10292,tc_fun(U_10293,tc_HOL_Obool)),tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10292,tc_HOL_Obool),tc_fun(tc_fun(U_10292,tc_fun(U_10293,tc_HOL_Obool)),tc_fun(U_10293,tc_HOL_Obool)),U_10294),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10292,tc_fun(U_10293,tc_HOL_Obool))),U_10296)),U_10297)),
    inference(clausify,[status(thm)],[f_2777_2]) ).

fof(f_2778_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_2778_2,plain,
    ! [U_10303,U_10302,U_10301,U_10300,U_10299,U_10298] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10298,tc_fun(U_10299,tc_HOL_Obool)),U_10300),hAPP(hAPP(c_COMBC(U_10298,tc_fun(U_10301,tc_fun(U_10299,tc_HOL_Obool)),tc_fun(U_10299,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10301,tc_HOL_Obool),tc_fun(tc_fun(U_10301,tc_fun(U_10299,tc_HOL_Obool)),tc_fun(U_10299,tc_HOL_Obool)),U_10298),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10301,tc_fun(U_10299,tc_HOL_Obool))),U_10302)),U_10303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10301,tc_fun(U_10299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10298,tc_fun(U_10301,tc_HOL_Obool)),U_10300),U_10302)),U_10303),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

cnf(f_2778_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10298,tc_fun(U_10299,tc_HOL_Obool)),U_10300),hAPP(hAPP(c_COMBC(U_10298,tc_fun(U_10301,tc_fun(U_10299,tc_HOL_Obool)),tc_fun(U_10299,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10301,tc_HOL_Obool),tc_fun(tc_fun(U_10301,tc_fun(U_10299,tc_HOL_Obool)),tc_fun(U_10299,tc_HOL_Obool)),U_10298),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10301,tc_fun(U_10299,tc_HOL_Obool))),U_10302)),U_10303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10301,tc_fun(U_10299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10298,tc_fun(U_10301,tc_HOL_Obool)),U_10300),U_10302)),U_10303),
    inference(clausify,[status(thm)],[f_2778_2]) ).

fof(f_2779_1,plain,
    ! [V_ca_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_ca_2))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_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_ca_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_ca_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).

fof(f_2779_2,plain,
    ! [U_10312,U_10311,U_10310,U_10309,U_10308,U_10307,U_10306] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10306,tc_fun(U_10307,tc_fun(U_10308,tc_HOL_Obool))),U_10309),U_10310),U_10311),U_10312))
        | ! [U_10305] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10310,U_10305),U_10311),U_10312))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10306),U_10305),U_10309)) ) )
      & ( ? [U_10304] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10310,U_10304),U_10311),U_10312))
            & hBOOL(hAPP(hAPP(c_member(U_10306),U_10304),U_10309)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10306,tc_fun(U_10307,tc_fun(U_10308,tc_HOL_Obool))),U_10309),U_10310),U_10311),U_10312)) ) ),
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

fof(f_2779_3,plain,
    ( ! [U_10326,U_10324,U_10322,U_10320,U_10318,U_10316,U_10314] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10314,tc_fun(U_10316,tc_fun(U_10318,tc_HOL_Obool))),U_10320),U_10322),U_10324),U_10326))
        | ! [U_10305] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10322,U_10305),U_10324),U_10326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10314),U_10305),U_10320)) ) )
    & ! [U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313] :
        ( ? [U_10304] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10321,U_10304),U_10323),U_10325))
            & hBOOL(hAPP(hAPP(c_member(U_10313),U_10304),U_10319)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10313,tc_fun(U_10315,tc_fun(U_10317,tc_HOL_Obool))),U_10319),U_10321),U_10323),U_10325)) ) ),
    inference(miniscope,[status(thm)],[f_2779_2]) ).

fof(f_2779_4,plain,
    ( ! [U_10326,U_10324,U_10322,U_10320,U_10318,U_10316,U_10314] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10314,tc_fun(U_10316,tc_fun(U_10318,tc_HOL_Obool))),U_10320),U_10322),U_10324),U_10326))
        | ! [U_10305] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10322,U_10305),U_10324),U_10326))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10314),U_10305),U_10320)) ) )
    & ! [U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_10321,sK227(U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313)),U_10323),U_10325))
          & hBOOL(hAPP(hAPP(c_member(U_10313),sK227(U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313)),U_10319)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10313,tc_fun(U_10315,tc_fun(U_10317,tc_HOL_Obool))),U_10319),U_10321),U_10323),U_10325)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_10304,sK227(U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313))],[f_2779_3]) ).

cnf(f_2779_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10313),sK227(U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313)),U_10319))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10313,tc_fun(U_10315,tc_fun(U_10317,tc_HOL_Obool))),U_10319),U_10321),U_10323),U_10325)) ),
    inference(clausify,[status(thm)],[f_2779_4]) ).

cnf(f_2779_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_10321,sK227(U_10325,U_10323,U_10321,U_10319,U_10317,U_10315,U_10313)),U_10323),U_10325))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10313,tc_fun(U_10315,tc_fun(U_10317,tc_HOL_Obool))),U_10319),U_10321),U_10323),U_10325)) ),
    inference(clausify,[status(thm)],[f_2779_4]) ).

cnf(f_2779_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10314,tc_fun(U_10316,tc_fun(U_10318,tc_HOL_Obool))),U_10320),U_10322),U_10324),U_10326))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_10322,U_10305),U_10324),U_10326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10314),U_10305),U_10320)) ),
    inference(clausify,[status(thm)],[f_2779_4]) ).

fof(f_2780_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_2780_2,plain,
    ! [U_10333,U_10332,U_10331,U_10330,U_10329] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10329,tc_fun(U_10330,tc_HOL_Obool)),U_10331),U_10332),U_10333))
        | ! [U_10328] :
            ( ~ hBOOL(hAPP(hAPP(U_10332,U_10328),U_10333))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10329),U_10328),U_10331)) ) )
      & ( ? [U_10327] :
            ( hBOOL(hAPP(hAPP(U_10332,U_10327),U_10333))
            & hBOOL(hAPP(hAPP(c_member(U_10329),U_10327),U_10331)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10329,tc_fun(U_10330,tc_HOL_Obool)),U_10331),U_10332),U_10333)) ) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ( ! [U_10343,U_10341,U_10339,U_10337,U_10335] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10335,tc_fun(U_10337,tc_HOL_Obool)),U_10339),U_10341),U_10343))
        | ! [U_10328] :
            ( ~ hBOOL(hAPP(hAPP(U_10341,U_10328),U_10343))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10335),U_10328),U_10339)) ) )
    & ! [U_10342,U_10340,U_10338,U_10336,U_10334] :
        ( ? [U_10327] :
            ( hBOOL(hAPP(hAPP(U_10340,U_10327),U_10342))
            & hBOOL(hAPP(hAPP(c_member(U_10334),U_10327),U_10338)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10334,tc_fun(U_10336,tc_HOL_Obool)),U_10338),U_10340),U_10342)) ) ),
    inference(miniscope,[status(thm)],[f_2780_2]) ).

fof(f_2780_4,plain,
    ( ! [U_10343,U_10341,U_10339,U_10337,U_10335] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10335,tc_fun(U_10337,tc_HOL_Obool)),U_10339),U_10341),U_10343))
        | ! [U_10328] :
            ( ~ hBOOL(hAPP(hAPP(U_10341,U_10328),U_10343))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10335),U_10328),U_10339)) ) )
    & ! [U_10342,U_10340,U_10338,U_10336,U_10334] :
        ( ( hBOOL(hAPP(hAPP(U_10340,sK228(U_10342,U_10340,U_10338,U_10336,U_10334)),U_10342))
          & hBOOL(hAPP(hAPP(c_member(U_10334),sK228(U_10342,U_10340,U_10338,U_10336,U_10334)),U_10338)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10334,tc_fun(U_10336,tc_HOL_Obool)),U_10338),U_10340),U_10342)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_10327,sK228(U_10342,U_10340,U_10338,U_10336,U_10334))],[f_2780_3]) ).

cnf(f_2780_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10334),sK228(U_10342,U_10340,U_10338,U_10336,U_10334)),U_10338))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10334,tc_fun(U_10336,tc_HOL_Obool)),U_10338),U_10340),U_10342)) ),
    inference(clausify,[status(thm)],[f_2780_4]) ).

cnf(f_2780_6,plain,
    ( hBOOL(hAPP(hAPP(U_10340,sK228(U_10342,U_10340,U_10338,U_10336,U_10334)),U_10342))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10334,tc_fun(U_10336,tc_HOL_Obool)),U_10338),U_10340),U_10342)) ),
    inference(clausify,[status(thm)],[f_2780_4]) ).

cnf(f_2780_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10335,tc_fun(U_10337,tc_HOL_Obool)),U_10339),U_10341),U_10343))
    | ~ hBOOL(hAPP(hAPP(U_10341,U_10328),U_10343))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10335),U_10328),U_10339)) ),
    inference(clausify,[status(thm)],[f_2780_4]) ).

fof(f_2781_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_2781_2,plain,
    ! [U_10345,U_10344] :
      ( ( hAPP(c_Int_ORep__Integ,U_10344) = hAPP(c_Int_ORep__Integ,U_10345)
        | U_10344 != U_10345 )
      & ( U_10344 = U_10345
        | hAPP(c_Int_ORep__Integ,U_10344) != hAPP(c_Int_ORep__Integ,U_10345) ) ),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

fof(f_2781_3,plain,
    ( ! [U_10349,U_10347] :
        ( hAPP(c_Int_ORep__Integ,U_10347) = hAPP(c_Int_ORep__Integ,U_10349)
        | U_10347 != U_10349 )
    & ! [U_10348,U_10346] :
        ( U_10346 = U_10348
        | hAPP(c_Int_ORep__Integ,U_10346) != hAPP(c_Int_ORep__Integ,U_10348) ) ),
    inference(miniscope,[status(thm)],[f_2781_2]) ).

cnf(f_2781_4,plain,
    ( U_10346 = U_10348
    | hAPP(c_Int_ORep__Integ,U_10346) != hAPP(c_Int_ORep__Integ,U_10348) ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

cnf(f_2781_5,plain,
    ( hAPP(c_Int_ORep__Integ,U_10347) = hAPP(c_Int_ORep__Integ,U_10349)
    | U_10347 != U_10349 ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

fof(f_2782_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_2782_2,plain,
    ! [U_10352,U_10351,U_10350] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10351) = hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10352)
          | U_10351 != U_10352 )
        & ( U_10351 = U_10352
          | hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10351) != hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10352) ) )
      | ~ class_Orderings_Olinorder(U_10350) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

cnf(f_2782_3,plain,
    ( U_10351 = U_10352
    | hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10351) != hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10352)
    | ~ class_Orderings_Olinorder(U_10350) ),
    inference(clausify,[status(thm)],[f_2782_2]) ).

cnf(f_2782_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10351) = hAPP(c_SetInterval_Oord__class_OatMost(U_10350),U_10352)
    | U_10351 != U_10352
    | ~ class_Orderings_Olinorder(U_10350) ),
    inference(clausify,[status(thm)],[f_2782_2]) ).

fof(f_2783_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_2783_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_2783_1]) ).

fof(f_2784_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_2784_2,plain,
    ! [U_10353] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10353) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10353),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

cnf(f_2784_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10353) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10353),
    inference(clausify,[status(thm)],[f_2784_2]) ).

fof(f_2785_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_2785_2,plain,
    ! [U_10354] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10354)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10354),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

cnf(f_2785_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10354)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10354),
    inference(clausify,[status(thm)],[f_2785_2]) ).

fof(f_2786_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_2786_2,plain,
    ! [U_10355] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10355)) = hAPP(c_Nat_OSuc,U_10355),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

cnf(f_2786_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10355)) = hAPP(c_Nat_OSuc,U_10355),
    inference(clausify,[status(thm)],[f_2786_2]) ).

fof(f_2787_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_2787_2,plain,
    ! [U_10356] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10356)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10356)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10356)),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

cnf(f_2787_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10356)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10356)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10356)),
    inference(clausify,[status(thm)],[f_2787_2]) ).

fof(f_2788_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_2788_2,plain,
    ! [U_10359,U_10358,U_10357] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_10357),U_10358),hAPP(c_SetInterval_Oord__class_OatMost(U_10357),U_10359)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10357),U_10358),U_10359)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10357),U_10358),U_10359))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10357),U_10358),hAPP(c_SetInterval_Oord__class_OatMost(U_10357),U_10359))) ) )
      | ~ class_Orderings_Oord(U_10357) ),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

cnf(f_2788_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10357),U_10358),U_10359))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10357),U_10358),hAPP(c_SetInterval_Oord__class_OatMost(U_10357),U_10359)))
    | ~ class_Orderings_Oord(U_10357) ),
    inference(clausify,[status(thm)],[f_2788_2]) ).

cnf(f_2788_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10357),U_10358),hAPP(c_SetInterval_Oord__class_OatMost(U_10357),U_10359)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10357),U_10358),U_10359))
    | ~ class_Orderings_Oord(U_10357) ),
    inference(clausify,[status(thm)],[f_2788_2]) ).

fof(f_2789_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_2789_2,plain,
    ! [U_10362,U_10361,U_10360] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10360,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10361)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10362)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10360),U_10361),U_10362)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10360),U_10361),U_10362))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10360,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10361)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10362))) ) )
      | ~ class_Orderings_Oorder(U_10360) ),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

cnf(f_2789_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10360),U_10361),U_10362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10360,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10361)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10362)))
    | ~ class_Orderings_Oorder(U_10360) ),
    inference(clausify,[status(thm)],[f_2789_2]) ).

cnf(f_2789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10360,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10361)),hAPP(c_SetInterval_Oord__class_OatMost(U_10360),U_10362)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10360),U_10361),U_10362))
    | ~ class_Orderings_Oorder(U_10360) ),
    inference(clausify,[status(thm)],[f_2789_2]) ).

fof(f_2790_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_2790_2,plain,
    ! [U_10366,U_10365,U_10364,U_10363] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10364)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool),tc_Nat_Onat),U_10365),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10366))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10366,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10364),U_10366))),U_10365),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

cnf(f_2790_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10364)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool),tc_Nat_Onat),U_10365),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10366))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10363,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10366,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10364),U_10366))),U_10365),
    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_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_2791_2,plain,
    ! [U_10369,U_10368,U_10367] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10367),U_10368),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10369))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10367),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10367),U_10368),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10369))),hAPP(U_10368,hAPP(c_Nat_OSuc,U_10369)))
      | ~ class_Groups_Ocomm__monoid__add(U_10367) ),
    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_10367),U_10368),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10369))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10367),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10367),U_10368),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10369))),hAPP(U_10368,hAPP(c_Nat_OSuc,U_10369)))
    | ~ class_Groups_Ocomm__monoid__add(U_10367) ),
    inference(clausify,[status(thm)],[f_2791_2]) ).

fof(f_2792_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_2792_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_2792_1]) ).

fof(f_2793_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_2793_2,plain,
    ! [U_10373,U_10372,U_10371,U_10370] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10370,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_10370,U_10371,U_10372)),hAPP(c_SetInterval_Oord__class_OatMost(U_10370),U_10373)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10370,U_10371,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10370),U_10372),U_10373))
      | ~ class_Orderings_Olinorder(U_10370) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

cnf(f_2793_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10370,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_10370,U_10371,U_10372)),hAPP(c_SetInterval_Oord__class_OatMost(U_10370),U_10373)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10370,U_10371,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10370),U_10372),U_10373))
    | ~ class_Orderings_Olinorder(U_10370) ),
    inference(clausify,[status(thm)],[f_2793_2]) ).

fof(f_2794_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_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_2794_2,plain,
    ! [U_10377,U_10376,U_10375,U_10374] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10374,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10374),U_10375)),c_SetInterval_Oord__class_OatLeastAtMost(U_10374,U_10376,U_10377)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10374,U_10376,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10374),U_10375),U_10377))
      | ~ class_Orderings_Olinorder(U_10374) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

cnf(f_2794_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10374,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10374),U_10375)),c_SetInterval_Oord__class_OatLeastAtMost(U_10374,U_10376,U_10377)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10374,U_10376,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10374),U_10375),U_10377))
    | ~ class_Orderings_Olinorder(U_10374) ),
    inference(clausify,[status(thm)],[f_2794_2]) ).

fof(f_2795_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_2795_2,plain,
    ! [U_10380,U_10379,U_10378] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10378,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10378),U_10379)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10378,U_10379,U_10380)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10378),U_10380)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10378),U_10379),U_10380))
      | ~ class_Orderings_Olinorder(U_10378) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

cnf(f_2795_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10378,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10378),U_10379)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10378,U_10379,U_10380)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10378),U_10380)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10378),U_10379),U_10380))
    | ~ class_Orderings_Olinorder(U_10378) ),
    inference(clausify,[status(thm)],[f_2795_2]) ).

fof(f_2796_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_2796_2,plain,
    ! [U_10383,U_10382,U_10381] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10381,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10381),U_10382)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10381,U_10382,U_10383)) = c_Orderings_Obot__class_Obot(tc_fun(U_10381,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10381) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

cnf(f_2796_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10381,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10381),U_10382)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10381,U_10382,U_10383)) = c_Orderings_Obot__class_Obot(tc_fun(U_10381,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10381) ),
    inference(clausify,[status(thm)],[f_2796_2]) ).

fof(f_2797_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_2797_2,plain,
    ! [U_10386,U_10385,U_10384] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10384),U_10385)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10384,U_10385,U_10386)) = c_Orderings_Obot__class_Obot(tc_fun(U_10384,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10384) ),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

cnf(f_2797_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10384),U_10385)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10384,U_10385,U_10386)) = c_Orderings_Obot__class_Obot(tc_fun(U_10384,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10384) ),
    inference(clausify,[status(thm)],[f_2797_2]) ).

fof(f_2798_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_2798_2,plain,
    ! [U_10389,U_10388,U_10387] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10388)),U_10389) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10387,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10387,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10388)),U_10389)),hAPP(U_10389,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

cnf(f_2798_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10388)),U_10389) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10387,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10387,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10388)),U_10389)),hAPP(U_10389,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2798_2]) ).

fof(f_2799_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_2799_2,plain,
    ! [U_10390] : c_Wellfounded_Omeasure(U_10390) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_10390),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

cnf(f_2799_3,plain,
    c_Wellfounded_Omeasure(U_10390) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_10390),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2799_2]) ).

fof(f_2800_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_2800_2,plain,
    ! [U_10392,U_10391] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10391,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10391),U_10392)),hAPP(hAPP(c_Set_Oinsert(U_10391),U_10392),c_Orderings_Obot__class_Obot(tc_fun(U_10391,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_10391),U_10392)
      | ~ class_Orderings_Olinorder(U_10391) ),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

cnf(f_2800_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10391,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10391),U_10392)),hAPP(hAPP(c_Set_Oinsert(U_10391),U_10392),c_Orderings_Obot__class_Obot(tc_fun(U_10391,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_10391),U_10392)
    | ~ class_Orderings_Olinorder(U_10391) ),
    inference(clausify,[status(thm)],[f_2800_2]) ).

fof(f_2801_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_2801_2,plain,
    ! [U_10395,U_10394,U_10393] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10393,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10393),U_10394)),c_SetInterval_Oord__class_OatLeastAtMost(U_10393,U_10394,U_10395)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10393),U_10395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10393),U_10394),U_10395))
      | ~ class_Orderings_Olinorder(U_10393) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

cnf(f_2801_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10393,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10393),U_10394)),c_SetInterval_Oord__class_OatLeastAtMost(U_10393,U_10394,U_10395)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10393),U_10395)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10393),U_10394),U_10395))
    | ~ class_Orderings_Olinorder(U_10393) ),
    inference(clausify,[status(thm)],[f_2801_2]) ).

fof(f_2802_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_2802_2,plain,
    ! [U_10401,U_10400,U_10399,U_10398,U_10397,U_10396] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10396,U_10396)),hAPP(hAPP(c_Product__Type_OPair(U_10396,U_10396),U_10397),U_10398)),hAPP(hAPP(c_Relation_Oinv__image(U_10399,U_10396),U_10400),U_10401)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10399,U_10399)),hAPP(hAPP(c_Product__Type_OPair(U_10399,U_10399),hAPP(U_10401,U_10397)),hAPP(U_10401,U_10398))),U_10400)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10399,U_10399)),hAPP(hAPP(c_Product__Type_OPair(U_10399,U_10399),hAPP(U_10401,U_10397)),hAPP(U_10401,U_10398))),U_10400))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10396,U_10396)),hAPP(hAPP(c_Product__Type_OPair(U_10396,U_10396),U_10397),U_10398)),hAPP(hAPP(c_Relation_Oinv__image(U_10399,U_10396),U_10400),U_10401))) ) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ( ! [U_10413,U_10411,U_10409,U_10407,U_10405] :
        ( ! [U_10403] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10403,U_10403)),hAPP(hAPP(c_Product__Type_OPair(U_10403,U_10403),U_10405),U_10407)),hAPP(hAPP(c_Relation_Oinv__image(U_10409,U_10403),U_10411),U_10413)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10409,U_10409)),hAPP(hAPP(c_Product__Type_OPair(U_10409,U_10409),hAPP(U_10413,U_10405)),hAPP(U_10413,U_10407))),U_10411)) )
    & ! [U_10412,U_10410,U_10408,U_10406,U_10404] :
        ( ! [U_10402] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10402,U_10402)),hAPP(hAPP(c_Product__Type_OPair(U_10402,U_10402),U_10404),U_10406)),hAPP(hAPP(c_Relation_Oinv__image(U_10408,U_10402),U_10410),U_10412)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10408,U_10408)),hAPP(hAPP(c_Product__Type_OPair(U_10408,U_10408),hAPP(U_10412,U_10404)),hAPP(U_10412,U_10406))),U_10410)) ) ),
    inference(miniscope,[status(thm)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10402,U_10402)),hAPP(hAPP(c_Product__Type_OPair(U_10402,U_10402),U_10404),U_10406)),hAPP(hAPP(c_Relation_Oinv__image(U_10408,U_10402),U_10410),U_10412)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10408,U_10408)),hAPP(hAPP(c_Product__Type_OPair(U_10408,U_10408),hAPP(U_10412,U_10404)),hAPP(U_10412,U_10406))),U_10410)) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

cnf(f_2802_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10403,U_10403)),hAPP(hAPP(c_Product__Type_OPair(U_10403,U_10403),U_10405),U_10407)),hAPP(hAPP(c_Relation_Oinv__image(U_10409,U_10403),U_10411),U_10413)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10409,U_10409)),hAPP(hAPP(c_Product__Type_OPair(U_10409,U_10409),hAPP(U_10413,U_10405)),hAPP(U_10413,U_10407))),U_10411)) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_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_2803_2,plain,
    ! [U_10416,U_10415,U_10414] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10414),hAPP(c_Power_Opower__class_Opower(U_10414),U_10415)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10416)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10414),hAPP(hAPP(c_Power_Opower__class_Opower(U_10414),U_10415),U_10416)),c_Groups_Oone__class_Oone(U_10414))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10414),U_10415),c_Groups_Oone__class_Oone(U_10414)))
      | U_10415 = c_Groups_Oone__class_Oone(U_10414)
      | ~ class_Fields_Ofield(U_10414) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

cnf(f_2803_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10414),hAPP(c_Power_Opower__class_Opower(U_10414),U_10415)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10416)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10414),hAPP(hAPP(c_Power_Opower__class_Opower(U_10414),U_10415),U_10416)),c_Groups_Oone__class_Oone(U_10414))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10414),U_10415),c_Groups_Oone__class_Oone(U_10414)))
    | U_10415 = c_Groups_Oone__class_Oone(U_10414)
    | ~ class_Fields_Ofield(U_10414) ),
    inference(clausify,[status(thm)],[f_2803_2]) ).

fof(f_2804_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_2804_2,plain,
    ! [U_10420,U_10419,U_10418,U_10417] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10417,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_10417,U_10418,U_10419)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10417,U_10419,U_10420)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10417,U_10418),U_10420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10417),U_10419),U_10420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10417),U_10418),U_10419))
      | ~ class_Orderings_Olinorder(U_10417) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

cnf(f_2804_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10417,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_10417,U_10418,U_10419)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10417,U_10419,U_10420)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10417,U_10418),U_10420)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10417),U_10419),U_10420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10417),U_10418),U_10419))
    | ~ class_Orderings_Olinorder(U_10417) ),
    inference(clausify,[status(thm)],[f_2804_2]) ).

fof(f_2805_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_2805_2,plain,
    ! [U_10422,U_10421] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10421),U_10422))),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

cnf(f_2805_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10421),U_10422))),
    inference(clausify,[status(thm)],[f_2805_2]) ).

fof(f_2806_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_2806_2,plain,
    ! [U_10424,U_10423] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10423),U_10424))),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

cnf(f_2806_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10423),U_10424))),
    inference(clausify,[status(thm)],[f_2806_2]) ).

fof(f_2807_1,plain,
    ! [V_d_2,V_ca_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_ca_2),V_d_2)
          | V_b_2 != V_d_2
          | V_a_2 != V_ca_2 )
        & ( ( V_b_2 = V_d_2
            & V_a_2 = V_ca_2 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_2807_2,plain,
    ! [U_10429,U_10428,U_10427,U_10426,U_10425] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10426),U_10427) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10428),U_10429)
          | U_10427 != U_10429
          | U_10426 != U_10428 )
        & ( ( U_10427 = U_10429
            & U_10426 = U_10428 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10426),U_10427) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10428),U_10429) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10428),U_10429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10426),U_10427))
      | ~ class_Orderings_Olinorder(U_10425) ),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

cnf(f_2807_3,plain,
    ( U_10426 = U_10428
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10426),U_10427) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10428),U_10429)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10428),U_10429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10426),U_10427))
    | ~ class_Orderings_Olinorder(U_10425) ),
    inference(clausify,[status(thm)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    ( U_10427 = U_10429
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10426),U_10427) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10428),U_10429)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10428),U_10429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10426),U_10427))
    | ~ class_Orderings_Olinorder(U_10425) ),
    inference(clausify,[status(thm)],[f_2807_2]) ).

cnf(f_2807_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10426),U_10427) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10425,U_10428),U_10429)
    | U_10427 != U_10429
    | U_10426 != U_10428
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10428),U_10429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10425),U_10426),U_10427))
    | ~ class_Orderings_Olinorder(U_10425) ),
    inference(clausify,[status(thm)],[f_2807_2]) ).

fof(f_2808_1,plain,
    ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
      ( V_a_2 = V_ca_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_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_ca_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).

fof(f_2808_2,plain,
    ! [U_10434,U_10433,U_10432,U_10431,U_10430] :
      ( U_10431 = U_10433
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10430),U_10433),U_10434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10430),U_10431),U_10432))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10430,U_10431),U_10432) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10430,U_10433),U_10434)
      | ~ class_Orderings_Olinorder(U_10430) ),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

cnf(f_2808_3,plain,
    ( U_10431 = U_10433
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10430),U_10433),U_10434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10430),U_10431),U_10432))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10430,U_10431),U_10432) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10430,U_10433),U_10434)
    | ~ class_Orderings_Olinorder(U_10430) ),
    inference(clausify,[status(thm)],[f_2808_2]) ).

fof(f_2809_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).

fof(f_2809_2,plain,
    ! [U_10439,U_10438,U_10437,U_10436,U_10435] :
      ( U_10437 = U_10439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10435),U_10438),U_10439))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10435),U_10436),U_10437))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10435,U_10436),U_10437) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10435,U_10438),U_10439)
      | ~ class_Orderings_Olinorder(U_10435) ),
    inference(variable_rename,[status(thm)],[f_2809_1]) ).

cnf(f_2809_3,plain,
    ( U_10437 = U_10439
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10435),U_10438),U_10439))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10435),U_10436),U_10437))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10435,U_10436),U_10437) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10435,U_10438),U_10439)
    | ~ class_Orderings_Olinorder(U_10435) ),
    inference(clausify,[status(thm)],[f_2809_2]) ).

fof(f_2810_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_Pa_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_2810_2,plain,
    ! [U_10445,U_10444] :
      ( ( ? [U_10443] :
            ( hBOOL(hAPP(U_10445,U_10443))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10443),U_10444)) )
        | ! [U_10442] :
            ( ~ hBOOL(hAPP(U_10445,U_10442))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10444))) ) )
      & ( ? [U_10441] :
            ( hBOOL(hAPP(U_10445,U_10441))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10444))) )
        | ! [U_10440] :
            ( ~ hBOOL(hAPP(U_10445,U_10440))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10444)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

fof(f_2810_3,plain,
    ( ! [U_10449,U_10447] :
        ( ? [U_10443] :
            ( hBOOL(hAPP(U_10449,U_10443))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10443),U_10447)) )
        | ! [U_10442] :
            ( ~ hBOOL(hAPP(U_10449,U_10442))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447))) ) )
    & ! [U_10448,U_10446] :
        ( ? [U_10441] :
            ( hBOOL(hAPP(U_10448,U_10441))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10446))) )
        | ! [U_10440] :
            ( ~ hBOOL(hAPP(U_10448,U_10440))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10446)) ) ) ),
    inference(miniscope,[status(thm)],[f_2810_2]) ).

fof(f_2810_4,plain,
    ( ! [U_10449,U_10447] :
        ( ? [U_10443] :
            ( hBOOL(hAPP(U_10449,U_10443))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10443),U_10447)) )
        | ! [U_10442] :
            ( ~ hBOOL(hAPP(U_10449,U_10442))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447))) ) )
    & ! [U_10448,U_10446] :
        ( ( hBOOL(hAPP(U_10448,sK229(U_10448,U_10446)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK229(U_10448,U_10446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10446))) )
        | ! [U_10440] :
            ( ~ hBOOL(hAPP(U_10448,U_10440))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10446)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_10441,sK229(U_10448,U_10446))],[f_2810_3]) ).

fof(f_2810_5,plain,
    ( ! [U_10449,U_10447] :
        ( ( hBOOL(hAPP(U_10449,sK230(U_10449,U_10447)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK230(U_10449,U_10447)),U_10447)) )
        | ! [U_10442] :
            ( ~ hBOOL(hAPP(U_10449,U_10442))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447))) ) )
    & ! [U_10448,U_10446] :
        ( ( hBOOL(hAPP(U_10448,sK229(U_10448,U_10446)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK229(U_10448,U_10446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10446))) )
        | ! [U_10440] :
            ( ~ hBOOL(hAPP(U_10448,U_10440))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10446)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_10443,sK230(U_10449,U_10447))],[f_2810_4]) ).

cnf(f_2810_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK229(U_10448,U_10446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10446)))
    | ~ hBOOL(hAPP(U_10448,U_10440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10446)) ),
    inference(clausify,[status(thm)],[f_2810_5]) ).

cnf(f_2810_7,plain,
    ( hBOOL(hAPP(U_10448,sK229(U_10448,U_10446)))
    | ~ hBOOL(hAPP(U_10448,U_10440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10440),U_10446)) ),
    inference(clausify,[status(thm)],[f_2810_5]) ).

cnf(f_2810_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK230(U_10449,U_10447)),U_10447))
    | ~ hBOOL(hAPP(U_10449,U_10442))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447))) ),
    inference(clausify,[status(thm)],[f_2810_5]) ).

cnf(f_2810_9,plain,
    ( hBOOL(hAPP(U_10449,sK230(U_10449,U_10447)))
    | ~ hBOOL(hAPP(U_10449,U_10442))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10442),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447))) ),
    inference(clausify,[status(thm)],[f_2810_5]) ).

fof(f_2811_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_Pa_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_2811_2,plain,
    ! [U_10455,U_10454] :
      ( ( ! [U_10453] :
            ( hBOOL(hAPP(U_10455,U_10453))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10454)) )
        | ? [U_10452] :
            ( ~ hBOOL(hAPP(U_10455,U_10452))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10454))) ) )
      & ( ! [U_10451] :
            ( hBOOL(hAPP(U_10455,U_10451))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10454))) )
        | ? [U_10450] :
            ( ~ hBOOL(hAPP(U_10455,U_10450))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10450),U_10454)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2811_1]) ).

fof(f_2811_3,plain,
    ( ! [U_10459,U_10457] :
        ( ! [U_10453] :
            ( hBOOL(hAPP(U_10459,U_10453))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10457)) )
        | ? [U_10452] :
            ( ~ hBOOL(hAPP(U_10459,U_10452))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10457))) ) )
    & ! [U_10458,U_10456] :
        ( ! [U_10451] :
            ( hBOOL(hAPP(U_10458,U_10451))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10456))) )
        | ? [U_10450] :
            ( ~ hBOOL(hAPP(U_10458,U_10450))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10450),U_10456)) ) ) ),
    inference(miniscope,[status(thm)],[f_2811_2]) ).

fof(f_2811_4,plain,
    ( ! [U_10459,U_10457] :
        ( ! [U_10453] :
            ( hBOOL(hAPP(U_10459,U_10453))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10457)) )
        | ? [U_10452] :
            ( ~ hBOOL(hAPP(U_10459,U_10452))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10452),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10457))) ) )
    & ! [U_10458,U_10456] :
        ( ! [U_10451] :
            ( hBOOL(hAPP(U_10458,U_10451))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10456))) )
        | ( ~ hBOOL(hAPP(U_10458,sK231(U_10458,U_10456)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK231(U_10458,U_10456)),U_10456)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_10450,sK231(U_10458,U_10456))],[f_2811_3]) ).

fof(f_2811_5,plain,
    ( ! [U_10459,U_10457] :
        ( ! [U_10453] :
            ( hBOOL(hAPP(U_10459,U_10453))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10457)) )
        | ( ~ hBOOL(hAPP(U_10459,sK232(U_10459,U_10457)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK232(U_10459,U_10457)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10457))) ) )
    & ! [U_10458,U_10456] :
        ( ! [U_10451] :
            ( hBOOL(hAPP(U_10458,U_10451))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10456))) )
        | ( ~ hBOOL(hAPP(U_10458,sK231(U_10458,U_10456)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK231(U_10458,U_10456)),U_10456)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_10452,sK232(U_10459,U_10457))],[f_2811_4]) ).

cnf(f_2811_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK231(U_10458,U_10456)),U_10456))
    | hBOOL(hAPP(U_10458,U_10451))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10456))) ),
    inference(clausify,[status(thm)],[f_2811_5]) ).

cnf(f_2811_7,plain,
    ( ~ hBOOL(hAPP(U_10458,sK231(U_10458,U_10456)))
    | hBOOL(hAPP(U_10458,U_10451))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10456))) ),
    inference(clausify,[status(thm)],[f_2811_5]) ).

cnf(f_2811_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK232(U_10459,U_10457)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10457)))
    | hBOOL(hAPP(U_10459,U_10453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10457)) ),
    inference(clausify,[status(thm)],[f_2811_5]) ).

cnf(f_2811_9,plain,
    ( ~ hBOOL(hAPP(U_10459,sK232(U_10459,U_10457)))
    | hBOOL(hAPP(U_10459,U_10453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10453),U_10457)) ),
    inference(clausify,[status(thm)],[f_2811_5]) ).

fof(f_2812_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_2812_2,plain,
    ! [U_10462,U_10461,U_10460] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10461),U_10462)) = 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_10460),U_10461)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10461),U_10462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10460),U_10461)) ),
    inference(variable_rename,[status(thm)],[f_2812_1]) ).

cnf(f_2812_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10461),U_10462)) = 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_10460),U_10461)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10461),U_10462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10460),U_10461)) ),
    inference(clausify,[status(thm)],[f_2812_2]) ).

fof(f_2813_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_2813_2,plain,
    ! [U_10464,U_10463] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10463),hAPP(c_Nat_OSuc,U_10464)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10463,U_10464),
    inference(variable_rename,[status(thm)],[f_2813_1]) ).

cnf(f_2813_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10463),hAPP(c_Nat_OSuc,U_10464)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10463,U_10464),
    inference(clausify,[status(thm)],[f_2813_2]) ).

fof(f_2814_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_2814_2,plain,
    ! [U_10465] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10465),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_2814_1]) ).

cnf(f_2814_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10465),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_2814_2]) ).

fof(f_2815_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_2815_2,plain,
    ! [U_10466] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10466) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10466),
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

cnf(f_2815_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10466) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10466),
    inference(clausify,[status(thm)],[f_2815_2]) ).

fof(f_2816_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_2816_2,plain,
    ! [U_10468,U_10467] :
      ( U_10467 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10468),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10467)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10467),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10468),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10467))))) ),
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

cnf(f_2816_3,plain,
    ( U_10467 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10468),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10467),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10468),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10467))))) ),
    inference(clausify,[status(thm)],[f_2816_2]) ).

fof(f_2817_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_2817_2,plain,
    ! [U_10470,U_10469] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10469),U_10470)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10470),U_10469),
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

cnf(f_2817_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10469),U_10470)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10470),U_10469),
    inference(clausify,[status(thm)],[f_2817_2]) ).

fof(f_2818_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_2818_2,plain,
    ! [U_10473,U_10472,U_10471] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10471,U_10473),U_10472) = c_Orderings_Obot__class_Obot(tc_fun(U_10471,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10471),U_10472),U_10473))
      | ~ class_Orderings_Oorder(U_10471) ),
    inference(variable_rename,[status(thm)],[f_2818_1]) ).

cnf(f_2818_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10471,U_10473),U_10472) = c_Orderings_Obot__class_Obot(tc_fun(U_10471,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10471),U_10472),U_10473))
    | ~ class_Orderings_Oorder(U_10471) ),
    inference(clausify,[status(thm)],[f_2818_2]) ).

fof(f_2819_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_2819_2,plain,
    ! [U_10476,U_10475,U_10474] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10474,U_10475),U_10476) = c_Orderings_Obot__class_Obot(tc_fun(U_10474,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10474),U_10475),U_10476)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10474),U_10475),U_10476))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10474,U_10475),U_10476) != c_Orderings_Obot__class_Obot(tc_fun(U_10474,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_10474) ),
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

cnf(f_2819_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10474),U_10475),U_10476))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10474,U_10475),U_10476) != c_Orderings_Obot__class_Obot(tc_fun(U_10474,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10474) ),
    inference(clausify,[status(thm)],[f_2819_2]) ).

cnf(f_2819_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10474,U_10475),U_10476) = c_Orderings_Obot__class_Obot(tc_fun(U_10474,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10474),U_10475),U_10476))
    | ~ class_Orderings_Oorder(U_10474) ),
    inference(clausify,[status(thm)],[f_2819_2]) ).

fof(f_2820_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_2820_2,plain,
    ! [U_10479,U_10478,U_10477] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10477,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10477,U_10478),U_10479)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10477),U_10478),U_10479)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10477),U_10478),U_10479))
          | c_Orderings_Obot__class_Obot(tc_fun(U_10477,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10477,U_10478),U_10479) ) )
      | ~ class_Orderings_Oorder(U_10477) ),
    inference(variable_rename,[status(thm)],[f_2820_1]) ).

cnf(f_2820_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10477),U_10478),U_10479))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10477,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10477,U_10478),U_10479)
    | ~ class_Orderings_Oorder(U_10477) ),
    inference(clausify,[status(thm)],[f_2820_2]) ).

cnf(f_2820_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10477,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10477,U_10478),U_10479)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10477),U_10478),U_10479))
    | ~ class_Orderings_Oorder(U_10477) ),
    inference(clausify,[status(thm)],[f_2820_2]) ).

fof(f_2821_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).

fof(f_2821_2,plain,
    ! [U_10484,U_10483,U_10482,U_10481,U_10480] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10482),U_10484))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10483),U_10481)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10482),U_10481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10481),U_10482)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10483),U_10484)))
      | ~ class_Orderings_Olinorder(U_10480) ),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

cnf(f_2821_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10483),U_10481))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10482),U_10481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10481),U_10482)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10483),U_10484)))
    | ~ class_Orderings_Olinorder(U_10480) ),
    inference(clausify,[status(thm)],[f_2821_2]) ).

cnf(f_2821_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10482),U_10484))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10480),U_10482),U_10481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10481),U_10482)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10480,U_10483),U_10484)))
    | ~ class_Orderings_Olinorder(U_10480) ),
    inference(clausify,[status(thm)],[f_2821_2]) ).

fof(f_2822_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_2822_2,plain,
    ! [U_10488,U_10487,U_10486,U_10485] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10485),U_10486),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10487)),hAPP(c_Nat_OSuc,U_10488))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10485),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10485,tc_Nat_Onat),U_10486),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10487),U_10488))
      | ~ class_Groups_Ocomm__monoid__add(U_10485) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

cnf(f_2822_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10485),U_10486),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10487)),hAPP(c_Nat_OSuc,U_10488))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10485),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10485,tc_Nat_Onat),U_10486),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10487),U_10488))
    | ~ class_Groups_Ocomm__monoid__add(U_10485) ),
    inference(clausify,[status(thm)],[f_2822_2]) ).

fof(f_2823_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_2823_2,plain,
    ! [U_10492,U_10491,U_10490,U_10489] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10489,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10490),U_10491)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10491),U_10492)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10490),U_10492)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10489),U_10491),U_10492))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10489),U_10490),U_10491))
      | ~ class_Orderings_Olinorder(U_10489) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

cnf(f_2823_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10489,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10490),U_10491)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10491),U_10492)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10489,U_10490),U_10492)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10489),U_10491),U_10492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10489),U_10490),U_10491))
    | ~ class_Orderings_Olinorder(U_10489) ),
    inference(clausify,[status(thm)],[f_2823_2]) ).

fof(f_2824_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_2824_2,plain,
    ! [U_10497,U_10496,U_10495,U_10494,U_10493] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10493),U_10494),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10495),U_10496)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10497),U_10496))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10493),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10493,tc_Nat_Onat),U_10494),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10496))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10495),U_10497))
      | ~ class_Groups_Ocomm__monoid__add(U_10493) ),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

cnf(f_2824_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10493),U_10494),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10495),U_10496)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10497),U_10496))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10493),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10493,tc_Nat_Onat),U_10494),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10496))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10495),U_10497))
    | ~ class_Groups_Ocomm__monoid__add(U_10493) ),
    inference(clausify,[status(thm)],[f_2824_2]) ).

fof(f_2825_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_2825_2,plain,
    ! [U_10501,U_10500,U_10499,U_10498] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10498,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10499),U_10501)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10499),U_10500)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10500),U_10501)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10498),U_10499),U_10500))
      | ~ class_Orderings_Olinorder(U_10498) ),
    inference(variable_rename,[status(thm)],[f_2825_1]) ).

cnf(f_2825_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10498,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10499),U_10501)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10499),U_10500)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10498,U_10500),U_10501)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10498),U_10499),U_10500))
    | ~ class_Orderings_Olinorder(U_10498) ),
    inference(clausify,[status(thm)],[f_2825_2]) ).

fof(f_2826_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_2826_2,plain,
    ! [U_10505,U_10504,U_10503,U_10502] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10502,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10502,U_10503),U_10504)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10502,U_10504),U_10505)) = c_Orderings_Obot__class_Obot(tc_fun(U_10502,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10502) ),
    inference(variable_rename,[status(thm)],[f_2826_1]) ).

cnf(f_2826_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10502,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10502,U_10503),U_10504)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10502,U_10504),U_10505)) = c_Orderings_Obot__class_Obot(tc_fun(U_10502,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10502) ),
    inference(clausify,[status(thm)],[f_2826_2]) ).

fof(f_2827_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_2827_2,plain,
    ! [U_10507,U_10506] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10506)),U_10507) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10506,U_10507),
    inference(variable_rename,[status(thm)],[f_2827_1]) ).

cnf(f_2827_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10506)),U_10507) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10506,U_10507),
    inference(clausify,[status(thm)],[f_2827_2]) ).

fof(f_2828_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_2828_2,plain,
    ! [U_10508] : 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_10508))),
    inference(variable_rename,[status(thm)],[f_2828_1]) ).

cnf(f_2828_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_10508))),
    inference(clausify,[status(thm)],[f_2828_2]) ).

fof(f_2829_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_2829_2,plain,
    ! [U_10513,U_10512,U_10511,U_10510,U_10509] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10510),U_10511))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10511),U_10512))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10510),U_10512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10511),U_10512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10510),U_10511))
      | ~ class_Groups_Ocomm__monoid__add(U_10509) ),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

cnf(f_2829_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10510),U_10511))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10511),U_10512))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10509),U_10513),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10510),U_10512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10511),U_10512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10510),U_10511))
    | ~ class_Groups_Ocomm__monoid__add(U_10509) ),
    inference(clausify,[status(thm)],[f_2829_2]) ).

fof(f_2830_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_2830_2,plain,
    ! [U_10518,U_10517,U_10516,U_10515,U_10514] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10514),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10515),U_10517))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10515),U_10516))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10516),U_10517))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10516),U_10517))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10515),U_10516))
      | ~ class_Groups_Oab__group__add(U_10514) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

cnf(f_2830_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10514),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10515),U_10517))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10515),U_10516))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10514),U_10518),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10516),U_10517))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10516),U_10517))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10515),U_10516))
    | ~ class_Groups_Oab__group__add(U_10514) ),
    inference(clausify,[status(thm)],[f_2830_2]) ).

fof(f_2831_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_2831_2,plain,
    ! [U_10519] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10519),hAPP(c_Nat_OSuc,U_10519)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10519),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

cnf(f_2831_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10519),hAPP(c_Nat_OSuc,U_10519)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10519),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2831_2]) ).

fof(f_2832_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_2832_2,plain,
    ! [U_10521,U_10520] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,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_10520,tc_HOL_Obool)),tc_fun(U_10520,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_10520,tc_HOL_Obool)),tc_fun(U_10520,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_10521)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10521),
    inference(variable_rename,[status(thm)],[f_2832_1]) ).

cnf(f_2832_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,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_10520,tc_HOL_Obool)),tc_fun(U_10520,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_10520,tc_HOL_Obool)),tc_fun(U_10520,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_10521)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10520,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10521),
    inference(clausify,[status(thm)],[f_2832_2]) ).

fof(f_2833_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_2833_2,plain,
    ! [U_10523,U_10522] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10523),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_10522,U_10523),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

cnf(f_2833_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10523),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_10522,U_10523),
    inference(clausify,[status(thm)],[f_2833_2]) ).

fof(f_2834_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_2834_2,plain,
    ! [U_10527,U_10526,U_10525,U_10524] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10524,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10524,U_10525),U_10526)),c_SetInterval_Oord__class_OatLeastAtMost(U_10524,U_10526,U_10527)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10524,U_10525,U_10527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10524),U_10526),U_10527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10524),U_10525),U_10526))
      | ~ class_Orderings_Olinorder(U_10524) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

cnf(f_2834_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10524,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10524,U_10525),U_10526)),c_SetInterval_Oord__class_OatLeastAtMost(U_10524,U_10526,U_10527)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10524,U_10525,U_10527)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10524),U_10526),U_10527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10524),U_10525),U_10526))
    | ~ class_Orderings_Olinorder(U_10524) ),
    inference(clausify,[status(thm)],[f_2834_2]) ).

fof(f_2835_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_2835_2,plain,
    ! [U_10531,U_10530,U_10529,U_10528] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10528,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10528,U_10529),U_10530)),c_SetInterval_Oord__class_OatLeastAtMost(U_10528,U_10530,U_10531)) = c_Orderings_Obot__class_Obot(tc_fun(U_10528,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10528) ),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

cnf(f_2835_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10528,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10528,U_10529),U_10530)),c_SetInterval_Oord__class_OatLeastAtMost(U_10528,U_10530,U_10531)) = c_Orderings_Obot__class_Obot(tc_fun(U_10528,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10528) ),
    inference(clausify,[status(thm)],[f_2835_2]) ).

fof(f_2836_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_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_2836_2,plain,
    ! [U_10536,U_10535,U_10534,U_10533,U_10532] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,U_10533),U_10534)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,U_10535),U_10536)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10532),U_10533),U_10535)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10532),U_10534),U_10536))
      | ~ class_Orderings_Olinorder(U_10532) ),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

cnf(f_2836_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10532,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,U_10533),U_10534)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,U_10535),U_10536)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10532,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10532),U_10533),U_10535)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10532),U_10534),U_10536))
    | ~ class_Orderings_Olinorder(U_10532) ),
    inference(clausify,[status(thm)],[f_2836_2]) ).

fof(f_2837_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_2837_2,plain,
    ! [U_10539,U_10538,U_10537] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10537,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10537),U_10538)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10537,U_10538),U_10539)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_10537),U_10539)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10537),U_10538),U_10539))
      | ~ class_Orderings_Olinorder(U_10537) ),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

cnf(f_2837_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10537,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10537),U_10538)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10537,U_10538),U_10539)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_10537),U_10539)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10537),U_10538),U_10539))
    | ~ class_Orderings_Olinorder(U_10537) ),
    inference(clausify,[status(thm)],[f_2837_2]) ).

fof(f_2838_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_2838_2,plain,
    ! [U_10542,U_10541,U_10540] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10540,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10540),U_10541)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10540,U_10541),U_10542)) = c_Orderings_Obot__class_Obot(tc_fun(U_10540,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10540) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

cnf(f_2838_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10540,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_10540),U_10541)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10540,U_10541),U_10542)) = c_Orderings_Obot__class_Obot(tc_fun(U_10540,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10540) ),
    inference(clausify,[status(thm)],[f_2838_2]) ).

fof(f_2839_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_2839_2,plain,
    ! [U_10546,U_10545,U_10544,U_10543] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10543,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10543,U_10544,U_10545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10543,U_10545),U_10546)) = c_Orderings_Obot__class_Obot(tc_fun(U_10543,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10543) ),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

cnf(f_2839_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10543,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10543,U_10544,U_10545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10543,U_10545),U_10546)) = c_Orderings_Obot__class_Obot(tc_fun(U_10543,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10543) ),
    inference(clausify,[status(thm)],[f_2839_2]) ).

fof(f_2840_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_2840_2,plain,
    ! [U_10549,U_10548,U_10547] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10547),U_10548),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_10549)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10547),U_10548),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10549))
      | hAPP(U_10548,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_10547)
      | ~ class_Groups_Ocomm__monoid__add(U_10547) ),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

cnf(f_2840_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10547),U_10548),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_10549)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10547),U_10548),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10549))
    | hAPP(U_10548,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_10547)
    | ~ class_Groups_Ocomm__monoid__add(U_10547) ),
    inference(clausify,[status(thm)],[f_2840_2]) ).

fof(f_2841_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_2841_2,plain,
    ! [U_10553,U_10552,U_10551,U_10550] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10550),U_10553),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10551),U_10552)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10550),hAPP(U_10553,U_10551)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10550),U_10553),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10551)),U_10552)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10551),U_10552))
      | ~ class_Groups_Ocomm__monoid__add(U_10550) ),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

cnf(f_2841_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10550),U_10553),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10551),U_10552)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10550),hAPP(U_10553,U_10551)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10550),U_10553),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10551)),U_10552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10551),U_10552))
    | ~ class_Groups_Ocomm__monoid__add(U_10550) ),
    inference(clausify,[status(thm)],[f_2841_2]) ).

fof(f_2842_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_2842_2,plain,
    ! [U_10554] : 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_10554)) = hAPP(c_Int_Onat,U_10554),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

cnf(f_2842_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_10554)) = hAPP(c_Int_Onat,U_10554),
    inference(clausify,[status(thm)],[f_2842_2]) ).

fof(f_2843_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_2843_2,plain,
    ! [U_10556,U_10555] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10555),U_10556)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10556),U_10555)),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

cnf(f_2843_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10555),U_10556)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10556),U_10555)),
    inference(clausify,[status(thm)],[f_2843_2]) ).

fof(f_2844_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_2844_2,plain,
    ! [U_10558,U_10557] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10557),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_10558) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10557,U_10558),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

cnf(f_2844_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10557),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_10558) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10557,U_10558),
    inference(clausify,[status(thm)],[f_2844_2]) ).

fof(f_2845_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_2845_2,plain,
    ! [U_10560,U_10559] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10559),hAPP(c_Nat_OSuc,U_10560)) = 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_10559),U_10560)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10559),hAPP(c_Nat_OSuc,U_10560)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10560),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10559),U_10560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10559),U_10560)) ) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

fof(f_2845_3,plain,
    ( ! [U_10564,U_10562] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10562),hAPP(c_Nat_OSuc,U_10564)) = 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_10562),U_10564)) )
    & ! [U_10563,U_10561] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10561),hAPP(c_Nat_OSuc,U_10563)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10563),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10561),U_10563))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10561),U_10563)) ) ),
    inference(miniscope,[status(thm)],[f_2845_2]) ).

cnf(f_2845_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10561),hAPP(c_Nat_OSuc,U_10563)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10563),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10561),U_10563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10561),U_10563)) ),
    inference(clausify,[status(thm)],[f_2845_3]) ).

cnf(f_2845_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10562),hAPP(c_Nat_OSuc,U_10564)) = 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_10562),U_10564)) ),
    inference(clausify,[status(thm)],[f_2845_3]) ).

fof(f_2846_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_2846_2,plain,
    ! [U_10568,U_10567,U_10566,U_10565] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),hAPP(c_Nat_OSuc,U_10566))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10565),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),U_10566))),hAPP(U_10568,U_10566))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10566),U_10567)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),hAPP(c_Nat_OSuc,U_10566))) = c_Groups_Ozero__class_Ozero(U_10565)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10566),U_10567)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_10565) ),
    inference(variable_rename,[status(thm)],[f_2846_1]) ).

cnf(f_2846_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),hAPP(c_Nat_OSuc,U_10566))) = c_Groups_Ozero__class_Ozero(U_10565)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10566),U_10567))
    | ~ class_Groups_Ocomm__monoid__add(U_10565) ),
    inference(clausify,[status(thm)],[f_2846_2]) ).

cnf(f_2846_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),hAPP(c_Nat_OSuc,U_10566))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10565),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10565),U_10568),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10567),U_10566))),hAPP(U_10568,U_10566))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10566),U_10567))
    | ~ class_Groups_Ocomm__monoid__add(U_10565) ),
    inference(clausify,[status(thm)],[f_2846_2]) ).

fof(f_2847_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_2847_2,plain,
    ! [U_10572,U_10571,U_10570,U_10569] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10569,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10569,U_10570,U_10571)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10569,U_10571),U_10572)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10569,U_10570,U_10572)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10569),U_10571),U_10572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10569),U_10570),U_10571))
      | ~ class_Orderings_Olinorder(U_10569) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

cnf(f_2847_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10569,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10569,U_10570,U_10571)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10569,U_10571),U_10572)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10569,U_10570,U_10572)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10569),U_10571),U_10572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10569),U_10570),U_10571))
    | ~ class_Orderings_Olinorder(U_10569) ),
    inference(clausify,[status(thm)],[f_2847_2]) ).

fof(f_2848_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_2848_2,plain,
    ! [U_10575,U_10574,U_10573] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10573,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10573,U_10574),U_10575)),hAPP(hAPP(c_Set_Oinsert(U_10573),U_10575),c_Orderings_Obot__class_Obot(tc_fun(U_10573,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_10573,U_10574,U_10575)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10573),U_10574),U_10575))
      | ~ class_Orderings_Olinorder(U_10573) ),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

cnf(f_2848_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10573,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10573,U_10574),U_10575)),hAPP(hAPP(c_Set_Oinsert(U_10573),U_10575),c_Orderings_Obot__class_Obot(tc_fun(U_10573,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_10573,U_10574,U_10575)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10573),U_10574),U_10575))
    | ~ class_Orderings_Olinorder(U_10573) ),
    inference(clausify,[status(thm)],[f_2848_2]) ).

fof(f_2849_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_2849_2,plain,
    ! [U_10578,U_10577,U_10576] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10576,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10576),U_10577),c_Orderings_Obot__class_Obot(tc_fun(U_10576,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10576,U_10577,U_10578)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10576,U_10577),U_10578)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10576),U_10577),U_10578))
      | ~ class_Orderings_Olinorder(U_10576) ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

cnf(f_2849_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10576,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10576),U_10577),c_Orderings_Obot__class_Obot(tc_fun(U_10576,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10576,U_10577,U_10578)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10576,U_10577),U_10578)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10576),U_10577),U_10578))
    | ~ class_Orderings_Olinorder(U_10576) ),
    inference(clausify,[status(thm)],[f_2849_2]) ).

fof(f_2850_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_2850_2,plain,
    ! [U_10582,U_10581] :
      ( ( c_Relation_Oirrefl(U_10581,U_10582)
        | ? [U_10580] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10581,U_10581)),hAPP(hAPP(c_Product__Type_OPair(U_10581,U_10581),U_10580),U_10580)),U_10582)) )
      & ( ! [U_10579] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10581,U_10581)),hAPP(hAPP(c_Product__Type_OPair(U_10581,U_10581),U_10579),U_10579)),U_10582))
        | ~ c_Relation_Oirrefl(U_10581,U_10582) ) ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

fof(f_2850_3,plain,
    ( ! [U_10586,U_10584] :
        ( c_Relation_Oirrefl(U_10584,U_10586)
        | ? [U_10580] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10584,U_10584)),hAPP(hAPP(c_Product__Type_OPair(U_10584,U_10584),U_10580),U_10580)),U_10586)) )
    & ! [U_10585,U_10583] :
        ( ! [U_10579] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10583,U_10583)),hAPP(hAPP(c_Product__Type_OPair(U_10583,U_10583),U_10579),U_10579)),U_10585))
        | ~ c_Relation_Oirrefl(U_10583,U_10585) ) ),
    inference(miniscope,[status(thm)],[f_2850_2]) ).

fof(f_2850_4,plain,
    ( ! [U_10586,U_10584] :
        ( c_Relation_Oirrefl(U_10584,U_10586)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10584,U_10584)),hAPP(hAPP(c_Product__Type_OPair(U_10584,U_10584),sK233(U_10586,U_10584)),sK233(U_10586,U_10584))),U_10586)) )
    & ! [U_10585,U_10583] :
        ( ! [U_10579] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10583,U_10583)),hAPP(hAPP(c_Product__Type_OPair(U_10583,U_10583),U_10579),U_10579)),U_10585))
        | ~ c_Relation_Oirrefl(U_10583,U_10585) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_10580,sK233(U_10586,U_10584))],[f_2850_3]) ).

cnf(f_2850_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10583,U_10583)),hAPP(hAPP(c_Product__Type_OPair(U_10583,U_10583),U_10579),U_10579)),U_10585))
    | ~ c_Relation_Oirrefl(U_10583,U_10585) ),
    inference(clausify,[status(thm)],[f_2850_4]) ).

cnf(f_2850_6,plain,
    ( c_Relation_Oirrefl(U_10584,U_10586)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10584,U_10584)),hAPP(hAPP(c_Product__Type_OPair(U_10584,U_10584),sK233(U_10586,U_10584)),sK233(U_10586,U_10584))),U_10586)) ),
    inference(clausify,[status(thm)],[f_2850_4]) ).

fof(f_2851_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_2851_2,plain,
    ! [U_10591,U_10590,U_10589,U_10588] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10591)))
      | ? [U_10587] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10587)),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,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_10587),U_10590))),U_10591))) ),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

fof(f_2851_3,plain,
    ! [U_10591,U_10590,U_10589,U_10588] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10591)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK234(U_10591,U_10590,U_10589,U_10588))),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,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),sK234(U_10591,U_10590,U_10589,U_10588)),U_10590))),U_10591))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_10587,sK234(U_10591,U_10590,U_10589,U_10588))],[f_2851_2]) ).

cnf(f_2851_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10591)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK234(U_10591,U_10590,U_10589,U_10588))),U_10589)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10588,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),sK234(U_10591,U_10590,U_10589,U_10588)),U_10590))),U_10591))) ),
    inference(clausify,[status(thm)],[f_2851_3]) ).

fof(f_2852_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_2852_2,plain,
    ! [U_10595,U_10594,U_10593,U_10592] : hAPP(c_Relation_OField(U_10592),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10592,U_10592)),hAPP(hAPP(c_Product__Type_OPair(U_10592,U_10592),U_10593),U_10594)),U_10595)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10592,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10592),U_10593),hAPP(hAPP(c_Set_Oinsert(U_10592),U_10594),c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_10592),U_10595)),
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

cnf(f_2852_3,plain,
    hAPP(c_Relation_OField(U_10592),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10592,U_10592)),hAPP(hAPP(c_Product__Type_OPair(U_10592,U_10592),U_10593),U_10594)),U_10595)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10592,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10592),U_10593),hAPP(hAPP(c_Set_Oinsert(U_10592),U_10594),c_Orderings_Obot__class_Obot(tc_fun(U_10592,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_10592),U_10595)),
    inference(clausify,[status(thm)],[f_2852_2]) ).

fof(f_2853_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_2853_2,plain,
    ! [U_10596] : hAPP(c_Relation_OField(U_10596),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10596,U_10596),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10596,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2853_1]) ).

cnf(f_2853_3,plain,
    hAPP(c_Relation_OField(U_10596),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10596,U_10596),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10596,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2853_2]) ).

fof(f_2854_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_2854_2,plain,
    ! [U_10599,U_10598,U_10597] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10597,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10597),U_10598)),hAPP(c_Relation_OField(U_10597),U_10599)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10597,U_10597),tc_HOL_Obool)),U_10598),U_10599)) ),
    inference(variable_rename,[status(thm)],[f_2854_1]) ).

cnf(f_2854_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10597,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10597),U_10598)),hAPP(c_Relation_OField(U_10597),U_10599)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10597,U_10597),tc_HOL_Obool)),U_10598),U_10599)) ),
    inference(clausify,[status(thm)],[f_2854_2]) ).

fof(f_2855_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_2855_2,plain,
    ! [U_10602,U_10601,U_10600] : hAPP(c_Relation_OField(U_10600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10600,U_10600),tc_HOL_Obool)),U_10601),U_10602)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10600,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10600),U_10601)),hAPP(c_Relation_OField(U_10600),U_10602)),
    inference(variable_rename,[status(thm)],[f_2855_1]) ).

cnf(f_2855_3,plain,
    hAPP(c_Relation_OField(U_10600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10600,U_10600),tc_HOL_Obool)),U_10601),U_10602)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10600,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10600),U_10601)),hAPP(c_Relation_OField(U_10600),U_10602)),
    inference(clausify,[status(thm)],[f_2855_2]) ).

fof(f_2856_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_2856_2,plain,
    ! [U_10604,U_10603] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10603),hAPP(c_Relation_OField(U_10603),U_10604)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_10603,U_10603)),U_10604)) ),
    inference(variable_rename,[status(thm)],[f_2856_1]) ).

cnf(f_2856_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10603),hAPP(c_Relation_OField(U_10603),U_10604)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_10603,U_10603)),U_10604)) ),
    inference(clausify,[status(thm)],[f_2856_2]) ).

fof(f_2857_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_2857_2,plain,
    ! [U_10609,U_10608,U_10607,U_10606] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10609)
      | ? [U_10605] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10605)),U_10607) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,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_10605),U_10608))),U_10609) ),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

fof(f_2857_3,plain,
    ! [U_10609,U_10608,U_10607,U_10606] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10609)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK235(U_10609,U_10608,U_10607,U_10606))),U_10607) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,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),sK235(U_10609,U_10608,U_10607,U_10606)),U_10608))),U_10609) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_10605,sK235(U_10609,U_10608,U_10607,U_10606))],[f_2857_2]) ).

cnf(f_2857_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10609)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK235(U_10609,U_10608,U_10607,U_10606))),U_10607) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10606,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),sK235(U_10609,U_10608,U_10607,U_10606)),U_10608))),U_10609) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

fof(f_2858_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_2858_2,plain,
    ! [U_10613,U_10612,U_10611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10612)),U_10613))
      | ? [U_10610] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10610)),U_10612)),U_10613)) ),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

fof(f_2858_3,plain,
    ! [U_10613,U_10612,U_10611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10612)),U_10613))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK236(U_10613,U_10612,U_10611))),U_10612)),U_10613)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_10610,sK236(U_10613,U_10612,U_10611))],[f_2858_2]) ).

cnf(f_2858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_10612)),U_10613))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10611,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10611,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK236(U_10613,U_10612,U_10611))),U_10612)),U_10613)) ),
    inference(clausify,[status(thm)],[f_2858_3]) ).

fof(f_2859_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_2859_2,plain,
    ! [U_10615,U_10614] : c_Relation_OId__on(U_10614,U_10615) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10614,tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),U_10615),hAPP(hAPP(c_COMBC(U_10614,tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool),tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10614,U_10614),tc_fun(tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool),tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),U_10614),c_Set_Oinsert(tc_prod(U_10614,U_10614))),hAPP(hAPP(c_COMBS(U_10614,U_10614,tc_prod(U_10614,U_10614)),c_Product__Type_OPair(U_10614,U_10614)),c_COMBI(U_10614)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

cnf(f_2859_3,plain,
    c_Relation_OId__on(U_10614,U_10615) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10614,tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),U_10615),hAPP(hAPP(c_COMBC(U_10614,tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool),tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10614,U_10614),tc_fun(tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool),tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)),U_10614),c_Set_Oinsert(tc_prod(U_10614,U_10614))),hAPP(hAPP(c_COMBS(U_10614,U_10614,tc_prod(U_10614,U_10614)),c_Product__Type_OPair(U_10614,U_10614)),c_COMBI(U_10614)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10614,U_10614),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2859_2]) ).

fof(f_2860_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_2860_2,plain,
    ! [U_10617,U_10616] : c_Relation_OId__on(U_10616,U_10617) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10616,U_10616,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10616,tc_HOL_Obool,tc_fun(U_10616,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10616,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10616,tc_HOL_Obool)),U_10616),c_COMBC(U_10616,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10616,tc_HOL_Obool),tc_fun(U_10616,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10616),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10616),c_fconj)),c_fequal))),U_10617)),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

cnf(f_2860_3,plain,
    c_Relation_OId__on(U_10616,U_10617) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10616,U_10616,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10616,tc_HOL_Obool,tc_fun(U_10616,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10616,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10616,tc_HOL_Obool)),U_10616),c_COMBC(U_10616,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10616,tc_HOL_Obool),tc_fun(U_10616,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10616),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10616),c_fconj)),c_fequal))),U_10617)),
    inference(clausify,[status(thm)],[f_2860_2]) ).

fof(f_2861_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_2861_2,plain,
    ! [U_10618] : c_Relation_OId__on(U_10618,c_Orderings_Obot__class_Obot(tc_fun(U_10618,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10618,U_10618),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

cnf(f_2861_3,plain,
    c_Relation_OId__on(U_10618,c_Orderings_Obot__class_Obot(tc_fun(U_10618,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10618,U_10618),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2861_2]) ).

fof(f_2862_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_2862_2,plain,
    ! [U_10622,U_10621,U_10620,U_10619] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10619,U_10619)),hAPP(hAPP(c_Product__Type_OPair(U_10619,U_10619),U_10620),U_10621)),c_Relation_OId__on(U_10619,U_10622)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10619),U_10620),U_10622))
        | U_10620 != U_10621 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_10619),U_10620),U_10622))
          & U_10620 = U_10621 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10619,U_10619)),hAPP(hAPP(c_Product__Type_OPair(U_10619,U_10619),U_10620),U_10621)),c_Relation_OId__on(U_10619,U_10622))) ) ),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ( ! [U_10630,U_10628,U_10626,U_10624] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10624,U_10624)),hAPP(hAPP(c_Product__Type_OPair(U_10624,U_10624),U_10626),U_10628)),c_Relation_OId__on(U_10624,U_10630)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10624),U_10626),U_10630))
        | U_10626 != U_10628 )
    & ! [U_10629,U_10627,U_10625,U_10623] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_10623),U_10625),U_10629))
          & U_10625 = U_10627 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10623,U_10623)),hAPP(hAPP(c_Product__Type_OPair(U_10623,U_10623),U_10625),U_10627)),c_Relation_OId__on(U_10623,U_10629))) ) ),
    inference(miniscope,[status(thm)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    ( U_10625 = U_10627
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10623,U_10623)),hAPP(hAPP(c_Product__Type_OPair(U_10623,U_10623),U_10625),U_10627)),c_Relation_OId__on(U_10623,U_10629))) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

cnf(f_2862_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10623),U_10625),U_10629))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10623,U_10623)),hAPP(hAPP(c_Product__Type_OPair(U_10623,U_10623),U_10625),U_10627)),c_Relation_OId__on(U_10623,U_10629))) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

cnf(f_2862_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10624,U_10624)),hAPP(hAPP(c_Product__Type_OPair(U_10624,U_10624),U_10626),U_10628)),c_Relation_OId__on(U_10624,U_10630)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10624),U_10626),U_10630))
    | U_10626 != U_10628 ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_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_2863_2,plain,
    ! [U_10634,U_10633,U_10632,U_10631] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10633,U_10633)),hAPP(hAPP(c_Product__Type_OPair(U_10633,U_10633),U_10631),U_10632)),c_Relation_OId__on(U_10633,U_10634)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10633),U_10631),U_10634))
      | U_10631 != U_10632 ),
    inference(variable_rename,[status(thm)],[f_2863_1]) ).

cnf(f_2863_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10633,U_10633)),hAPP(hAPP(c_Product__Type_OPair(U_10633,U_10633),U_10631),U_10632)),c_Relation_OId__on(U_10633,U_10634)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10633),U_10631),U_10634))
    | U_10631 != U_10632 ),
    inference(clausify,[status(thm)],[f_2863_2]) ).

fof(f_2864_1,plain,
    ! [V_A_2,V_ca_2,T_b] :
      ( ? [B_x] :
          ( V_ca_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_ca_2),c_Relation_OId__on(T_b,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).

fof(f_2864_2,plain,
    ! [U_10638,U_10637,U_10636] :
      ( ? [U_10635] :
          ( U_10637 = hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10636),U_10635),U_10635)
          & hBOOL(hAPP(hAPP(c_member(U_10636),U_10635),U_10638)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10636,U_10636)),U_10637),c_Relation_OId__on(U_10636,U_10638))) ),
    inference(variable_rename,[status(thm)],[f_2864_1]) ).

fof(f_2864_3,plain,
    ! [U_10638,U_10637,U_10636] :
      ( ( U_10637 = hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10636),sK237(U_10638,U_10637,U_10636)),sK237(U_10638,U_10637,U_10636))
        & hBOOL(hAPP(hAPP(c_member(U_10636),sK237(U_10638,U_10637,U_10636)),U_10638)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10636,U_10636)),U_10637),c_Relation_OId__on(U_10636,U_10638))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_10635,sK237(U_10638,U_10637,U_10636))],[f_2864_2]) ).

cnf(f_2864_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10636),sK237(U_10638,U_10637,U_10636)),U_10638))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10636,U_10636)),U_10637),c_Relation_OId__on(U_10636,U_10638))) ),
    inference(clausify,[status(thm)],[f_2864_3]) ).

cnf(f_2864_5,plain,
    ( U_10637 = hAPP(hAPP(c_Product__Type_OPair(U_10636,U_10636),sK237(U_10638,U_10637,U_10636)),sK237(U_10638,U_10637,U_10636))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10636,U_10636)),U_10637),c_Relation_OId__on(U_10636,U_10638))) ),
    inference(clausify,[status(thm)],[f_2864_3]) ).

fof(f_2865_1,plain,
    ! [V_x_2,V_y_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).

fof(f_2865_2,plain,
    ! [U_10641,U_10640,U_10639] :
      ( ( ( ( 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_10639)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10641),U_10640)) = 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_10641),U_10640)) )
          & ( 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_10639)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10641),U_10640)) = 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_10641),U_10640)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10639),U_10640)) )
      & ( 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_10639)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10641),U_10640)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10641),U_10639)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10640),U_10639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10639),U_10640)) ) ),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

fof(f_2865_3,plain,
    ( ! [U_10647,U_10645,U_10643] :
        ( ( ( 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_10643)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10647),U_10645)) = 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_10647),U_10645)) )
          & ( 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_10643)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10647),U_10645)) = 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_10647),U_10645)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10643),U_10645)) )
    & ! [U_10646,U_10644,U_10642] :
        ( 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_10642)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10646),U_10644)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10646),U_10642)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10644),U_10642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10642),U_10644)) ) ),
    inference(miniscope,[status(thm)],[f_2865_2]) ).

cnf(f_2865_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_10642)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10646),U_10644)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10646),U_10642)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10644),U_10642))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10642),U_10644)) ),
    inference(clausify,[status(thm)],[f_2865_3]) ).

cnf(f_2865_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_10643)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10647),U_10645)) = 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_10647),U_10645))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10643),U_10645)) ),
    inference(clausify,[status(thm)],[f_2865_3]) ).

cnf(f_2865_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_10643)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10647),U_10645)) = 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_10647),U_10645))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10643),U_10645)) ),
    inference(clausify,[status(thm)],[f_2865_3]) ).

fof(f_2866_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_2866_2,plain,
    ! [U_10648] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10648) = 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_10648)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10648)) ),
    inference(variable_rename,[status(thm)],[f_2866_1]) ).

cnf(f_2866_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10648) = 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_10648)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10648)) ),
    inference(clausify,[status(thm)],[f_2866_2]) ).

fof(f_2867_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_2867_2,plain,
    ! [U_10654,U_10653,U_10652,U_10651,U_10650,U_10649] :
      ( hBOOL(hAPP(hAPP(c_member(U_10654),U_10649),hAPP(c_Set_Oimage(U_10652,U_10654,U_10650),U_10653)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10652),U_10651),U_10653))
      | U_10649 != hAPP(U_10650,U_10651) ),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

cnf(f_2867_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10654),U_10649),hAPP(c_Set_Oimage(U_10652,U_10654,U_10650),U_10653)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10652),U_10651),U_10653))
    | U_10649 != hAPP(U_10650,U_10651) ),
    inference(clausify,[status(thm)],[f_2867_2]) ).

fof(f_2868_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_2868_2,plain,
    ! [U_10658,U_10657,U_10656,U_10655] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10657),hAPP(c_Set_Oimage(U_10655,U_10657,U_10658),U_10656)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10655),U_10656)) ),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

cnf(f_2868_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10657),hAPP(c_Set_Oimage(U_10655,U_10657,U_10658),U_10656)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10655),U_10656)) ),
    inference(clausify,[status(thm)],[f_2868_2]) ).

fof(f_2869_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_2869_2,plain,
    ! [U_10664,U_10663,U_10662,U_10661,U_10660,U_10659] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10659,tc_fun(U_10660,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10661,U_10659,U_10662),U_10663)),U_10664) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10661,tc_fun(U_10660,tc_HOL_Obool)),U_10663),hAPP(hAPP(c_COMBB(U_10659,tc_fun(U_10660,tc_HOL_Obool),U_10661),U_10664),U_10662)),
    inference(variable_rename,[status(thm)],[f_2869_1]) ).

cnf(f_2869_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10659,tc_fun(U_10660,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10661,U_10659,U_10662),U_10663)),U_10664) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10661,tc_fun(U_10660,tc_HOL_Obool)),U_10663),hAPP(hAPP(c_COMBB(U_10659,tc_fun(U_10660,tc_HOL_Obool),U_10661),U_10664),U_10662)),
    inference(clausify,[status(thm)],[f_2869_2]) ).

fof(f_2870_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_2870_2,plain,
    ! [U_10670,U_10669,U_10668,U_10667,U_10666,U_10665] : hAPP(c_Set_Oimage(U_10665,U_10666,U_10667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10668,tc_fun(U_10665,tc_HOL_Obool)),U_10669),U_10670)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10668,tc_fun(U_10666,tc_HOL_Obool)),U_10669),hAPP(hAPP(c_COMBB(tc_fun(U_10665,tc_HOL_Obool),tc_fun(U_10666,tc_HOL_Obool),U_10668),c_Set_Oimage(U_10665,U_10666,U_10667)),U_10670)),
    inference(variable_rename,[status(thm)],[f_2870_1]) ).

cnf(f_2870_3,plain,
    hAPP(c_Set_Oimage(U_10665,U_10666,U_10667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10668,tc_fun(U_10665,tc_HOL_Obool)),U_10669),U_10670)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10668,tc_fun(U_10666,tc_HOL_Obool)),U_10669),hAPP(hAPP(c_COMBB(tc_fun(U_10665,tc_HOL_Obool),tc_fun(U_10666,tc_HOL_Obool),U_10668),c_Set_Oimage(U_10665,U_10666,U_10667)),U_10670)),
    inference(clausify,[status(thm)],[f_2870_2]) ).

fof(f_2871_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_2871_2,plain,
    ! [U_10676,U_10675,U_10674,U_10673,U_10672,U_10671] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10671,tc_fun(U_10672,tc_HOL_Obool)),U_10673),hAPP(hAPP(c_COMBB(U_10674,tc_fun(U_10672,tc_HOL_Obool),U_10671),U_10675),U_10676)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10672,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10671,U_10674,U_10676),U_10673)),U_10675),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

cnf(f_2871_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10671,tc_fun(U_10672,tc_HOL_Obool)),U_10673),hAPP(hAPP(c_COMBB(U_10674,tc_fun(U_10672,tc_HOL_Obool),U_10671),U_10675),U_10676)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10674,tc_fun(U_10672,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10671,U_10674,U_10676),U_10673)),U_10675),
    inference(clausify,[status(thm)],[f_2871_2]) ).

fof(f_2872_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_2872_2,plain,
    ! [U_10681,U_10680,U_10679,U_10678,U_10677] : hAPP(c_Set_Oimage(U_10677,U_10678,hAPP(hAPP(c_COMBB(U_10679,U_10678,U_10677),U_10680),U_10681)),c_Orderings_Otop__class_Otop(tc_fun(U_10677,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_10679,U_10678,U_10680),hAPP(c_Set_Oimage(U_10677,U_10679,U_10681),c_Orderings_Otop__class_Otop(tc_fun(U_10677,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

cnf(f_2872_3,plain,
    hAPP(c_Set_Oimage(U_10677,U_10678,hAPP(hAPP(c_COMBB(U_10679,U_10678,U_10677),U_10680),U_10681)),c_Orderings_Otop__class_Otop(tc_fun(U_10677,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_10679,U_10678,U_10680),hAPP(c_Set_Oimage(U_10677,U_10679,U_10681),c_Orderings_Otop__class_Otop(tc_fun(U_10677,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2872_2]) ).

fof(f_2873_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_2873_2,plain,
    ! [U_10687,U_10686,U_10685,U_10684,U_10683,U_10682] : hAPP(c_Set_Oimage(U_10682,U_10683,U_10684),hAPP(c_Set_Oimage(U_10685,U_10682,U_10686),U_10687)) = hAPP(c_Set_Oimage(U_10685,U_10683,hAPP(hAPP(c_COMBB(U_10682,U_10683,U_10685),U_10684),U_10686)),U_10687),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

cnf(f_2873_3,plain,
    hAPP(c_Set_Oimage(U_10682,U_10683,U_10684),hAPP(c_Set_Oimage(U_10685,U_10682,U_10686),U_10687)) = hAPP(c_Set_Oimage(U_10685,U_10683,hAPP(hAPP(c_COMBB(U_10682,U_10683,U_10685),U_10684),U_10686)),U_10687),
    inference(clausify,[status(thm)],[f_2873_2]) ).

fof(f_2874_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_2874_2,plain,
    ! [U_10689,U_10688] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10688),U_10689))
        | ~ 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_10688)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10689))) )
      & ( 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_10688)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10689)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10688),U_10689)) ) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

fof(f_2874_3,plain,
    ( ! [U_10693,U_10691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10691),U_10693))
        | ~ 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_10691)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10693))) )
    & ! [U_10692,U_10690] :
        ( 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_10690)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10692)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10690),U_10692)) ) ),
    inference(miniscope,[status(thm)],[f_2874_2]) ).

cnf(f_2874_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_10690)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10692)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10690),U_10692)) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

cnf(f_2874_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10691),U_10693))
    | ~ 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_10691)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10693))) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

fof(f_2875_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_2875_2,plain,
    ! [U_10695,U_10694] :
      ( ( U_10694 = U_10695
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10694) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10695) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10694) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10695)
        | U_10694 != U_10695 ) ),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

fof(f_2875_3,plain,
    ( ! [U_10699,U_10697] :
        ( U_10697 = U_10699
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10697) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10699) )
    & ! [U_10698,U_10696] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10696) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10698)
        | U_10696 != U_10698 ) ),
    inference(miniscope,[status(thm)],[f_2875_2]) ).

cnf(f_2875_4,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10696) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10698)
    | U_10696 != U_10698 ),
    inference(clausify,[status(thm)],[f_2875_3]) ).

cnf(f_2875_5,plain,
    ( U_10697 = U_10699
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10697) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10699) ),
    inference(clausify,[status(thm)],[f_2875_3]) ).

fof(f_2876_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_2876_2,plain,
    ! [U_10704,U_10703,U_10702,U_10701,U_10700] :
      ( hAPP(c_Set_Oimage(tc_fun(U_10700,tc_HOL_Obool),tc_fun(U_10701,tc_HOL_Obool),c_Set_Oimage(U_10700,U_10701,U_10702)),hAPP(c_Set_OPow(U_10700),U_10703)) = hAPP(c_Set_OPow(U_10701),U_10704)
      | hAPP(c_Set_Oimage(U_10700,U_10701,U_10702),U_10703) != U_10704 ),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

cnf(f_2876_3,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_10700,tc_HOL_Obool),tc_fun(U_10701,tc_HOL_Obool),c_Set_Oimage(U_10700,U_10701,U_10702)),hAPP(c_Set_OPow(U_10700),U_10703)) = hAPP(c_Set_OPow(U_10701),U_10704)
    | hAPP(c_Set_Oimage(U_10700,U_10701,U_10702),U_10703) != U_10704 ),
    inference(clausify,[status(thm)],[f_2876_2]) ).

fof(f_2877_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_2877_2,plain,
    ! [U_10710,U_10709,U_10708,U_10707,U_10706,U_10705] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10705,tc_fun(U_10706,tc_HOL_Obool)),U_10707),hAPP(hAPP(c_COMBB(U_10708,tc_fun(U_10706,tc_HOL_Obool),U_10705),U_10709),U_10710)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10708,tc_fun(U_10706,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10705,U_10708,U_10710),U_10707)),U_10709),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

cnf(f_2877_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10705,tc_fun(U_10706,tc_HOL_Obool)),U_10707),hAPP(hAPP(c_COMBB(U_10708,tc_fun(U_10706,tc_HOL_Obool),U_10705),U_10709),U_10710)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10708,tc_fun(U_10706,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10705,U_10708,U_10710),U_10707)),U_10709),
    inference(clausify,[status(thm)],[f_2877_2]) ).

fof(f_2878_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_2878_2,plain,
    ! [U_10716,U_10715,U_10714,U_10713,U_10712,U_10711] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10711,tc_fun(U_10712,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10713,U_10711,U_10714),U_10715)),U_10716) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10713,tc_fun(U_10712,tc_HOL_Obool)),U_10715),hAPP(hAPP(c_COMBB(U_10711,tc_fun(U_10712,tc_HOL_Obool),U_10713),U_10716),U_10714)),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

cnf(f_2878_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10711,tc_fun(U_10712,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10713,U_10711,U_10714),U_10715)),U_10716) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10713,tc_fun(U_10712,tc_HOL_Obool)),U_10715),hAPP(hAPP(c_COMBB(U_10711,tc_fun(U_10712,tc_HOL_Obool),U_10713),U_10716),U_10714)),
    inference(clausify,[status(thm)],[f_2878_2]) ).

fof(f_2879_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_2879_2,plain,
    ! [U_10723,U_10722,U_10721,U_10720,U_10719] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10719),U_10720),hAPP(c_Set_Oimage(U_10721,U_10719,U_10722),U_10723)))
        | ! [U_10718] :
            ( U_10720 != hAPP(U_10722,U_10718)
            | ~ hBOOL(hAPP(hAPP(c_member(U_10721),U_10718),U_10723)) ) )
      & ( ? [U_10717] :
            ( U_10720 = hAPP(U_10722,U_10717)
            & hBOOL(hAPP(hAPP(c_member(U_10721),U_10717),U_10723)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10719),U_10720),hAPP(c_Set_Oimage(U_10721,U_10719,U_10722),U_10723))) ) ),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

fof(f_2879_3,plain,
    ( ! [U_10733,U_10731,U_10729,U_10727] :
        ( ! [U_10725] : hBOOL(hAPP(hAPP(c_member(U_10725),U_10727),hAPP(c_Set_Oimage(U_10729,U_10725,U_10731),U_10733)))
        | ! [U_10718] :
            ( U_10727 != hAPP(U_10731,U_10718)
            | ~ hBOOL(hAPP(hAPP(c_member(U_10729),U_10718),U_10733)) ) )
    & ! [U_10732,U_10730,U_10728,U_10726] :
        ( ! [U_10724] : ~ hBOOL(hAPP(hAPP(c_member(U_10724),U_10726),hAPP(c_Set_Oimage(U_10728,U_10724,U_10730),U_10732)))
        | ? [U_10717] :
            ( U_10726 = hAPP(U_10730,U_10717)
            & hBOOL(hAPP(hAPP(c_member(U_10728),U_10717),U_10732)) ) ) ),
    inference(miniscope,[status(thm)],[f_2879_2]) ).

fof(f_2879_4,plain,
    ( ! [U_10733,U_10731,U_10729,U_10727] :
        ( ! [U_10725] : hBOOL(hAPP(hAPP(c_member(U_10725),U_10727),hAPP(c_Set_Oimage(U_10729,U_10725,U_10731),U_10733)))
        | ! [U_10718] :
            ( U_10727 != hAPP(U_10731,U_10718)
            | ~ hBOOL(hAPP(hAPP(c_member(U_10729),U_10718),U_10733)) ) )
    & ! [U_10732,U_10730,U_10728,U_10726] :
        ( ! [U_10724] : ~ hBOOL(hAPP(hAPP(c_member(U_10724),U_10726),hAPP(c_Set_Oimage(U_10728,U_10724,U_10730),U_10732)))
        | ( U_10726 = hAPP(U_10730,sK238(U_10732,U_10730,U_10728,U_10726))
          & hBOOL(hAPP(hAPP(c_member(U_10728),sK238(U_10732,U_10730,U_10728,U_10726)),U_10732)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_10717,sK238(U_10732,U_10730,U_10728,U_10726))],[f_2879_3]) ).

cnf(f_2879_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10728),sK238(U_10732,U_10730,U_10728,U_10726)),U_10732))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10724),U_10726),hAPP(c_Set_Oimage(U_10728,U_10724,U_10730),U_10732))) ),
    inference(clausify,[status(thm)],[f_2879_4]) ).

cnf(f_2879_6,plain,
    ( U_10726 = hAPP(U_10730,sK238(U_10732,U_10730,U_10728,U_10726))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10724),U_10726),hAPP(c_Set_Oimage(U_10728,U_10724,U_10730),U_10732))) ),
    inference(clausify,[status(thm)],[f_2879_4]) ).

cnf(f_2879_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10725),U_10727),hAPP(c_Set_Oimage(U_10729,U_10725,U_10731),U_10733)))
    | U_10727 != hAPP(U_10731,U_10718)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10729),U_10718),U_10733)) ),
    inference(clausify,[status(thm)],[f_2879_4]) ).

fof(f_2880_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_2880_2,plain,
    ! [U_10738,U_10737,U_10736,U_10735,U_10734] :
      ( hBOOL(hAPP(hAPP(c_member(U_10737),hAPP(U_10738,U_10735)),hAPP(c_Set_Oimage(U_10734,U_10737,U_10738),U_10736)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10736)) ),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

cnf(f_2880_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10737),hAPP(U_10738,U_10735)),hAPP(c_Set_Oimage(U_10734,U_10737,U_10738),U_10736)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10736)) ),
    inference(clausify,[status(thm)],[f_2880_2]) ).

fof(f_2881_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_2881_2,plain,
    ! [U_10744,U_10743,U_10742,U_10741,U_10740,U_10739] :
      ( hBOOL(hAPP(hAPP(c_member(U_10744),U_10742),hAPP(c_Set_Oimage(U_10739,U_10744,U_10743),U_10741)))
      | U_10742 != hAPP(U_10743,U_10740)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10740),U_10741)) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

cnf(f_2881_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10744),U_10742),hAPP(c_Set_Oimage(U_10739,U_10744,U_10743),U_10741)))
    | U_10742 != hAPP(U_10743,U_10740)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10740),U_10741)) ),
    inference(clausify,[status(thm)],[f_2881_2]) ).

fof(f_2882_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_2882_2,plain,
    ! [U_10748,U_10747,U_10746,U_10745] :
      ( ( hAPP(c_Set_Oimage(U_10745,U_10746,U_10747),U_10748) = c_Orderings_Obot__class_Obot(tc_fun(U_10746,tc_HOL_Obool))
        | U_10748 != c_Orderings_Obot__class_Obot(tc_fun(U_10745,tc_HOL_Obool)) )
      & ( U_10748 = c_Orderings_Obot__class_Obot(tc_fun(U_10745,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_10745,U_10746,U_10747),U_10748) != c_Orderings_Obot__class_Obot(tc_fun(U_10746,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ( ! [U_10756,U_10754,U_10752,U_10750] :
        ( hAPP(c_Set_Oimage(U_10750,U_10752,U_10754),U_10756) = c_Orderings_Obot__class_Obot(tc_fun(U_10752,tc_HOL_Obool))
        | U_10756 != c_Orderings_Obot__class_Obot(tc_fun(U_10750,tc_HOL_Obool)) )
    & ! [U_10755,U_10753,U_10751,U_10749] :
        ( U_10755 = c_Orderings_Obot__class_Obot(tc_fun(U_10749,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_10749,U_10751,U_10753),U_10755) != c_Orderings_Obot__class_Obot(tc_fun(U_10751,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( U_10755 = c_Orderings_Obot__class_Obot(tc_fun(U_10749,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_10749,U_10751,U_10753),U_10755) != c_Orderings_Obot__class_Obot(tc_fun(U_10751,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

cnf(f_2882_5,plain,
    ( hAPP(c_Set_Oimage(U_10750,U_10752,U_10754),U_10756) = c_Orderings_Obot__class_Obot(tc_fun(U_10752,tc_HOL_Obool))
    | U_10756 != c_Orderings_Obot__class_Obot(tc_fun(U_10750,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_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_2883_2,plain,
    ! [U_10759,U_10758,U_10757] : hAPP(c_Set_Oimage(U_10757,U_10758,U_10759),c_Orderings_Obot__class_Obot(tc_fun(U_10757,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10758,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

cnf(f_2883_3,plain,
    hAPP(c_Set_Oimage(U_10757,U_10758,U_10759),c_Orderings_Obot__class_Obot(tc_fun(U_10757,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10758,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2883_2]) ).

fof(f_2884_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_2884_2,plain,
    ! [U_10763,U_10762,U_10761,U_10760] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10760,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_10761,U_10760,U_10762),U_10763)
        | U_10763 != c_Orderings_Obot__class_Obot(tc_fun(U_10761,tc_HOL_Obool)) )
      & ( U_10763 = c_Orderings_Obot__class_Obot(tc_fun(U_10761,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10760,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_10761,U_10760,U_10762),U_10763) ) ),
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

fof(f_2884_3,plain,
    ( ! [U_10771,U_10769,U_10767] :
        ( ! [U_10765] : c_Orderings_Obot__class_Obot(tc_fun(U_10765,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_10767,U_10765,U_10769),U_10771)
        | U_10771 != c_Orderings_Obot__class_Obot(tc_fun(U_10767,tc_HOL_Obool)) )
    & ! [U_10770,U_10768,U_10766] :
        ( ! [U_10764] : c_Orderings_Obot__class_Obot(tc_fun(U_10764,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_10766,U_10764,U_10768),U_10770)
        | U_10770 = c_Orderings_Obot__class_Obot(tc_fun(U_10766,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2884_2]) ).

cnf(f_2884_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10764,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_10766,U_10764,U_10768),U_10770)
    | U_10770 = c_Orderings_Obot__class_Obot(tc_fun(U_10766,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2884_3]) ).

cnf(f_2884_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10765,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_10767,U_10765,U_10769),U_10771)
    | U_10771 != c_Orderings_Obot__class_Obot(tc_fun(U_10767,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2884_3]) ).

fof(f_2885_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_2885_2,plain,
    ! [U_10776,U_10775,U_10774,U_10773,U_10772] : hAPP(c_Set_Oimage(U_10772,U_10773,U_10774),hAPP(hAPP(c_Set_Oinsert(U_10772),U_10775),U_10776)) = hAPP(hAPP(c_Set_Oinsert(U_10773),hAPP(U_10774,U_10775)),hAPP(c_Set_Oimage(U_10772,U_10773,U_10774),U_10776)),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

cnf(f_2885_3,plain,
    hAPP(c_Set_Oimage(U_10772,U_10773,U_10774),hAPP(hAPP(c_Set_Oinsert(U_10772),U_10775),U_10776)) = hAPP(hAPP(c_Set_Oinsert(U_10773),hAPP(U_10774,U_10775)),hAPP(c_Set_Oimage(U_10772,U_10773,U_10774),U_10776)),
    inference(clausify,[status(thm)],[f_2885_2]) ).

fof(f_2886_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_2886_2,plain,
    ! [U_10781,U_10780,U_10779,U_10778,U_10777] : hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10777,tc_HOL_Obool)),U_10780),U_10781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10778,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),U_10780)),hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),U_10781)),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

cnf(f_2886_3,plain,
    hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10777,tc_HOL_Obool)),U_10780),U_10781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10778,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),U_10780)),hAPP(c_Set_Oimage(U_10777,U_10778,U_10779),U_10781)),
    inference(clausify,[status(thm)],[f_2886_2]) ).

fof(f_2887_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_2887_2,plain,
    ! [U_10786,U_10785,U_10784,U_10783,U_10782] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10782,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10783,tc_HOL_Obool),tc_fun(U_10782,tc_HOL_Obool),c_Set_Oimage(U_10783,U_10782,U_10784)),hAPP(c_Set_OPow(U_10783),U_10785))),hAPP(c_Set_OPow(U_10782),U_10786)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10783,U_10782,U_10784),U_10785)),U_10786)) ),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

cnf(f_2887_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10782,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10783,tc_HOL_Obool),tc_fun(U_10782,tc_HOL_Obool),c_Set_Oimage(U_10783,U_10782,U_10784)),hAPP(c_Set_OPow(U_10783),U_10785))),hAPP(c_Set_OPow(U_10782),U_10786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10783,U_10782,U_10784),U_10785)),U_10786)) ),
    inference(clausify,[status(thm)],[f_2887_2]) ).

fof(f_2888_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_2888_2,plain,
    ! [U_10793,U_10792,U_10791,U_10790,U_10789] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10789,tc_HOL_Obool)),U_10790),hAPP(c_Set_Oimage(U_10791,U_10789,U_10792),U_10793)))
        | ! [U_10788] :
            ( U_10790 != hAPP(c_Set_Oimage(U_10791,U_10789,U_10792),U_10788)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10791,tc_HOL_Obool)),U_10788),U_10793)) ) )
      & ( ? [U_10787] :
            ( U_10790 = hAPP(c_Set_Oimage(U_10791,U_10789,U_10792),U_10787)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10791,tc_HOL_Obool)),U_10787),U_10793)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10789,tc_HOL_Obool)),U_10790),hAPP(c_Set_Oimage(U_10791,U_10789,U_10792),U_10793))) ) ),
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

fof(f_2888_3,plain,
    ( ! [U_10803,U_10801,U_10799,U_10797,U_10795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10795,tc_HOL_Obool)),U_10797),hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10803)))
        | ! [U_10788] :
            ( U_10797 != hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10788)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10799,tc_HOL_Obool)),U_10788),U_10803)) ) )
    & ! [U_10802,U_10800,U_10798,U_10796,U_10794] :
        ( ? [U_10787] :
            ( U_10796 = hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),U_10787)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10798,tc_HOL_Obool)),U_10787),U_10802)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10794,tc_HOL_Obool)),U_10796),hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),U_10802))) ) ),
    inference(miniscope,[status(thm)],[f_2888_2]) ).

fof(f_2888_4,plain,
    ( ! [U_10803,U_10801,U_10799,U_10797,U_10795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10795,tc_HOL_Obool)),U_10797),hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10803)))
        | ! [U_10788] :
            ( U_10797 != hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10788)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10799,tc_HOL_Obool)),U_10788),U_10803)) ) )
    & ! [U_10802,U_10800,U_10798,U_10796,U_10794] :
        ( ( U_10796 = hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),sK239(U_10802,U_10800,U_10798,U_10796,U_10794))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10798,tc_HOL_Obool)),sK239(U_10802,U_10800,U_10798,U_10796,U_10794)),U_10802)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10794,tc_HOL_Obool)),U_10796),hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),U_10802))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_10787,sK239(U_10802,U_10800,U_10798,U_10796,U_10794))],[f_2888_3]) ).

cnf(f_2888_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10798,tc_HOL_Obool)),sK239(U_10802,U_10800,U_10798,U_10796,U_10794)),U_10802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10794,tc_HOL_Obool)),U_10796),hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),U_10802))) ),
    inference(clausify,[status(thm)],[f_2888_4]) ).

cnf(f_2888_6,plain,
    ( U_10796 = hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),sK239(U_10802,U_10800,U_10798,U_10796,U_10794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10794,tc_HOL_Obool)),U_10796),hAPP(c_Set_Oimage(U_10798,U_10794,U_10800),U_10802))) ),
    inference(clausify,[status(thm)],[f_2888_4]) ).

cnf(f_2888_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10795,tc_HOL_Obool)),U_10797),hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10803)))
    | U_10797 != hAPP(c_Set_Oimage(U_10799,U_10795,U_10801),U_10788)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10799,tc_HOL_Obool)),U_10788),U_10803)) ),
    inference(clausify,[status(thm)],[f_2888_4]) ).

fof(f_2889_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_2889_2,plain,
    ! [U_10808,U_10807,U_10806,U_10805,U_10804] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10807,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10804,U_10807,U_10808),U_10805)),hAPP(c_Set_Oimage(U_10804,U_10807,U_10808),U_10806)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10804,tc_HOL_Obool)),U_10805),U_10806)) ),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

cnf(f_2889_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10807,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10804,U_10807,U_10808),U_10805)),hAPP(c_Set_Oimage(U_10804,U_10807,U_10808),U_10806)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10804,tc_HOL_Obool)),U_10805),U_10806)) ),
    inference(clausify,[status(thm)],[f_2889_2]) ).

fof(f_2890_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_2890_2,plain,
    ! [U_10813,U_10812,U_10811,U_10810,U_10809] :
      ( hAPP(hAPP(c_Set_Oinsert(U_10812),hAPP(U_10813,U_10810)),hAPP(c_Set_Oimage(U_10809,U_10812,U_10813),U_10811)) = hAPP(c_Set_Oimage(U_10809,U_10812,U_10813),U_10811)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10809),U_10810),U_10811)) ),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

cnf(f_2890_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_10812),hAPP(U_10813,U_10810)),hAPP(c_Set_Oimage(U_10809,U_10812,U_10813),U_10811)) = hAPP(c_Set_Oimage(U_10809,U_10812,U_10813),U_10811)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10809),U_10810),U_10811)) ),
    inference(clausify,[status(thm)],[f_2890_2]) ).

fof(f_2891_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_2891_2,plain,
    ! [U_10818,U_10817,U_10816,U_10815,U_10814] :
      ( hBOOL(hAPP(hAPP(c_member(U_10817),U_10814),hAPP(c_Set_Oimage(U_10818,U_10817,U_10815),c_Orderings_Otop__class_Otop(tc_fun(U_10818,tc_HOL_Obool)))))
      | U_10814 != hAPP(U_10815,U_10816) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

cnf(f_2891_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10817),U_10814),hAPP(c_Set_Oimage(U_10818,U_10817,U_10815),c_Orderings_Otop__class_Otop(tc_fun(U_10818,tc_HOL_Obool)))))
    | U_10814 != hAPP(U_10815,U_10816) ),
    inference(clausify,[status(thm)],[f_2891_2]) ).

fof(f_2892_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_2892_2,plain,
    ! [U_10822,U_10821,U_10820,U_10819] : hBOOL(hAPP(hAPP(c_member(U_10819),hAPP(U_10820,U_10821)),hAPP(c_Set_Oimage(U_10822,U_10819,U_10820),c_Orderings_Otop__class_Otop(tc_fun(U_10822,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

cnf(f_2892_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_10819),hAPP(U_10820,U_10821)),hAPP(c_Set_Oimage(U_10822,U_10819,U_10820),c_Orderings_Otop__class_Otop(tc_fun(U_10822,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2892_2]) ).

fof(f_2893_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_2893_2,plain,
    ! [U_10827,U_10826,U_10825,U_10824,U_10823] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10825),U_10826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10825,tc_HOL_Obool)),U_10826),hAPP(c_Set_Oimage(U_10823,U_10825,U_10827),U_10824)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10824)) ),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

cnf(f_2893_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10825),U_10826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10825,tc_HOL_Obool)),U_10826),hAPP(c_Set_Oimage(U_10823,U_10825,U_10827),U_10824)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10824)) ),
    inference(clausify,[status(thm)],[f_2893_2]) ).

fof(f_2894_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_2894_2,plain,
    ! [U_10832,U_10831,U_10830,U_10829,U_10828] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10828,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10829,tc_HOL_Obool)),U_10831),U_10832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10828,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),U_10831)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),U_10832)))),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

cnf(f_2894_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10828,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10829,tc_HOL_Obool)),U_10831),U_10832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10828,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),U_10831)),hAPP(c_Set_Oimage(U_10829,U_10828,U_10830),U_10832)))),
    inference(clausify,[status(thm)],[f_2894_2]) ).

fof(f_2895_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_2895_2,plain,
    ! [U_10837,U_10836,U_10835,U_10834,U_10833] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10833,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),U_10836)),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),U_10837))),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10834,tc_HOL_Obool)),U_10836),U_10837)))),
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

cnf(f_2895_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10833,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),U_10836)),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),U_10837))),hAPP(c_Set_Oimage(U_10834,U_10833,U_10835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10834,tc_HOL_Obool)),U_10836),U_10837)))),
    inference(clausify,[status(thm)],[f_2895_2]) ).

fof(f_2896_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_2896_2,plain,
    ! [U_10840,U_10839,U_10838] :
      ( hAPP(c_Set_Oimage(U_10838,U_10838,c_Groups_Ouminus__class_Ouminus(U_10838)),c_SetInterval_Oord__class_OatLeastAtMost(U_10838,U_10839,U_10840)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10838,hAPP(c_Groups_Ouminus__class_Ouminus(U_10838),U_10840),hAPP(c_Groups_Ouminus__class_Ouminus(U_10838),U_10839))
      | ~ class_Groups_Oordered__ab__group__add(U_10838) ),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

cnf(f_2896_3,plain,
    ( hAPP(c_Set_Oimage(U_10838,U_10838,c_Groups_Ouminus__class_Ouminus(U_10838)),c_SetInterval_Oord__class_OatLeastAtMost(U_10838,U_10839,U_10840)) = c_SetInterval_Oord__class_OatLeastAtMost(U_10838,hAPP(c_Groups_Ouminus__class_Ouminus(U_10838),U_10840),hAPP(c_Groups_Ouminus__class_Ouminus(U_10838),U_10839))
    | ~ class_Groups_Oordered__ab__group__add(U_10838) ),
    inference(clausify,[status(thm)],[f_2896_2]) ).

fof(f_2897_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_2897_2,plain,
    ! [U_10842,U_10841] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10841),U_10842)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10841)),hAPP(c_Nat_OSuc,U_10842)),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

cnf(f_2897_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_10841),U_10842)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10841)),hAPP(c_Nat_OSuc,U_10842)),
    inference(clausify,[status(thm)],[f_2897_2]) ).

fof(f_2898_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_2898_2,plain,
    ! [U_10844,U_10843] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10843,U_10844)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10843),hAPP(c_Nat_OSuc,U_10844)),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

cnf(f_2898_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10843,U_10844)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10843),hAPP(c_Nat_OSuc,U_10844)),
    inference(clausify,[status(thm)],[f_2898_2]) ).

fof(f_2899_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_2899_2,plain,
    ! [U_10847,U_10846,U_10845] :
      ( hAPP(c_Set_Oimage(U_10845,U_10845,c_Groups_Ouminus__class_Ouminus(U_10845)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10845,U_10846,U_10847)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10845,hAPP(c_Groups_Ouminus__class_Ouminus(U_10845),U_10847),hAPP(c_Groups_Ouminus__class_Ouminus(U_10845),U_10846))
      | ~ class_Groups_Oordered__ab__group__add(U_10845) ),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

cnf(f_2899_3,plain,
    ( hAPP(c_Set_Oimage(U_10845,U_10845,c_Groups_Ouminus__class_Ouminus(U_10845)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10845,U_10846,U_10847)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10845,hAPP(c_Groups_Ouminus__class_Ouminus(U_10845),U_10847),hAPP(c_Groups_Ouminus__class_Ouminus(U_10845),U_10846))
    | ~ class_Groups_Oordered__ab__group__add(U_10845) ),
    inference(clausify,[status(thm)],[f_2899_2]) ).

fof(f_2900_1,plain,
    ! [V_ca_2,T_c,T_b,V_A_2] :
      ( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_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_ca_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_2900_2,plain,
    ! [U_10851,U_10850,U_10849,U_10848] :
      ( ( hAPP(c_Set_Oimage(U_10849,U_10850,hAPP(c_COMBK(U_10850,U_10849),U_10851)),U_10848) = hAPP(hAPP(c_Set_Oinsert(U_10850),U_10851),c_Orderings_Obot__class_Obot(tc_fun(U_10850,tc_HOL_Obool)))
        | U_10848 = c_Orderings_Obot__class_Obot(tc_fun(U_10849,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_10849,U_10850,hAPP(c_COMBK(U_10850,U_10849),U_10851)),U_10848) = c_Orderings_Obot__class_Obot(tc_fun(U_10850,tc_HOL_Obool))
        | U_10848 != c_Orderings_Obot__class_Obot(tc_fun(U_10849,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

fof(f_2900_3,plain,
    ( ! [U_10859,U_10857,U_10855,U_10853] :
        ( hAPP(c_Set_Oimage(U_10855,U_10857,hAPP(c_COMBK(U_10857,U_10855),U_10859)),U_10853) = hAPP(hAPP(c_Set_Oinsert(U_10857),U_10859),c_Orderings_Obot__class_Obot(tc_fun(U_10857,tc_HOL_Obool)))
        | U_10853 = c_Orderings_Obot__class_Obot(tc_fun(U_10855,tc_HOL_Obool)) )
    & ! [U_10858,U_10856,U_10854,U_10852] :
        ( hAPP(c_Set_Oimage(U_10854,U_10856,hAPP(c_COMBK(U_10856,U_10854),U_10858)),U_10852) = c_Orderings_Obot__class_Obot(tc_fun(U_10856,tc_HOL_Obool))
        | U_10852 != c_Orderings_Obot__class_Obot(tc_fun(U_10854,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2900_2]) ).

cnf(f_2900_4,plain,
    ( hAPP(c_Set_Oimage(U_10854,U_10856,hAPP(c_COMBK(U_10856,U_10854),U_10858)),U_10852) = c_Orderings_Obot__class_Obot(tc_fun(U_10856,tc_HOL_Obool))
    | U_10852 != c_Orderings_Obot__class_Obot(tc_fun(U_10854,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2900_3]) ).

cnf(f_2900_5,plain,
    ( hAPP(c_Set_Oimage(U_10855,U_10857,hAPP(c_COMBK(U_10857,U_10855),U_10859)),U_10853) = hAPP(hAPP(c_Set_Oinsert(U_10857),U_10859),c_Orderings_Obot__class_Obot(tc_fun(U_10857,tc_HOL_Obool)))
    | U_10853 = c_Orderings_Obot__class_Obot(tc_fun(U_10855,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2900_3]) ).

fof(f_2901_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_2901_2,plain,
    ! [U_10864,U_10863,U_10862,U_10861,U_10860] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10863),hAPP(c_Set_Oimage(U_10861,U_10863,hAPP(hAPP(c_COMBB(U_10860,U_10863,U_10861),U_10864),U_10862)),c_Orderings_Otop__class_Otop(tc_fun(U_10861,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10860),hAPP(c_Set_Oimage(U_10861,U_10860,U_10862),c_Orderings_Otop__class_Otop(tc_fun(U_10861,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

cnf(f_2901_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10863),hAPP(c_Set_Oimage(U_10861,U_10863,hAPP(hAPP(c_COMBB(U_10860,U_10863,U_10861),U_10864),U_10862)),c_Orderings_Otop__class_Otop(tc_fun(U_10861,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10860),hAPP(c_Set_Oimage(U_10861,U_10860,U_10862),c_Orderings_Otop__class_Otop(tc_fun(U_10861,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2901_2]) ).

fof(f_2902_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_2902_2,plain,
    ! [U_10866,U_10865] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10865),U_10866))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10865)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10866))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10865)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10866)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10865),U_10866)) ) ),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

fof(f_2902_3,plain,
    ( ! [U_10870,U_10868] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10868),U_10870))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10868)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10870))) )
    & ! [U_10869,U_10867] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10867)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10869)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10867),U_10869)) ) ),
    inference(miniscope,[status(thm)],[f_2902_2]) ).

cnf(f_2902_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10867)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10869)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10867),U_10869)) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

cnf(f_2902_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_10868),U_10870))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10868)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10870))) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

fof(f_2903_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_2903_2,plain,
    ! [U_10873,U_10872,U_10871] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10871),U_10872),U_10873) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10871),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10871,tc_Int_Oint),U_10872),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10873))
      | ~ class_Groups_Ocomm__monoid__mult(U_10871)
      | ~ class_Groups_Ocomm__monoid__add(U_10871) ),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

cnf(f_2903_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10871),U_10872),U_10873) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10871),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10871,tc_Int_Oint),U_10872),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10873))
    | ~ class_Groups_Ocomm__monoid__mult(U_10871)
    | ~ class_Groups_Ocomm__monoid__add(U_10871) ),
    inference(clausify,[status(thm)],[f_2903_2]) ).

fof(f_2904_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_2904_2,plain,
    ! [U_10876,U_10875,U_10874] : 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_10874)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10875),U_10876)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10875),U_10874)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10876),U_10874)),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

cnf(f_2904_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_10874)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10875),U_10876)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10875),U_10874)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10876),U_10874)),
    inference(clausify,[status(thm)],[f_2904_2]) ).

fof(f_2905_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_2905_2,plain,
    ! [U_10879,U_10878,U_10877] : 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_10877)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10878,U_10879)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10878),U_10877),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10879),U_10877)),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

cnf(f_2905_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_10877)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10878,U_10879)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10878),U_10877),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10879),U_10877)),
    inference(clausify,[status(thm)],[f_2905_2]) ).

fof(f_2906_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_2906_2,plain,
    ! [U_10881,U_10880] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10880),U_10881))
        | ~ 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_10880)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10881))) )
      & ( 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_10880)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10881)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10880),U_10881)) ) ),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

fof(f_2906_3,plain,
    ( ! [U_10885,U_10883] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10883),U_10885))
        | ~ 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_10883)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10885))) )
    & ! [U_10884,U_10882] :
        ( 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_10882)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10884)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10882),U_10884)) ) ),
    inference(miniscope,[status(thm)],[f_2906_2]) ).

cnf(f_2906_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_10882)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10884)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10882),U_10884)) ),
    inference(clausify,[status(thm)],[f_2906_3]) ).

cnf(f_2906_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10883),U_10885))
    | ~ 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_10883)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10885))) ),
    inference(clausify,[status(thm)],[f_2906_3]) ).

fof(f_2907_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_2907_2,plain,
    ! [U_10889,U_10888,U_10887,U_10886] : hAPP(c_Set_Oimage(U_10886,U_10887,U_10888),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10886,tc_HOL_Obool),U_10889)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10886,tc_HOL_Obool),tc_fun(U_10887,tc_HOL_Obool)),U_10889),c_Set_Oimage(U_10886,U_10887,U_10888)),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

cnf(f_2907_3,plain,
    hAPP(c_Set_Oimage(U_10886,U_10887,U_10888),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10886,tc_HOL_Obool),U_10889)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10886,tc_HOL_Obool),tc_fun(U_10887,tc_HOL_Obool)),U_10889),c_Set_Oimage(U_10886,U_10887,U_10888)),
    inference(clausify,[status(thm)],[f_2907_2]) ).

fof(f_2908_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_2908_2,plain,
    ! [U_10893,U_10892,U_10891,U_10890] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10892),hAPP(c_Set_Oimage(U_10890,U_10892,U_10893),U_10891))),hAPP(c_Finite__Set_Ocard(U_10890),U_10891)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10890),U_10891)) ),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

cnf(f_2908_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10892),hAPP(c_Set_Oimage(U_10890,U_10892,U_10893),U_10891))),hAPP(c_Finite__Set_Ocard(U_10890),U_10891)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10890),U_10891)) ),
    inference(clausify,[status(thm)],[f_2908_2]) ).

fof(f_2909_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_2909_2,plain,
    ! [U_10896,U_10895,U_10894] :
      ( hAPP(c_Set_Oimage(U_10894,U_10894,c_Groups_Ouminus__class_Ouminus(U_10894)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10894,U_10895,U_10896)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10894,hAPP(c_Groups_Ouminus__class_Ouminus(U_10894),U_10896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10894),U_10895))
      | ~ class_Groups_Oordered__ab__group__add(U_10894) ),
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

cnf(f_2909_3,plain,
    ( hAPP(c_Set_Oimage(U_10894,U_10894,c_Groups_Ouminus__class_Ouminus(U_10894)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10894,U_10895,U_10896)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10894,hAPP(c_Groups_Ouminus__class_Ouminus(U_10894),U_10896)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10894),U_10895))
    | ~ class_Groups_Oordered__ab__group__add(U_10894) ),
    inference(clausify,[status(thm)],[f_2909_2]) ).

fof(f_2910_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_2910_2,plain,
    ! [U_10899,U_10898,U_10897] :
      ( hAPP(c_Set_Oimage(U_10897,U_10897,c_Groups_Ouminus__class_Ouminus(U_10897)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10897,U_10898),U_10899)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10897,hAPP(c_Groups_Ouminus__class_Ouminus(U_10897),U_10899),hAPP(c_Groups_Ouminus__class_Ouminus(U_10897),U_10898))
      | ~ class_Groups_Oordered__ab__group__add(U_10897) ),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

cnf(f_2910_3,plain,
    ( hAPP(c_Set_Oimage(U_10897,U_10897,c_Groups_Ouminus__class_Ouminus(U_10897)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10897,U_10898),U_10899)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10897,hAPP(c_Groups_Ouminus__class_Ouminus(U_10897),U_10899),hAPP(c_Groups_Ouminus__class_Ouminus(U_10897),U_10898))
    | ~ class_Groups_Oordered__ab__group__add(U_10897) ),
    inference(clausify,[status(thm)],[f_2910_2]) ).

fof(f_2911_1,plain,
    ! [V_ca_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_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_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_2911_2,plain,
    ! [U_10904,U_10903,U_10902,U_10901,U_10900] :
      ( hAPP(c_Set_Oimage(U_10900,U_10903,hAPP(c_COMBK(U_10903,U_10900),U_10904)),U_10902) = hAPP(hAPP(c_Set_Oinsert(U_10903),U_10904),c_Orderings_Obot__class_Obot(tc_fun(U_10903,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10900),U_10901),U_10902)) ),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

cnf(f_2911_3,plain,
    ( hAPP(c_Set_Oimage(U_10900,U_10903,hAPP(c_COMBK(U_10903,U_10900),U_10904)),U_10902) = hAPP(hAPP(c_Set_Oinsert(U_10903),U_10904),c_Orderings_Obot__class_Obot(tc_fun(U_10903,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10900),U_10901),U_10902)) ),
    inference(clausify,[status(thm)],[f_2911_2]) ).

fof(f_2912_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_2912_2,plain,
    ! [U_10908,U_10907,U_10906,U_10905] : hAPP(c_Set_Oimage(U_10905,U_10906,U_10907),U_10908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10906,tc_HOL_Obool)),U_10908),hAPP(hAPP(c_COMBC(U_10905,tc_fun(U_10906,tc_HOL_Obool),tc_fun(U_10906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10906,tc_fun(tc_fun(U_10906,tc_HOL_Obool),tc_fun(U_10906,tc_HOL_Obool)),U_10905),c_Set_Oinsert(U_10906)),U_10907)),c_Orderings_Obot__class_Obot(tc_fun(U_10906,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

cnf(f_2912_3,plain,
    hAPP(c_Set_Oimage(U_10905,U_10906,U_10907),U_10908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10906,tc_HOL_Obool)),U_10908),hAPP(hAPP(c_COMBC(U_10905,tc_fun(U_10906,tc_HOL_Obool),tc_fun(U_10906,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10906,tc_fun(tc_fun(U_10906,tc_HOL_Obool),tc_fun(U_10906,tc_HOL_Obool)),U_10905),c_Set_Oinsert(U_10906)),U_10907)),c_Orderings_Obot__class_Obot(tc_fun(U_10906,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2912_2]) ).

fof(f_2913_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_2913_2,plain,
    ! [U_10911,U_10910,U_10909] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10909),U_10910),U_10911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10909),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10909,tc_Int_Oint),U_10910),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10911))
      | ~ class_Groups_Ocomm__monoid__mult(U_10909)
      | ~ class_Groups_Ocomm__monoid__add(U_10909) ),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

cnf(f_2913_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10909),U_10910),U_10911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10909),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10909,tc_Int_Oint),U_10910),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10911))
    | ~ class_Groups_Ocomm__monoid__mult(U_10909)
    | ~ class_Groups_Ocomm__monoid__add(U_10909) ),
    inference(clausify,[status(thm)],[f_2913_2]) ).

fof(f_2914_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_2914_2,plain,
    ! [U_10912] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10912))
        | ~ 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_10912))) )
      & ( 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_10912)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10912)) ) ),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

fof(f_2914_3,plain,
    ( ! [U_10914] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10914))
        | ~ 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_10914))) )
    & ! [U_10913] :
        ( 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_10913)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10913)) ) ),
    inference(miniscope,[status(thm)],[f_2914_2]) ).

cnf(f_2914_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_10913)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10913)) ),
    inference(clausify,[status(thm)],[f_2914_3]) ).

cnf(f_2914_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_10914))
    | ~ 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_10914))) ),
    inference(clausify,[status(thm)],[f_2914_3]) ).

fof(f_2915_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_2915_2,plain,
    ! [U_10915] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10915) = 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_10915)),
    inference(variable_rename,[status(thm)],[f_2915_1]) ).

cnf(f_2915_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10915) = 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_10915)),
    inference(clausify,[status(thm)],[f_2915_2]) ).

fof(f_2916_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_2916_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_2916_1]) ).

fof(f_2917_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_2917_2,plain,
    ! [U_10919,U_10918,U_10917,U_10916] :
      ( hAPP(c_Set_Oimage(U_10916,U_10918,U_10919),U_10917) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10918,tc_HOL_Obool),U_10916,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10918,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10916,tc_fun(U_10918,tc_HOL_Obool),tc_fun(U_10918,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10918,tc_fun(tc_fun(U_10918,tc_HOL_Obool),tc_fun(U_10918,tc_HOL_Obool)),U_10916),c_Set_Oinsert(U_10918)),U_10919)),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool))),U_10917)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10916),U_10917)) ),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

cnf(f_2917_3,plain,
    ( hAPP(c_Set_Oimage(U_10916,U_10918,U_10919),U_10917) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10918,tc_HOL_Obool),U_10916,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10918,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10916,tc_fun(U_10918,tc_HOL_Obool),tc_fun(U_10918,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10918,tc_fun(tc_fun(U_10918,tc_HOL_Obool),tc_fun(U_10918,tc_HOL_Obool)),U_10916),c_Set_Oinsert(U_10918)),U_10919)),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10918,tc_HOL_Obool))),U_10917)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10916),U_10917)) ),
    inference(clausify,[status(thm)],[f_2917_2]) ).

fof(f_2918_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_2918_2,plain,
    ! [U_10920] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10920)) = 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_10920))),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

cnf(f_2918_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10920)) = 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_10920))),
    inference(clausify,[status(thm)],[f_2918_2]) ).

fof(f_2919_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_2919_2,plain,
    ! [U_10922,U_10921] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10921),c_Big__Operators_Olinorder__class_OMin(U_10921,U_10922)) = c_Big__Operators_Olinorder__class_OMax(U_10921,hAPP(c_Set_Oimage(U_10921,U_10921,c_Groups_Ouminus__class_Ouminus(U_10921)),U_10922))
      | U_10922 = c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10922))
      | ~ class_Groups_Olinordered__ab__group__add(U_10921) ),
    inference(variable_rename,[status(thm)],[f_2919_1]) ).

cnf(f_2919_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10921),c_Big__Operators_Olinorder__class_OMin(U_10921,U_10922)) = c_Big__Operators_Olinorder__class_OMax(U_10921,hAPP(c_Set_Oimage(U_10921,U_10921,c_Groups_Ouminus__class_Ouminus(U_10921)),U_10922))
    | U_10922 = c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10921),U_10922))
    | ~ class_Groups_Olinordered__ab__group__add(U_10921) ),
    inference(clausify,[status(thm)],[f_2919_2]) ).

fof(f_2920_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_2920_2,plain,
    ! [U_10924,U_10923] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10923),c_Big__Operators_Olinorder__class_OMax(U_10923,U_10924)) = c_Big__Operators_Olinorder__class_OMin(U_10923,hAPP(c_Set_Oimage(U_10923,U_10923,c_Groups_Ouminus__class_Ouminus(U_10923)),U_10924))
      | U_10924 = c_Orderings_Obot__class_Obot(tc_fun(U_10923,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10923),U_10924))
      | ~ class_Groups_Olinordered__ab__group__add(U_10923) ),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

cnf(f_2920_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10923),c_Big__Operators_Olinorder__class_OMax(U_10923,U_10924)) = c_Big__Operators_Olinorder__class_OMin(U_10923,hAPP(c_Set_Oimage(U_10923,U_10923,c_Groups_Ouminus__class_Ouminus(U_10923)),U_10924))
    | U_10924 = c_Orderings_Obot__class_Obot(tc_fun(U_10923,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10923),U_10924))
    | ~ class_Groups_Olinordered__ab__group__add(U_10923) ),
    inference(clausify,[status(thm)],[f_2920_2]) ).

fof(f_2921_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_2921_2,plain,
    ! [U_10926,U_10925] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_10925,U_10926) = 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_10925),hAPP(c_Int_Onat,U_10926)))
      | ~ c_Nat__Transfer_Ois__nat(U_10926)
      | ~ c_Nat__Transfer_Ois__nat(U_10925) ),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

cnf(f_2921_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_10925,U_10926) = 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_10925),hAPP(c_Int_Onat,U_10926)))
    | ~ c_Nat__Transfer_Ois__nat(U_10926)
    | ~ c_Nat__Transfer_Ois__nat(U_10925) ),
    inference(clausify,[status(thm)],[f_2921_2]) ).

fof(f_2922_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_2922_2,plain,
    ! [U_10930,U_10929,U_10928,U_10927] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),U_10930))),hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10927,tc_HOL_Obool)),U_10930))))
      | hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),c_Orderings_Otop__class_Otop(tc_fun(U_10927,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10928,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

cnf(f_2922_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),U_10930))),hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10927,tc_HOL_Obool)),U_10930))))
    | hAPP(c_Set_Oimage(U_10927,U_10928,U_10929),c_Orderings_Otop__class_Otop(tc_fun(U_10927,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10928,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2922_2]) ).

fof(f_2923_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_2923_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_2923_1]) ).

fof(f_2924_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_2924_2,plain,
    ! [U_10935,U_10934,U_10933] :
      ( hAPP(U_10934,c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),U_10935)) = c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),hAPP(c_Set_Oimage(U_10933,U_10933,U_10934),U_10935))
      | U_10935 = c_Orderings_Obot__class_Obot(tc_fun(U_10933,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10933),U_10935))
      | ? [U_10932,U_10931] : hAPP(U_10934,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),U_10932),U_10931)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),hAPP(U_10934,U_10932)),hAPP(U_10934,U_10931))
      | ~ class_Orderings_Olinorder(U_10933) ),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

fof(f_2924_3,plain,
    ! [U_10935,U_10934,U_10933] :
      ( hAPP(U_10934,c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),U_10935)) = c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),hAPP(c_Set_Oimage(U_10933,U_10933,U_10934),U_10935))
      | U_10935 = c_Orderings_Obot__class_Obot(tc_fun(U_10933,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10933),U_10935))
      | ? [U_10931] : hAPP(U_10934,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),sK240(U_10935,U_10934,U_10933)),U_10931)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),hAPP(U_10934,sK240(U_10935,U_10934,U_10933))),hAPP(U_10934,U_10931))
      | ~ class_Orderings_Olinorder(U_10933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_10932,sK240(U_10935,U_10934,U_10933))],[f_2924_2]) ).

fof(f_2924_4,plain,
    ! [U_10935,U_10934,U_10933] :
      ( hAPP(U_10934,c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),U_10935)) = c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),hAPP(c_Set_Oimage(U_10933,U_10933,U_10934),U_10935))
      | U_10935 = c_Orderings_Obot__class_Obot(tc_fun(U_10933,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10933),U_10935))
      | hAPP(U_10934,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),sK240(U_10935,U_10934,U_10933)),sK241(U_10935,U_10934,U_10933))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),hAPP(U_10934,sK240(U_10935,U_10934,U_10933))),hAPP(U_10934,sK241(U_10935,U_10934,U_10933)))
      | ~ class_Orderings_Olinorder(U_10933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_10931,sK241(U_10935,U_10934,U_10933))],[f_2924_3]) ).

cnf(f_2924_5,plain,
    ( hAPP(U_10934,c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),U_10935)) = c_Big__Operators_Olattice_OSup__fin(U_10933,c_Orderings_Oord__class_Omax(U_10933),hAPP(c_Set_Oimage(U_10933,U_10933,U_10934),U_10935))
    | U_10935 = c_Orderings_Obot__class_Obot(tc_fun(U_10933,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10933),U_10935))
    | hAPP(U_10934,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),sK240(U_10935,U_10934,U_10933)),sK241(U_10935,U_10934,U_10933))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10933),hAPP(U_10934,sK240(U_10935,U_10934,U_10933))),hAPP(U_10934,sK241(U_10935,U_10934,U_10933)))
    | ~ class_Orderings_Olinorder(U_10933) ),
    inference(clausify,[status(thm)],[f_2924_4]) ).

fof(f_2925_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_2925_2,plain,
    ! [U_10942,U_10941,U_10940,U_10939,U_10938,U_10937,U_10936] :
      ( hBOOL(hAPP(hAPP(c_member(U_10941),hAPP(hAPP(U_10942,U_10938),U_10939)),hAPP(c_Set_Oimage(tc_prod(U_10936,U_10937),U_10941,hAPP(c_Product__Type_Oprod_Oprod__case(U_10936,U_10937,U_10941),U_10942)),U_10940)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10936,U_10937)),hAPP(hAPP(c_Product__Type_OPair(U_10936,U_10937),U_10938),U_10939)),U_10940)) ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

cnf(f_2925_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10941),hAPP(hAPP(U_10942,U_10938),U_10939)),hAPP(c_Set_Oimage(tc_prod(U_10936,U_10937),U_10941,hAPP(c_Product__Type_Oprod_Oprod__case(U_10936,U_10937,U_10941),U_10942)),U_10940)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10936,U_10937)),hAPP(hAPP(c_Product__Type_OPair(U_10936,U_10937),U_10938),U_10939)),U_10940)) ),
    inference(clausify,[status(thm)],[f_2925_2]) ).

fof(f_2926_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_2926_2,plain,
    ! [U_10945,U_10944,U_10943] : hAPP(c_Set_Oimage(U_10944,tc_fun(U_10944,tc_HOL_Obool),U_10943),U_10945) != hAPP(c_Set_OPow(U_10944),U_10945),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

cnf(f_2926_3,plain,
    hAPP(c_Set_Oimage(U_10944,tc_fun(U_10944,tc_HOL_Obool),U_10943),U_10945) != hAPP(c_Set_OPow(U_10944),U_10945),
    inference(clausify,[status(thm)],[f_2926_2]) ).

fof(f_2927_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_2927_2,plain,
    ! [U_10948,U_10947,U_10946] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10947) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10948)
          | U_10947 != U_10948 )
        & ( U_10947 = U_10948
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10947) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10948) ) )
      | ~ class_Orderings_Olinorder(U_10946) ),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

cnf(f_2927_3,plain,
    ( U_10947 = U_10948
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10947) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10948)
    | ~ class_Orderings_Olinorder(U_10946) ),
    inference(clausify,[status(thm)],[f_2927_2]) ).

cnf(f_2927_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10947) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10946),U_10948)
    | U_10947 != U_10948
    | ~ class_Orderings_Olinorder(U_10946) ),
    inference(clausify,[status(thm)],[f_2927_2]) ).

fof(f_2928_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_2928_2,plain,
    ! [U_10950,U_10949] : hAPP(c_Relation_OField(U_10949),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_10949,U_10949),tc_HOL_Obool),U_10950)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10949,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_10949,U_10949),tc_HOL_Obool),tc_fun(U_10949,tc_HOL_Obool),c_Relation_OField(U_10949)),U_10950)),
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

cnf(f_2928_3,plain,
    hAPP(c_Relation_OField(U_10949),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_10949,U_10949),tc_HOL_Obool),U_10950)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10949,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_10949,U_10949),tc_HOL_Obool),tc_fun(U_10949,tc_HOL_Obool),c_Relation_OField(U_10949)),U_10950)),
    inference(clausify,[status(thm)],[f_2928_2]) ).

fof(f_2929_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_2929_2,plain,
    ! [U_10954,U_10953,U_10952,U_10951] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10951,tc_fun(U_10952,tc_HOL_Obool)),U_10953),U_10954) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10952,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10951,tc_fun(U_10952,tc_HOL_Obool),U_10954),U_10953)),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

cnf(f_2929_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10951,tc_fun(U_10952,tc_HOL_Obool)),U_10953),U_10954) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10952,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10951,tc_fun(U_10952,tc_HOL_Obool),U_10954),U_10953)),
    inference(clausify,[status(thm)],[f_2929_2]) ).

fof(f_2930_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_2930_2,plain,
    ! [U_10958,U_10957,U_10956,U_10955] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10955,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10956,tc_fun(U_10955,tc_HOL_Obool),U_10957),U_10958)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10955,tc_HOL_Obool)),U_10958),U_10957),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

cnf(f_2930_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10955,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10956,tc_fun(U_10955,tc_HOL_Obool),U_10957),U_10958)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10955,tc_HOL_Obool)),U_10958),U_10957),
    inference(clausify,[status(thm)],[f_2930_2]) ).

fof(f_2931_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_2931_2,plain,
    ! [U_10962,U_10961,U_10960,U_10959] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10959,tc_fun(U_10960,tc_HOL_Obool)),U_10961),U_10962) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10960,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10959,tc_fun(U_10960,tc_HOL_Obool),U_10962),U_10961)),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

cnf(f_2931_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10959,tc_fun(U_10960,tc_HOL_Obool)),U_10961),U_10962) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10960,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10959,tc_fun(U_10960,tc_HOL_Obool),U_10962),U_10961)),
    inference(clausify,[status(thm)],[f_2931_2]) ).

fof(f_2932_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_2932_2,plain,
    ! [U_10966,U_10965,U_10964,U_10963] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10963,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10964,tc_fun(U_10963,tc_HOL_Obool),U_10965),U_10966)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10964,tc_fun(U_10963,tc_HOL_Obool)),U_10966),U_10965),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

cnf(f_2932_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10963,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10964,tc_fun(U_10963,tc_HOL_Obool),U_10965),U_10966)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10964,tc_fun(U_10963,tc_HOL_Obool)),U_10966),U_10965),
    inference(clausify,[status(thm)],[f_2932_2]) ).

fof(f_2933_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_2933_2,plain,
    ! [U_10967] : 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_10967)) = U_10967,
    inference(variable_rename,[status(thm)],[f_2933_1]) ).

cnf(f_2933_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_10967)) = U_10967,
    inference(clausify,[status(thm)],[f_2933_2]) ).

fof(f_2934_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_2934_2,plain,
    ! [U_10969,U_10968] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10968),U_10969) = 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_10968)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10969))),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

cnf(f_2934_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10968),U_10969) = 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_10968)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10969))),
    inference(clausify,[status(thm)],[f_2934_2]) ).

fof(f_2935_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_2935_2,plain,
    ! [U_10972,U_10971,U_10970] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_10970),U_10971),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10970),U_10972)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10970),U_10972),U_10971)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10970),U_10972),U_10971))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10970),U_10971),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10970),U_10972))) ) )
      | ~ class_Orderings_Oord(U_10970) ),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

cnf(f_2935_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10970),U_10972),U_10971))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10970),U_10971),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10970),U_10972)))
    | ~ class_Orderings_Oord(U_10970) ),
    inference(clausify,[status(thm)],[f_2935_2]) ).

cnf(f_2935_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10970),U_10971),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10970),U_10972)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10970),U_10972),U_10971))
    | ~ class_Orderings_Oord(U_10970) ),
    inference(clausify,[status(thm)],[f_2935_2]) ).

fof(f_2936_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_2936_2,plain,
    ! [U_10975,U_10974,U_10973] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10973,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10974)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10975)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10975),U_10974)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10975),U_10974))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10973,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10974)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10975))) ) )
      | ~ class_Orderings_Olinorder(U_10973) ),
    inference(variable_rename,[status(thm)],[f_2936_1]) ).

cnf(f_2936_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10975),U_10974))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10973,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10974)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10975)))
    | ~ class_Orderings_Olinorder(U_10973) ),
    inference(clausify,[status(thm)],[f_2936_2]) ).

cnf(f_2936_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10973,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10974)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10973),U_10975)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10975),U_10974))
    | ~ class_Orderings_Olinorder(U_10973) ),
    inference(clausify,[status(thm)],[f_2936_2]) ).

fof(f_2937_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_2937_2,plain,
    ! [U_10980,U_10979,U_10978,U_10977,U_10976] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10976,tc_fun(U_10977,tc_HOL_Obool)),U_10978),hAPP(hAPP(c_COMBS(U_10976,tc_fun(U_10977,tc_HOL_Obool),tc_fun(U_10977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10977,tc_HOL_Obool),tc_fun(tc_fun(U_10977,tc_HOL_Obool),tc_fun(U_10977,tc_HOL_Obool)),U_10976),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10977,tc_HOL_Obool))),U_10979)),U_10980)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10977,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10977,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10976,tc_fun(U_10977,tc_HOL_Obool),U_10979),U_10978))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10977,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10976,tc_fun(U_10977,tc_HOL_Obool),U_10980),U_10978))),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

cnf(f_2937_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10976,tc_fun(U_10977,tc_HOL_Obool)),U_10978),hAPP(hAPP(c_COMBS(U_10976,tc_fun(U_10977,tc_HOL_Obool),tc_fun(U_10977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10977,tc_HOL_Obool),tc_fun(tc_fun(U_10977,tc_HOL_Obool),tc_fun(U_10977,tc_HOL_Obool)),U_10976),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10977,tc_HOL_Obool))),U_10979)),U_10980)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10977,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10977,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10976,tc_fun(U_10977,tc_HOL_Obool),U_10979),U_10978))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10977,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10976,tc_fun(U_10977,tc_HOL_Obool),U_10980),U_10978))),
    inference(clausify,[status(thm)],[f_2937_2]) ).

fof(f_2938_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_2938_2,plain,
    ! [U_10985,U_10984,U_10983,U_10982,U_10981] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10981,tc_fun(U_10982,tc_HOL_Obool)),U_10983),hAPP(hAPP(c_COMBS(U_10981,tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10982,tc_HOL_Obool),tc_fun(tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool)),U_10981),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool))),U_10984)),U_10985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10982,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10981,tc_fun(U_10982,tc_HOL_Obool),U_10984),U_10983))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10982,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10981,tc_fun(U_10982,tc_HOL_Obool),U_10985),U_10983))),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

cnf(f_2938_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10981,tc_fun(U_10982,tc_HOL_Obool)),U_10983),hAPP(hAPP(c_COMBS(U_10981,tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10982,tc_HOL_Obool),tc_fun(tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool)),U_10981),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool))),U_10984)),U_10985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10982,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10981,tc_fun(U_10982,tc_HOL_Obool),U_10984),U_10983))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10982,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10981,tc_fun(U_10982,tc_HOL_Obool),U_10985),U_10983))),
    inference(clausify,[status(thm)],[f_2938_2]) ).

fof(f_2939_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_2939_2,plain,
    ! [U_10988,U_10987,U_10986] : hAPP(c_Set_OPow(U_10986),hAPP(hAPP(c_Set_Oinsert(U_10986),U_10987),U_10988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10986,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10986),U_10988)),hAPP(c_Set_Oimage(tc_fun(U_10986,tc_HOL_Obool),tc_fun(U_10986,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10986),U_10987)),hAPP(c_Set_OPow(U_10986),U_10988))),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

cnf(f_2939_3,plain,
    hAPP(c_Set_OPow(U_10986),hAPP(hAPP(c_Set_Oinsert(U_10986),U_10987),U_10988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10986,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10986),U_10988)),hAPP(c_Set_Oimage(tc_fun(U_10986,tc_HOL_Obool),tc_fun(U_10986,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10986),U_10987)),hAPP(c_Set_OPow(U_10986),U_10988))),
    inference(clausify,[status(thm)],[f_2939_2]) ).

fof(f_2940_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_2940_2,plain,
    ! [U_10990,U_10989] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10989,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10989),U_10990)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10989),U_10990)
      | ~ class_Orderings_Olinorder(U_10989) ),
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

cnf(f_2940_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10989,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_10989),U_10990)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10989),U_10990)
    | ~ class_Orderings_Olinorder(U_10989) ),
    inference(clausify,[status(thm)],[f_2940_2]) ).

fof(f_2941_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_2941_2,plain,
    ! [U_10992,U_10991] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10991,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10991),U_10992)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10991),U_10992)
      | ~ class_Orderings_Olinorder(U_10991) ),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

cnf(f_2941_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10991,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_10991),U_10992)) = hAPP(c_SetInterval_Oord__class_OatMost(U_10991),U_10992)
    | ~ class_Orderings_Olinorder(U_10991) ),
    inference(clausify,[status(thm)],[f_2941_2]) ).

fof(f_2942_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_2942_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_2942_1]) ).

fof(f_2943_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_2943_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_2943_1]) ).

fof(f_2944_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_2944_2,plain,
    ! [U_10994,U_10993] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10993,U_10994) = 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_10993),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10994))),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

cnf(f_2944_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10993,U_10994) = 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_10993),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10994))),
    inference(clausify,[status(thm)],[f_2944_2]) ).

fof(f_2945_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_2945_2,plain,
    ! [U_10996,U_10995] : 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_10995)),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_10996),U_10995))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10995),U_10996),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

cnf(f_2945_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_10995)),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_10996),U_10995))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10995),U_10996),
    inference(clausify,[status(thm)],[f_2945_2]) ).

fof(f_2946_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_2946_2,plain,
    ! [U_10998,U_10997] : hAPP(c_Set_Oimage(U_10997,U_10997,c_COMBI(U_10997)),U_10998) = U_10998,
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

cnf(f_2946_3,plain,
    hAPP(c_Set_Oimage(U_10997,U_10997,c_COMBI(U_10997)),U_10998) = U_10998,
    inference(clausify,[status(thm)],[f_2946_2]) ).

fof(f_2947_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_2947_2,plain,
    ! [U_11000,U_10999] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10999),U_11000) = 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_10999)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_11000))),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

cnf(f_2947_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10999),U_11000) = 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_10999)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_11000))),
    inference(clausify,[status(thm)],[f_2947_2]) ).

fof(f_2948_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_2948_2,plain,
    ! [U_11003,U_11002,U_11001] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11001,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11001,U_11002,U_11003)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11001),U_11003)) = c_Orderings_Obot__class_Obot(tc_fun(U_11001,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11001) ),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

cnf(f_2948_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11001,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11001,U_11002,U_11003)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11001),U_11003)) = c_Orderings_Obot__class_Obot(tc_fun(U_11001,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11001) ),
    inference(clausify,[status(thm)],[f_2948_2]) ).

fof(f_2949_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_2949_2,plain,
    ! [U_11006,U_11005,U_11004] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11004,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11004,U_11005,U_11006)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11004),U_11006)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11004),U_11005)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11004),U_11005),U_11006))
      | ~ class_Orderings_Olinorder(U_11004) ),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

cnf(f_2949_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11004,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11004,U_11005,U_11006)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11004),U_11006)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11004),U_11005)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11004),U_11005),U_11006))
    | ~ class_Orderings_Olinorder(U_11004) ),
    inference(clausify,[status(thm)],[f_2949_2]) ).

fof(f_2950_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_2950_2,plain,
    ! [U_11008,U_11007] :
      ( hAPP(c_Set_Oimage(U_11007,U_11007,c_Groups_Ouminus__class_Ouminus(U_11007)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11007),U_11008)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11007),hAPP(c_Groups_Ouminus__class_Ouminus(U_11007),U_11008))
      | ~ class_Groups_Oordered__ab__group__add(U_11007) ),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

cnf(f_2950_3,plain,
    ( hAPP(c_Set_Oimage(U_11007,U_11007,c_Groups_Ouminus__class_Ouminus(U_11007)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11007),U_11008)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11007),hAPP(c_Groups_Ouminus__class_Ouminus(U_11007),U_11008))
    | ~ class_Groups_Oordered__ab__group__add(U_11007) ),
    inference(clausify,[status(thm)],[f_2950_2]) ).

fof(f_2951_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_2951_2,plain,
    ! [U_11010,U_11009] :
      ( hAPP(c_Set_Oimage(U_11009,U_11009,c_Groups_Ouminus__class_Ouminus(U_11009)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11009),U_11010)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11009),hAPP(c_Groups_Ouminus__class_Ouminus(U_11009),U_11010))
      | ~ class_Groups_Oordered__ab__group__add(U_11009) ),
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

cnf(f_2951_3,plain,
    ( hAPP(c_Set_Oimage(U_11009,U_11009,c_Groups_Ouminus__class_Ouminus(U_11009)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11009),U_11010)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11009),hAPP(c_Groups_Ouminus__class_Ouminus(U_11009),U_11010))
    | ~ class_Groups_Oordered__ab__group__add(U_11009) ),
    inference(clausify,[status(thm)],[f_2951_2]) ).

fof(f_2952_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_2952_2,plain,
    ! [U_11013,U_11012,U_11011] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11011,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11011,U_11012,U_11013)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11011),U_11013)) = c_Orderings_Obot__class_Obot(tc_fun(U_11011,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11011) ),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

cnf(f_2952_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11011,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11011,U_11012,U_11013)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11011),U_11013)) = c_Orderings_Obot__class_Obot(tc_fun(U_11011,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11011) ),
    inference(clausify,[status(thm)],[f_2952_2]) ).

fof(f_2953_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_2953_2,plain,
    ! [U_11014] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11014)) = 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_11014)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11014)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

cnf(f_2953_3,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11014)) = 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_11014)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11014)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2953_2]) ).

fof(f_2954_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_2954_2,plain,
    ! [U_11015] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11015) = 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_11015))),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

cnf(f_2954_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_11015) = 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_11015))),
    inference(clausify,[status(thm)],[f_2954_2]) ).

fof(f_2955_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_2955_2,plain,
    ! [U_11018,U_11017,U_11016] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11016),U_11018),U_11017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_11016),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_11016,tc_Nat_Onat),U_11018),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11017))
      | ~ c_Nat__Transfer_Onat__set(U_11017)
      | ~ class_Groups_Ocomm__monoid__mult(U_11016)
      | ~ class_Groups_Ocomm__monoid__add(U_11016) ),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

cnf(f_2955_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11016),U_11018),U_11017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_11016),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_11016,tc_Nat_Onat),U_11018),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11017))
    | ~ c_Nat__Transfer_Onat__set(U_11017)
    | ~ class_Groups_Ocomm__monoid__mult(U_11016)
    | ~ class_Groups_Ocomm__monoid__add(U_11016) ),
    inference(clausify,[status(thm)],[f_2955_2]) ).

fof(f_2956_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_2956_2,plain,
    ! [U_11024,U_11023,U_11022,U_11021,U_11020,U_11019] :
      ( ( hAPP(c_Set_Oimage(U_11019,U_11022,c_Fun_Ofun__upd(U_11019,U_11022,U_11023,U_11020,U_11024)),U_11021) = hAPP(c_Set_Oimage(U_11019,U_11022,U_11023),U_11021)
        | hBOOL(hAPP(hAPP(c_member(U_11019),U_11020),U_11021)) )
      & ( hAPP(c_Set_Oimage(U_11019,U_11022,c_Fun_Ofun__upd(U_11019,U_11022,U_11023,U_11020,U_11024)),U_11021) = hAPP(hAPP(c_Set_Oinsert(U_11022),U_11024),hAPP(c_Set_Oimage(U_11019,U_11022,U_11023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11019,tc_HOL_Obool)),U_11021),hAPP(hAPP(c_Set_Oinsert(U_11019),U_11020),c_Orderings_Obot__class_Obot(tc_fun(U_11019,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11019),U_11020),U_11021)) ) ),
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

fof(f_2956_3,plain,
    ( ! [U_11036,U_11034,U_11032,U_11030,U_11028,U_11026] :
        ( hAPP(c_Set_Oimage(U_11026,U_11032,c_Fun_Ofun__upd(U_11026,U_11032,U_11034,U_11028,U_11036)),U_11030) = hAPP(c_Set_Oimage(U_11026,U_11032,U_11034),U_11030)
        | hBOOL(hAPP(hAPP(c_member(U_11026),U_11028),U_11030)) )
    & ! [U_11035,U_11033,U_11031,U_11029,U_11027,U_11025] :
        ( hAPP(c_Set_Oimage(U_11025,U_11031,c_Fun_Ofun__upd(U_11025,U_11031,U_11033,U_11027,U_11035)),U_11029) = hAPP(hAPP(c_Set_Oinsert(U_11031),U_11035),hAPP(c_Set_Oimage(U_11025,U_11031,U_11033),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11025,tc_HOL_Obool)),U_11029),hAPP(hAPP(c_Set_Oinsert(U_11025),U_11027),c_Orderings_Obot__class_Obot(tc_fun(U_11025,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11025),U_11027),U_11029)) ) ),
    inference(miniscope,[status(thm)],[f_2956_2]) ).

cnf(f_2956_4,plain,
    ( hAPP(c_Set_Oimage(U_11025,U_11031,c_Fun_Ofun__upd(U_11025,U_11031,U_11033,U_11027,U_11035)),U_11029) = hAPP(hAPP(c_Set_Oinsert(U_11031),U_11035),hAPP(c_Set_Oimage(U_11025,U_11031,U_11033),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11025,tc_HOL_Obool)),U_11029),hAPP(hAPP(c_Set_Oinsert(U_11025),U_11027),c_Orderings_Obot__class_Obot(tc_fun(U_11025,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11025),U_11027),U_11029)) ),
    inference(clausify,[status(thm)],[f_2956_3]) ).

cnf(f_2956_5,plain,
    ( hAPP(c_Set_Oimage(U_11026,U_11032,c_Fun_Ofun__upd(U_11026,U_11032,U_11034,U_11028,U_11036)),U_11030) = hAPP(c_Set_Oimage(U_11026,U_11032,U_11034),U_11030)
    | hBOOL(hAPP(hAPP(c_member(U_11026),U_11028),U_11030)) ),
    inference(clausify,[status(thm)],[f_2956_3]) ).

fof(f_2957_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_2957_2,plain,
    ! [U_11038,U_11037] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11037),U_11038) = 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_11037)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11038)))
      | ~ c_Nat__Transfer_Onat__set(U_11038)
      | ~ c_Nat__Transfer_Onat__set(U_11037) ),
    inference(variable_rename,[status(thm)],[f_2957_1]) ).

cnf(f_2957_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11037),U_11038) = 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_11037)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11038)))
    | ~ c_Nat__Transfer_Onat__set(U_11038)
    | ~ c_Nat__Transfer_Onat__set(U_11037) ),
    inference(clausify,[status(thm)],[f_2957_2]) ).

fof(f_2958_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_2958_2,plain,
    ! [U_11042,U_11041,U_11040,U_11039] : c_Fun_Ofun__upd(U_11039,U_11040,U_11041,U_11042,hAPP(U_11041,U_11042)) = U_11041,
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

cnf(f_2958_3,plain,
    c_Fun_Ofun__upd(U_11039,U_11040,U_11041,U_11042,hAPP(U_11041,U_11042)) = U_11041,
    inference(clausify,[status(thm)],[f_2958_2]) ).

fof(f_2959_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_2959_2,plain,
    ! [U_11044,U_11043] :
      ( ( ( U_11043 = U_11044
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11043) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11044) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11043) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11044)
          | U_11043 != U_11044 ) )
      | ~ c_Nat__Transfer_Onat__set(U_11044)
      | ~ c_Nat__Transfer_Onat__set(U_11043) ),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

cnf(f_2959_3,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11043) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11044)
    | U_11043 != U_11044
    | ~ c_Nat__Transfer_Onat__set(U_11044)
    | ~ c_Nat__Transfer_Onat__set(U_11043) ),
    inference(clausify,[status(thm)],[f_2959_2]) ).

cnf(f_2959_4,plain,
    ( U_11043 = U_11044
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11043) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11044)
    | ~ c_Nat__Transfer_Onat__set(U_11044)
    | ~ c_Nat__Transfer_Onat__set(U_11043) ),
    inference(clausify,[status(thm)],[f_2959_2]) ).

fof(f_2960_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_2960_2,plain,
    ! [U_11049,U_11048,U_11047,U_11046,U_11045] :
      ( ( c_Fun_Ofun__upd(U_11045,U_11046,U_11047,U_11048,U_11049) = U_11047
        | hAPP(U_11047,U_11048) != U_11049 )
      & ( hAPP(U_11047,U_11048) = U_11049
        | c_Fun_Ofun__upd(U_11045,U_11046,U_11047,U_11048,U_11049) != U_11047 ) ),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

fof(f_2960_3,plain,
    ( ! [U_11059,U_11057,U_11055] :
        ( ! [U_11053,U_11051] : c_Fun_Ofun__upd(U_11051,U_11053,U_11055,U_11057,U_11059) = U_11055
        | hAPP(U_11055,U_11057) != U_11059 )
    & ! [U_11058,U_11056,U_11054] :
        ( ! [U_11052,U_11050] : c_Fun_Ofun__upd(U_11050,U_11052,U_11054,U_11056,U_11058) != U_11054
        | hAPP(U_11054,U_11056) = U_11058 ) ),
    inference(miniscope,[status(thm)],[f_2960_2]) ).

cnf(f_2960_4,plain,
    ( c_Fun_Ofun__upd(U_11050,U_11052,U_11054,U_11056,U_11058) != U_11054
    | hAPP(U_11054,U_11056) = U_11058 ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

cnf(f_2960_5,plain,
    ( c_Fun_Ofun__upd(U_11051,U_11053,U_11055,U_11057,U_11059) = U_11055
    | hAPP(U_11055,U_11057) != U_11059 ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

fof(f_2961_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_2961_2,plain,
    ! [U_11065,U_11064,U_11063,U_11062,U_11061,U_11060] : c_Fun_Ofun__upd(U_11060,U_11061,c_Fun_Ofun__upd(U_11060,U_11061,U_11062,U_11063,U_11064),U_11063,U_11065) = c_Fun_Ofun__upd(U_11060,U_11061,U_11062,U_11063,U_11065),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

cnf(f_2961_3,plain,
    c_Fun_Ofun__upd(U_11060,U_11061,c_Fun_Ofun__upd(U_11060,U_11061,U_11062,U_11063,U_11064),U_11063,U_11065) = c_Fun_Ofun__upd(U_11060,U_11061,U_11062,U_11063,U_11065),
    inference(clausify,[status(thm)],[f_2961_2]) ).

fof(f_2962_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_2962_2,plain,
    ! [U_11070,U_11069,U_11068,U_11067,U_11066] : hAPP(c_Fun_Ofun__upd(U_11066,U_11067,U_11068,U_11069,U_11070),U_11069) = U_11070,
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

cnf(f_2962_3,plain,
    hAPP(c_Fun_Ofun__upd(U_11066,U_11067,U_11068,U_11069,U_11070),U_11069) = U_11070,
    inference(clausify,[status(thm)],[f_2962_2]) ).

fof(f_2963_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_2963_2,plain,
    ! [U_11076,U_11075,U_11074,U_11073,U_11072,U_11071] :
      ( ( hAPP(c_Fun_Ofun__upd(U_11073,U_11074,U_11075,U_11072,U_11076),U_11071) = hAPP(U_11075,U_11071)
        | U_11071 = U_11072 )
      & ( hAPP(c_Fun_Ofun__upd(U_11073,U_11074,U_11075,U_11072,U_11076),U_11071) = U_11076
        | U_11071 != U_11072 ) ),
    inference(variable_rename,[status(thm)],[f_2963_1]) ).

fof(f_2963_3,plain,
    ( ! [U_11088,U_11086,U_11084,U_11082,U_11080,U_11078] :
        ( hAPP(c_Fun_Ofun__upd(U_11082,U_11084,U_11086,U_11080,U_11088),U_11078) = hAPP(U_11086,U_11078)
        | U_11078 = U_11080 )
    & ! [U_11087,U_11085,U_11083,U_11081,U_11079,U_11077] :
        ( hAPP(c_Fun_Ofun__upd(U_11081,U_11083,U_11085,U_11079,U_11087),U_11077) = U_11087
        | U_11077 != U_11079 ) ),
    inference(miniscope,[status(thm)],[f_2963_2]) ).

cnf(f_2963_4,plain,
    ( hAPP(c_Fun_Ofun__upd(U_11081,U_11083,U_11085,U_11079,U_11087),U_11077) = U_11087
    | U_11077 != U_11079 ),
    inference(clausify,[status(thm)],[f_2963_3]) ).

cnf(f_2963_5,plain,
    ( hAPP(c_Fun_Ofun__upd(U_11082,U_11084,U_11086,U_11080,U_11088),U_11078) = hAPP(U_11086,U_11078)
    | U_11078 = U_11080 ),
    inference(clausify,[status(thm)],[f_2963_3]) ).

fof(f_2964_1,plain,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_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_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2)
      | V_a_2 = V_ca_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).

fof(f_2964_2,plain,
    ! [U_11095,U_11094,U_11093,U_11092,U_11091,U_11090,U_11089] :
      ( c_Fun_Ofun__upd(U_11091,U_11092,c_Fun_Ofun__upd(U_11091,U_11092,U_11093,U_11089,U_11094),U_11090,U_11095) = c_Fun_Ofun__upd(U_11091,U_11092,c_Fun_Ofun__upd(U_11091,U_11092,U_11093,U_11090,U_11095),U_11089,U_11094)
      | U_11089 = U_11090 ),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

cnf(f_2964_3,plain,
    ( c_Fun_Ofun__upd(U_11091,U_11092,c_Fun_Ofun__upd(U_11091,U_11092,U_11093,U_11089,U_11094),U_11090,U_11095) = c_Fun_Ofun__upd(U_11091,U_11092,c_Fun_Ofun__upd(U_11091,U_11092,U_11093,U_11090,U_11095),U_11089,U_11094)
    | U_11089 = U_11090 ),
    inference(clausify,[status(thm)],[f_2964_2]) ).

fof(f_2965_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_2965_2,plain,
    ! [U_11101,U_11100,U_11099,U_11098,U_11097,U_11096] :
      ( hAPP(c_Fun_Ofun__upd(U_11098,U_11099,U_11100,U_11097,U_11101),U_11096) = hAPP(U_11100,U_11096)
      | U_11096 = U_11097 ),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

cnf(f_2965_3,plain,
    ( hAPP(c_Fun_Ofun__upd(U_11098,U_11099,U_11100,U_11097,U_11101),U_11096) = hAPP(U_11100,U_11096)
    | U_11096 = U_11097 ),
    inference(clausify,[status(thm)],[f_2965_2]) ).

fof(f_2966_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_2966_2,plain,
    ! [U_11106,U_11105,U_11104,U_11103,U_11102] :
      ( c_Fun_Ofun__upd(U_11105,U_11106,U_11102,U_11103,U_11104) = U_11102
      | hAPP(U_11102,U_11103) != U_11104 ),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

cnf(f_2966_3,plain,
    ( c_Fun_Ofun__upd(U_11105,U_11106,U_11102,U_11103,U_11104) = U_11102
    | hAPP(U_11102,U_11103) != U_11104 ),
    inference(clausify,[status(thm)],[f_2966_2]) ).

fof(f_2967_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_2967_2,plain,
    ! [U_11112,U_11111,U_11110,U_11109,U_11108,U_11107] :
      ( ( hAPP(c_Fun_Ofun__upd(U_11109,U_11110,U_11111,U_11108,U_11112),U_11107) = hAPP(U_11111,U_11107)
        | U_11107 = U_11108 )
      & ( hAPP(c_Fun_Ofun__upd(U_11109,U_11110,U_11111,U_11108,U_11112),U_11107) = U_11112
        | U_11107 != U_11108 ) ),
    inference(variable_rename,[status(thm)],[f_2967_1]) ).

fof(f_2967_3,plain,
    ( ! [U_11124,U_11122,U_11120,U_11118,U_11116,U_11114] :
        ( hAPP(c_Fun_Ofun__upd(U_11118,U_11120,U_11122,U_11116,U_11124),U_11114) = hAPP(U_11122,U_11114)
        | U_11114 = U_11116 )
    & ! [U_11123,U_11121,U_11119,U_11117,U_11115,U_11113] :
        ( hAPP(c_Fun_Ofun__upd(U_11117,U_11119,U_11121,U_11115,U_11123),U_11113) = U_11123
        | U_11113 != U_11115 ) ),
    inference(miniscope,[status(thm)],[f_2967_2]) ).

cnf(f_2967_4,plain,
    ( hAPP(c_Fun_Ofun__upd(U_11117,U_11119,U_11121,U_11115,U_11123),U_11113) = U_11123
    | U_11113 != U_11115 ),
    inference(clausify,[status(thm)],[f_2967_3]) ).

cnf(f_2967_5,plain,
    ( hAPP(c_Fun_Ofun__upd(U_11118,U_11120,U_11122,U_11116,U_11124),U_11114) = hAPP(U_11122,U_11114)
    | U_11114 = U_11116 ),
    inference(clausify,[status(thm)],[f_2967_3]) ).

fof(f_2968_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_2968_2,plain,
    ! [U_11126,U_11125] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11125),U_11126))
      | ~ c_Nat__Transfer_Onat__set(U_11126)
      | ~ c_Nat__Transfer_Onat__set(U_11125) ),
    inference(variable_rename,[status(thm)],[f_2968_1]) ).

cnf(f_2968_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11125),U_11126))
    | ~ c_Nat__Transfer_Onat__set(U_11126)
    | ~ c_Nat__Transfer_Onat__set(U_11125) ),
    inference(clausify,[status(thm)],[f_2968_2]) ).

fof(f_2969_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_2969_2,plain,
    ! [U_11128,U_11127] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11127),U_11128))
      | ~ c_Nat__Transfer_Onat__set(U_11128)
      | ~ c_Nat__Transfer_Onat__set(U_11127) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

cnf(f_2969_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11127),U_11128))
    | ~ c_Nat__Transfer_Onat__set(U_11128)
    | ~ c_Nat__Transfer_Onat__set(U_11127) ),
    inference(clausify,[status(thm)],[f_2969_2]) ).

fof(f_2970_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_2970_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_2970_1]) ).

fof(f_2971_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_2971_2,plain,
    ! [U_11131] :
      ( ( c_Nat__Transfer_Onat__set(U_11131)
        | ? [U_11130] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11130))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11130),U_11131)) ) )
      & ( ! [U_11129] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11129))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11129),U_11131)) )
        | ~ c_Nat__Transfer_Onat__set(U_11131) ) ),
    inference(variable_rename,[status(thm)],[f_2971_1]) ).

fof(f_2971_3,plain,
    ( ! [U_11133] :
        ( c_Nat__Transfer_Onat__set(U_11133)
        | ? [U_11130] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11130))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11130),U_11133)) ) )
    & ! [U_11132] :
        ( ! [U_11129] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11129))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11129),U_11132)) )
        | ~ c_Nat__Transfer_Onat__set(U_11132) ) ),
    inference(miniscope,[status(thm)],[f_2971_2]) ).

fof(f_2971_4,plain,
    ( ! [U_11133] :
        ( c_Nat__Transfer_Onat__set(U_11133)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK242(U_11133)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK242(U_11133)),U_11133)) ) )
    & ! [U_11132] :
        ( ! [U_11129] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11129))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11129),U_11132)) )
        | ~ c_Nat__Transfer_Onat__set(U_11132) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_11130,sK242(U_11133))],[f_2971_3]) ).

cnf(f_2971_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11129))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11129),U_11132))
    | ~ c_Nat__Transfer_Onat__set(U_11132) ),
    inference(clausify,[status(thm)],[f_2971_4]) ).

cnf(f_2971_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK242(U_11133)),U_11133))
    | c_Nat__Transfer_Onat__set(U_11133) ),
    inference(clausify,[status(thm)],[f_2971_4]) ).

cnf(f_2971_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK242(U_11133)))
    | c_Nat__Transfer_Onat__set(U_11133) ),
    inference(clausify,[status(thm)],[f_2971_4]) ).

fof(f_2972_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_2972_2,plain,
    ! [U_11134] : 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_11134)),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

cnf(f_2972_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_11134)),
    inference(clausify,[status(thm)],[f_2972_2]) ).

fof(f_2973_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_2973_2,plain,
    ! [U_11136,U_11135] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11135,U_11136))
      | ~ c_Nat__Transfer_Ois__nat(U_11135) ),
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

cnf(f_2973_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11135,U_11136))
    | ~ c_Nat__Transfer_Ois__nat(U_11135) ),
    inference(clausify,[status(thm)],[f_2973_2]) ).

fof(f_2974_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_2974_2,plain,
    ! [U_11138,U_11137] :
      ( c_Nat__Transfer_Ois__nat(U_11138)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11138),U_11137))
      | ~ c_Nat__Transfer_Onat__set(U_11137) ),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

cnf(f_2974_3,plain,
    ( c_Nat__Transfer_Ois__nat(U_11138)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11138),U_11137))
    | ~ c_Nat__Transfer_Onat__set(U_11137) ),
    inference(clausify,[status(thm)],[f_2974_2]) ).

fof(f_2975_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_2975_2,plain,
    ! [U_11140,U_11139] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11139,U_11140))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11139)) ),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

cnf(f_2975_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11139,U_11140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11139)) ),
    inference(clausify,[status(thm)],[f_2975_2]) ).

fof(f_2976_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_2976_2,plain,
    ! [U_11141] :
      ( 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_11141)) = U_11141
      | ~ c_Nat__Transfer_Onat__set(U_11141) ),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

cnf(f_2976_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_11141)) = U_11141
    | ~ c_Nat__Transfer_Onat__set(U_11141) ),
    inference(clausify,[status(thm)],[f_2976_2]) ).

fof(f_2977_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_2977_2,plain,
    ! [U_11143,U_11142] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11142),U_11143) = 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_11142)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11143)))
      | ~ c_Nat__Transfer_Onat__set(U_11143)
      | ~ c_Nat__Transfer_Onat__set(U_11142) ),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

cnf(f_2977_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11142),U_11143) = 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_11142)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11143)))
    | ~ c_Nat__Transfer_Onat__set(U_11143)
    | ~ c_Nat__Transfer_Onat__set(U_11142) ),
    inference(clausify,[status(thm)],[f_2977_2]) ).

fof(f_2978_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_2978_2,plain,
    ! [U_11145,U_11144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11145))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11145),U_11144))
      | ~ c_Nat__Transfer_Onat__set(U_11144) ),
    inference(variable_rename,[status(thm)],[f_2978_1]) ).

cnf(f_2978_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11145))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11145),U_11144))
    | ~ c_Nat__Transfer_Onat__set(U_11144) ),
    inference(clausify,[status(thm)],[f_2978_2]) ).

fof(f_2979_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_2979_2,plain,
    ! [U_11146] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_11146))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11146))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11146)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_11146)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_11146) ),
    inference(variable_rename,[status(thm)],[f_2979_1]) ).

cnf(f_2979_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_11146)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_11146))
    | ~ c_Nat__Transfer_Onat__set(U_11146) ),
    inference(clausify,[status(thm)],[f_2979_2]) ).

cnf(f_2979_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_11146))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11146)))
    | ~ c_Nat__Transfer_Onat__set(U_11146) ),
    inference(clausify,[status(thm)],[f_2979_2]) ).

fof(f_2980_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_2980_2,plain,
    ! [U_11147] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_11147) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11147))
      | ~ c_Nat__Transfer_Onat__set(U_11147) ),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

cnf(f_2980_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_11147) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11147))
    | ~ c_Nat__Transfer_Onat__set(U_11147) ),
    inference(clausify,[status(thm)],[f_2980_2]) ).

fof(f_2981_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_2981_2,plain,
    ! [U_11149,U_11148] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11148),U_11149))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_11148)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11149))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_11148)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11149)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11148),U_11149)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_11149)
      | ~ c_Nat__Transfer_Ois__nat(U_11148) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

cnf(f_2981_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_11148)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11149)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11148),U_11149))
    | ~ c_Nat__Transfer_Onat__set(U_11149)
    | ~ c_Nat__Transfer_Ois__nat(U_11148) ),
    inference(clausify,[status(thm)],[f_2981_2]) ).

cnf(f_2981_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11148),U_11149))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_11148)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11149)))
    | ~ c_Nat__Transfer_Onat__set(U_11149)
    | ~ c_Nat__Transfer_Ois__nat(U_11148) ),
    inference(clausify,[status(thm)],[f_2981_2]) ).

fof(f_2982_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_2982_2,plain,
    ! [U_11151,U_11150] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11150),U_11151))
          | ~ 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_11150)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11151))) )
        & ( 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_11150)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11151)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11150),U_11151)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_11151)
      | ~ c_Nat__Transfer_Onat__set(U_11150) ),
    inference(variable_rename,[status(thm)],[f_2982_1]) ).

cnf(f_2982_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_11150)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11151)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11150),U_11151))
    | ~ c_Nat__Transfer_Onat__set(U_11151)
    | ~ c_Nat__Transfer_Onat__set(U_11150) ),
    inference(clausify,[status(thm)],[f_2982_2]) ).

cnf(f_2982_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11150),U_11151))
    | ~ 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_11150)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11151)))
    | ~ c_Nat__Transfer_Onat__set(U_11151)
    | ~ c_Nat__Transfer_Onat__set(U_11150) ),
    inference(clausify,[status(thm)],[f_2982_2]) ).

fof(f_2983_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_2983_2,plain,
    ! [U_11153,U_11152] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11152),U_11153))
          | ~ 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_11152)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11153))) )
        & ( 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_11152)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11153)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11152),U_11153)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_11153)
      | ~ c_Nat__Transfer_Onat__set(U_11152) ),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

cnf(f_2983_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_11152)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11152),U_11153))
    | ~ c_Nat__Transfer_Onat__set(U_11153)
    | ~ c_Nat__Transfer_Onat__set(U_11152) ),
    inference(clausify,[status(thm)],[f_2983_2]) ).

cnf(f_2983_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11152),U_11153))
    | ~ 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_11152)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11153)))
    | ~ c_Nat__Transfer_Onat__set(U_11153)
    | ~ c_Nat__Transfer_Onat__set(U_11152) ),
    inference(clausify,[status(thm)],[f_2983_2]) ).

fof(f_2984_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_2984_2,plain,
    ! [U_11156,U_11155,U_11154] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11154),U_11156),U_11155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_11154),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_11154,tc_Nat_Onat),U_11156),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11155))
      | ~ c_Nat__Transfer_Onat__set(U_11155)
      | ~ class_Groups_Ocomm__monoid__mult(U_11154)
      | ~ class_Groups_Ocomm__monoid__add(U_11154) ),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

cnf(f_2984_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11154),U_11156),U_11155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_11154),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_11154,tc_Nat_Onat),U_11156),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11155))
    | ~ c_Nat__Transfer_Onat__set(U_11155)
    | ~ class_Groups_Ocomm__monoid__mult(U_11154)
    | ~ class_Groups_Ocomm__monoid__add(U_11154) ),
    inference(clausify,[status(thm)],[f_2984_2]) ).

fof(f_2985_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_2985_2,plain,
    ! [U_11157] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11157)) = 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_11157)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11157),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

cnf(f_2985_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11157)) = 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_11157)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11157),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2985_2]) ).

fof(f_2986_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_2986_2,plain,
    ! [U_11162,U_11161,U_11160] :
      ( hAPP(U_11161,c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),U_11162)) = c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),hAPP(c_Set_Oimage(U_11160,U_11160,U_11161),U_11162))
      | U_11162 = c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11162))
      | ? [U_11159,U_11158] : hAPP(U_11161,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),U_11159),U_11158)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),hAPP(U_11161,U_11159)),hAPP(U_11161,U_11158))
      | ~ class_Orderings_Olinorder(U_11160) ),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

fof(f_2986_3,plain,
    ! [U_11162,U_11161,U_11160] :
      ( hAPP(U_11161,c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),U_11162)) = c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),hAPP(c_Set_Oimage(U_11160,U_11160,U_11161),U_11162))
      | U_11162 = c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11162))
      | ? [U_11158] : hAPP(U_11161,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),sK243(U_11162,U_11161,U_11160)),U_11158)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),hAPP(U_11161,sK243(U_11162,U_11161,U_11160))),hAPP(U_11161,U_11158))
      | ~ class_Orderings_Olinorder(U_11160) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_11159,sK243(U_11162,U_11161,U_11160))],[f_2986_2]) ).

fof(f_2986_4,plain,
    ! [U_11162,U_11161,U_11160] :
      ( hAPP(U_11161,c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),U_11162)) = c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),hAPP(c_Set_Oimage(U_11160,U_11160,U_11161),U_11162))
      | U_11162 = c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11162))
      | hAPP(U_11161,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),sK243(U_11162,U_11161,U_11160)),sK244(U_11162,U_11161,U_11160))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),hAPP(U_11161,sK243(U_11162,U_11161,U_11160))),hAPP(U_11161,sK244(U_11162,U_11161,U_11160)))
      | ~ class_Orderings_Olinorder(U_11160) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_11158,sK244(U_11162,U_11161,U_11160))],[f_2986_3]) ).

cnf(f_2986_5,plain,
    ( hAPP(U_11161,c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),U_11162)) = c_Big__Operators_Olattice_OInf__fin(U_11160,c_Orderings_Oord__class_Omin(U_11160),hAPP(c_Set_Oimage(U_11160,U_11160,U_11161),U_11162))
    | U_11162 = c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11162))
    | hAPP(U_11161,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),sK243(U_11162,U_11161,U_11160)),sK244(U_11162,U_11161,U_11160))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11160),hAPP(U_11161,sK243(U_11162,U_11161,U_11160))),hAPP(U_11161,sK244(U_11162,U_11161,U_11160)))
    | ~ class_Orderings_Olinorder(U_11160) ),
    inference(clausify,[status(thm)],[f_2986_4]) ).

fof(f_2987_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_2987_2,plain,
    ! [U_11167,U_11166,U_11165] :
      ( hAPP(U_11166,c_Big__Operators_Olinorder__class_OMax(U_11165,U_11167)) = c_Big__Operators_Olinorder__class_OMax(U_11165,hAPP(c_Set_Oimage(U_11165,U_11165,U_11166),U_11167))
      | U_11167 = c_Orderings_Obot__class_Obot(tc_fun(U_11165,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),U_11167))
      | ? [U_11164,U_11163] : hAPP(U_11166,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),U_11164),U_11163)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),hAPP(U_11166,U_11164)),hAPP(U_11166,U_11163))
      | ~ class_Orderings_Olinorder(U_11165) ),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

fof(f_2987_3,plain,
    ! [U_11167,U_11166,U_11165] :
      ( hAPP(U_11166,c_Big__Operators_Olinorder__class_OMax(U_11165,U_11167)) = c_Big__Operators_Olinorder__class_OMax(U_11165,hAPP(c_Set_Oimage(U_11165,U_11165,U_11166),U_11167))
      | U_11167 = c_Orderings_Obot__class_Obot(tc_fun(U_11165,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),U_11167))
      | ? [U_11163] : hAPP(U_11166,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),sK245(U_11167,U_11166,U_11165)),U_11163)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),hAPP(U_11166,sK245(U_11167,U_11166,U_11165))),hAPP(U_11166,U_11163))
      | ~ class_Orderings_Olinorder(U_11165) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_11164,sK245(U_11167,U_11166,U_11165))],[f_2987_2]) ).

fof(f_2987_4,plain,
    ! [U_11167,U_11166,U_11165] :
      ( hAPP(U_11166,c_Big__Operators_Olinorder__class_OMax(U_11165,U_11167)) = c_Big__Operators_Olinorder__class_OMax(U_11165,hAPP(c_Set_Oimage(U_11165,U_11165,U_11166),U_11167))
      | U_11167 = c_Orderings_Obot__class_Obot(tc_fun(U_11165,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),U_11167))
      | hAPP(U_11166,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),sK245(U_11167,U_11166,U_11165)),sK246(U_11167,U_11166,U_11165))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),hAPP(U_11166,sK245(U_11167,U_11166,U_11165))),hAPP(U_11166,sK246(U_11167,U_11166,U_11165)))
      | ~ class_Orderings_Olinorder(U_11165) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_11163,sK246(U_11167,U_11166,U_11165))],[f_2987_3]) ).

cnf(f_2987_5,plain,
    ( hAPP(U_11166,c_Big__Operators_Olinorder__class_OMax(U_11165,U_11167)) = c_Big__Operators_Olinorder__class_OMax(U_11165,hAPP(c_Set_Oimage(U_11165,U_11165,U_11166),U_11167))
    | U_11167 = c_Orderings_Obot__class_Obot(tc_fun(U_11165,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11165),U_11167))
    | hAPP(U_11166,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),sK245(U_11167,U_11166,U_11165)),sK246(U_11167,U_11166,U_11165))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11165),hAPP(U_11166,sK245(U_11167,U_11166,U_11165))),hAPP(U_11166,sK246(U_11167,U_11166,U_11165)))
    | ~ class_Orderings_Olinorder(U_11165) ),
    inference(clausify,[status(thm)],[f_2987_4]) ).

fof(f_2988_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_2988_2,plain,
    ! [U_11170,U_11169,U_11168] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11169) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11170)
          | U_11169 != U_11170 )
        & ( U_11169 = U_11170
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11169) != hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11170) ) )
      | ~ class_Orderings_Olinorder(U_11168) ),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

cnf(f_2988_3,plain,
    ( U_11169 = U_11170
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11169) != hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11170)
    | ~ class_Orderings_Olinorder(U_11168) ),
    inference(clausify,[status(thm)],[f_2988_2]) ).

cnf(f_2988_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11169) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11168),U_11170)
    | U_11169 != U_11170
    | ~ class_Orderings_Olinorder(U_11168) ),
    inference(clausify,[status(thm)],[f_2988_2]) ).

fof(f_2989_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_2989_2,plain,
    ! [U_11173,U_11172,U_11171] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11171),U_11172),hAPP(c_SetInterval_Oord__class_OatLeast(U_11171),U_11173)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11171),U_11173),U_11172)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11171),U_11173),U_11172))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11171),U_11172),hAPP(c_SetInterval_Oord__class_OatLeast(U_11171),U_11173))) ) )
      | ~ class_Orderings_Oord(U_11171) ),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

cnf(f_2989_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11171),U_11173),U_11172))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11171),U_11172),hAPP(c_SetInterval_Oord__class_OatLeast(U_11171),U_11173)))
    | ~ class_Orderings_Oord(U_11171) ),
    inference(clausify,[status(thm)],[f_2989_2]) ).

cnf(f_2989_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11171),U_11172),hAPP(c_SetInterval_Oord__class_OatLeast(U_11171),U_11173)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11171),U_11173),U_11172))
    | ~ class_Orderings_Oord(U_11171) ),
    inference(clausify,[status(thm)],[f_2989_2]) ).

fof(f_2990_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_2990_2,plain,
    ! [U_11176,U_11175,U_11174] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11175)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11176)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11174),U_11176),U_11175)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11174),U_11176),U_11175))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11175)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11176))) ) )
      | ~ class_Orderings_Oorder(U_11174) ),
    inference(variable_rename,[status(thm)],[f_2990_1]) ).

cnf(f_2990_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11174),U_11176),U_11175))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11175)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11176)))
    | ~ class_Orderings_Oorder(U_11174) ),
    inference(clausify,[status(thm)],[f_2990_2]) ).

cnf(f_2990_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11175)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11174),U_11176)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11174),U_11176),U_11175))
    | ~ class_Orderings_Oorder(U_11174) ),
    inference(clausify,[status(thm)],[f_2990_2]) ).

fof(f_2991_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_2991_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_2991_1]) ).

fof(f_2992_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_2992_2,plain,
    ! [U_11178,U_11177] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11177,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11177),U_11178)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11177),U_11178)
      | ~ class_Orderings_Olinorder(U_11177) ),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

cnf(f_2992_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11177,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11177),U_11178)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11177),U_11178)
    | ~ class_Orderings_Olinorder(U_11177) ),
    inference(clausify,[status(thm)],[f_2992_2]) ).

fof(f_2993_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_2993_2,plain,
    ! [U_11180,U_11179] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11179,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11179),U_11180)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11179),U_11180)
      | ~ class_Orderings_Olinorder(U_11179) ),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

cnf(f_2993_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11179,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11179),U_11180)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_11179),U_11180)
    | ~ class_Orderings_Olinorder(U_11179) ),
    inference(clausify,[status(thm)],[f_2993_2]) ).

fof(f_2994_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_2994_2,plain,
    ! [U_11181] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11181)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_11181),
    inference(variable_rename,[status(thm)],[f_2994_1]) ).

cnf(f_2994_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11181)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_11181),
    inference(clausify,[status(thm)],[f_2994_2]) ).

fof(f_2995_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_2995_2,plain,
    ! [U_11184,U_11183,U_11182] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11182,U_11183),U_11184)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11182),U_11184)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11182),U_11183)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11182),U_11183),U_11184))
      | ~ class_Orderings_Olinorder(U_11182) ),
    inference(variable_rename,[status(thm)],[f_2995_1]) ).

cnf(f_2995_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11182,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11182,U_11183),U_11184)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11182),U_11184)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11182),U_11183)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11182),U_11183),U_11184))
    | ~ class_Orderings_Olinorder(U_11182) ),
    inference(clausify,[status(thm)],[f_2995_2]) ).

fof(f_2996_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_2996_2,plain,
    ! [U_11187,U_11186,U_11185] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11185,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11185,U_11186),U_11187)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11185),U_11187)) = c_Orderings_Obot__class_Obot(tc_fun(U_11185,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11185) ),
    inference(variable_rename,[status(thm)],[f_2996_1]) ).

cnf(f_2996_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11185,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11185,U_11186),U_11187)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11185),U_11187)) = c_Orderings_Obot__class_Obot(tc_fun(U_11185,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11185) ),
    inference(clausify,[status(thm)],[f_2996_2]) ).

fof(f_2997_1,plain,
    ! [V_d_2,V_ca_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_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).

fof(f_2997_2,plain,
    ! [U_11191,U_11190,U_11189,U_11188] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11188,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11188),U_11189)),c_SetInterval_Oord__class_OatLeastAtMost(U_11188,U_11190,U_11191)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11188,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11188),U_11189),U_11190),U_11191)
      | ~ class_Orderings_Olinorder(U_11188) ),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

cnf(f_2997_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11188,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11188),U_11189)),c_SetInterval_Oord__class_OatLeastAtMost(U_11188,U_11190,U_11191)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11188,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11188),U_11189),U_11190),U_11191)
    | ~ class_Orderings_Olinorder(U_11188) ),
    inference(clausify,[status(thm)],[f_2997_2]) ).

fof(f_2998_1,plain,
    ! [V_ca_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_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).

fof(f_2998_2,plain,
    ! [U_11195,U_11194,U_11193,U_11192] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11192,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11192,U_11193,U_11194)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11192),U_11195)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11192,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11192),U_11193),U_11195),U_11194)
      | ~ class_Orderings_Olinorder(U_11192) ),
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

cnf(f_2998_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11192,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11192,U_11193,U_11194)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11192),U_11195)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11192,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11192),U_11193),U_11195),U_11194)
    | ~ class_Orderings_Olinorder(U_11192) ),
    inference(clausify,[status(thm)],[f_2998_2]) ).

fof(f_2999_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_2999_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_2999_1]) ).

fof(f_3000_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_3000_2,plain,
    ! [U_11198,U_11197,U_11196] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11196,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11196,U_11197,U_11198)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11196),U_11198)) = c_Orderings_Obot__class_Obot(tc_fun(U_11196,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11196) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

cnf(f_3000_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11196,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11196,U_11197,U_11198)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11196),U_11198)) = c_Orderings_Obot__class_Obot(tc_fun(U_11196,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11196) ),
    inference(clausify,[status(thm)],[f_3000_2]) ).

fof(f_3001_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_3001_2,plain,
    ! [U_11200,U_11199] :
      ( hAPP(c_Set_Oimage(U_11199,U_11199,c_Groups_Ouminus__class_Ouminus(U_11199)),hAPP(c_SetInterval_Oord__class_OatMost(U_11199),U_11200)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11199),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11200))
      | ~ class_Groups_Oordered__ab__group__add(U_11199) ),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

cnf(f_3001_3,plain,
    ( hAPP(c_Set_Oimage(U_11199,U_11199,c_Groups_Ouminus__class_Ouminus(U_11199)),hAPP(c_SetInterval_Oord__class_OatMost(U_11199),U_11200)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11199),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11200))
    | ~ class_Groups_Oordered__ab__group__add(U_11199) ),
    inference(clausify,[status(thm)],[f_3001_2]) ).

fof(f_3002_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_3002_2,plain,
    ! [U_11202,U_11201] :
      ( hAPP(c_Set_Oimage(U_11201,U_11201,c_Groups_Ouminus__class_Ouminus(U_11201)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11201),U_11202)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11201),hAPP(c_Groups_Ouminus__class_Ouminus(U_11201),U_11202))
      | ~ class_Groups_Oordered__ab__group__add(U_11201) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

cnf(f_3002_3,plain,
    ( hAPP(c_Set_Oimage(U_11201,U_11201,c_Groups_Ouminus__class_Ouminus(U_11201)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11201),U_11202)) = hAPP(c_SetInterval_Oord__class_OatMost(U_11201),hAPP(c_Groups_Ouminus__class_Ouminus(U_11201),U_11202))
    | ~ class_Groups_Oordered__ab__group__add(U_11201) ),
    inference(clausify,[status(thm)],[f_3002_2]) ).

fof(f_3003_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_3003_2,plain,
    ! [U_11204,U_11203] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11203,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11203),U_11204)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11203),U_11204)) = hAPP(hAPP(c_Set_Oinsert(U_11203),U_11204),c_Orderings_Obot__class_Obot(tc_fun(U_11203,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11203) ),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

cnf(f_3003_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11203,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11203),U_11204)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11203),U_11204)) = hAPP(hAPP(c_Set_Oinsert(U_11203),U_11204),c_Orderings_Obot__class_Obot(tc_fun(U_11203,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_11203) ),
    inference(clausify,[status(thm)],[f_3003_2]) ).

fof(f_3004_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_3004_2,plain,
    ! [U_11206,U_11205] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),c_Orderings_Obot__class_Obot(tc_fun(U_11205,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11205),U_11206)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11205),U_11206)
      | ~ class_Orderings_Olinorder(U_11205) ),
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

cnf(f_3004_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),c_Orderings_Obot__class_Obot(tc_fun(U_11205,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11205),U_11206)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11205),U_11206)
    | ~ class_Orderings_Olinorder(U_11205) ),
    inference(clausify,[status(thm)],[f_3004_2]) ).

fof(f_3005_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_3005_2,plain,
    ! [U_11209,U_11208,U_11207] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11207,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11207,U_11208,U_11209)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11207),U_11209)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11207),U_11208)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11207),U_11208),U_11209))
      | ~ class_Orderings_Olinorder(U_11207) ),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

cnf(f_3005_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11207,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11207,U_11208,U_11209)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11207),U_11209)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_11207),U_11208)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11207),U_11208),U_11209))
    | ~ class_Orderings_Olinorder(U_11207) ),
    inference(clausify,[status(thm)],[f_3005_2]) ).

fof(f_3006_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_3006_2,plain,
    ! [U_11212,U_11211,U_11210] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11210,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11210,U_11211,U_11212)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11210),U_11212)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11210),U_11211)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11210),U_11211),U_11212))
      | ~ class_Orderings_Olinorder(U_11210) ),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

cnf(f_3006_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11210,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11210,U_11211,U_11212)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11210),U_11212)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11210),U_11211)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11210),U_11211),U_11212))
    | ~ class_Orderings_Olinorder(U_11210) ),
    inference(clausify,[status(thm)],[f_3006_2]) ).

fof(f_3007_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_3007_2,plain,
    ! [U_11217,U_11216,U_11215] :
      ( hAPP(U_11216,c_Big__Operators_Olinorder__class_OMin(U_11215,U_11217)) = c_Big__Operators_Olinorder__class_OMin(U_11215,hAPP(c_Set_Oimage(U_11215,U_11215,U_11216),U_11217))
      | U_11217 = c_Orderings_Obot__class_Obot(tc_fun(U_11215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11215),U_11217))
      | ? [U_11214,U_11213] : hAPP(U_11216,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),U_11214),U_11213)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),hAPP(U_11216,U_11214)),hAPP(U_11216,U_11213))
      | ~ class_Orderings_Olinorder(U_11215) ),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

fof(f_3007_3,plain,
    ! [U_11217,U_11216,U_11215] :
      ( hAPP(U_11216,c_Big__Operators_Olinorder__class_OMin(U_11215,U_11217)) = c_Big__Operators_Olinorder__class_OMin(U_11215,hAPP(c_Set_Oimage(U_11215,U_11215,U_11216),U_11217))
      | U_11217 = c_Orderings_Obot__class_Obot(tc_fun(U_11215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11215),U_11217))
      | ? [U_11213] : hAPP(U_11216,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),sK247(U_11217,U_11216,U_11215)),U_11213)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),hAPP(U_11216,sK247(U_11217,U_11216,U_11215))),hAPP(U_11216,U_11213))
      | ~ class_Orderings_Olinorder(U_11215) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_11214,sK247(U_11217,U_11216,U_11215))],[f_3007_2]) ).

fof(f_3007_4,plain,
    ! [U_11217,U_11216,U_11215] :
      ( hAPP(U_11216,c_Big__Operators_Olinorder__class_OMin(U_11215,U_11217)) = c_Big__Operators_Olinorder__class_OMin(U_11215,hAPP(c_Set_Oimage(U_11215,U_11215,U_11216),U_11217))
      | U_11217 = c_Orderings_Obot__class_Obot(tc_fun(U_11215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11215),U_11217))
      | hAPP(U_11216,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),sK247(U_11217,U_11216,U_11215)),sK248(U_11217,U_11216,U_11215))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),hAPP(U_11216,sK247(U_11217,U_11216,U_11215))),hAPP(U_11216,sK248(U_11217,U_11216,U_11215)))
      | ~ class_Orderings_Olinorder(U_11215) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_11213,sK248(U_11217,U_11216,U_11215))],[f_3007_3]) ).

cnf(f_3007_5,plain,
    ( hAPP(U_11216,c_Big__Operators_Olinorder__class_OMin(U_11215,U_11217)) = c_Big__Operators_Olinorder__class_OMin(U_11215,hAPP(c_Set_Oimage(U_11215,U_11215,U_11216),U_11217))
    | U_11217 = c_Orderings_Obot__class_Obot(tc_fun(U_11215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11215),U_11217))
    | hAPP(U_11216,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),sK247(U_11217,U_11216,U_11215)),sK248(U_11217,U_11216,U_11215))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11215),hAPP(U_11216,sK247(U_11217,U_11216,U_11215))),hAPP(U_11216,sK248(U_11217,U_11216,U_11215)))
    | ~ class_Orderings_Olinorder(U_11215) ),
    inference(clausify,[status(thm)],[f_3007_4]) ).

fof(f_3008_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_3008_2,plain,
    ! [U_11222,U_11221,U_11220] :
      ( hAPP(U_11221,c_Big__Operators_Olattice__class_OInf__fin(U_11220,U_11222)) = c_Big__Operators_Olattice__class_OInf__fin(U_11220,hAPP(c_Set_Oimage(U_11220,U_11220,U_11221),U_11222))
      | U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
      | ? [U_11219,U_11218] : hAPP(U_11221,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),U_11219),U_11218)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),hAPP(U_11221,U_11219)),hAPP(U_11221,U_11218))
      | ~ class_Lattices_Olattice(U_11220) ),
    inference(variable_rename,[status(thm)],[f_3008_1]) ).

fof(f_3008_3,plain,
    ! [U_11222,U_11221,U_11220] :
      ( hAPP(U_11221,c_Big__Operators_Olattice__class_OInf__fin(U_11220,U_11222)) = c_Big__Operators_Olattice__class_OInf__fin(U_11220,hAPP(c_Set_Oimage(U_11220,U_11220,U_11221),U_11222))
      | U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
      | ? [U_11218] : hAPP(U_11221,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),sK249(U_11222,U_11221,U_11220)),U_11218)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),hAPP(U_11221,sK249(U_11222,U_11221,U_11220))),hAPP(U_11221,U_11218))
      | ~ class_Lattices_Olattice(U_11220) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_11219,sK249(U_11222,U_11221,U_11220))],[f_3008_2]) ).

fof(f_3008_4,plain,
    ! [U_11222,U_11221,U_11220] :
      ( hAPP(U_11221,c_Big__Operators_Olattice__class_OInf__fin(U_11220,U_11222)) = c_Big__Operators_Olattice__class_OInf__fin(U_11220,hAPP(c_Set_Oimage(U_11220,U_11220,U_11221),U_11222))
      | U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
      | hAPP(U_11221,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),sK249(U_11222,U_11221,U_11220)),sK250(U_11222,U_11221,U_11220))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),hAPP(U_11221,sK249(U_11222,U_11221,U_11220))),hAPP(U_11221,sK250(U_11222,U_11221,U_11220)))
      | ~ class_Lattices_Olattice(U_11220) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_11218,sK250(U_11222,U_11221,U_11220))],[f_3008_3]) ).

cnf(f_3008_5,plain,
    ( hAPP(U_11221,c_Big__Operators_Olattice__class_OInf__fin(U_11220,U_11222)) = c_Big__Operators_Olattice__class_OInf__fin(U_11220,hAPP(c_Set_Oimage(U_11220,U_11220,U_11221),U_11222))
    | U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
    | hAPP(U_11221,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),sK249(U_11222,U_11221,U_11220)),sK250(U_11222,U_11221,U_11220))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11220),hAPP(U_11221,sK249(U_11222,U_11221,U_11220))),hAPP(U_11221,sK250(U_11222,U_11221,U_11220)))
    | ~ class_Lattices_Olattice(U_11220) ),
    inference(clausify,[status(thm)],[f_3008_4]) ).

fof(f_3009_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_3009_2,plain,
    ! [U_11227,U_11226,U_11225] :
      ( hAPP(U_11226,c_Big__Operators_Olattice__class_OSup__fin(U_11225,U_11227)) = c_Big__Operators_Olattice__class_OSup__fin(U_11225,hAPP(c_Set_Oimage(U_11225,U_11225,U_11226),U_11227))
      | U_11227 = c_Orderings_Obot__class_Obot(tc_fun(U_11225,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11225),U_11227))
      | ? [U_11224,U_11223] : hAPP(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),U_11224),U_11223)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),hAPP(U_11226,U_11224)),hAPP(U_11226,U_11223))
      | ~ class_Lattices_Olattice(U_11225) ),
    inference(variable_rename,[status(thm)],[f_3009_1]) ).

fof(f_3009_3,plain,
    ! [U_11227,U_11226,U_11225] :
      ( hAPP(U_11226,c_Big__Operators_Olattice__class_OSup__fin(U_11225,U_11227)) = c_Big__Operators_Olattice__class_OSup__fin(U_11225,hAPP(c_Set_Oimage(U_11225,U_11225,U_11226),U_11227))
      | U_11227 = c_Orderings_Obot__class_Obot(tc_fun(U_11225,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11225),U_11227))
      | ? [U_11223] : hAPP(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),sK251(U_11227,U_11226,U_11225)),U_11223)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),hAPP(U_11226,sK251(U_11227,U_11226,U_11225))),hAPP(U_11226,U_11223))
      | ~ class_Lattices_Olattice(U_11225) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_11224,sK251(U_11227,U_11226,U_11225))],[f_3009_2]) ).

fof(f_3009_4,plain,
    ! [U_11227,U_11226,U_11225] :
      ( hAPP(U_11226,c_Big__Operators_Olattice__class_OSup__fin(U_11225,U_11227)) = c_Big__Operators_Olattice__class_OSup__fin(U_11225,hAPP(c_Set_Oimage(U_11225,U_11225,U_11226),U_11227))
      | U_11227 = c_Orderings_Obot__class_Obot(tc_fun(U_11225,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11225),U_11227))
      | hAPP(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),sK251(U_11227,U_11226,U_11225)),sK252(U_11227,U_11226,U_11225))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),hAPP(U_11226,sK251(U_11227,U_11226,U_11225))),hAPP(U_11226,sK252(U_11227,U_11226,U_11225)))
      | ~ class_Lattices_Olattice(U_11225) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_11223,sK252(U_11227,U_11226,U_11225))],[f_3009_3]) ).

cnf(f_3009_5,plain,
    ( hAPP(U_11226,c_Big__Operators_Olattice__class_OSup__fin(U_11225,U_11227)) = c_Big__Operators_Olattice__class_OSup__fin(U_11225,hAPP(c_Set_Oimage(U_11225,U_11225,U_11226),U_11227))
    | U_11227 = c_Orderings_Obot__class_Obot(tc_fun(U_11225,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11225),U_11227))
    | hAPP(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),sK251(U_11227,U_11226,U_11225)),sK252(U_11227,U_11226,U_11225))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11225),hAPP(U_11226,sK251(U_11227,U_11226,U_11225))),hAPP(U_11226,sK252(U_11227,U_11226,U_11225)))
    | ~ class_Lattices_Olattice(U_11225) ),
    inference(clausify,[status(thm)],[f_3009_4]) ).

fof(f_3010_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_3010_2,plain,
    ! [U_11232,U_11231,U_11230] :
      ( hAPP(U_11231,hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),U_11232)) = hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),hAPP(c_Set_Oimage(U_11230,U_11230,U_11231),U_11232))
      | U_11232 = c_Orderings_Obot__class_Obot(tc_fun(U_11230,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11230),U_11232))
      | ? [U_11229,U_11228] : hAPP(U_11231,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),U_11229),U_11228)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),hAPP(U_11231,U_11229)),hAPP(U_11231,U_11228))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_11230) ),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

fof(f_3010_3,plain,
    ! [U_11232,U_11231,U_11230] :
      ( hAPP(U_11231,hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),U_11232)) = hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),hAPP(c_Set_Oimage(U_11230,U_11230,U_11231),U_11232))
      | U_11232 = c_Orderings_Obot__class_Obot(tc_fun(U_11230,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11230),U_11232))
      | ? [U_11228] : hAPP(U_11231,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),sK253(U_11232,U_11231,U_11230)),U_11228)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),hAPP(U_11231,sK253(U_11232,U_11231,U_11230))),hAPP(U_11231,U_11228))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_11230) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_11229,sK253(U_11232,U_11231,U_11230))],[f_3010_2]) ).

fof(f_3010_4,plain,
    ! [U_11232,U_11231,U_11230] :
      ( hAPP(U_11231,hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),U_11232)) = hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),hAPP(c_Set_Oimage(U_11230,U_11230,U_11231),U_11232))
      | U_11232 = c_Orderings_Obot__class_Obot(tc_fun(U_11230,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11230),U_11232))
      | hAPP(U_11231,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),sK253(U_11232,U_11231,U_11230)),sK254(U_11232,U_11231,U_11230))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),hAPP(U_11231,sK253(U_11232,U_11231,U_11230))),hAPP(U_11231,sK254(U_11232,U_11231,U_11230)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_11230) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_11228,sK254(U_11232,U_11231,U_11230))],[f_3010_3]) ).

cnf(f_3010_5,plain,
    ( hAPP(U_11231,hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),U_11232)) = hAPP(c_Finite__Set_Ofold1(U_11230,c_Groups_Otimes__class_Otimes(U_11230)),hAPP(c_Set_Oimage(U_11230,U_11230,U_11231),U_11232))
    | U_11232 = c_Orderings_Obot__class_Obot(tc_fun(U_11230,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11230),U_11232))
    | hAPP(U_11231,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),sK253(U_11232,U_11231,U_11230)),sK254(U_11232,U_11231,U_11230))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11230),hAPP(U_11231,sK253(U_11232,U_11231,U_11230))),hAPP(U_11231,sK254(U_11232,U_11231,U_11230)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_11230) ),
    inference(clausify,[status(thm)],[f_3010_4]) ).

fof(f_3011_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_3011_2,plain,
    ! [U_11234,U_11233] :
      ( ( 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_11233),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_11234),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_11233),U_11234)),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_11233),U_11234)),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_11233),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_11234),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

fof(f_3011_3,plain,
    ( ! [U_11238,U_11236] :
        ( 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_11236),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_11238),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_11236),U_11238)),c_Int_Ointrel)) )
    & ! [U_11237,U_11235] :
        ( 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_11235),U_11237)),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_11235),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_11237),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3011_2]) ).

cnf(f_3011_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_11235),U_11237)),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_11235),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_11237),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3011_3]) ).

cnf(f_3011_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_11236),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_11238),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_11236),U_11238)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3011_3]) ).

fof(f_3012_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_3012_2,plain,
    ! [U_11244,U_11243,U_11242,U_11241,U_11240] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11243),U_11241) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11244),U_11242)
      | ? [U_11239] :
          ( hAPP(U_11243,U_11239) != hAPP(U_11244,U_11239)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11239)) )
      | ~ c_Nat__Transfer_Onat__set(U_11242)
      | U_11241 != U_11242
      | ~ class_Groups_Ocomm__monoid__mult(U_11240)
      | ~ class_Groups_Ocomm__monoid__add(U_11240) ),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

fof(f_3012_3,plain,
    ! [U_11244,U_11243,U_11242,U_11241,U_11240] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11243),U_11241) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11244),U_11242)
      | ( hAPP(U_11243,sK255(U_11244,U_11243,U_11242,U_11241,U_11240)) != hAPP(U_11244,sK255(U_11244,U_11243,U_11242,U_11241,U_11240))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK255(U_11244,U_11243,U_11242,U_11241,U_11240))) )
      | ~ c_Nat__Transfer_Onat__set(U_11242)
      | U_11241 != U_11242
      | ~ class_Groups_Ocomm__monoid__mult(U_11240)
      | ~ class_Groups_Ocomm__monoid__add(U_11240) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_11239,sK255(U_11244,U_11243,U_11242,U_11241,U_11240))],[f_3012_2]) ).

cnf(f_3012_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK255(U_11244,U_11243,U_11242,U_11241,U_11240)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11243),U_11241) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11244),U_11242)
    | ~ c_Nat__Transfer_Onat__set(U_11242)
    | U_11241 != U_11242
    | ~ class_Groups_Ocomm__monoid__mult(U_11240)
    | ~ class_Groups_Ocomm__monoid__add(U_11240) ),
    inference(clausify,[status(thm)],[f_3012_3]) ).

cnf(f_3012_5,plain,
    ( hAPP(U_11243,sK255(U_11244,U_11243,U_11242,U_11241,U_11240)) != hAPP(U_11244,sK255(U_11244,U_11243,U_11242,U_11241,U_11240))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11243),U_11241) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11240),U_11244),U_11242)
    | ~ c_Nat__Transfer_Onat__set(U_11242)
    | U_11241 != U_11242
    | ~ class_Groups_Ocomm__monoid__mult(U_11240)
    | ~ class_Groups_Ocomm__monoid__add(U_11240) ),
    inference(clausify,[status(thm)],[f_3012_3]) ).

fof(f_3013_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_3013_2,plain,
    ! [U_11249,U_11248,U_11247,U_11246,U_11245] : hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11245,tc_HOL_Obool)),U_11248),U_11249)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11246,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),U_11248)),hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),U_11249)),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

cnf(f_3013_3,plain,
    hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11245,tc_HOL_Obool)),U_11248),U_11249)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11246,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),U_11248)),hAPP(c_Relation_OImage(U_11245,U_11246,U_11247),U_11249)),
    inference(clausify,[status(thm)],[f_3013_2]) ).

fof(f_3014_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_3014_2,plain,
    ! [U_11252,U_11251,U_11250] : hAPP(c_Relation_OImage(U_11250,U_11251,U_11252),c_Orderings_Obot__class_Obot(tc_fun(U_11250,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11251,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

cnf(f_3014_3,plain,
    hAPP(c_Relation_OImage(U_11250,U_11251,U_11252),c_Orderings_Obot__class_Obot(tc_fun(U_11250,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11251,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3014_2]) ).

fof(f_3015_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_3015_2,plain,
    ! [U_11258,U_11257,U_11256,U_11255,U_11254,U_11253] : hAPP(c_Relation_OImage(U_11253,U_11254,U_11255),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11256,tc_fun(U_11253,tc_HOL_Obool)),U_11257),U_11258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11256,tc_fun(U_11254,tc_HOL_Obool)),U_11257),hAPP(hAPP(c_COMBB(tc_fun(U_11253,tc_HOL_Obool),tc_fun(U_11254,tc_HOL_Obool),U_11256),c_Relation_OImage(U_11253,U_11254,U_11255)),U_11258)),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

cnf(f_3015_3,plain,
    hAPP(c_Relation_OImage(U_11253,U_11254,U_11255),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11256,tc_fun(U_11253,tc_HOL_Obool)),U_11257),U_11258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11256,tc_fun(U_11254,tc_HOL_Obool)),U_11257),hAPP(hAPP(c_COMBB(tc_fun(U_11253,tc_HOL_Obool),tc_fun(U_11254,tc_HOL_Obool),U_11256),c_Relation_OImage(U_11253,U_11254,U_11255)),U_11258)),
    inference(clausify,[status(thm)],[f_3015_2]) ).

fof(f_3016_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_3016_2,plain,
    ! [U_11263,U_11262,U_11261,U_11260,U_11259] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11259,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),U_11263))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11259,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),U_11262)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),U_11263)))),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

cnf(f_3016_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11259,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),U_11263))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11259,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),U_11262)),hAPP(c_Relation_OImage(U_11260,U_11259,U_11261),U_11263)))),
    inference(clausify,[status(thm)],[f_3016_2]) ).

fof(f_3017_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_3017_2,plain,
    ! [U_11269,U_11268,U_11267,U_11266,U_11265,U_11264] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11264,U_11265,U_11266),U_11268)),hAPP(c_Relation_OImage(U_11264,U_11265,U_11267),U_11269)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11264,tc_HOL_Obool)),U_11268),U_11269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11264,U_11265),tc_HOL_Obool)),U_11266),U_11267)) ),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

cnf(f_3017_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11265,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11264,U_11265,U_11266),U_11268)),hAPP(c_Relation_OImage(U_11264,U_11265,U_11267),U_11269)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11264,tc_HOL_Obool)),U_11268),U_11269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11264,U_11265),tc_HOL_Obool)),U_11266),U_11267)) ),
    inference(clausify,[status(thm)],[f_3017_2]) ).

fof(f_3018_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_3018_2,plain,
    ! [U_11274,U_11273,U_11272,U_11271,U_11270] : hAPP(c_Relation_OImage(U_11270,U_11271,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11270,U_11271),tc_HOL_Obool)),U_11272),U_11273)),U_11274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11271,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11270,U_11271,U_11272),U_11274)),hAPP(c_Relation_OImage(U_11270,U_11271,U_11273),U_11274)),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

cnf(f_3018_3,plain,
    hAPP(c_Relation_OImage(U_11270,U_11271,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11270,U_11271),tc_HOL_Obool)),U_11272),U_11273)),U_11274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11271,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11270,U_11271,U_11272),U_11274)),hAPP(c_Relation_OImage(U_11270,U_11271,U_11273),U_11274)),
    inference(clausify,[status(thm)],[f_3018_2]) ).

fof(f_3019_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_3019_2,plain,
    ! [U_11277,U_11276,U_11275] : hAPP(c_Relation_OImage(U_11275,U_11275,c_Relation_OId__on(U_11275,U_11276)),U_11277) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11277),
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

cnf(f_3019_3,plain,
    hAPP(c_Relation_OImage(U_11275,U_11275,c_Relation_OId__on(U_11275,U_11276)),U_11277) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11277),
    inference(clausify,[status(thm)],[f_3019_2]) ).

fof(f_3020_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_3020_2,plain,
    ! [U_11283,U_11282,U_11281,U_11280,U_11279,U_11278] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11278,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11279,U_11278,U_11280),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11281,tc_fun(U_11279,tc_HOL_Obool)),U_11282),U_11283))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11281,tc_fun(U_11278,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11279,tc_HOL_Obool),tc_fun(U_11278,tc_HOL_Obool),U_11281),c_Relation_OImage(U_11279,U_11278,U_11280)),U_11283)))),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

cnf(f_3020_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11278,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11279,U_11278,U_11280),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11281,tc_fun(U_11279,tc_HOL_Obool)),U_11282),U_11283))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11281,tc_fun(U_11278,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11279,tc_HOL_Obool),tc_fun(U_11278,tc_HOL_Obool),U_11281),c_Relation_OImage(U_11279,U_11278,U_11280)),U_11283)))),
    inference(clausify,[status(thm)],[f_3020_2]) ).

fof(f_3021_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_3021_2,plain,
    ! [U_11289,U_11288,U_11287,U_11286,U_11285,U_11284] :
      ( hBOOL(hAPP(hAPP(c_member(U_11287),U_11288),hAPP(c_Relation_OImage(U_11284,U_11287,U_11289),U_11286)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11284,U_11287)),hAPP(hAPP(c_Product__Type_OPair(U_11284,U_11287),U_11285),U_11288)),U_11289))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11284),U_11285),U_11286)) ),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

cnf(f_3021_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11287),U_11288),hAPP(c_Relation_OImage(U_11284,U_11287,U_11289),U_11286)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11284,U_11287)),hAPP(hAPP(c_Product__Type_OPair(U_11284,U_11287),U_11285),U_11288)),U_11289))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11284),U_11285),U_11286)) ),
    inference(clausify,[status(thm)],[f_3021_2]) ).

fof(f_3022_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_3022_2,plain,
    ! [U_11296,U_11295,U_11294,U_11293,U_11292] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11292),U_11293),hAPP(c_Relation_OImage(U_11294,U_11292,U_11295),U_11296)))
        | ! [U_11291] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11294,U_11292)),hAPP(hAPP(c_Product__Type_OPair(U_11294,U_11292),U_11291),U_11293)),U_11295))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11294),U_11291),U_11296)) ) )
      & ( ? [U_11290] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11294,U_11292)),hAPP(hAPP(c_Product__Type_OPair(U_11294,U_11292),U_11290),U_11293)),U_11295))
            & hBOOL(hAPP(hAPP(c_member(U_11294),U_11290),U_11296)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11292),U_11293),hAPP(c_Relation_OImage(U_11294,U_11292,U_11295),U_11296))) ) ),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

fof(f_3022_3,plain,
    ( ! [U_11306,U_11304,U_11302,U_11300,U_11298] :
        ( hBOOL(hAPP(hAPP(c_member(U_11298),U_11300),hAPP(c_Relation_OImage(U_11302,U_11298,U_11304),U_11306)))
        | ! [U_11291] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11302,U_11298)),hAPP(hAPP(c_Product__Type_OPair(U_11302,U_11298),U_11291),U_11300)),U_11304))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11302),U_11291),U_11306)) ) )
    & ! [U_11305,U_11303,U_11301,U_11299,U_11297] :
        ( ? [U_11290] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11301,U_11297)),hAPP(hAPP(c_Product__Type_OPair(U_11301,U_11297),U_11290),U_11299)),U_11303))
            & hBOOL(hAPP(hAPP(c_member(U_11301),U_11290),U_11305)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11297),U_11299),hAPP(c_Relation_OImage(U_11301,U_11297,U_11303),U_11305))) ) ),
    inference(miniscope,[status(thm)],[f_3022_2]) ).

fof(f_3022_4,plain,
    ( ! [U_11306,U_11304,U_11302,U_11300,U_11298] :
        ( hBOOL(hAPP(hAPP(c_member(U_11298),U_11300),hAPP(c_Relation_OImage(U_11302,U_11298,U_11304),U_11306)))
        | ! [U_11291] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11302,U_11298)),hAPP(hAPP(c_Product__Type_OPair(U_11302,U_11298),U_11291),U_11300)),U_11304))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11302),U_11291),U_11306)) ) )
    & ! [U_11305,U_11303,U_11301,U_11299,U_11297] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11301,U_11297)),hAPP(hAPP(c_Product__Type_OPair(U_11301,U_11297),sK256(U_11305,U_11303,U_11301,U_11299,U_11297)),U_11299)),U_11303))
          & hBOOL(hAPP(hAPP(c_member(U_11301),sK256(U_11305,U_11303,U_11301,U_11299,U_11297)),U_11305)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11297),U_11299),hAPP(c_Relation_OImage(U_11301,U_11297,U_11303),U_11305))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_11290,sK256(U_11305,U_11303,U_11301,U_11299,U_11297))],[f_3022_3]) ).

cnf(f_3022_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11301),sK256(U_11305,U_11303,U_11301,U_11299,U_11297)),U_11305))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11297),U_11299),hAPP(c_Relation_OImage(U_11301,U_11297,U_11303),U_11305))) ),
    inference(clausify,[status(thm)],[f_3022_4]) ).

cnf(f_3022_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11301,U_11297)),hAPP(hAPP(c_Product__Type_OPair(U_11301,U_11297),sK256(U_11305,U_11303,U_11301,U_11299,U_11297)),U_11299)),U_11303))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11297),U_11299),hAPP(c_Relation_OImage(U_11301,U_11297,U_11303),U_11305))) ),
    inference(clausify,[status(thm)],[f_3022_4]) ).

cnf(f_3022_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11298),U_11300),hAPP(c_Relation_OImage(U_11302,U_11298,U_11304),U_11306)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11302,U_11298)),hAPP(hAPP(c_Product__Type_OPair(U_11302,U_11298),U_11291),U_11300)),U_11304))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11302),U_11291),U_11306)) ),
    inference(clausify,[status(thm)],[f_3022_4]) ).

fof(f_3023_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_3023_2,plain,
    ! [U_11310,U_11309,U_11308,U_11307] : hAPP(c_Relation_OImage(U_11307,U_11308,U_11309),U_11310) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(U_11308,tc_HOL_Obool)),U_11310),hAPP(hAPP(c_COMBB(tc_fun(U_11307,tc_HOL_Obool),tc_fun(U_11308,tc_HOL_Obool),U_11307),c_Relation_OImage(U_11307,U_11308,U_11309)),hAPP(hAPP(c_COMBC(U_11307,tc_fun(U_11307,tc_HOL_Obool),tc_fun(U_11307,tc_HOL_Obool)),c_Set_Oinsert(U_11307)),c_Orderings_Obot__class_Obot(tc_fun(U_11307,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

cnf(f_3023_3,plain,
    hAPP(c_Relation_OImage(U_11307,U_11308,U_11309),U_11310) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(U_11308,tc_HOL_Obool)),U_11310),hAPP(hAPP(c_COMBB(tc_fun(U_11307,tc_HOL_Obool),tc_fun(U_11308,tc_HOL_Obool),U_11307),c_Relation_OImage(U_11307,U_11308,U_11309)),hAPP(hAPP(c_COMBC(U_11307,tc_fun(U_11307,tc_HOL_Obool),tc_fun(U_11307,tc_HOL_Obool)),c_Set_Oinsert(U_11307)),c_Orderings_Obot__class_Obot(tc_fun(U_11307,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3023_2]) ).

fof(f_3024_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_3024_2,plain,
    ! [U_11315,U_11314,U_11313,U_11312,U_11311] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11311),U_11312),hAPP(c_Relation_OImage(U_11313,U_11311,U_11314),hAPP(hAPP(c_Set_Oinsert(U_11313),U_11315),c_Orderings_Obot__class_Obot(tc_fun(U_11313,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11313,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11313,U_11311),U_11315),U_11312)),U_11314)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11313,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11313,U_11311),U_11315),U_11312)),U_11314))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11311),U_11312),hAPP(c_Relation_OImage(U_11313,U_11311,U_11314),hAPP(hAPP(c_Set_Oinsert(U_11313),U_11315),c_Orderings_Obot__class_Obot(tc_fun(U_11313,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3024_1]) ).

fof(f_3024_3,plain,
    ( ! [U_11325,U_11323,U_11321,U_11319,U_11317] :
        ( hBOOL(hAPP(hAPP(c_member(U_11317),U_11319),hAPP(c_Relation_OImage(U_11321,U_11317,U_11323),hAPP(hAPP(c_Set_Oinsert(U_11321),U_11325),c_Orderings_Obot__class_Obot(tc_fun(U_11321,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11321,U_11317)),hAPP(hAPP(c_Product__Type_OPair(U_11321,U_11317),U_11325),U_11319)),U_11323)) )
    & ! [U_11324,U_11322,U_11320,U_11318,U_11316] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11320,U_11316)),hAPP(hAPP(c_Product__Type_OPair(U_11320,U_11316),U_11324),U_11318)),U_11322))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11316),U_11318),hAPP(c_Relation_OImage(U_11320,U_11316,U_11322),hAPP(hAPP(c_Set_Oinsert(U_11320),U_11324),c_Orderings_Obot__class_Obot(tc_fun(U_11320,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_3024_2]) ).

cnf(f_3024_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11320,U_11316)),hAPP(hAPP(c_Product__Type_OPair(U_11320,U_11316),U_11324),U_11318)),U_11322))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11316),U_11318),hAPP(c_Relation_OImage(U_11320,U_11316,U_11322),hAPP(hAPP(c_Set_Oinsert(U_11320),U_11324),c_Orderings_Obot__class_Obot(tc_fun(U_11320,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_3024_3]) ).

cnf(f_3024_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11317),U_11319),hAPP(c_Relation_OImage(U_11321,U_11317,U_11323),hAPP(hAPP(c_Set_Oinsert(U_11321),U_11325),c_Orderings_Obot__class_Obot(tc_fun(U_11321,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11321,U_11317)),hAPP(hAPP(c_Product__Type_OPair(U_11321,U_11317),U_11325),U_11319)),U_11323)) ),
    inference(clausify,[status(thm)],[f_3024_3]) ).

fof(f_3025_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_3025_2,plain,
    ! [U_11328,U_11327,U_11326] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_11326),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_11327),U_11328)),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_11326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11326),U_11327)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11326),U_11328))
      | ~ class_Rings_Oring__1(U_11326) ),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

cnf(f_3025_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11326),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_11327),U_11328)),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_11326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11326),U_11327)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11326),U_11328))
    | ~ class_Rings_Oring__1(U_11326) ),
    inference(clausify,[status(thm)],[f_3025_2]) ).

fof(f_3026_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_3026_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_3026_1]) ).

fof(f_3027_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_3027_2,plain,
    ! [U_11332,U_11331,U_11330,U_11329] : 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_11329),U_11330)),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_11331),U_11332)),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_11329),U_11331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11330),U_11332))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11329),U_11332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11330),U_11331)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

cnf(f_3027_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_11329),U_11330)),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_11331),U_11332)),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_11329),U_11331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11330),U_11332))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11329),U_11332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11330),U_11331)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3027_2]) ).

fof(f_3028_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_3028_2,plain,
    ! [U_11333] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11333)) = U_11333,
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

cnf(f_3028_3,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11333)) = U_11333,
    inference(clausify,[status(thm)],[f_3028_2]) ).

fof(f_3029_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_3029_2,plain,
    ! [U_11335,U_11334] : 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_11334),U_11335)),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_11335),U_11334)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

cnf(f_3029_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_11334),U_11335)),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_11335),U_11334)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3029_2]) ).

fof(f_3030_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_3030_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_3030_1]) ).

fof(f_3031_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_3031_2,plain,
    ! [U_11336] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11336) = 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_11336),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_3031_1]) ).

cnf(f_3031_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11336) = 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_11336),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_3031_2]) ).

fof(f_3032_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_3032_2,plain,
    ! [U_11340,U_11339,U_11338,U_11337] : 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_11337),U_11338)),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_11339),U_11340)),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_11337),U_11339)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11338),U_11340))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

cnf(f_3032_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_11337),U_11338)),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_11339),U_11340)),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_11337),U_11339)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11338),U_11340))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3032_2]) ).

fof(f_3033_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_3033_2,plain,
    ! [U_11342,U_11341] : 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_11341),U_11342)),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_11341),U_11342),
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

cnf(f_3033_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_11341),U_11342)),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_11341),U_11342),
    inference(clausify,[status(thm)],[f_3033_2]) ).

fof(f_3034_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_3034_2,plain,
    ! [U_11343] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11343) = 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_11343)),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_3034_1]) ).

cnf(f_3034_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11343) = 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_11343)),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_3034_2]) ).

fof(f_3035_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_3035_2,plain,
    ! [U_11347,U_11346,U_11345,U_11344] :
      ( ( 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_11344),U_11345)),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_11346),U_11347)),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_11344),U_11347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11346),U_11345))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11344),U_11347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11346),U_11345)))
        | ~ 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_11344),U_11345)),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_11346),U_11347)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

fof(f_3035_3,plain,
    ( ! [U_11355,U_11353,U_11351,U_11349] :
        ( 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_11349),U_11351)),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_11353),U_11355)),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_11349),U_11355)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11353),U_11351))) )
    & ! [U_11354,U_11352,U_11350,U_11348] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11348),U_11354)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11352),U_11350)))
        | ~ 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_11348),U_11350)),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_11352),U_11354)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3035_2]) ).

cnf(f_3035_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11348),U_11354)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11352),U_11350)))
    | ~ 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_11348),U_11350)),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_11352),U_11354)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

cnf(f_3035_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_11349),U_11351)),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_11353),U_11355)),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_11349),U_11355)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11353),U_11351))) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

fof(f_3036_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_3036_2,plain,
    ! [U_11359,U_11358,U_11357,U_11356] :
      ( ( 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_11356),U_11357)),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_11358),U_11359)),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_11356),U_11359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11358),U_11357))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11356),U_11359)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11358),U_11357)))
        | ~ 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_11356),U_11357)),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_11358),U_11359)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

fof(f_3036_3,plain,
    ( ! [U_11367,U_11365,U_11363,U_11361] :
        ( 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_11361),U_11363)),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_11365),U_11367)),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_11361),U_11367)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11365),U_11363))) )
    & ! [U_11366,U_11364,U_11362,U_11360] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11360),U_11366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11364),U_11362)))
        | ~ 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_11360),U_11362)),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_11364),U_11366)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3036_2]) ).

cnf(f_3036_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_11360),U_11366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11364),U_11362)))
    | ~ 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_11360),U_11362)),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_11364),U_11366)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3036_3]) ).

cnf(f_3036_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_11361),U_11363)),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_11365),U_11367)),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_11361),U_11367)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11365),U_11363))) ),
    inference(clausify,[status(thm)],[f_3036_3]) ).

fof(f_3037_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_3037_2,plain,
    ! [U_11370] :
    ? [U_11369,U_11368] : U_11370 = 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_11369),U_11368)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

fof(f_3037_3,plain,
    ! [U_11370] :
    ? [U_11368] : U_11370 = 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),sK257(U_11370)),U_11368)),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,[sK257]),skolemize(U_11369,sK257(U_11370))],[f_3037_2]) ).

fof(f_3037_4,plain,
    ! [U_11370] : U_11370 = 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),sK257(U_11370)),sK258(U_11370))),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,[sK258]),skolemize(U_11368,sK258(U_11370))],[f_3037_3]) ).

cnf(f_3037_5,plain,
    U_11370 = 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),sK257(U_11370)),sK258(U_11370))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3037_4]) ).

fof(f_3038_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_3038_2,plain,
    ! [U_11373,U_11372,U_11371] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11371),U_11372),U_11373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11371,tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),U_11372),hAPP(hAPP(c_COMBC(U_11371,tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11371,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),U_11371),c_Set_Oinsert(tc_fun(U_11371,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11371,tc_HOL_Obool),tc_fun(U_11371,tc_HOL_Obool),U_11371),c_Relation_OImage(U_11371,U_11371,U_11373)),hAPP(hAPP(c_COMBC(U_11371,tc_fun(U_11371,tc_HOL_Obool),tc_fun(U_11371,tc_HOL_Obool)),c_Set_Oinsert(U_11371)),c_Orderings_Obot__class_Obot(tc_fun(U_11371,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

cnf(f_3038_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11371),U_11372),U_11373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11371,tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),U_11372),hAPP(hAPP(c_COMBC(U_11371,tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11371,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)),U_11371),c_Set_Oinsert(tc_fun(U_11371,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11371,tc_HOL_Obool),tc_fun(U_11371,tc_HOL_Obool),U_11371),c_Relation_OImage(U_11371,U_11371,U_11373)),hAPP(hAPP(c_COMBC(U_11371,tc_fun(U_11371,tc_HOL_Obool),tc_fun(U_11371,tc_HOL_Obool)),c_Set_Oinsert(U_11371)),c_Orderings_Obot__class_Obot(tc_fun(U_11371,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11371,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3038_2]) ).

fof(f_3039_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_3039_2,plain,
    ! [U_11379,U_11378,U_11377,U_11376,U_11375] :
      ( ? [U_11374] :
          ( hBOOL(hAPP(hAPP(c_member(U_11377),U_11374),U_11379))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11375)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11375),U_11374),U_11376)),U_11378)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11375),U_11376),hAPP(c_Relation_OImage(U_11377,U_11375,U_11378),U_11379))) ),
    inference(variable_rename,[status(thm)],[f_3039_1]) ).

fof(f_3039_3,plain,
    ! [U_11379,U_11378,U_11377,U_11376,U_11375] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11377),sK259(U_11379,U_11378,U_11377,U_11376,U_11375)),U_11379))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11375)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11375),sK259(U_11379,U_11378,U_11377,U_11376,U_11375)),U_11376)),U_11378)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11375),U_11376),hAPP(c_Relation_OImage(U_11377,U_11375,U_11378),U_11379))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_11374,sK259(U_11379,U_11378,U_11377,U_11376,U_11375))],[f_3039_2]) ).

cnf(f_3039_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11375)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11375),sK259(U_11379,U_11378,U_11377,U_11376,U_11375)),U_11376)),U_11378))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11375),U_11376),hAPP(c_Relation_OImage(U_11377,U_11375,U_11378),U_11379))) ),
    inference(clausify,[status(thm)],[f_3039_3]) ).

cnf(f_3039_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11377),sK259(U_11379,U_11378,U_11377,U_11376,U_11375)),U_11379))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11375),U_11376),hAPP(c_Relation_OImage(U_11377,U_11375,U_11378),U_11379))) ),
    inference(clausify,[status(thm)],[f_3039_3]) ).

fof(f_3040_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_3040_2,plain,
    ! [U_11382,U_11381,U_11380] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11380),U_11381),U_11382) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11380,tc_HOL_Obool),tc_HOL_Obool))
        | U_11381 != c_Orderings_Obot__class_Obot(tc_fun(U_11380,tc_HOL_Obool)) )
      & ( U_11381 = c_Orderings_Obot__class_Obot(tc_fun(U_11380,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11380),U_11381),U_11382) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11380,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3040_1]) ).

fof(f_3040_3,plain,
    ( ! [U_11388,U_11386,U_11384] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11384),U_11386),U_11388) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11384,tc_HOL_Obool),tc_HOL_Obool))
        | U_11386 != c_Orderings_Obot__class_Obot(tc_fun(U_11384,tc_HOL_Obool)) )
    & ! [U_11387,U_11385,U_11383] :
        ( U_11385 = c_Orderings_Obot__class_Obot(tc_fun(U_11383,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11383),U_11385),U_11387) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3040_2]) ).

cnf(f_3040_4,plain,
    ( U_11385 = c_Orderings_Obot__class_Obot(tc_fun(U_11383,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11383),U_11385),U_11387) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3040_3]) ).

cnf(f_3040_5,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11384),U_11386),U_11388) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11384,tc_HOL_Obool),tc_HOL_Obool))
    | U_11386 != c_Orderings_Obot__class_Obot(tc_fun(U_11384,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3040_3]) ).

fof(f_3041_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_3041_2,plain,
    ! [U_11391,U_11390,U_11389] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11389,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11389),U_11390),U_11391)
        | U_11390 != c_Orderings_Obot__class_Obot(tc_fun(U_11389,tc_HOL_Obool)) )
      & ( U_11390 = c_Orderings_Obot__class_Obot(tc_fun(U_11389,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11389,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11389),U_11390),U_11391) ) ),
    inference(variable_rename,[status(thm)],[f_3041_1]) ).

fof(f_3041_3,plain,
    ( ! [U_11397,U_11395,U_11393] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11393,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11393),U_11395),U_11397)
        | U_11395 != c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool)) )
    & ! [U_11396,U_11394,U_11392] :
        ( U_11394 = c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11392,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11392),U_11394),U_11396) ) ),
    inference(miniscope,[status(thm)],[f_3041_2]) ).

cnf(f_3041_4,plain,
    ( U_11394 = c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11392,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11392),U_11394),U_11396) ),
    inference(clausify,[status(thm)],[f_3041_3]) ).

cnf(f_3041_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11393,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11393),U_11395),U_11397)
    | U_11395 != c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3041_3]) ).

fof(f_3042_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_3042_2,plain,
    ! [U_11399,U_11398] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11398),c_Orderings_Obot__class_Obot(tc_fun(U_11398,tc_HOL_Obool))),U_11399) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11398,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3042_1]) ).

cnf(f_3042_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11398),c_Orderings_Obot__class_Obot(tc_fun(U_11398,tc_HOL_Obool))),U_11399) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11398,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3042_2]) ).

fof(f_3043_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_3043_2,plain,
    ! [U_11403,U_11402,U_11401,U_11400] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11400,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11400,U_11400,U_11403),hAPP(hAPP(c_Set_Oinsert(U_11400),U_11401),c_Orderings_Obot__class_Obot(tc_fun(U_11400,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11400),U_11402),U_11403)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11400),U_11401),U_11402)) ),
    inference(variable_rename,[status(thm)],[f_3043_1]) ).

cnf(f_3043_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11400,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11400,U_11400,U_11403),hAPP(hAPP(c_Set_Oinsert(U_11400),U_11401),c_Orderings_Obot__class_Obot(tc_fun(U_11400,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11400),U_11402),U_11403)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11400),U_11401),U_11402)) ),
    inference(clausify,[status(thm)],[f_3043_2]) ).

fof(f_3044_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_3044_2,plain,
    ! [U_11406,U_11405,U_11404] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11404),hAPP(hAPP(c_Set_Oinsert(U_11404),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool)))),U_11406) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11404,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11404,U_11404,U_11406),hAPP(hAPP(c_Set_Oinsert(U_11404),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11404,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3044_1]) ).

cnf(f_3044_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11404),hAPP(hAPP(c_Set_Oinsert(U_11404),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool)))),U_11406) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11404,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11404,U_11404,U_11406),hAPP(hAPP(c_Set_Oinsert(U_11404),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11404,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3044_2]) ).

fof(f_3045_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_3045_2,plain,
    ! [U_11412,U_11411,U_11410,U_11409,U_11408,U_11407] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11407,U_11407)),hAPP(hAPP(c_Product__Type_OPair(U_11407,U_11407),U_11411),U_11412)),U_11409))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11407),U_11410),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11407,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11407,U_11407,U_11409),hAPP(hAPP(c_Set_Oinsert(U_11407),U_11411),c_Orderings_Obot__class_Obot(tc_fun(U_11407,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11407,U_11407,U_11409),hAPP(hAPP(c_Set_Oinsert(U_11407),U_11412),c_Orderings_Obot__class_Obot(tc_fun(U_11407,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_11407,U_11408,U_11409) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

cnf(f_3045_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11407,U_11407)),hAPP(hAPP(c_Product__Type_OPair(U_11407,U_11407),U_11411),U_11412)),U_11409))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11407),U_11410),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11407,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11407,U_11407,U_11409),hAPP(hAPP(c_Set_Oinsert(U_11407),U_11411),c_Orderings_Obot__class_Obot(tc_fun(U_11407,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11407,U_11407,U_11409),hAPP(hAPP(c_Set_Oinsert(U_11407),U_11412),c_Orderings_Obot__class_Obot(tc_fun(U_11407,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_11407,U_11408,U_11409) ),
    inference(clausify,[status(thm)],[f_3045_2]) ).

fof(f_3046_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_3046_2,plain,
    ! [U_11417,U_11416,U_11415,U_11414,U_11413] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11417),U_11416)),U_11415))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11413),U_11416),U_11414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11413,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11413,U_11413,U_11415),hAPP(hAPP(c_Set_Oinsert(U_11413),U_11416),c_Orderings_Obot__class_Obot(tc_fun(U_11413,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11413,U_11413,U_11415),hAPP(hAPP(c_Set_Oinsert(U_11413),U_11417),c_Orderings_Obot__class_Obot(tc_fun(U_11413,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_11413,U_11414,U_11415) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

cnf(f_3046_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11417),U_11416)),U_11415))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11413),U_11416),U_11414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11413,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11413,U_11413,U_11415),hAPP(hAPP(c_Set_Oinsert(U_11413),U_11416),c_Orderings_Obot__class_Obot(tc_fun(U_11413,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11413,U_11413,U_11415),hAPP(hAPP(c_Set_Oinsert(U_11413),U_11417),c_Orderings_Obot__class_Obot(tc_fun(U_11413,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_11413,U_11414,U_11415) ),
    inference(clausify,[status(thm)],[f_3046_2]) ).

fof(f_3047_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_3047_2,plain,
    ! [U_11422,U_11421,U_11420,U_11419] :
      ( ? [U_11418] :
          ( hBOOL(hAPP(hAPP(c_member(U_11419),U_11418),U_11421))
          & U_11420 = hAPP(c_Relation_OImage(U_11419,U_11419,U_11422),hAPP(hAPP(c_Set_Oinsert(U_11419),U_11418),c_Orderings_Obot__class_Obot(tc_fun(U_11419,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11419,tc_HOL_Obool)),U_11420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11419),U_11421),U_11422))) ),
    inference(variable_rename,[status(thm)],[f_3047_1]) ).

fof(f_3047_3,plain,
    ! [U_11422,U_11421,U_11420,U_11419] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11419),sK260(U_11422,U_11421,U_11420,U_11419)),U_11421))
        & U_11420 = hAPP(c_Relation_OImage(U_11419,U_11419,U_11422),hAPP(hAPP(c_Set_Oinsert(U_11419),sK260(U_11422,U_11421,U_11420,U_11419)),c_Orderings_Obot__class_Obot(tc_fun(U_11419,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11419,tc_HOL_Obool)),U_11420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11419),U_11421),U_11422))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_11418,sK260(U_11422,U_11421,U_11420,U_11419))],[f_3047_2]) ).

cnf(f_3047_4,plain,
    ( U_11420 = hAPP(c_Relation_OImage(U_11419,U_11419,U_11422),hAPP(hAPP(c_Set_Oinsert(U_11419),sK260(U_11422,U_11421,U_11420,U_11419)),c_Orderings_Obot__class_Obot(tc_fun(U_11419,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11419,tc_HOL_Obool)),U_11420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11419),U_11421),U_11422))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

cnf(f_3047_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11419),sK260(U_11422,U_11421,U_11420,U_11419)),U_11421))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11419,tc_HOL_Obool)),U_11420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11419),U_11421),U_11422))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

fof(f_3048_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_3048_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_3048_1]) ).

fof(f_3049_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_3049_2,plain,
    ! [U_11425,U_11424,U_11423] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_11423,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11423),U_11424),U_11425)) = U_11424
      | ~ c_Equiv__Relations_Oequiv(U_11423,U_11424,U_11425) ),
    inference(variable_rename,[status(thm)],[f_3049_1]) ).

cnf(f_3049_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_11423,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11423),U_11424),U_11425)) = U_11424
    | ~ c_Equiv__Relations_Oequiv(U_11423,U_11424,U_11425) ),
    inference(clausify,[status(thm)],[f_3049_2]) ).

fof(f_3050_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_3050_2,plain,
    ! [U_11429,U_11428,U_11427,U_11426] :
      ( hBOOL(hAPP(hAPP(c_member(U_11426),U_11429),hAPP(c_Relation_OImage(U_11426,U_11426,U_11428),hAPP(hAPP(c_Set_Oinsert(U_11426),U_11429),c_Orderings_Obot__class_Obot(tc_fun(U_11426,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11426),U_11429),U_11427))
      | ~ c_Equiv__Relations_Oequiv(U_11426,U_11427,U_11428) ),
    inference(variable_rename,[status(thm)],[f_3050_1]) ).

cnf(f_3050_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11426),U_11429),hAPP(c_Relation_OImage(U_11426,U_11426,U_11428),hAPP(hAPP(c_Set_Oinsert(U_11426),U_11429),c_Orderings_Obot__class_Obot(tc_fun(U_11426,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11426),U_11429),U_11427))
    | ~ c_Equiv__Relations_Oequiv(U_11426,U_11427,U_11428) ),
    inference(clausify,[status(thm)],[f_3050_2]) ).

fof(f_3051_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_3051_2,plain,
    ! [U_11434,U_11433,U_11432,U_11431,U_11430] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11430,tc_HOL_Obool)),U_11433),U_11434) = c_Orderings_Obot__class_Obot(tc_fun(U_11430,tc_HOL_Obool))
      | U_11433 = U_11434
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11430,tc_HOL_Obool)),U_11434),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11430),U_11431),U_11432)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11430,tc_HOL_Obool)),U_11433),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11430),U_11431),U_11432)))
      | ~ c_Equiv__Relations_Oequiv(U_11430,U_11431,U_11432) ),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

cnf(f_3051_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11430,tc_HOL_Obool)),U_11433),U_11434) = c_Orderings_Obot__class_Obot(tc_fun(U_11430,tc_HOL_Obool))
    | U_11433 = U_11434
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11430,tc_HOL_Obool)),U_11434),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11430),U_11431),U_11432)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11430,tc_HOL_Obool)),U_11433),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11430),U_11431),U_11432)))
    | ~ c_Equiv__Relations_Oequiv(U_11430,U_11431,U_11432) ),
    inference(clausify,[status(thm)],[f_3051_2]) ).

fof(f_3052_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_3052_2,plain,
    ! [U_11439,U_11438,U_11437,U_11436,U_11435] :
      ( hAPP(c_Relation_OImage(U_11435,U_11435,U_11437),hAPP(hAPP(c_Set_Oinsert(U_11435),U_11438),c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11435,U_11435,U_11437),hAPP(hAPP(c_Set_Oinsert(U_11435),U_11439),c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11435,U_11435)),hAPP(hAPP(c_Product__Type_OPair(U_11435,U_11435),U_11438),U_11439)),U_11437))
      | ~ c_Equiv__Relations_Oequiv(U_11435,U_11436,U_11437) ),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

cnf(f_3052_3,plain,
    ( hAPP(c_Relation_OImage(U_11435,U_11435,U_11437),hAPP(hAPP(c_Set_Oinsert(U_11435),U_11438),c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11435,U_11435,U_11437),hAPP(hAPP(c_Set_Oinsert(U_11435),U_11439),c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11435,U_11435)),hAPP(hAPP(c_Product__Type_OPair(U_11435,U_11435),U_11438),U_11439)),U_11437))
    | ~ c_Equiv__Relations_Oequiv(U_11435,U_11436,U_11437) ),
    inference(clausify,[status(thm)],[f_3052_2]) ).

fof(f_3053_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_3053_2,plain,
    ! [U_11446,U_11445,U_11444,U_11443,U_11442,U_11441,U_11440] :
      ( U_11443 = U_11444
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11440,U_11440)),hAPP(hAPP(c_Product__Type_OPair(U_11440,U_11440),U_11445),U_11446)),U_11442))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11440),U_11446),U_11444))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11440),U_11445),U_11443))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11440,tc_HOL_Obool)),U_11444),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11440),U_11441),U_11442)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11440,tc_HOL_Obool)),U_11443),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11440),U_11441),U_11442)))
      | ~ c_Equiv__Relations_Oequiv(U_11440,U_11441,U_11442) ),
    inference(variable_rename,[status(thm)],[f_3053_1]) ).

cnf(f_3053_3,plain,
    ( U_11443 = U_11444
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11440,U_11440)),hAPP(hAPP(c_Product__Type_OPair(U_11440,U_11440),U_11445),U_11446)),U_11442))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11440),U_11446),U_11444))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11440),U_11445),U_11443))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11440,tc_HOL_Obool)),U_11444),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11440),U_11441),U_11442)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11440,tc_HOL_Obool)),U_11443),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11440),U_11441),U_11442)))
    | ~ c_Equiv__Relations_Oequiv(U_11440,U_11441,U_11442) ),
    inference(clausify,[status(thm)],[f_3053_2]) ).

fof(f_3054_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_3054_2,plain,
    ! [U_11453,U_11452,U_11451,U_11450,U_11449,U_11448,U_11447] :
      ( ( ( U_11450 = U_11451
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),U_11452),U_11453)),U_11449)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),U_11452),U_11453)),U_11449))
          | U_11450 != U_11451 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11453),U_11451))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11452),U_11450))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11451),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
      | ~ c_Equiv__Relations_Oequiv(U_11447,U_11448,U_11449) ),
    inference(variable_rename,[status(thm)],[f_3054_1]) ).

cnf(f_3054_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),U_11452),U_11453)),U_11449))
    | U_11450 != U_11451
    | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11453),U_11451))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11452),U_11450))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11451),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
    | ~ c_Equiv__Relations_Oequiv(U_11447,U_11448,U_11449) ),
    inference(clausify,[status(thm)],[f_3054_2]) ).

cnf(f_3054_4,plain,
    ( U_11450 = U_11451
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),U_11452),U_11453)),U_11449))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11453),U_11451))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11447),U_11452),U_11450))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11451),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11447,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11447),U_11448),U_11449)))
    | ~ c_Equiv__Relations_Oequiv(U_11447,U_11448,U_11449) ),
    inference(clausify,[status(thm)],[f_3054_2]) ).

fof(f_3055_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_3055_2,plain,
    ! [U_11458,U_11457,U_11456,U_11455,U_11454] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11454,U_11454)),hAPP(hAPP(c_Product__Type_OPair(U_11454,U_11454),U_11456),U_11457)),U_11455))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11454),U_11457),U_11458))
      | ~ c_Equiv__Relations_Oequiv(U_11454,U_11458,U_11455)
      | hAPP(c_Relation_OImage(U_11454,U_11454,U_11455),hAPP(hAPP(c_Set_Oinsert(U_11454),U_11456),c_Orderings_Obot__class_Obot(tc_fun(U_11454,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11454,U_11454,U_11455),hAPP(hAPP(c_Set_Oinsert(U_11454),U_11457),c_Orderings_Obot__class_Obot(tc_fun(U_11454,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

cnf(f_3055_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11454,U_11454)),hAPP(hAPP(c_Product__Type_OPair(U_11454,U_11454),U_11456),U_11457)),U_11455))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11454),U_11457),U_11458))
    | ~ c_Equiv__Relations_Oequiv(U_11454,U_11458,U_11455)
    | hAPP(c_Relation_OImage(U_11454,U_11454,U_11455),hAPP(hAPP(c_Set_Oinsert(U_11454),U_11456),c_Orderings_Obot__class_Obot(tc_fun(U_11454,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11454,U_11454,U_11455),hAPP(hAPP(c_Set_Oinsert(U_11454),U_11457),c_Orderings_Obot__class_Obot(tc_fun(U_11454,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3055_2]) ).

fof(f_3056_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_3056_2,plain,
    ! [U_11463,U_11462,U_11461,U_11460,U_11459] :
      ( ( ( hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11462),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11459,U_11459)),hAPP(hAPP(c_Product__Type_OPair(U_11459,U_11459),U_11462),U_11463)),U_11461)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11459,U_11459)),hAPP(hAPP(c_Product__Type_OPair(U_11459,U_11459),U_11462),U_11463)),U_11461))
          | hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11462),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11463),U_11460))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11462),U_11460))
      | ~ c_Equiv__Relations_Oequiv(U_11459,U_11460,U_11461) ),
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

cnf(f_3056_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11459,U_11459)),hAPP(hAPP(c_Product__Type_OPair(U_11459,U_11459),U_11462),U_11463)),U_11461))
    | hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11462),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11463),U_11460))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11462),U_11460))
    | ~ c_Equiv__Relations_Oequiv(U_11459,U_11460,U_11461) ),
    inference(clausify,[status(thm)],[f_3056_2]) ).

cnf(f_3056_4,plain,
    ( hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11462),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11459,U_11459,U_11461),hAPP(hAPP(c_Set_Oinsert(U_11459),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11459,U_11459)),hAPP(hAPP(c_Product__Type_OPair(U_11459,U_11459),U_11462),U_11463)),U_11461))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11463),U_11460))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11459),U_11462),U_11460))
    | ~ c_Equiv__Relations_Oequiv(U_11459,U_11460,U_11461) ),
    inference(clausify,[status(thm)],[f_3056_2]) ).

fof(f_3057_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_3057_2,plain,
    ! [U_11468,U_11467,U_11466,U_11465,U_11464] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11464),U_11468),U_11465))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11464),U_11467),U_11465))
          | hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11467),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11468),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_11464),U_11468),U_11465))
            & hBOOL(hAPP(hAPP(c_member(U_11464),U_11467),U_11465))
            & hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11467),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11468),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_11464,U_11465,U_11466) ),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

cnf(f_3057_3,plain,
    ( hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11467),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11468),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466))
    | ~ c_Equiv__Relations_Oequiv(U_11464,U_11465,U_11466) ),
    inference(clausify,[status(thm)],[f_3057_2]) ).

cnf(f_3057_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11464),U_11467),U_11465))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466))
    | ~ c_Equiv__Relations_Oequiv(U_11464,U_11465,U_11466) ),
    inference(clausify,[status(thm)],[f_3057_2]) ).

cnf(f_3057_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11464),U_11468),U_11465))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466))
    | ~ c_Equiv__Relations_Oequiv(U_11464,U_11465,U_11466) ),
    inference(clausify,[status(thm)],[f_3057_2]) ).

cnf(f_3057_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11464,U_11464)),hAPP(hAPP(c_Product__Type_OPair(U_11464,U_11464),U_11467),U_11468)),U_11466))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11464),U_11468),U_11465))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11464),U_11467),U_11465))
    | hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11467),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11464,U_11464,U_11466),hAPP(hAPP(c_Set_Oinsert(U_11464),U_11468),c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))))
    | ~ c_Equiv__Relations_Oequiv(U_11464,U_11465,U_11466) ),
    inference(clausify,[status(thm)],[f_3057_2]) ).

fof(f_3058_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_3058_2,plain,
    ! [U_11473,U_11472,U_11471,U_11470,U_11469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11469,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11469,U_11469,U_11471),hAPP(hAPP(c_Set_Oinsert(U_11469),U_11472),c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11469,U_11469,U_11471),hAPP(hAPP(c_Set_Oinsert(U_11469),U_11473),c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11469,U_11469)),hAPP(hAPP(c_Product__Type_OPair(U_11469,U_11469),U_11472),U_11473)),U_11471))
      | ~ c_Equiv__Relations_Oequiv(U_11469,U_11470,U_11471) ),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

cnf(f_3058_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11469,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11469,U_11469,U_11471),hAPP(hAPP(c_Set_Oinsert(U_11469),U_11472),c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11469,U_11469,U_11471),hAPP(hAPP(c_Set_Oinsert(U_11469),U_11473),c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11469,U_11469)),hAPP(hAPP(c_Product__Type_OPair(U_11469,U_11469),U_11472),U_11473)),U_11471))
    | ~ c_Equiv__Relations_Oequiv(U_11469,U_11470,U_11471) ),
    inference(clausify,[status(thm)],[f_3058_2]) ).

fof(f_3059_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_3059_2,plain,
    ! [U_11478,U_11477,U_11476,U_11475,U_11474] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11477),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11478),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11474,U_11474)),hAPP(hAPP(c_Product__Type_OPair(U_11474,U_11474),U_11477),U_11478)),U_11476)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11474,U_11474)),hAPP(hAPP(c_Product__Type_OPair(U_11474,U_11474),U_11477),U_11478)),U_11476))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11477),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11478),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11478),U_11475))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11477),U_11475))
      | ~ c_Equiv__Relations_Oequiv(U_11474,U_11475,U_11476) ),
    inference(variable_rename,[status(thm)],[f_3059_1]) ).

cnf(f_3059_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11474,U_11474)),hAPP(hAPP(c_Product__Type_OPair(U_11474,U_11474),U_11477),U_11478)),U_11476))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11477),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11478),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11478),U_11475))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11477),U_11475))
    | ~ c_Equiv__Relations_Oequiv(U_11474,U_11475,U_11476) ),
    inference(clausify,[status(thm)],[f_3059_2]) ).

cnf(f_3059_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11477),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11474),hAPP(hAPP(c_Set_Oinsert(U_11474),U_11478),c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool)))),U_11476)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11474,U_11474)),hAPP(hAPP(c_Product__Type_OPair(U_11474,U_11474),U_11477),U_11478)),U_11476))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11478),U_11475))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11474),U_11477),U_11475))
    | ~ c_Equiv__Relations_Oequiv(U_11474,U_11475,U_11476) ),
    inference(clausify,[status(thm)],[f_3059_2]) ).

fof(f_3060_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_3060_2,plain,
    ! [U_11488,U_11487,U_11486,U_11485,U_11484,U_11483,U_11482,U_11481,U_11480,U_11479] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11479,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11479,U_11479,U_11481),hAPP(hAPP(c_Set_Oinsert(U_11479),U_11487),c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_11482,tc_fun(U_11485,tc_HOL_Obool)),tc_fun(U_11485,tc_HOL_Obool),U_11479),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11482,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11482,U_11482,U_11484),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11488),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool)))))),U_11486)) = hAPP(hAPP(U_11486,U_11487),U_11488)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11482),U_11488),U_11483))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11487),U_11480))
      | ~ c_Equiv__Relations_Ocongruent2(U_11479,U_11482,tc_fun(U_11485,tc_HOL_Obool),U_11481,U_11484,U_11486)
      | ~ c_Equiv__Relations_Oequiv(U_11482,U_11483,U_11484)
      | ~ c_Equiv__Relations_Oequiv(U_11479,U_11480,U_11481) ),
    inference(variable_rename,[status(thm)],[f_3060_1]) ).

cnf(f_3060_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11479,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11479,U_11479,U_11481),hAPP(hAPP(c_Set_Oinsert(U_11479),U_11487),c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_11482,tc_fun(U_11485,tc_HOL_Obool)),tc_fun(U_11485,tc_HOL_Obool),U_11479),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11482,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11482,U_11482,U_11484),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11488),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool)))))),U_11486)) = hAPP(hAPP(U_11486,U_11487),U_11488)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11482),U_11488),U_11483))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11487),U_11480))
    | ~ c_Equiv__Relations_Ocongruent2(U_11479,U_11482,tc_fun(U_11485,tc_HOL_Obool),U_11481,U_11484,U_11486)
    | ~ c_Equiv__Relations_Oequiv(U_11482,U_11483,U_11484)
    | ~ c_Equiv__Relations_Oequiv(U_11479,U_11480,U_11481) ),
    inference(clausify,[status(thm)],[f_3060_2]) ).

fof(f_3061_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_3061_2,plain,
    ! [U_11494,U_11493,U_11492,U_11491,U_11490,U_11489] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11489,tc_fun(U_11492,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11489,U_11489,U_11491),hAPP(hAPP(c_Set_Oinsert(U_11489),U_11494),c_Orderings_Obot__class_Obot(tc_fun(U_11489,tc_HOL_Obool))))),U_11493) = hAPP(U_11493,U_11494)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11489),U_11494),U_11490))
      | ~ c_Equiv__Relations_Ocongruent(U_11489,tc_fun(U_11492,tc_HOL_Obool),U_11491,U_11493)
      | ~ c_Equiv__Relations_Oequiv(U_11489,U_11490,U_11491) ),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

cnf(f_3061_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11489,tc_fun(U_11492,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11489,U_11489,U_11491),hAPP(hAPP(c_Set_Oinsert(U_11489),U_11494),c_Orderings_Obot__class_Obot(tc_fun(U_11489,tc_HOL_Obool))))),U_11493) = hAPP(U_11493,U_11494)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11489),U_11494),U_11490))
    | ~ c_Equiv__Relations_Ocongruent(U_11489,tc_fun(U_11492,tc_HOL_Obool),U_11491,U_11493)
    | ~ c_Equiv__Relations_Oequiv(U_11489,U_11490,U_11491) ),
    inference(clausify,[status(thm)],[f_3061_2]) ).

fof(f_3062_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_3062_2,plain,
    ! [U_11496,U_11495] :
      ( ( c_Equiv__Relations_Oequiv(U_11495,c_Orderings_Otop__class_Otop(tc_fun(U_11495,tc_HOL_Obool)),U_11496)
        | ~ c_Equiv__Relations_Oequivp(U_11495,hAPP(hAPP(c_COMBC(U_11495,tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11495),c_COMBC(U_11495,tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11495,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11495),hAPP(c_COMBB(tc_prod(U_11495,U_11495),tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11495,U_11495)))),c_Product__Type_OPair(U_11495,U_11495)))),U_11496)) )
      & ( c_Equiv__Relations_Oequivp(U_11495,hAPP(hAPP(c_COMBC(U_11495,tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11495),c_COMBC(U_11495,tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11495,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11495),hAPP(c_COMBB(tc_prod(U_11495,U_11495),tc_fun(tc_fun(tc_prod(U_11495,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11495,U_11495)))),c_Product__Type_OPair(U_11495,U_11495)))),U_11496))
        | ~ c_Equiv__Relations_Oequiv(U_11495,c_Orderings_Otop__class_Otop(tc_fun(U_11495,tc_HOL_Obool)),U_11496) ) ),
    inference(variable_rename,[status(thm)],[f_3062_1]) ).

fof(f_3062_3,plain,
    ( ! [U_11500,U_11498] :
        ( c_Equiv__Relations_Oequiv(U_11498,c_Orderings_Otop__class_Otop(tc_fun(U_11498,tc_HOL_Obool)),U_11500)
        | ~ c_Equiv__Relations_Oequivp(U_11498,hAPP(hAPP(c_COMBC(U_11498,tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11498,tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool)),U_11498),c_COMBC(U_11498,tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11498,tc_prod(U_11498,U_11498)),tc_fun(U_11498,tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),U_11498),hAPP(c_COMBB(tc_prod(U_11498,U_11498),tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool),U_11498),c_member(tc_prod(U_11498,U_11498)))),c_Product__Type_OPair(U_11498,U_11498)))),U_11500)) )
    & ! [U_11499,U_11497] :
        ( c_Equiv__Relations_Oequivp(U_11497,hAPP(hAPP(c_COMBC(U_11497,tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_fun(U_11497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11497,tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_fun(U_11497,tc_HOL_Obool)),U_11497),c_COMBC(U_11497,tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11497,tc_prod(U_11497,U_11497)),tc_fun(U_11497,tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),U_11497),hAPP(c_COMBB(tc_prod(U_11497,U_11497),tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool),U_11497),c_member(tc_prod(U_11497,U_11497)))),c_Product__Type_OPair(U_11497,U_11497)))),U_11499))
        | ~ c_Equiv__Relations_Oequiv(U_11497,c_Orderings_Otop__class_Otop(tc_fun(U_11497,tc_HOL_Obool)),U_11499) ) ),
    inference(miniscope,[status(thm)],[f_3062_2]) ).

cnf(f_3062_4,plain,
    ( c_Equiv__Relations_Oequivp(U_11497,hAPP(hAPP(c_COMBC(U_11497,tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_fun(U_11497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11497,tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_fun(U_11497,tc_HOL_Obool)),U_11497),c_COMBC(U_11497,tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11497,tc_prod(U_11497,U_11497)),tc_fun(U_11497,tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool)),U_11497),hAPP(c_COMBB(tc_prod(U_11497,U_11497),tc_fun(tc_fun(tc_prod(U_11497,U_11497),tc_HOL_Obool),tc_HOL_Obool),U_11497),c_member(tc_prod(U_11497,U_11497)))),c_Product__Type_OPair(U_11497,U_11497)))),U_11499))
    | ~ c_Equiv__Relations_Oequiv(U_11497,c_Orderings_Otop__class_Otop(tc_fun(U_11497,tc_HOL_Obool)),U_11499) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

cnf(f_3062_5,plain,
    ( c_Equiv__Relations_Oequiv(U_11498,c_Orderings_Otop__class_Otop(tc_fun(U_11498,tc_HOL_Obool)),U_11500)
    | ~ c_Equiv__Relations_Oequivp(U_11498,hAPP(hAPP(c_COMBC(U_11498,tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11498,tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_fun(U_11498,tc_HOL_Obool)),U_11498),c_COMBC(U_11498,tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11498,tc_prod(U_11498,U_11498)),tc_fun(U_11498,tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool)),U_11498),hAPP(c_COMBB(tc_prod(U_11498,U_11498),tc_fun(tc_fun(tc_prod(U_11498,U_11498),tc_HOL_Obool),tc_HOL_Obool),U_11498),c_member(tc_prod(U_11498,U_11498)))),c_Product__Type_OPair(U_11498,U_11498)))),U_11500)) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

fof(f_3063_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_3063_2,plain,
    ! [U_11505,U_11504,U_11503,U_11502,U_11501] :
      ( hBOOL(hAPP(hAPP(U_11502,U_11503),U_11505))
      | ~ hBOOL(hAPP(hAPP(U_11502,U_11504),U_11505))
      | ~ hBOOL(hAPP(hAPP(U_11502,U_11503),U_11504))
      | ~ c_Equiv__Relations_Oequivp(U_11501,U_11502) ),
    inference(variable_rename,[status(thm)],[f_3063_1]) ).

fof(f_3063_3,plain,
    ! [U_11505,U_11504,U_11503,U_11502] :
      ( ! [U_11501] : ~ c_Equiv__Relations_Oequivp(U_11501,U_11502)
      | hBOOL(hAPP(hAPP(U_11502,U_11503),U_11505))
      | ~ hBOOL(hAPP(hAPP(U_11502,U_11504),U_11505))
      | ~ hBOOL(hAPP(hAPP(U_11502,U_11503),U_11504)) ),
    inference(miniscope,[status(thm)],[f_3063_2]) ).

cnf(f_3063_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_11501,U_11502)
    | hBOOL(hAPP(hAPP(U_11502,U_11503),U_11505))
    | ~ hBOOL(hAPP(hAPP(U_11502,U_11504),U_11505))
    | ~ hBOOL(hAPP(hAPP(U_11502,U_11503),U_11504)) ),
    inference(clausify,[status(thm)],[f_3063_3]) ).

fof(f_3064_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_3064_2,plain,
    ! [U_11509,U_11508,U_11507,U_11506] :
      ( hBOOL(hAPP(hAPP(U_11507,U_11509),U_11508))
      | ~ hBOOL(hAPP(hAPP(U_11507,U_11508),U_11509))
      | ~ c_Equiv__Relations_Oequivp(U_11506,U_11507) ),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

fof(f_3064_3,plain,
    ! [U_11509,U_11508,U_11507] :
      ( ! [U_11506] : ~ c_Equiv__Relations_Oequivp(U_11506,U_11507)
      | hBOOL(hAPP(hAPP(U_11507,U_11509),U_11508))
      | ~ hBOOL(hAPP(hAPP(U_11507,U_11508),U_11509)) ),
    inference(miniscope,[status(thm)],[f_3064_2]) ).

cnf(f_3064_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_11506,U_11507)
    | hBOOL(hAPP(hAPP(U_11507,U_11509),U_11508))
    | ~ hBOOL(hAPP(hAPP(U_11507,U_11508),U_11509)) ),
    inference(clausify,[status(thm)],[f_3064_3]) ).

fof(f_3065_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_3065_2,plain,
    ! [U_11512,U_11511,U_11510] :
      ( hBOOL(hAPP(hAPP(U_11511,U_11512),U_11512))
      | ~ c_Equiv__Relations_Oequivp(U_11510,U_11511) ),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

fof(f_3065_3,plain,
    ! [U_11512,U_11511] :
      ( ! [U_11510] : ~ c_Equiv__Relations_Oequivp(U_11510,U_11511)
      | hBOOL(hAPP(hAPP(U_11511,U_11512),U_11512)) ),
    inference(miniscope,[status(thm)],[f_3065_2]) ).

cnf(f_3065_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_11510,U_11511)
    | hBOOL(hAPP(hAPP(U_11511,U_11512),U_11512)) ),
    inference(clausify,[status(thm)],[f_3065_3]) ).

fof(f_3066_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_3066_2,plain,
    ! [U_11518,U_11517] :
      ( ( c_Equiv__Relations_Oequivp(U_11517,U_11518)
        | ? [U_11516,U_11515] :
            ( ( ~ hBOOL(hAPP(hAPP(U_11518,U_11516),U_11515))
              & hAPP(U_11518,U_11516) = hAPP(U_11518,U_11515) )
            | ( hAPP(U_11518,U_11516) != hAPP(U_11518,U_11515)
              & hBOOL(hAPP(hAPP(U_11518,U_11516),U_11515)) ) ) )
      & ( ! [U_11514,U_11513] :
            ( ( hBOOL(hAPP(hAPP(U_11518,U_11514),U_11513))
              | hAPP(U_11518,U_11514) != hAPP(U_11518,U_11513) )
            & ( hAPP(U_11518,U_11514) = hAPP(U_11518,U_11513)
              | ~ hBOOL(hAPP(hAPP(U_11518,U_11514),U_11513)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_11517,U_11518) ) ),
    inference(variable_rename,[status(thm)],[f_3066_1]) ).

fof(f_3066_3,plain,
    ( ! [U_11530] :
        ( ! [U_11528] : c_Equiv__Relations_Oequivp(U_11528,U_11530)
        | ? [U_11526,U_11524] :
            ( ~ hBOOL(hAPP(hAPP(U_11530,U_11526),U_11524))
            & hAPP(U_11530,U_11526) = hAPP(U_11530,U_11524) )
        | ? [U_11525,U_11523] :
            ( hAPP(U_11530,U_11525) != hAPP(U_11530,U_11523)
            & hBOOL(hAPP(hAPP(U_11530,U_11525),U_11523)) ) )
    & ! [U_11529] :
        ( ! [U_11527] : ~ c_Equiv__Relations_Oequivp(U_11527,U_11529)
        | ( ! [U_11522,U_11520] :
              ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
              | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520) )
          & ! [U_11521,U_11519] :
              ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
              | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3066_2]) ).

fof(f_3066_4,plain,
    ( ! [U_11530] :
        ( ! [U_11528] : c_Equiv__Relations_Oequivp(U_11528,U_11530)
        | ? [U_11526,U_11524] :
            ( ~ hBOOL(hAPP(hAPP(U_11530,U_11526),U_11524))
            & hAPP(U_11530,U_11526) = hAPP(U_11530,U_11524) )
        | ? [U_11523] :
            ( hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,U_11523)
            & hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),U_11523)) ) )
    & ! [U_11529] :
        ( ! [U_11527] : ~ c_Equiv__Relations_Oequivp(U_11527,U_11529)
        | ( ! [U_11522,U_11520] :
              ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
              | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520) )
          & ! [U_11521,U_11519] :
              ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
              | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_11525,sK261(U_11530))],[f_3066_3]) ).

fof(f_3066_5,plain,
    ( ! [U_11530] :
        ( ! [U_11528] : c_Equiv__Relations_Oequivp(U_11528,U_11530)
        | ? [U_11526,U_11524] :
            ( ~ hBOOL(hAPP(hAPP(U_11530,U_11526),U_11524))
            & hAPP(U_11530,U_11526) = hAPP(U_11530,U_11524) )
        | ( hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,sK262(U_11530))
          & hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),sK262(U_11530))) ) )
    & ! [U_11529] :
        ( ! [U_11527] : ~ c_Equiv__Relations_Oequivp(U_11527,U_11529)
        | ( ! [U_11522,U_11520] :
              ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
              | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520) )
          & ! [U_11521,U_11519] :
              ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
              | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_11523,sK262(U_11530))],[f_3066_4]) ).

fof(f_3066_6,plain,
    ( ! [U_11530] :
        ( ! [U_11528] : c_Equiv__Relations_Oequivp(U_11528,U_11530)
        | ? [U_11524] :
            ( ~ hBOOL(hAPP(hAPP(U_11530,sK263(U_11530)),U_11524))
            & hAPP(U_11530,sK263(U_11530)) = hAPP(U_11530,U_11524) )
        | ( hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,sK262(U_11530))
          & hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),sK262(U_11530))) ) )
    & ! [U_11529] :
        ( ! [U_11527] : ~ c_Equiv__Relations_Oequivp(U_11527,U_11529)
        | ( ! [U_11522,U_11520] :
              ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
              | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520) )
          & ! [U_11521,U_11519] :
              ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
              | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_11526,sK263(U_11530))],[f_3066_5]) ).

fof(f_3066_7,plain,
    ( ! [U_11530] :
        ( ! [U_11528] : c_Equiv__Relations_Oequivp(U_11528,U_11530)
        | ( ~ hBOOL(hAPP(hAPP(U_11530,sK263(U_11530)),sK264(U_11530)))
          & hAPP(U_11530,sK263(U_11530)) = hAPP(U_11530,sK264(U_11530)) )
        | ( hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,sK262(U_11530))
          & hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),sK262(U_11530))) ) )
    & ! [U_11529] :
        ( ! [U_11527] : ~ c_Equiv__Relations_Oequivp(U_11527,U_11529)
        | ( ! [U_11522,U_11520] :
              ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
              | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520) )
          & ! [U_11521,U_11519] :
              ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
              | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_11524,sK264(U_11530))],[f_3066_6]) ).

cnf(f_3066_8,plain,
    ( hAPP(U_11529,U_11521) = hAPP(U_11529,U_11519)
    | ~ hBOOL(hAPP(hAPP(U_11529,U_11521),U_11519))
    | ~ c_Equiv__Relations_Oequivp(U_11527,U_11529) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

cnf(f_3066_9,plain,
    ( hBOOL(hAPP(hAPP(U_11529,U_11522),U_11520))
    | hAPP(U_11529,U_11522) != hAPP(U_11529,U_11520)
    | ~ c_Equiv__Relations_Oequivp(U_11527,U_11529) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

cnf(f_3066_10,plain,
    ( hAPP(U_11530,sK263(U_11530)) = hAPP(U_11530,sK264(U_11530))
    | hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),sK262(U_11530)))
    | c_Equiv__Relations_Oequivp(U_11528,U_11530) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

cnf(f_3066_11,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11530,sK263(U_11530)),sK264(U_11530)))
    | hBOOL(hAPP(hAPP(U_11530,sK261(U_11530)),sK262(U_11530)))
    | c_Equiv__Relations_Oequivp(U_11528,U_11530) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

cnf(f_3066_12,plain,
    ( hAPP(U_11530,sK263(U_11530)) = hAPP(U_11530,sK264(U_11530))
    | hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,sK262(U_11530))
    | c_Equiv__Relations_Oequivp(U_11528,U_11530) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

cnf(f_3066_13,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11530,sK263(U_11530)),sK264(U_11530)))
    | hAPP(U_11530,sK261(U_11530)) != hAPP(U_11530,sK262(U_11530))
    | c_Equiv__Relations_Oequivp(U_11528,U_11530) ),
    inference(clausify,[status(thm)],[f_3066_7]) ).

fof(f_3067_1,plain,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3067_2,plain,
    ! [U_11531] : c_Equiv__Relations_Oequivp(U_11531,c_fequal),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

cnf(f_3067_3,plain,
    c_Equiv__Relations_Oequivp(U_11531,c_fequal),
    inference(clausify,[status(thm)],[f_3067_2]) ).

fof(f_3068_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_3068_2,plain,
    ! [U_11539,U_11538,U_11537,U_11536,U_11535,U_11534,U_11533,U_11532] :
      ( c_Equiv__Relations_Ocongruent(U_11535,U_11536,U_11537,hAPP(U_11538,U_11539))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11532),U_11539),U_11533))
      | ~ c_Equiv__Relations_Ocongruent2(U_11532,U_11535,U_11536,U_11534,U_11537,U_11538)
      | ~ c_Equiv__Relations_Oequiv(U_11532,U_11533,U_11534) ),
    inference(variable_rename,[status(thm)],[f_3068_1]) ).

cnf(f_3068_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_11535,U_11536,U_11537,hAPP(U_11538,U_11539))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11532),U_11539),U_11533))
    | ~ c_Equiv__Relations_Ocongruent2(U_11532,U_11535,U_11536,U_11534,U_11537,U_11538)
    | ~ c_Equiv__Relations_Oequiv(U_11532,U_11533,U_11534) ),
    inference(clausify,[status(thm)],[f_3068_2]) ).

fof(f_3069_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_3069_2,plain,
    ! [U_11549,U_11548,U_11547,U_11546,U_11545,U_11544,U_11543,U_11542,U_11541,U_11540] :
      ( hAPP(hAPP(U_11545,U_11546),U_11548) = hAPP(hAPP(U_11545,U_11547),U_11549)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11541,U_11541)),hAPP(hAPP(c_Product__Type_OPair(U_11541,U_11541),U_11548),U_11549)),U_11544))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11540,U_11540)),hAPP(hAPP(c_Product__Type_OPair(U_11540,U_11540),U_11546),U_11547)),U_11543))
      | ~ c_Equiv__Relations_Ocongruent2(U_11540,U_11541,U_11542,U_11543,U_11544,U_11545) ),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

cnf(f_3069_3,plain,
    ( hAPP(hAPP(U_11545,U_11546),U_11548) = hAPP(hAPP(U_11545,U_11547),U_11549)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11541,U_11541)),hAPP(hAPP(c_Product__Type_OPair(U_11541,U_11541),U_11548),U_11549)),U_11544))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11540,U_11540)),hAPP(hAPP(c_Product__Type_OPair(U_11540,U_11540),U_11546),U_11547)),U_11543))
    | ~ c_Equiv__Relations_Ocongruent2(U_11540,U_11541,U_11542,U_11543,U_11544,U_11545) ),
    inference(clausify,[status(thm)],[f_3069_2]) ).

fof(f_3070_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_3070_2,plain,
    ! [U_11555,U_11554,U_11553,U_11552,U_11551,U_11550] :
      ( hAPP(U_11553,U_11554) = hAPP(U_11553,U_11555)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11550,U_11550)),hAPP(hAPP(c_Product__Type_OPair(U_11550,U_11550),U_11554),U_11555)),U_11552))
      | ~ c_Equiv__Relations_Ocongruent(U_11550,U_11551,U_11552,U_11553) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

cnf(f_3070_3,plain,
    ( hAPP(U_11553,U_11554) = hAPP(U_11553,U_11555)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11550,U_11550)),hAPP(hAPP(c_Product__Type_OPair(U_11550,U_11550),U_11554),U_11555)),U_11552))
    | ~ c_Equiv__Relations_Ocongruent(U_11550,U_11551,U_11552,U_11553) ),
    inference(clausify,[status(thm)],[f_3070_2]) ).

fof(f_3071_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_3071_2,plain,
    ! [U_11564,U_11563,U_11562,U_11561,U_11560,U_11559,U_11558,U_11557,U_11556] :
      ( c_Equiv__Relations_Ocongruent(U_11556,tc_fun(U_11562,tc_HOL_Obool),U_11558,hAPP(hAPP(c_COMBB(tc_fun(U_11559,tc_fun(U_11562,tc_HOL_Obool)),tc_fun(U_11562,tc_HOL_Obool),U_11556),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11559,tc_fun(U_11562,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11559,U_11559,U_11561),hAPP(hAPP(c_Set_Oinsert(U_11559),U_11564),c_Orderings_Obot__class_Obot(tc_fun(U_11559,tc_HOL_Obool)))))),U_11563))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11559),U_11564),U_11560))
      | ~ c_Equiv__Relations_Ocongruent2(U_11556,U_11559,tc_fun(U_11562,tc_HOL_Obool),U_11558,U_11561,U_11563)
      | ~ c_Equiv__Relations_Oequiv(U_11559,U_11560,U_11561)
      | ~ c_Equiv__Relations_Oequiv(U_11556,U_11557,U_11558) ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

cnf(f_3071_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_11556,tc_fun(U_11562,tc_HOL_Obool),U_11558,hAPP(hAPP(c_COMBB(tc_fun(U_11559,tc_fun(U_11562,tc_HOL_Obool)),tc_fun(U_11562,tc_HOL_Obool),U_11556),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11559,tc_fun(U_11562,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11559,U_11559,U_11561),hAPP(hAPP(c_Set_Oinsert(U_11559),U_11564),c_Orderings_Obot__class_Obot(tc_fun(U_11559,tc_HOL_Obool)))))),U_11563))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11559),U_11564),U_11560))
    | ~ c_Equiv__Relations_Ocongruent2(U_11556,U_11559,tc_fun(U_11562,tc_HOL_Obool),U_11558,U_11561,U_11563)
    | ~ c_Equiv__Relations_Oequiv(U_11559,U_11560,U_11561)
    | ~ c_Equiv__Relations_Oequiv(U_11556,U_11557,U_11558) ),
    inference(clausify,[status(thm)],[f_3071_2]) ).

fof(f_3072_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_3072_2,plain,
    ! [U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567] :
      ( U_11572 = U_11573
      | ? [U_11566] :
          ( ? [U_11565] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11567,U_11567)),hAPP(hAPP(c_Product__Type_OPair(U_11567,U_11567),U_11566),U_11565)),U_11569))
              & hAPP(U_11571,U_11566) = hAPP(U_11571,U_11565)
              & hBOOL(hAPP(hAPP(c_member(U_11567),U_11565),U_11568)) )
          & hBOOL(hAPP(hAPP(c_member(U_11567),U_11566),U_11568)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
      | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
      | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

fof(f_3072_3,plain,
    ! [U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567] :
      ( U_11572 = U_11573
      | ( ? [U_11565] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11567,U_11567)),hAPP(hAPP(c_Product__Type_OPair(U_11567,U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11565)),U_11569))
            & hAPP(U_11571,sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)) = hAPP(U_11571,U_11565)
            & hBOOL(hAPP(hAPP(c_member(U_11567),U_11565),U_11568)) )
        & hBOOL(hAPP(hAPP(c_member(U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11568)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
      | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
      | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_11566,sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))],[f_3072_2]) ).

fof(f_3072_4,plain,
    ! [U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567] :
      ( U_11572 = U_11573
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11567,U_11567)),hAPP(hAPP(c_Product__Type_OPair(U_11567,U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))),U_11569))
        & hAPP(U_11571,sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)) = hAPP(U_11571,sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))
        & hBOOL(hAPP(hAPP(c_member(U_11567),sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11568))
        & hBOOL(hAPP(hAPP(c_member(U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11568)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
      | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
      | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_11565,sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))],[f_3072_3]) ).

cnf(f_3072_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11568))
    | U_11572 = U_11573
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
    | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
    | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

cnf(f_3072_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11567),sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),U_11568))
    | U_11572 = U_11573
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
    | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
    | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

cnf(f_3072_7,plain,
    ( hAPP(U_11571,sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)) = hAPP(U_11571,sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))
    | U_11572 = U_11573
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
    | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
    | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

cnf(f_3072_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11567,U_11567)),hAPP(hAPP(c_Product__Type_OPair(U_11567,U_11567),sK265(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567)),sK266(U_11573,U_11572,U_11571,U_11570,U_11569,U_11568,U_11567))),U_11569))
    | U_11572 = U_11573
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11573),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11567,tc_HOL_Obool)),U_11572),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11567),U_11568),U_11569)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11572),U_11571) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11567,tc_fun(U_11570,tc_HOL_Obool)),U_11573),U_11571)
    | ~ c_Equiv__Relations_Ocongruent(U_11567,tc_fun(U_11570,tc_HOL_Obool),U_11569,U_11571)
    | ~ c_Equiv__Relations_Oequiv(U_11567,U_11568,U_11569) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

fof(f_3073_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_3073_2,plain,
    ! [U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
      | ? [U_11575] :
          ( ? [U_11574] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(U_11583,U_11575),U_11574)),U_11586))
              & hBOOL(hAPP(hAPP(c_member(U_11579),U_11574),U_11580)) )
          & hBOOL(hAPP(hAPP(c_member(U_11576),U_11575),U_11577)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
      | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
      | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

fof(f_3073_3,plain,
    ! [U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
      | ( ? [U_11574] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(U_11583,sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11574)),U_11586))
            & hBOOL(hAPP(hAPP(c_member(U_11579),U_11574),U_11580)) )
        & hBOOL(hAPP(hAPP(c_member(U_11576),sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11577)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
      | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
      | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_11575,sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576))],[f_3073_2]) ).

fof(f_3073_4,plain,
    ! [U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(U_11583,sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),sK268(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576))),U_11586))
        & hBOOL(hAPP(hAPP(c_member(U_11579),sK268(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11580))
        & hBOOL(hAPP(hAPP(c_member(U_11576),sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11577)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
      | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
      | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_11574,sK268(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576))],[f_3073_3]) ).

cnf(f_3073_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11576),sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11577))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
    | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
    | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
    | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(clausify,[status(thm)],[f_3073_4]) ).

cnf(f_3073_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11579),sK268(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),U_11580))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
    | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
    | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
    | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(clausify,[status(thm)],[f_3073_4]) ).

cnf(f_3073_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(U_11583,sK267(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576)),sK268(U_11586,U_11585,U_11584,U_11583,U_11582,U_11581,U_11580,U_11579,U_11578,U_11577,U_11576))),U_11586))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_11582,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11576,tc_fun(U_11582,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_COMBB(tc_fun(U_11579,tc_fun(U_11582,tc_HOL_Obool)),tc_fun(U_11582,tc_HOL_Obool),U_11576),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11579,tc_fun(U_11582,tc_HOL_Obool)),U_11585)),U_11583))),U_11586))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11579,tc_HOL_Obool)),U_11585),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11579),U_11580),U_11581)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11576,tc_HOL_Obool)),U_11584),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11576),U_11577),U_11578)))
    | ~ c_Equiv__Relations_Ocongruent2(U_11576,U_11579,tc_fun(U_11582,tc_HOL_Obool),U_11578,U_11581,U_11583)
    | ~ c_Equiv__Relations_Oequiv(U_11579,U_11580,U_11581)
    | ~ c_Equiv__Relations_Oequiv(U_11576,U_11577,U_11578) ),
    inference(clausify,[status(thm)],[f_3073_4]) ).

fof(f_3074_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_3074_2,plain,
    ! [U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11588,tc_fun(U_11591,tc_HOL_Obool)),U_11593),U_11592)),U_11594))
      | ? [U_11587] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(U_11592,U_11587)),U_11594))
          & hBOOL(hAPP(hAPP(c_member(U_11588),U_11587),U_11589)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11588,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11588),U_11589),U_11590)))
      | ~ c_Equiv__Relations_Ocongruent(U_11588,tc_fun(U_11591,tc_HOL_Obool),U_11590,U_11592)
      | ~ c_Equiv__Relations_Oequiv(U_11588,U_11589,U_11590) ),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

fof(f_3074_3,plain,
    ! [U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11588,tc_fun(U_11591,tc_HOL_Obool)),U_11593),U_11592)),U_11594))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(U_11592,sK269(U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588))),U_11594))
        & hBOOL(hAPP(hAPP(c_member(U_11588),sK269(U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588)),U_11589)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11588,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11588),U_11589),U_11590)))
      | ~ c_Equiv__Relations_Ocongruent(U_11588,tc_fun(U_11591,tc_HOL_Obool),U_11590,U_11592)
      | ~ c_Equiv__Relations_Oequiv(U_11588,U_11589,U_11590) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_11587,sK269(U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588))],[f_3074_2]) ).

cnf(f_3074_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11588),sK269(U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588)),U_11589))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11588,tc_fun(U_11591,tc_HOL_Obool)),U_11593),U_11592)),U_11594))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11588,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11588),U_11589),U_11590)))
    | ~ c_Equiv__Relations_Ocongruent(U_11588,tc_fun(U_11591,tc_HOL_Obool),U_11590,U_11592)
    | ~ c_Equiv__Relations_Oequiv(U_11588,U_11589,U_11590) ),
    inference(clausify,[status(thm)],[f_3074_3]) ).

cnf(f_3074_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(U_11592,sK269(U_11594,U_11593,U_11592,U_11591,U_11590,U_11589,U_11588))),U_11594))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11588,tc_fun(U_11591,tc_HOL_Obool)),U_11593),U_11592)),U_11594))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11588,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11588),U_11589),U_11590)))
    | ~ c_Equiv__Relations_Ocongruent(U_11588,tc_fun(U_11591,tc_HOL_Obool),U_11590,U_11592)
    | ~ c_Equiv__Relations_Oequiv(U_11588,U_11589,U_11590) ),
    inference(clausify,[status(thm)],[f_3074_3]) ).

fof(f_3075_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_3075_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_3075_1]) ).

fof(f_3076_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_3076_2,plain,
    ! [U_11597,U_11596,U_11595] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11595,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11595),U_11596),U_11597)) = hAPP(c_Finite__Set_Ocard(U_11595),U_11596)
      | ~ c_Fun_Oinj__on(U_11595,tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11595,tc_fun(tc_prod(U_11595,U_11595),tc_HOL_Obool),tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11595,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11595,U_11595),tc_HOL_Obool),tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool)),U_11595),c_Equiv__Relations_Oquotient(U_11595)),hAPP(hAPP(c_COMBC(U_11595,tc_fun(U_11595,tc_HOL_Obool),tc_fun(U_11595,tc_HOL_Obool)),c_Set_Oinsert(U_11595)),c_Orderings_Obot__class_Obot(tc_fun(U_11595,tc_HOL_Obool))))),U_11597),U_11596)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11595),U_11596)) ),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

cnf(f_3076_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11595,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11595),U_11596),U_11597)) = hAPP(c_Finite__Set_Ocard(U_11595),U_11596)
    | ~ c_Fun_Oinj__on(U_11595,tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11595,tc_fun(tc_prod(U_11595,U_11595),tc_HOL_Obool),tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11595,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11595,U_11595),tc_HOL_Obool),tc_fun(tc_fun(U_11595,tc_HOL_Obool),tc_HOL_Obool)),U_11595),c_Equiv__Relations_Oquotient(U_11595)),hAPP(hAPP(c_COMBC(U_11595,tc_fun(U_11595,tc_HOL_Obool),tc_fun(U_11595,tc_HOL_Obool)),c_Set_Oinsert(U_11595)),c_Orderings_Obot__class_Obot(tc_fun(U_11595,tc_HOL_Obool))))),U_11597),U_11596)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11595),U_11596)) ),
    inference(clausify,[status(thm)],[f_3076_2]) ).

fof(f_3077_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_3077_2,plain,
    ! [U_11603,U_11602,U_11601,U_11600,U_11599] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11602),U_11600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11603),U_11601)
      | ? [U_11598] :
          ( hAPP(U_11602,U_11598) != hAPP(U_11603,U_11598)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11598)) )
      | ~ c_Nat__Transfer_Onat__set(U_11601)
      | U_11600 != U_11601
      | ~ class_Groups_Ocomm__monoid__mult(U_11599)
      | ~ class_Groups_Ocomm__monoid__add(U_11599) ),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

fof(f_3077_3,plain,
    ! [U_11603,U_11602,U_11601,U_11600,U_11599] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11602),U_11600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11603),U_11601)
      | ( hAPP(U_11602,sK270(U_11603,U_11602,U_11601,U_11600,U_11599)) != hAPP(U_11603,sK270(U_11603,U_11602,U_11601,U_11600,U_11599))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK270(U_11603,U_11602,U_11601,U_11600,U_11599))) )
      | ~ c_Nat__Transfer_Onat__set(U_11601)
      | U_11600 != U_11601
      | ~ class_Groups_Ocomm__monoid__mult(U_11599)
      | ~ class_Groups_Ocomm__monoid__add(U_11599) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_11598,sK270(U_11603,U_11602,U_11601,U_11600,U_11599))],[f_3077_2]) ).

cnf(f_3077_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK270(U_11603,U_11602,U_11601,U_11600,U_11599)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11602),U_11600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11603),U_11601)
    | ~ c_Nat__Transfer_Onat__set(U_11601)
    | U_11600 != U_11601
    | ~ class_Groups_Ocomm__monoid__mult(U_11599)
    | ~ class_Groups_Ocomm__monoid__add(U_11599) ),
    inference(clausify,[status(thm)],[f_3077_3]) ).

cnf(f_3077_5,plain,
    ( hAPP(U_11602,sK270(U_11603,U_11602,U_11601,U_11600,U_11599)) != hAPP(U_11603,sK270(U_11603,U_11602,U_11601,U_11600,U_11599))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11602),U_11600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_11599),U_11603),U_11601)
    | ~ c_Nat__Transfer_Onat__set(U_11601)
    | U_11600 != U_11601
    | ~ class_Groups_Ocomm__monoid__mult(U_11599)
    | ~ class_Groups_Ocomm__monoid__add(U_11599) ),
    inference(clausify,[status(thm)],[f_3077_3]) ).

fof(f_3078_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_3078_2,plain,
    ! [U_11606,U_11605,U_11604] : c_Fun_Oinj__on(U_11604,U_11605,U_11606,c_Orderings_Obot__class_Obot(tc_fun(U_11604,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3078_1]) ).

cnf(f_3078_3,plain,
    c_Fun_Oinj__on(U_11604,U_11605,U_11606,c_Orderings_Obot__class_Obot(tc_fun(U_11604,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3078_2]) ).

fof(f_3079_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_3079_2,plain,
    ! [U_11608,U_11607] :
      ( c_Fun_Oinj__on(U_11607,U_11607,c_Groups_Ouminus__class_Ouminus(U_11607),U_11608)
      | ~ class_Groups_Oordered__ab__group__add(U_11607) ),
    inference(variable_rename,[status(thm)],[f_3079_1]) ).

cnf(f_3079_3,plain,
    ( c_Fun_Oinj__on(U_11607,U_11607,c_Groups_Ouminus__class_Ouminus(U_11607),U_11608)
    | ~ class_Groups_Oordered__ab__group__add(U_11607) ),
    inference(clausify,[status(thm)],[f_3079_2]) ).

fof(f_3080_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_3080_2,plain,
    ! [U_11613,U_11612,U_11611,U_11610,U_11609] :
      ( c_Fun_Oinj__on(U_11609,U_11610,U_11611,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11612),U_11613))
      | ~ c_Fun_Oinj__on(U_11609,U_11610,U_11611,U_11612) ),
    inference(variable_rename,[status(thm)],[f_3080_1]) ).

cnf(f_3080_3,plain,
    ( c_Fun_Oinj__on(U_11609,U_11610,U_11611,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11612),U_11613))
    | ~ c_Fun_Oinj__on(U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3080_2]) ).

fof(f_3081_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_3081_2,plain,
    ! [U_11618,U_11617,U_11616,U_11615,U_11614] :
      ( c_Fun_Oinj__on(U_11614,U_11615,U_11616,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11614,tc_HOL_Obool)),U_11617),U_11618))
      | ~ c_Fun_Oinj__on(U_11614,U_11615,U_11616,U_11618)
      | ~ c_Fun_Oinj__on(U_11614,U_11615,U_11616,U_11617) ),
    inference(variable_rename,[status(thm)],[f_3081_1]) ).

cnf(f_3081_3,plain,
    ( c_Fun_Oinj__on(U_11614,U_11615,U_11616,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11614,tc_HOL_Obool)),U_11617),U_11618))
    | ~ c_Fun_Oinj__on(U_11614,U_11615,U_11616,U_11618)
    | ~ c_Fun_Oinj__on(U_11614,U_11615,U_11616,U_11617) ),
    inference(clausify,[status(thm)],[f_3081_2]) ).

fof(f_3082_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_3082_2,plain,
    ! [U_11620,U_11619] : c_Fun_Oinj__on(U_11619,U_11619,c_COMBI(U_11619),U_11620),
    inference(variable_rename,[status(thm)],[f_3082_1]) ).

cnf(f_3082_3,plain,
    c_Fun_Oinj__on(U_11619,U_11619,c_COMBI(U_11619),U_11620),
    inference(clausify,[status(thm)],[f_3082_2]) ).

fof(f_3083_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_3083_2,plain,
    ! [U_11628,U_11627,U_11626,U_11625] :
      ( ( c_Fun_Oinj__on(U_11625,U_11626,U_11627,U_11628)
        | ? [U_11624] :
            ( ? [U_11623] :
                ( U_11624 != U_11623
                & hAPP(U_11627,U_11624) = hAPP(U_11627,U_11623)
                & hBOOL(hAPP(hAPP(c_member(U_11625),U_11623),U_11628)) )
            & hBOOL(hAPP(hAPP(c_member(U_11625),U_11624),U_11628)) ) )
      & ( ! [U_11622] :
            ( ! [U_11621] :
                ( U_11622 = U_11621
                | hAPP(U_11627,U_11622) != hAPP(U_11627,U_11621)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11625),U_11621),U_11628)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11625),U_11622),U_11628)) )
        | ~ c_Fun_Oinj__on(U_11625,U_11626,U_11627,U_11628) ) ),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

fof(f_3083_3,plain,
    ( ! [U_11636,U_11634,U_11632,U_11630] :
        ( c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636)
        | ? [U_11624] :
            ( ? [U_11623] :
                ( U_11624 != U_11623
                & hAPP(U_11634,U_11624) = hAPP(U_11634,U_11623)
                & hBOOL(hAPP(hAPP(c_member(U_11630),U_11623),U_11636)) )
            & hBOOL(hAPP(hAPP(c_member(U_11630),U_11624),U_11636)) ) )
    & ! [U_11635,U_11633,U_11631,U_11629] :
        ( ! [U_11622] :
            ( ! [U_11621] :
                ( U_11622 = U_11621
                | hAPP(U_11633,U_11622) != hAPP(U_11633,U_11621)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11621),U_11635)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11622),U_11635)) )
        | ~ c_Fun_Oinj__on(U_11629,U_11631,U_11633,U_11635) ) ),
    inference(miniscope,[status(thm)],[f_3083_2]) ).

fof(f_3083_4,plain,
    ( ! [U_11636,U_11634,U_11632,U_11630] :
        ( c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636)
        | ( ? [U_11623] :
              ( sK271(U_11636,U_11634,U_11632,U_11630) != U_11623
              & hAPP(U_11634,sK271(U_11636,U_11634,U_11632,U_11630)) = hAPP(U_11634,U_11623)
              & hBOOL(hAPP(hAPP(c_member(U_11630),U_11623),U_11636)) )
          & hBOOL(hAPP(hAPP(c_member(U_11630),sK271(U_11636,U_11634,U_11632,U_11630)),U_11636)) ) )
    & ! [U_11635,U_11633,U_11631,U_11629] :
        ( ! [U_11622] :
            ( ! [U_11621] :
                ( U_11622 = U_11621
                | hAPP(U_11633,U_11622) != hAPP(U_11633,U_11621)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11621),U_11635)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11622),U_11635)) )
        | ~ c_Fun_Oinj__on(U_11629,U_11631,U_11633,U_11635) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_11624,sK271(U_11636,U_11634,U_11632,U_11630))],[f_3083_3]) ).

fof(f_3083_5,plain,
    ( ! [U_11636,U_11634,U_11632,U_11630] :
        ( c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636)
        | ( sK271(U_11636,U_11634,U_11632,U_11630) != sK272(U_11636,U_11634,U_11632,U_11630)
          & hAPP(U_11634,sK271(U_11636,U_11634,U_11632,U_11630)) = hAPP(U_11634,sK272(U_11636,U_11634,U_11632,U_11630))
          & hBOOL(hAPP(hAPP(c_member(U_11630),sK272(U_11636,U_11634,U_11632,U_11630)),U_11636))
          & hBOOL(hAPP(hAPP(c_member(U_11630),sK271(U_11636,U_11634,U_11632,U_11630)),U_11636)) ) )
    & ! [U_11635,U_11633,U_11631,U_11629] :
        ( ! [U_11622] :
            ( ! [U_11621] :
                ( U_11622 = U_11621
                | hAPP(U_11633,U_11622) != hAPP(U_11633,U_11621)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11621),U_11635)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11622),U_11635)) )
        | ~ c_Fun_Oinj__on(U_11629,U_11631,U_11633,U_11635) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_11623,sK272(U_11636,U_11634,U_11632,U_11630))],[f_3083_4]) ).

cnf(f_3083_6,plain,
    ( U_11622 = U_11621
    | hAPP(U_11633,U_11622) != hAPP(U_11633,U_11621)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11621),U_11635))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11629),U_11622),U_11635))
    | ~ c_Fun_Oinj__on(U_11629,U_11631,U_11633,U_11635) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11630),sK271(U_11636,U_11634,U_11632,U_11630)),U_11636))
    | c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11630),sK272(U_11636,U_11634,U_11632,U_11630)),U_11636))
    | c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_9,plain,
    ( hAPP(U_11634,sK271(U_11636,U_11634,U_11632,U_11630)) = hAPP(U_11634,sK272(U_11636,U_11634,U_11632,U_11630))
    | c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_10,plain,
    ( sK271(U_11636,U_11634,U_11632,U_11630) != sK272(U_11636,U_11634,U_11632,U_11630)
    | c_Fun_Oinj__on(U_11630,U_11632,U_11634,U_11636) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

fof(f_3084_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_3084_2,plain,
    ! [U_11642,U_11641,U_11640,U_11639,U_11638,U_11637] :
      ( hAPP(U_11639,U_11641) != hAPP(U_11639,U_11642)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11637),U_11642),U_11640))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11637),U_11641),U_11640))
      | U_11641 = U_11642
      | ~ c_Fun_Oinj__on(U_11637,U_11638,U_11639,U_11640) ),
    inference(variable_rename,[status(thm)],[f_3084_1]) ).

cnf(f_3084_3,plain,
    ( hAPP(U_11639,U_11641) != hAPP(U_11639,U_11642)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11637),U_11642),U_11640))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11637),U_11641),U_11640))
    | U_11641 = U_11642
    | ~ c_Fun_Oinj__on(U_11637,U_11638,U_11639,U_11640) ),
    inference(clausify,[status(thm)],[f_3084_2]) ).

fof(f_3085_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_3085_2,plain,
    ! [U_11648,U_11647,U_11646,U_11645,U_11644,U_11643] :
      ( ( ( hAPP(U_11645,U_11647) = hAPP(U_11645,U_11648)
          | U_11647 != U_11648 )
        & ( U_11647 = U_11648
          | hAPP(U_11645,U_11647) != hAPP(U_11645,U_11648) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11648),U_11646))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11647),U_11646))
      | ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
    inference(variable_rename,[status(thm)],[f_3085_1]) ).

cnf(f_3085_3,plain,
    ( U_11647 = U_11648
    | hAPP(U_11645,U_11647) != hAPP(U_11645,U_11648)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11648),U_11646))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11647),U_11646))
    | ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
    inference(clausify,[status(thm)],[f_3085_2]) ).

cnf(f_3085_4,plain,
    ( hAPP(U_11645,U_11647) = hAPP(U_11645,U_11648)
    | U_11647 != U_11648
    | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11648),U_11646))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11643),U_11647),U_11646))
    | ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
    inference(clausify,[status(thm)],[f_3085_2]) ).

fof(f_3086_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_3086_2,plain,
    ! [U_11654,U_11653,U_11652,U_11651,U_11650,U_11649] :
      ( U_11653 = U_11654
      | ~ hBOOL(hAPP(hAPP(c_member(U_11649),U_11654),U_11652))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11649),U_11653),U_11652))
      | hAPP(U_11651,U_11653) != hAPP(U_11651,U_11654)
      | ~ c_Fun_Oinj__on(U_11649,U_11650,U_11651,U_11652) ),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

cnf(f_3086_3,plain,
    ( U_11653 = U_11654
    | ~ hBOOL(hAPP(hAPP(c_member(U_11649),U_11654),U_11652))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11649),U_11653),U_11652))
    | hAPP(U_11651,U_11653) != hAPP(U_11651,U_11654)
    | ~ c_Fun_Oinj__on(U_11649,U_11650,U_11651,U_11652) ),
    inference(clausify,[status(thm)],[f_3086_2]) ).

fof(f_3087_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_3087_2,plain,
    ! [U_11659,U_11658,U_11657,U_11656,U_11655] :
      ( c_Fun_Oinj__on(U_11655,U_11656,U_11657,U_11659)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11659),U_11658))
      | ~ c_Fun_Oinj__on(U_11655,U_11656,U_11657,U_11658) ),
    inference(variable_rename,[status(thm)],[f_3087_1]) ).

cnf(f_3087_3,plain,
    ( c_Fun_Oinj__on(U_11655,U_11656,U_11657,U_11659)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11659),U_11658))
    | ~ c_Fun_Oinj__on(U_11655,U_11656,U_11657,U_11658) ),
    inference(clausify,[status(thm)],[f_3087_2]) ).

fof(f_3088_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_3088_2,plain,
    ! [U_11664,U_11663,U_11662,U_11661,U_11660] :
      ( ( ( hAPP(U_11662,U_11663) = hAPP(U_11662,U_11664)
          | U_11663 != U_11664 )
        & ( U_11663 = U_11664
          | hAPP(U_11662,U_11663) != hAPP(U_11662,U_11664) ) )
      | ~ c_Fun_Oinj__on(U_11660,U_11661,U_11662,c_Orderings_Otop__class_Otop(tc_fun(U_11660,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

fof(f_3088_3,plain,
    ! [U_11664,U_11663,U_11662] :
      ( ! [U_11661,U_11660] : ~ c_Fun_Oinj__on(U_11660,U_11661,U_11662,c_Orderings_Otop__class_Otop(tc_fun(U_11660,tc_HOL_Obool)))
      | ( ( hAPP(U_11662,U_11663) = hAPP(U_11662,U_11664)
          | U_11663 != U_11664 )
        & ( U_11663 = U_11664
          | hAPP(U_11662,U_11663) != hAPP(U_11662,U_11664) ) ) ),
    inference(miniscope,[status(thm)],[f_3088_2]) ).

cnf(f_3088_4,plain,
    ( U_11663 = U_11664
    | hAPP(U_11662,U_11663) != hAPP(U_11662,U_11664)
    | ~ c_Fun_Oinj__on(U_11660,U_11661,U_11662,c_Orderings_Otop__class_Otop(tc_fun(U_11660,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

cnf(f_3088_5,plain,
    ( hAPP(U_11662,U_11663) = hAPP(U_11662,U_11664)
    | U_11663 != U_11664
    | ~ c_Fun_Oinj__on(U_11660,U_11661,U_11662,c_Orderings_Otop__class_Otop(tc_fun(U_11660,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

fof(f_3089_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_3089_2,plain,
    ! [U_11669,U_11668,U_11667,U_11666,U_11665] :
      ( U_11668 = U_11669
      | hAPP(U_11667,U_11668) != hAPP(U_11667,U_11669)
      | ~ c_Fun_Oinj__on(U_11665,U_11666,U_11667,c_Orderings_Otop__class_Otop(tc_fun(U_11665,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3089_1]) ).

fof(f_3089_3,plain,
    ! [U_11669,U_11668,U_11667] :
      ( ! [U_11666,U_11665] : ~ c_Fun_Oinj__on(U_11665,U_11666,U_11667,c_Orderings_Otop__class_Otop(tc_fun(U_11665,tc_HOL_Obool)))
      | U_11668 = U_11669
      | hAPP(U_11667,U_11668) != hAPP(U_11667,U_11669) ),
    inference(miniscope,[status(thm)],[f_3089_2]) ).

cnf(f_3089_4,plain,
    ( ~ c_Fun_Oinj__on(U_11665,U_11666,U_11667,c_Orderings_Otop__class_Otop(tc_fun(U_11665,tc_HOL_Obool)))
    | U_11668 = U_11669
    | hAPP(U_11667,U_11668) != hAPP(U_11667,U_11669) ),
    inference(clausify,[status(thm)],[f_3089_3]) ).

fof(f_3090_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_3090_2,plain,
    ! [U_11673,U_11672,U_11671,U_11670] :
      ( c_Fun_Oinj__on(U_11670,tc_fun(U_11673,U_11671),hAPP(hAPP(c_COMBB(U_11671,tc_fun(U_11673,U_11671),U_11670),c_COMBK(U_11671,U_11673)),U_11672),c_Orderings_Otop__class_Otop(tc_fun(U_11670,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_11670,U_11671,U_11672,c_Orderings_Otop__class_Otop(tc_fun(U_11670,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

cnf(f_3090_3,plain,
    ( c_Fun_Oinj__on(U_11670,tc_fun(U_11673,U_11671),hAPP(hAPP(c_COMBB(U_11671,tc_fun(U_11673,U_11671),U_11670),c_COMBK(U_11671,U_11673)),U_11672),c_Orderings_Otop__class_Otop(tc_fun(U_11670,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_11670,U_11671,U_11672,c_Orderings_Otop__class_Otop(tc_fun(U_11670,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3090_2]) ).

fof(f_3091_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_3091_2,plain,
    ! [U_11677,U_11676,U_11675,U_11674] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11675),U_11677))
      | ~ c_Fun_Oinj__on(U_11675,U_11674,U_11676,U_11677)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11674),hAPP(c_Set_Oimage(U_11675,U_11674,U_11676),U_11677))) ),
    inference(variable_rename,[status(thm)],[f_3091_1]) ).

cnf(f_3091_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11675),U_11677))
    | ~ c_Fun_Oinj__on(U_11675,U_11674,U_11676,U_11677)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11674),hAPP(c_Set_Oimage(U_11675,U_11674,U_11676),U_11677))) ),
    inference(clausify,[status(thm)],[f_3091_2]) ).

fof(f_3092_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_3092_2,plain,
    ! [U_11682,U_11681,U_11680,U_11679,U_11678] :
      ( ( ( hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681) = hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11682)
          | U_11681 != U_11682 )
        & ( U_11681 = U_11682
          | hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681) != hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11682) ) )
      | ~ c_Fun_Oinj__on(U_11678,U_11679,U_11680,c_Orderings_Otop__class_Otop(tc_fun(U_11678,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

cnf(f_3092_3,plain,
    ( U_11681 = U_11682
    | hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681) != hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11682)
    | ~ c_Fun_Oinj__on(U_11678,U_11679,U_11680,c_Orderings_Otop__class_Otop(tc_fun(U_11678,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3092_2]) ).

cnf(f_3092_4,plain,
    ( hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681) = hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11682)
    | U_11681 != U_11682
    | ~ c_Fun_Oinj__on(U_11678,U_11679,U_11680,c_Orderings_Otop__class_Otop(tc_fun(U_11678,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3092_2]) ).

fof(f_3093_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_3093_2,plain,
    ! [U_11687,U_11686,U_11685,U_11684,U_11683] :
      ( ( ( hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11686) = hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11687)
          | U_11686 != U_11687 )
        & ( U_11686 = U_11687
          | hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11686) != hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11687) ) )
      | ~ c_Fun_Oinj__on(U_11683,U_11684,U_11685,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11683,tc_HOL_Obool)),U_11686),U_11687)) ),
    inference(variable_rename,[status(thm)],[f_3093_1]) ).

cnf(f_3093_3,plain,
    ( U_11686 = U_11687
    | hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11686) != hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11687)
    | ~ c_Fun_Oinj__on(U_11683,U_11684,U_11685,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11683,tc_HOL_Obool)),U_11686),U_11687)) ),
    inference(clausify,[status(thm)],[f_3093_2]) ).

cnf(f_3093_4,plain,
    ( hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11686) = hAPP(c_Set_Oimage(U_11683,U_11684,U_11685),U_11687)
    | U_11686 != U_11687
    | ~ c_Fun_Oinj__on(U_11683,U_11684,U_11685,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11683,tc_HOL_Obool)),U_11686),U_11687)) ),
    inference(clausify,[status(thm)],[f_3093_2]) ).

fof(f_3094_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_3094_2,plain,
    ! [U_11691,U_11690,U_11689,U_11688] :
      ( hAPP(c_Finite__Set_Ocard(U_11689),hAPP(c_Set_Oimage(U_11688,U_11689,U_11690),U_11691)) = hAPP(c_Finite__Set_Ocard(U_11688),U_11691)
      | ~ c_Fun_Oinj__on(U_11688,U_11689,U_11690,U_11691) ),
    inference(variable_rename,[status(thm)],[f_3094_1]) ).

cnf(f_3094_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11689),hAPP(c_Set_Oimage(U_11688,U_11689,U_11690),U_11691)) = hAPP(c_Finite__Set_Ocard(U_11688),U_11691)
    | ~ c_Fun_Oinj__on(U_11688,U_11689,U_11690,U_11691) ),
    inference(clausify,[status(thm)],[f_3094_2]) ).

fof(f_3095_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_3095_2,plain,
    ! [U_11696,U_11695,U_11694,U_11693,U_11692] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11693,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11692,U_11693,U_11694),U_11696)),hAPP(c_Set_Oimage(U_11692,U_11693,U_11694),U_11695)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11692,tc_HOL_Obool)),U_11696),U_11695))
      | ~ c_Fun_Oinj__on(U_11692,U_11693,U_11694,U_11695) ),
    inference(variable_rename,[status(thm)],[f_3095_1]) ).

cnf(f_3095_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11693,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11692,U_11693,U_11694),U_11696)),hAPP(c_Set_Oimage(U_11692,U_11693,U_11694),U_11695)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11692,tc_HOL_Obool)),U_11696),U_11695))
    | ~ c_Fun_Oinj__on(U_11692,U_11693,U_11694,U_11695) ),
    inference(clausify,[status(thm)],[f_3095_2]) ).

fof(f_3096_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_3096_2,plain,
    ! [U_11701,U_11700,U_11699,U_11698,U_11697] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11698),hAPP(U_11699,U_11700)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11701)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11697),U_11700),U_11701)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_11697),U_11700),U_11701))
          | ~ hBOOL(hAPP(hAPP(c_member(U_11698),hAPP(U_11699,U_11700)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11701))) ) )
      | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,c_Orderings_Otop__class_Otop(tc_fun(U_11697,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

cnf(f_3096_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11697),U_11700),U_11701))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11698),hAPP(U_11699,U_11700)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11701)))
    | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,c_Orderings_Otop__class_Otop(tc_fun(U_11697,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3096_2]) ).

cnf(f_3096_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11698),hAPP(U_11699,U_11700)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11701)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11697),U_11700),U_11701))
    | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,c_Orderings_Otop__class_Otop(tc_fun(U_11697,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3096_2]) ).

fof(f_3097_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_3097_2,plain,
    ! [U_11709,U_11708,U_11707,U_11706] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
          | ! [U_11705] :
              ( ? [U_11704] :
                  ( U_11704 != U_11705
                  & U_11709 = hAPP(U_11708,U_11704) )
              | U_11709 != hAPP(U_11708,U_11705) ) )
        & ( ? [U_11703] :
              ( ! [U_11702] :
                  ( U_11702 = U_11703
                  | U_11709 != hAPP(U_11708,U_11702) )
              & U_11709 = hAPP(U_11708,U_11703) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

fof(f_3097_3,plain,
    ! [U_11709,U_11708,U_11707,U_11706] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
          | ! [U_11705] :
              ( ? [U_11704] :
                  ( U_11704 != U_11705
                  & U_11709 = hAPP(U_11708,U_11704) )
              | U_11709 != hAPP(U_11708,U_11705) ) )
        & ( ( ! [U_11702] :
                ( U_11702 = sK273(U_11709,U_11708,U_11707,U_11706)
                | U_11709 != hAPP(U_11708,U_11702) )
            & U_11709 = hAPP(U_11708,sK273(U_11709,U_11708,U_11707,U_11706)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_11703,sK273(U_11709,U_11708,U_11707,U_11706))],[f_3097_2]) ).

fof(f_3097_4,plain,
    ! [U_11709,U_11708,U_11707,U_11706] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
          | ! [U_11705] :
              ( ( sK274(U_11709,U_11708,U_11707,U_11706,U_11705) != U_11705
                & U_11709 = hAPP(U_11708,sK274(U_11709,U_11708,U_11707,U_11706,U_11705)) )
              | U_11709 != hAPP(U_11708,U_11705) ) )
        & ( ( ! [U_11702] :
                ( U_11702 = sK273(U_11709,U_11708,U_11707,U_11706)
                | U_11709 != hAPP(U_11708,U_11702) )
            & U_11709 = hAPP(U_11708,sK273(U_11709,U_11708,U_11707,U_11706)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_11704,sK274(U_11709,U_11708,U_11707,U_11706,U_11705))],[f_3097_3]) ).

cnf(f_3097_5,plain,
    ( U_11709 = hAPP(U_11708,sK273(U_11709,U_11708,U_11707,U_11706))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3097_4]) ).

cnf(f_3097_6,plain,
    ( U_11702 = sK273(U_11709,U_11708,U_11707,U_11706)
    | U_11709 != hAPP(U_11708,U_11702)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3097_4]) ).

cnf(f_3097_7,plain,
    ( U_11709 = hAPP(U_11708,sK274(U_11709,U_11708,U_11707,U_11706,U_11705))
    | U_11709 != hAPP(U_11708,U_11705)
    | hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3097_4]) ).

cnf(f_3097_8,plain,
    ( sK274(U_11709,U_11708,U_11707,U_11706,U_11705) != U_11705
    | U_11709 != hAPP(U_11708,U_11705)
    | hBOOL(hAPP(hAPP(c_member(U_11707),U_11709),hAPP(c_Set_Oimage(U_11706,U_11707,U_11708),c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_11706,U_11707,U_11708,c_Orderings_Otop__class_Otop(tc_fun(U_11706,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3097_4]) ).

fof(f_3098_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_3098_2,plain,
    ! [U_11717,U_11716,U_11715,U_11714] :
      ( ( ( ? [U_11713] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11713),U_11714)),U_11717))
              & c_Fun_Oinj__on(U_11715,U_11716,U_11713,U_11714) )
          | ! [U_11712] : hAPP(c_Set_Oimage(U_11716,U_11715,U_11712),U_11717) != U_11714 )
        & ( ? [U_11711] : hAPP(c_Set_Oimage(U_11716,U_11715,U_11711),U_11717) = U_11714
          | ! [U_11710] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11710),U_11714)),U_11717))
              | ~ c_Fun_Oinj__on(U_11715,U_11716,U_11710,U_11714) ) ) )
      | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

fof(f_3098_3,plain,
    ! [U_11717,U_11716,U_11715,U_11714] :
      ( ( ( ? [U_11713] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11713),U_11714)),U_11717))
              & c_Fun_Oinj__on(U_11715,U_11716,U_11713,U_11714) )
          | ! [U_11712] : hAPP(c_Set_Oimage(U_11716,U_11715,U_11712),U_11717) != U_11714 )
        & ( hAPP(c_Set_Oimage(U_11716,U_11715,sK275(U_11717,U_11716,U_11715,U_11714)),U_11717) = U_11714
          | ! [U_11710] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11710),U_11714)),U_11717))
              | ~ c_Fun_Oinj__on(U_11715,U_11716,U_11710,U_11714) ) ) )
      | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_11711,sK275(U_11717,U_11716,U_11715,U_11714))],[f_3098_2]) ).

fof(f_3098_4,plain,
    ! [U_11717,U_11716,U_11715,U_11714] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,sK276(U_11717,U_11716,U_11715,U_11714)),U_11714)),U_11717))
            & c_Fun_Oinj__on(U_11715,U_11716,sK276(U_11717,U_11716,U_11715,U_11714),U_11714) )
          | ! [U_11712] : hAPP(c_Set_Oimage(U_11716,U_11715,U_11712),U_11717) != U_11714 )
        & ( hAPP(c_Set_Oimage(U_11716,U_11715,sK275(U_11717,U_11716,U_11715,U_11714)),U_11717) = U_11714
          | ! [U_11710] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11710),U_11714)),U_11717))
              | ~ c_Fun_Oinj__on(U_11715,U_11716,U_11710,U_11714) ) ) )
      | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_11713,sK276(U_11717,U_11716,U_11715,U_11714))],[f_3098_3]) ).

cnf(f_3098_5,plain,
    ( hAPP(c_Set_Oimage(U_11716,U_11715,sK275(U_11717,U_11716,U_11715,U_11714)),U_11717) = U_11714
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,U_11710),U_11714)),U_11717))
    | ~ c_Fun_Oinj__on(U_11715,U_11716,U_11710,U_11714)
    | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

cnf(f_3098_6,plain,
    ( c_Fun_Oinj__on(U_11715,U_11716,sK276(U_11717,U_11716,U_11715,U_11714),U_11714)
    | hAPP(c_Set_Oimage(U_11716,U_11715,U_11712),U_11717) != U_11714
    | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

cnf(f_3098_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11716,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11715,U_11716,sK276(U_11717,U_11716,U_11715,U_11714)),U_11714)),U_11717))
    | hAPP(c_Set_Oimage(U_11716,U_11715,U_11712),U_11717) != U_11714
    | U_11714 = c_Orderings_Obot__class_Obot(tc_fun(U_11715,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

fof(f_3099_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_3099_2,plain,
    ! [U_11720,U_11719,U_11718] :
      ( hAPP(c_Set_Oimage(U_11718,U_11718,U_11720),U_11719) = U_11719
      | ~ c_Fun_Oinj__on(U_11718,U_11718,U_11720,U_11719)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11718,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11718,U_11718,U_11720),U_11719)),U_11719))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11718),U_11719)) ),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

cnf(f_3099_3,plain,
    ( hAPP(c_Set_Oimage(U_11718,U_11718,U_11720),U_11719) = U_11719
    | ~ c_Fun_Oinj__on(U_11718,U_11718,U_11720,U_11719)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11718,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11718,U_11718,U_11720),U_11719)),U_11719))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11718),U_11719)) ),
    inference(clausify,[status(thm)],[f_3099_2]) ).

fof(f_3100_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_3100_2,plain,
    ! [U_11723,U_11722,U_11721] :
      ( c_Fun_Oinj__on(U_11721,U_11721,U_11723,U_11722)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11721,tc_HOL_Obool)),U_11722),hAPP(c_Set_Oimage(U_11721,U_11721,U_11723),U_11722)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11721),U_11722)) ),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

cnf(f_3100_3,plain,
    ( c_Fun_Oinj__on(U_11721,U_11721,U_11723,U_11722)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11721,tc_HOL_Obool)),U_11722),hAPP(c_Set_Oimage(U_11721,U_11721,U_11723),U_11722)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11721),U_11722)) ),
    inference(clausify,[status(thm)],[f_3100_2]) ).

fof(f_3101_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_3101_2,plain,
    ! [U_11725,U_11724] :
      ( c_Fun_Oinj__on(U_11724,U_11724,U_11725,c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_11724,U_11724,U_11725),c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11724),c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3101_1]) ).

cnf(f_3101_3,plain,
    ( c_Fun_Oinj__on(U_11724,U_11724,U_11725,c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_11724,U_11724,U_11725),c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11724),c_Orderings_Otop__class_Otop(tc_fun(U_11724,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3101_2]) ).

fof(f_3102_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_3102_2,plain,
    ! [U_11727,U_11726] :
      ( hAPP(c_Set_Oimage(U_11726,U_11726,U_11727),c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_11726,U_11726,U_11727,c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11726),c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

cnf(f_3102_3,plain,
    ( hAPP(c_Set_Oimage(U_11726,U_11726,U_11727),c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_11726,U_11726,U_11727,c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11726),c_Orderings_Otop__class_Otop(tc_fun(U_11726,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3102_2]) ).

fof(f_3103_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_3103_2,plain,
    ! [U_11732,U_11731,U_11730,U_11729,U_11728] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11729,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11731)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11732)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11728,tc_HOL_Obool)),U_11731),U_11732)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11728,tc_HOL_Obool)),U_11731),U_11732))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11729,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11731)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11732))) ) )
      | ~ c_Fun_Oinj__on(U_11728,U_11729,U_11730,c_Orderings_Otop__class_Otop(tc_fun(U_11728,tc_HOL_Obool))) ),
    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_11728,tc_HOL_Obool)),U_11731),U_11732))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11729,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11731)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11732)))
    | ~ c_Fun_Oinj__on(U_11728,U_11729,U_11730,c_Orderings_Otop__class_Otop(tc_fun(U_11728,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3103_2]) ).

cnf(f_3103_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11729,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11731)),hAPP(c_Set_Oimage(U_11728,U_11729,U_11730),U_11732)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11728,tc_HOL_Obool)),U_11731),U_11732))
    | ~ c_Fun_Oinj__on(U_11728,U_11729,U_11730,c_Orderings_Otop__class_Otop(tc_fun(U_11728,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3103_2]) ).

fof(f_3104_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_3104_2,plain,
    ! [U_11738,U_11737,U_11736,U_11735,U_11734,U_11733] :
      ( hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11733,tc_HOL_Obool)),U_11737),U_11738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11734,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11737)),hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11733,tc_HOL_Obool)),U_11738),U_11736))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11733,tc_HOL_Obool)),U_11737),U_11736))
      | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736) ),
    inference(variable_rename,[status(thm)],[f_3104_1]) ).

cnf(f_3104_3,plain,
    ( hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11733,tc_HOL_Obool)),U_11737),U_11738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11734,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11737)),hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11738))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11733,tc_HOL_Obool)),U_11738),U_11736))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11733,tc_HOL_Obool)),U_11737),U_11736))
    | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736) ),
    inference(clausify,[status(thm)],[f_3104_2]) ).

fof(f_3105_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_3105_2,plain,
    ! [U_11743,U_11742,U_11741,U_11740,U_11739] :
      ( hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11743)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11740,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),U_11742)),hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),U_11743))
      | ~ c_Fun_Oinj__on(U_11739,U_11740,U_11741,c_Orderings_Otop__class_Otop(tc_fun(U_11739,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

cnf(f_3105_3,plain,
    ( hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11743)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11740,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),U_11742)),hAPP(c_Set_Oimage(U_11739,U_11740,U_11741),U_11743))
    | ~ c_Fun_Oinj__on(U_11739,U_11740,U_11741,c_Orderings_Otop__class_Otop(tc_fun(U_11739,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3105_2]) ).

fof(f_3106_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_3106_2,plain,
    ! [U_11747,U_11746,U_11745,U_11744] :
      ( c_Fun_Oinj__on(U_11744,U_11746,U_11747,U_11745)
      | hAPP(c_Finite__Set_Ocard(U_11746),hAPP(c_Set_Oimage(U_11744,U_11746,U_11747),U_11745)) != hAPP(c_Finite__Set_Ocard(U_11744),U_11745)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11744),U_11745)) ),
    inference(variable_rename,[status(thm)],[f_3106_1]) ).

cnf(f_3106_3,plain,
    ( c_Fun_Oinj__on(U_11744,U_11746,U_11747,U_11745)
    | hAPP(c_Finite__Set_Ocard(U_11746),hAPP(c_Set_Oimage(U_11744,U_11746,U_11747),U_11745)) != hAPP(c_Finite__Set_Ocard(U_11744),U_11745)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11744),U_11745)) ),
    inference(clausify,[status(thm)],[f_3106_2]) ).

fof(f_3107_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_3107_2,plain,
    ! [U_11751,U_11750,U_11749,U_11748] :
      ( ( ( c_Fun_Oinj__on(U_11748,U_11750,U_11751,U_11749)
          | hAPP(c_Finite__Set_Ocard(U_11750),hAPP(c_Set_Oimage(U_11748,U_11750,U_11751),U_11749)) != hAPP(c_Finite__Set_Ocard(U_11748),U_11749) )
        & ( hAPP(c_Finite__Set_Ocard(U_11750),hAPP(c_Set_Oimage(U_11748,U_11750,U_11751),U_11749)) = hAPP(c_Finite__Set_Ocard(U_11748),U_11749)
          | ~ c_Fun_Oinj__on(U_11748,U_11750,U_11751,U_11749) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11749)) ),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

cnf(f_3107_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11750),hAPP(c_Set_Oimage(U_11748,U_11750,U_11751),U_11749)) = hAPP(c_Finite__Set_Ocard(U_11748),U_11749)
    | ~ c_Fun_Oinj__on(U_11748,U_11750,U_11751,U_11749)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11749)) ),
    inference(clausify,[status(thm)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    ( c_Fun_Oinj__on(U_11748,U_11750,U_11751,U_11749)
    | hAPP(c_Finite__Set_Ocard(U_11750),hAPP(c_Set_Oimage(U_11748,U_11750,U_11751),U_11749)) != hAPP(c_Finite__Set_Ocard(U_11748),U_11749)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11749)) ),
    inference(clausify,[status(thm)],[f_3107_2]) ).

fof(f_3108_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_3108_2,plain,
    ! [U_11757,U_11756,U_11755,U_11754,U_11753,U_11752] :
      ( hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11752,tc_HOL_Obool)),U_11756),U_11757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),U_11756)),hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),U_11757))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11752,tc_HOL_Obool)),U_11757),U_11755))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11752,tc_HOL_Obool)),U_11756),U_11755))
      | ~ c_Fun_Oinj__on(U_11752,U_11753,U_11754,U_11755) ),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

cnf(f_3108_3,plain,
    ( hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11752,tc_HOL_Obool)),U_11756),U_11757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),U_11756)),hAPP(c_Set_Oimage(U_11752,U_11753,U_11754),U_11757))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11752,tc_HOL_Obool)),U_11757),U_11755))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11752,tc_HOL_Obool)),U_11756),U_11755))
    | ~ c_Fun_Oinj__on(U_11752,U_11753,U_11754,U_11755) ),
    inference(clausify,[status(thm)],[f_3108_2]) ).

fof(f_3109_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_3109_2,plain,
    ! [U_11762,U_11761,U_11760,U_11759,U_11758] :
      ( hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11758,tc_HOL_Obool)),U_11761),U_11762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11759,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),U_11761)),hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),U_11762))
      | ~ c_Fun_Oinj__on(U_11758,U_11759,U_11760,c_Orderings_Otop__class_Otop(tc_fun(U_11758,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

cnf(f_3109_3,plain,
    ( hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11758,tc_HOL_Obool)),U_11761),U_11762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11759,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),U_11761)),hAPP(c_Set_Oimage(U_11758,U_11759,U_11760),U_11762))
    | ~ c_Fun_Oinj__on(U_11758,U_11759,U_11760,c_Orderings_Otop__class_Otop(tc_fun(U_11758,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3109_2]) ).

fof(f_3110_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_3110_2,plain,
    ! [U_11766,U_11765,U_11764,U_11763] :
      ( ~ c_Fun_Oinj__on(U_11764,U_11763,U_11765,U_11766)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11763),hAPP(c_Set_Oimage(U_11764,U_11763,U_11765),U_11766))),hAPP(c_Finite__Set_Ocard(U_11764),U_11766))) ),
    inference(variable_rename,[status(thm)],[f_3110_1]) ).

cnf(f_3110_3,plain,
    ( ~ c_Fun_Oinj__on(U_11764,U_11763,U_11765,U_11766)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11763),hAPP(c_Set_Oimage(U_11764,U_11763,U_11765),U_11766))),hAPP(c_Finite__Set_Ocard(U_11764),U_11766))) ),
    inference(clausify,[status(thm)],[f_3110_2]) ).

fof(f_3111_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_3111_2,plain,
    ! [U_11772,U_11771,U_11770,U_11769,U_11768,U_11767] :
      ( c_Fun_Oinj__on(U_11767,U_11768,c_Fun_Ofun__upd(U_11767,U_11768,U_11769,U_11772,U_11771),U_11770)
      | hBOOL(hAPP(hAPP(c_member(U_11768),U_11771),hAPP(c_Set_Oimage(U_11767,U_11768,U_11769),U_11770)))
      | ~ c_Fun_Oinj__on(U_11767,U_11768,U_11769,U_11770) ),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

cnf(f_3111_3,plain,
    ( c_Fun_Oinj__on(U_11767,U_11768,c_Fun_Ofun__upd(U_11767,U_11768,U_11769,U_11772,U_11771),U_11770)
    | hBOOL(hAPP(hAPP(c_member(U_11768),U_11771),hAPP(c_Set_Oimage(U_11767,U_11768,U_11769),U_11770)))
    | ~ c_Fun_Oinj__on(U_11767,U_11768,U_11769,U_11770) ),
    inference(clausify,[status(thm)],[f_3111_2]) ).

fof(f_3112_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_3112_2,plain,
    ! [U_11773] : c_Fun_Oinj__on(U_11773,tc_fun(U_11773,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11773,tc_fun(U_11773,tc_HOL_Obool),tc_fun(U_11773,tc_HOL_Obool)),c_Set_Oinsert(U_11773)),c_Orderings_Obot__class_Obot(tc_fun(U_11773,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11773,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

cnf(f_3112_3,plain,
    c_Fun_Oinj__on(U_11773,tc_fun(U_11773,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11773,tc_fun(U_11773,tc_HOL_Obool),tc_fun(U_11773,tc_HOL_Obool)),c_Set_Oinsert(U_11773)),c_Orderings_Obot__class_Obot(tc_fun(U_11773,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11773,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3112_2]) ).

fof(f_3113_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_3113_2,plain,
    ! [U_11774] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_11774)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

cnf(f_3113_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_11774)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3113_2]) ).

fof(f_3114_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_3114_2,plain,
    ! [U_11780,U_11779,U_11778,U_11777,U_11776,U_11775] :
      ( hAPP(c_Finite__Set_Ocard(U_11775),U_11778) = hAPP(c_Finite__Set_Ocard(U_11776),U_11779)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11776),U_11779))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11775),U_11778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11775,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11776,U_11775,U_11780),U_11779)),U_11778))
      | ~ c_Fun_Oinj__on(U_11776,U_11775,U_11780,U_11779)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11776,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11775,U_11776,U_11777),U_11778)),U_11779))
      | ~ c_Fun_Oinj__on(U_11775,U_11776,U_11777,U_11778) ),
    inference(variable_rename,[status(thm)],[f_3114_1]) ).

cnf(f_3114_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11775),U_11778) = hAPP(c_Finite__Set_Ocard(U_11776),U_11779)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11776),U_11779))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11775),U_11778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11775,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11776,U_11775,U_11780),U_11779)),U_11778))
    | ~ c_Fun_Oinj__on(U_11776,U_11775,U_11780,U_11779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11776,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11775,U_11776,U_11777),U_11778)),U_11779))
    | ~ c_Fun_Oinj__on(U_11775,U_11776,U_11777,U_11778) ),
    inference(clausify,[status(thm)],[f_3114_2]) ).

fof(f_3115_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_3115_2,plain,
    ! [U_11784,U_11783,U_11782,U_11781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11781,U_11782,U_11783),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11781,tc_HOL_Obool)),U_11784))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11781,U_11782,U_11783),U_11784))))
      | ~ c_Fun_Oinj__on(U_11781,U_11782,U_11783,c_Orderings_Otop__class_Otop(tc_fun(U_11781,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

cnf(f_3115_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11781,U_11782,U_11783),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11781,tc_HOL_Obool)),U_11784))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11782,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11781,U_11782,U_11783),U_11784))))
    | ~ c_Fun_Oinj__on(U_11781,U_11782,U_11783,c_Orderings_Otop__class_Otop(tc_fun(U_11781,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3115_2]) ).

fof(f_3116_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_3116_2,plain,
    ! [U_11789,U_11788,U_11787,U_11786,U_11785] :
      ( ( c_Fun_Oinj__on(U_11785,U_11786,U_11787,hAPP(hAPP(c_Set_Oinsert(U_11785),U_11788),U_11789))
        | hBOOL(hAPP(hAPP(c_member(U_11786),hAPP(U_11787,U_11788)),hAPP(c_Set_Oimage(U_11785,U_11786,U_11787),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11785,tc_HOL_Obool)),U_11789),hAPP(hAPP(c_Set_Oinsert(U_11785),U_11788),c_Orderings_Obot__class_Obot(tc_fun(U_11785,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11785,U_11786,U_11787,U_11789) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11786),hAPP(U_11787,U_11788)),hAPP(c_Set_Oimage(U_11785,U_11786,U_11787),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11785,tc_HOL_Obool)),U_11789),hAPP(hAPP(c_Set_Oinsert(U_11785),U_11788),c_Orderings_Obot__class_Obot(tc_fun(U_11785,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11785,U_11786,U_11787,U_11789) )
        | ~ c_Fun_Oinj__on(U_11785,U_11786,U_11787,hAPP(hAPP(c_Set_Oinsert(U_11785),U_11788),U_11789)) ) ),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

fof(f_3116_3,plain,
    ( ! [U_11799,U_11797,U_11795,U_11793,U_11791] :
        ( c_Fun_Oinj__on(U_11791,U_11793,U_11795,hAPP(hAPP(c_Set_Oinsert(U_11791),U_11797),U_11799))
        | hBOOL(hAPP(hAPP(c_member(U_11793),hAPP(U_11795,U_11797)),hAPP(c_Set_Oimage(U_11791,U_11793,U_11795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11791,tc_HOL_Obool)),U_11799),hAPP(hAPP(c_Set_Oinsert(U_11791),U_11797),c_Orderings_Obot__class_Obot(tc_fun(U_11791,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11791,U_11793,U_11795,U_11799) )
    & ! [U_11798,U_11796,U_11794,U_11792,U_11790] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11792),hAPP(U_11794,U_11796)),hAPP(c_Set_Oimage(U_11790,U_11792,U_11794),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11790,tc_HOL_Obool)),U_11798),hAPP(hAPP(c_Set_Oinsert(U_11790),U_11796),c_Orderings_Obot__class_Obot(tc_fun(U_11790,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11790,U_11792,U_11794,U_11798) )
        | ~ c_Fun_Oinj__on(U_11790,U_11792,U_11794,hAPP(hAPP(c_Set_Oinsert(U_11790),U_11796),U_11798)) ) ),
    inference(miniscope,[status(thm)],[f_3116_2]) ).

cnf(f_3116_4,plain,
    ( c_Fun_Oinj__on(U_11790,U_11792,U_11794,U_11798)
    | ~ c_Fun_Oinj__on(U_11790,U_11792,U_11794,hAPP(hAPP(c_Set_Oinsert(U_11790),U_11796),U_11798)) ),
    inference(clausify,[status(thm)],[f_3116_3]) ).

cnf(f_3116_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_11792),hAPP(U_11794,U_11796)),hAPP(c_Set_Oimage(U_11790,U_11792,U_11794),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11790,tc_HOL_Obool)),U_11798),hAPP(hAPP(c_Set_Oinsert(U_11790),U_11796),c_Orderings_Obot__class_Obot(tc_fun(U_11790,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_11790,U_11792,U_11794,hAPP(hAPP(c_Set_Oinsert(U_11790),U_11796),U_11798)) ),
    inference(clausify,[status(thm)],[f_3116_3]) ).

cnf(f_3116_6,plain,
    ( c_Fun_Oinj__on(U_11791,U_11793,U_11795,hAPP(hAPP(c_Set_Oinsert(U_11791),U_11797),U_11799))
    | hBOOL(hAPP(hAPP(c_member(U_11793),hAPP(U_11795,U_11797)),hAPP(c_Set_Oimage(U_11791,U_11793,U_11795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11791,tc_HOL_Obool)),U_11799),hAPP(hAPP(c_Set_Oinsert(U_11791),U_11797),c_Orderings_Obot__class_Obot(tc_fun(U_11791,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_11791,U_11793,U_11795,U_11799) ),
    inference(clausify,[status(thm)],[f_3116_3]) ).

fof(f_3117_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_3117_2,plain,
    ! [U_11804,U_11803,U_11802,U_11801,U_11800] :
      ( ( c_Fun_Oinj__on(U_11800,U_11801,U_11802,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11800,tc_HOL_Obool)),U_11803),U_11804))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11801,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11800,U_11801,U_11802),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11800,tc_HOL_Obool)),U_11803),U_11804))),hAPP(c_Set_Oimage(U_11800,U_11801,U_11802),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11800,tc_HOL_Obool)),U_11804),U_11803))) != c_Orderings_Obot__class_Obot(tc_fun(U_11801,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11800,U_11801,U_11802,U_11804)
        | ~ c_Fun_Oinj__on(U_11800,U_11801,U_11802,U_11803) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11801,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11800,U_11801,U_11802),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11800,tc_HOL_Obool)),U_11803),U_11804))),hAPP(c_Set_Oimage(U_11800,U_11801,U_11802),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11800,tc_HOL_Obool)),U_11804),U_11803))) = c_Orderings_Obot__class_Obot(tc_fun(U_11801,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11800,U_11801,U_11802,U_11804)
          & c_Fun_Oinj__on(U_11800,U_11801,U_11802,U_11803) )
        | ~ c_Fun_Oinj__on(U_11800,U_11801,U_11802,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11800,tc_HOL_Obool)),U_11803),U_11804)) ) ),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

fof(f_3117_3,plain,
    ( ! [U_11814,U_11812,U_11810,U_11808,U_11806] :
        ( c_Fun_Oinj__on(U_11806,U_11808,U_11810,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11806,tc_HOL_Obool)),U_11812),U_11814))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11808,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11806,U_11808,U_11810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11806,tc_HOL_Obool)),U_11812),U_11814))),hAPP(c_Set_Oimage(U_11806,U_11808,U_11810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11806,tc_HOL_Obool)),U_11814),U_11812))) != c_Orderings_Obot__class_Obot(tc_fun(U_11808,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11806,U_11808,U_11810,U_11814)
        | ~ c_Fun_Oinj__on(U_11806,U_11808,U_11810,U_11812) )
    & ! [U_11813,U_11811,U_11809,U_11807,U_11805] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11807,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11805,U_11807,U_11809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813))),hAPP(c_Set_Oimage(U_11805,U_11807,U_11809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11805,tc_HOL_Obool)),U_11813),U_11811))) = c_Orderings_Obot__class_Obot(tc_fun(U_11807,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11805,U_11807,U_11809,U_11813)
          & c_Fun_Oinj__on(U_11805,U_11807,U_11809,U_11811) )
        | ~ c_Fun_Oinj__on(U_11805,U_11807,U_11809,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813)) ) ),
    inference(miniscope,[status(thm)],[f_3117_2]) ).

cnf(f_3117_4,plain,
    ( c_Fun_Oinj__on(U_11805,U_11807,U_11809,U_11811)
    | ~ c_Fun_Oinj__on(U_11805,U_11807,U_11809,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813)) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

cnf(f_3117_5,plain,
    ( c_Fun_Oinj__on(U_11805,U_11807,U_11809,U_11813)
    | ~ c_Fun_Oinj__on(U_11805,U_11807,U_11809,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813)) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

cnf(f_3117_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11807,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11805,U_11807,U_11809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813))),hAPP(c_Set_Oimage(U_11805,U_11807,U_11809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11805,tc_HOL_Obool)),U_11813),U_11811))) = c_Orderings_Obot__class_Obot(tc_fun(U_11807,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_11805,U_11807,U_11809,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11805,tc_HOL_Obool)),U_11811),U_11813)) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

cnf(f_3117_7,plain,
    ( c_Fun_Oinj__on(U_11806,U_11808,U_11810,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11806,tc_HOL_Obool)),U_11812),U_11814))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11808,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11806,U_11808,U_11810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11806,tc_HOL_Obool)),U_11812),U_11814))),hAPP(c_Set_Oimage(U_11806,U_11808,U_11810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11806,tc_HOL_Obool)),U_11814),U_11812))) != c_Orderings_Obot__class_Obot(tc_fun(U_11808,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_11806,U_11808,U_11810,U_11814)
    | ~ c_Fun_Oinj__on(U_11806,U_11808,U_11810,U_11812) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

fof(f_3118_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_3118_2,plain,
    ! [U_11819,U_11818,U_11817,U_11816,U_11815] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11815),U_11818)),hAPP(c_Finite__Set_Ocard(U_11816),U_11819)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11816),U_11819))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11816,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11815,U_11816,U_11817),U_11818)),U_11819))
      | ~ c_Fun_Oinj__on(U_11815,U_11816,U_11817,U_11818) ),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

cnf(f_3118_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11815),U_11818)),hAPP(c_Finite__Set_Ocard(U_11816),U_11819)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11816),U_11819))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11816,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11815,U_11816,U_11817),U_11818)),U_11819))
    | ~ c_Fun_Oinj__on(U_11815,U_11816,U_11817,U_11818) ),
    inference(clausify,[status(thm)],[f_3118_2]) ).

fof(f_3119_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_3119_2,plain,
    ! [U_11825,U_11824,U_11823,U_11822] :
      ( ( ( ? [U_11821] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,U_11821),U_11823)),U_11825))
              & c_Fun_Oinj__on(U_11822,U_11824,U_11821,U_11823) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825)))
          | ! [U_11820] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,U_11820),U_11823)),U_11825))
              | ~ c_Fun_Oinj__on(U_11822,U_11824,U_11820,U_11823) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11824),U_11825))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11822),U_11823)) ),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

fof(f_3119_3,plain,
    ! [U_11825,U_11824,U_11823,U_11822] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,sK277(U_11825,U_11824,U_11823,U_11822)),U_11823)),U_11825))
            & c_Fun_Oinj__on(U_11822,U_11824,sK277(U_11825,U_11824,U_11823,U_11822),U_11823) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825)))
          | ! [U_11820] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,U_11820),U_11823)),U_11825))
              | ~ c_Fun_Oinj__on(U_11822,U_11824,U_11820,U_11823) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11824),U_11825))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11822),U_11823)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_11821,sK277(U_11825,U_11824,U_11823,U_11822))],[f_3119_2]) ).

cnf(f_3119_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,U_11820),U_11823)),U_11825))
    | ~ c_Fun_Oinj__on(U_11822,U_11824,U_11820,U_11823)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11824),U_11825))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11822),U_11823)) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

cnf(f_3119_5,plain,
    ( c_Fun_Oinj__on(U_11822,U_11824,sK277(U_11825,U_11824,U_11823,U_11822),U_11823)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11824),U_11825))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11822),U_11823)) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

cnf(f_3119_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11824,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11822,U_11824,sK277(U_11825,U_11824,U_11823,U_11822)),U_11823)),U_11825))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11822),U_11823)),hAPP(c_Finite__Set_Ocard(U_11824),U_11825)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11824),U_11825))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11822),U_11823)) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

fof(f_3120_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_3120_2,plain,
    ! [U_11829,U_11828,U_11827,U_11826] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11826,tc_HOL_Obool)),U_11828),hAPP(hAPP(c_Set_Oinsert(U_11826),U_11829),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool))))),U_11827) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),U_11828),U_11827)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),hAPP(hAPP(c_Set_Oinsert(U_11826),U_11829),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool)))),U_11827))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11826),U_11829),U_11828))
      | ~ c_Fun_Oinj__on(U_11826,tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11826,tc_fun(tc_prod(U_11826,U_11826),tc_HOL_Obool),tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11826,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11826,U_11826),tc_HOL_Obool),tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),U_11826),c_Equiv__Relations_Oquotient(U_11826)),hAPP(hAPP(c_COMBC(U_11826,tc_fun(U_11826,tc_HOL_Obool),tc_fun(U_11826,tc_HOL_Obool)),c_Set_Oinsert(U_11826)),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool))))),U_11827),U_11828) ),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

cnf(f_3120_3,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11826,tc_HOL_Obool)),U_11828),hAPP(hAPP(c_Set_Oinsert(U_11826),U_11829),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool))))),U_11827) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),U_11828),U_11827)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11826),hAPP(hAPP(c_Set_Oinsert(U_11826),U_11829),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool)))),U_11827))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11826),U_11829),U_11828))
    | ~ c_Fun_Oinj__on(U_11826,tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11826,tc_fun(tc_prod(U_11826,U_11826),tc_HOL_Obool),tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11826,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11826,U_11826),tc_HOL_Obool),tc_fun(tc_fun(U_11826,tc_HOL_Obool),tc_HOL_Obool)),U_11826),c_Equiv__Relations_Oquotient(U_11826)),hAPP(hAPP(c_COMBC(U_11826,tc_fun(U_11826,tc_HOL_Obool),tc_fun(U_11826,tc_HOL_Obool)),c_Set_Oinsert(U_11826)),c_Orderings_Obot__class_Obot(tc_fun(U_11826,tc_HOL_Obool))))),U_11827),U_11828) ),
    inference(clausify,[status(thm)],[f_3120_2]) ).

fof(f_3121_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_3121_2,plain,
    ! [U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831] :
      ( hAPP(c_Set_Oimage(U_11831,U_11832,U_11833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11831,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11832,tc_HOL_Obool)),U_11836),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11835),c_Set_Oimage(U_11831,U_11832,U_11833)),U_11837))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11838),U_11836))
      | ? [U_11830] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11831,tc_HOL_Obool)),hAPP(U_11837,U_11830)),U_11834))
          & hBOOL(hAPP(hAPP(c_member(U_11835),U_11830),U_11836)) )
      | ~ c_Fun_Oinj__on(U_11831,U_11832,U_11833,U_11834) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

fof(f_3121_3,plain,
    ! [U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831] :
      ( hAPP(c_Set_Oimage(U_11831,U_11832,U_11833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11831,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11832,tc_HOL_Obool)),U_11836),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11835),c_Set_Oimage(U_11831,U_11832,U_11833)),U_11837))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11838),U_11836))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11831,tc_HOL_Obool)),hAPP(U_11837,sK278(U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831))),U_11834))
        & hBOOL(hAPP(hAPP(c_member(U_11835),sK278(U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831)),U_11836)) )
      | ~ c_Fun_Oinj__on(U_11831,U_11832,U_11833,U_11834) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_11830,sK278(U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831))],[f_3121_2]) ).

cnf(f_3121_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11835),sK278(U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831)),U_11836))
    | hAPP(c_Set_Oimage(U_11831,U_11832,U_11833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11831,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11832,tc_HOL_Obool)),U_11836),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11835),c_Set_Oimage(U_11831,U_11832,U_11833)),U_11837))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11838),U_11836))
    | ~ c_Fun_Oinj__on(U_11831,U_11832,U_11833,U_11834) ),
    inference(clausify,[status(thm)],[f_3121_3]) ).

cnf(f_3121_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11831,tc_HOL_Obool)),hAPP(U_11837,sK278(U_11838,U_11837,U_11836,U_11835,U_11834,U_11833,U_11832,U_11831))),U_11834))
    | hAPP(c_Set_Oimage(U_11831,U_11832,U_11833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11831,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11835,tc_fun(U_11832,tc_HOL_Obool)),U_11836),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11835),c_Set_Oimage(U_11831,U_11832,U_11833)),U_11837))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11838),U_11836))
    | ~ c_Fun_Oinj__on(U_11831,U_11832,U_11833,U_11834) ),
    inference(clausify,[status(thm)],[f_3121_3]) ).

fof(f_3122_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_3122_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_3122_1]) ).

fof(f_3123_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_3123_2,plain,
    ! [U_11844,U_11843,U_11842,U_11841,U_11840,U_11839] :
      ( hBOOL(hAPP(hAPP(c_member(U_11839),hAPP(c_Fun_Othe__inv__into(U_11839,U_11840,U_11842,U_11841),U_11843)),U_11844))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11839,tc_HOL_Obool)),U_11842),U_11844))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11840),U_11843),hAPP(c_Set_Oimage(U_11839,U_11840,U_11841),U_11842)))
      | ~ c_Fun_Oinj__on(U_11839,U_11840,U_11841,U_11842) ),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

cnf(f_3123_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11839),hAPP(c_Fun_Othe__inv__into(U_11839,U_11840,U_11842,U_11841),U_11843)),U_11844))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11839,tc_HOL_Obool)),U_11842),U_11844))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11840),U_11843),hAPP(c_Set_Oimage(U_11839,U_11840,U_11841),U_11842)))
    | ~ c_Fun_Oinj__on(U_11839,U_11840,U_11841,U_11842) ),
    inference(clausify,[status(thm)],[f_3123_2]) ).

fof(f_3124_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_3124_2,plain,
    ! [U_11845] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11845),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

cnf(f_3124_3,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11845),
    inference(clausify,[status(thm)],[f_3124_2]) ).

fof(f_3125_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_3125_2,plain,
    ! [U_11847,U_11846] : 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_11846),U_11847),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

cnf(f_3125_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_11846),U_11847),
    inference(clausify,[status(thm)],[f_3125_2]) ).

fof(f_3126_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_3126_2,plain,
    ! [U_11848] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_11848,c_Nat_Osemiring__1__class_Oof__nat(U_11848),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_11848) ),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

cnf(f_3126_3,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_11848,c_Nat_Osemiring__1__class_Oof__nat(U_11848),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_11848) ),
    inference(clausify,[status(thm)],[f_3126_2]) ).

fof(f_3127_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_3127_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_3127_1]) ).

fof(f_3128_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_3128_2,plain,
    ! [U_11851,U_11850,U_11849] : c_Fun_Oinj__on(tc_prod(U_11849,U_11850),tc_prod(U_11850,U_11849),hAPP(c_Product__Type_Oprod_Oprod__case(U_11849,U_11850,tc_prod(U_11850,U_11849)),hAPP(c_COMBC(U_11850,U_11849,tc_prod(U_11850,U_11849)),c_Product__Type_OPair(U_11850,U_11849))),U_11851),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

cnf(f_3128_3,plain,
    c_Fun_Oinj__on(tc_prod(U_11849,U_11850),tc_prod(U_11850,U_11849),hAPP(c_Product__Type_Oprod_Oprod__case(U_11849,U_11850,tc_prod(U_11850,U_11849)),hAPP(c_COMBC(U_11850,U_11849,tc_prod(U_11850,U_11849)),c_Product__Type_OPair(U_11850,U_11849))),U_11851),
    inference(clausify,[status(thm)],[f_3128_2]) ).

fof(f_3129_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_3129_2,plain,
    ! [U_11857,U_11856,U_11855,U_11854,U_11853,U_11852] :
      ( hAPP(c_Fun_Othe__inv__into(U_11852,U_11853,U_11855,U_11854),U_11857) = U_11856
      | ~ hBOOL(hAPP(hAPP(c_member(U_11852),U_11856),U_11855))
      | hAPP(U_11854,U_11856) != U_11857
      | ~ c_Fun_Oinj__on(U_11852,U_11853,U_11854,U_11855) ),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

cnf(f_3129_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_11852,U_11853,U_11855,U_11854),U_11857) = U_11856
    | ~ hBOOL(hAPP(hAPP(c_member(U_11852),U_11856),U_11855))
    | hAPP(U_11854,U_11856) != U_11857
    | ~ c_Fun_Oinj__on(U_11852,U_11853,U_11854,U_11855) ),
    inference(clausify,[status(thm)],[f_3129_2]) ).

fof(f_3130_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_3130_2,plain,
    ! [U_11862,U_11861,U_11860,U_11859,U_11858] :
      ( hAPP(c_Fun_Othe__inv__into(U_11858,U_11859,U_11861,U_11860),hAPP(U_11860,U_11862)) = U_11862
      | ~ hBOOL(hAPP(hAPP(c_member(U_11858),U_11862),U_11861))
      | ~ c_Fun_Oinj__on(U_11858,U_11859,U_11860,U_11861) ),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

cnf(f_3130_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_11858,U_11859,U_11861,U_11860),hAPP(U_11860,U_11862)) = U_11862
    | ~ hBOOL(hAPP(hAPP(c_member(U_11858),U_11862),U_11861))
    | ~ c_Fun_Oinj__on(U_11858,U_11859,U_11860,U_11861) ),
    inference(clausify,[status(thm)],[f_3130_2]) ).

fof(f_3131_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_3131_2,plain,
    ! [U_11866,U_11865,U_11864,U_11863] :
      ( hAPP(c_Fun_Othe__inv__into(U_11863,U_11864,c_Orderings_Otop__class_Otop(tc_fun(U_11863,tc_HOL_Obool)),U_11865),hAPP(U_11865,U_11866)) = U_11866
      | ~ c_Fun_Oinj__on(U_11863,U_11864,U_11865,c_Orderings_Otop__class_Otop(tc_fun(U_11863,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

cnf(f_3131_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_11863,U_11864,c_Orderings_Otop__class_Otop(tc_fun(U_11863,tc_HOL_Obool)),U_11865),hAPP(U_11865,U_11866)) = U_11866
    | ~ c_Fun_Oinj__on(U_11863,U_11864,U_11865,c_Orderings_Otop__class_Otop(tc_fun(U_11863,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3131_2]) ).

fof(f_3132_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_3132_2,plain,
    ! [U_11870,U_11869,U_11868,U_11867] :
      ( c_Fun_Oinj__on(U_11868,U_11867,c_Fun_Othe__inv__into(U_11867,U_11868,U_11870,U_11869),hAPP(c_Set_Oimage(U_11867,U_11868,U_11869),U_11870))
      | ~ c_Fun_Oinj__on(U_11867,U_11868,U_11869,U_11870) ),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

cnf(f_3132_3,plain,
    ( c_Fun_Oinj__on(U_11868,U_11867,c_Fun_Othe__inv__into(U_11867,U_11868,U_11870,U_11869),hAPP(c_Set_Oimage(U_11867,U_11868,U_11869),U_11870))
    | ~ c_Fun_Oinj__on(U_11867,U_11868,U_11869,U_11870) ),
    inference(clausify,[status(thm)],[f_3132_2]) ).

fof(f_3133_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_3133_2,plain,
    ! [U_11874,U_11873,U_11872,U_11871] :
      ( hAPP(c_Set_Oimage(U_11872,U_11871,c_Fun_Othe__inv__into(U_11871,U_11872,U_11874,U_11873)),hAPP(c_Set_Oimage(U_11871,U_11872,U_11873),U_11874)) = U_11874
      | ~ c_Fun_Oinj__on(U_11871,U_11872,U_11873,U_11874) ),
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

cnf(f_3133_3,plain,
    ( hAPP(c_Set_Oimage(U_11872,U_11871,c_Fun_Othe__inv__into(U_11871,U_11872,U_11874,U_11873)),hAPP(c_Set_Oimage(U_11871,U_11872,U_11873),U_11874)) = U_11874
    | ~ c_Fun_Oinj__on(U_11871,U_11872,U_11873,U_11874) ),
    inference(clausify,[status(thm)],[f_3133_2]) ).

fof(f_3134_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_3134_2,plain,
    ! [U_11879,U_11878,U_11877,U_11876,U_11875] :
      ( hAPP(U_11877,hAPP(c_Fun_Othe__inv__into(U_11875,U_11876,U_11878,U_11877),U_11879)) = U_11879
      | ~ hBOOL(hAPP(hAPP(c_member(U_11876),U_11879),hAPP(c_Set_Oimage(U_11875,U_11876,U_11877),U_11878)))
      | ~ c_Fun_Oinj__on(U_11875,U_11876,U_11877,U_11878) ),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

cnf(f_3134_3,plain,
    ( hAPP(U_11877,hAPP(c_Fun_Othe__inv__into(U_11875,U_11876,U_11878,U_11877),U_11879)) = U_11879
    | ~ hBOOL(hAPP(hAPP(c_member(U_11876),U_11879),hAPP(c_Set_Oimage(U_11875,U_11876,U_11877),U_11878)))
    | ~ c_Fun_Oinj__on(U_11875,U_11876,U_11877,U_11878) ),
    inference(clausify,[status(thm)],[f_3134_2]) ).

fof(f_3135_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_3135_2,plain,
    ! [U_11884,U_11883,U_11882,U_11881,U_11880] :
      ( hAPP(c_Set_Oimage(U_11881,U_11880,U_11883),U_11884) = c_Orderings_Otop__class_Otop(tc_fun(U_11880,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_11880,U_11881,U_11882,U_11883,U_11884) ),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

cnf(f_3135_3,plain,
    ( hAPP(c_Set_Oimage(U_11881,U_11880,U_11883),U_11884) = c_Orderings_Otop__class_Otop(tc_fun(U_11880,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_11880,U_11881,U_11882,U_11883,U_11884) ),
    inference(clausify,[status(thm)],[f_3135_2]) ).

fof(f_3136_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_3136_2,plain,
    ! [U_11889,U_11888,U_11887,U_11886,U_11885] :
      ( hAPP(c_Set_Oimage(U_11885,U_11886,U_11887),c_Orderings_Otop__class_Otop(tc_fun(U_11885,tc_HOL_Obool))) = U_11889
      | ~ c_Typedef_Otype__definition(U_11885,U_11886,U_11887,U_11888,U_11889) ),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

cnf(f_3136_3,plain,
    ( hAPP(c_Set_Oimage(U_11885,U_11886,U_11887),c_Orderings_Otop__class_Otop(tc_fun(U_11885,tc_HOL_Obool))) = U_11889
    | ~ c_Typedef_Otype__definition(U_11885,U_11886,U_11887,U_11888,U_11889) ),
    inference(clausify,[status(thm)],[f_3136_2]) ).

fof(f_3137_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_3137_2,plain,
    ! [U_11895,U_11894,U_11893,U_11892,U_11891,U_11890] :
      ( hBOOL(hAPP(hAPP(c_member(U_11891),hAPP(U_11892,U_11895)),U_11894))
      | ~ c_Typedef_Otype__definition(U_11890,U_11891,U_11892,U_11893,U_11894) ),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

fof(f_3137_3,plain,
    ! [U_11895,U_11894,U_11893,U_11892,U_11891] :
      ( ! [U_11890] : ~ c_Typedef_Otype__definition(U_11890,U_11891,U_11892,U_11893,U_11894)
      | hBOOL(hAPP(hAPP(c_member(U_11891),hAPP(U_11892,U_11895)),U_11894)) ),
    inference(miniscope,[status(thm)],[f_3137_2]) ).

cnf(f_3137_4,plain,
    ( ~ c_Typedef_Otype__definition(U_11890,U_11891,U_11892,U_11893,U_11894)
    | hBOOL(hAPP(hAPP(c_member(U_11891),hAPP(U_11892,U_11895)),U_11894)) ),
    inference(clausify,[status(thm)],[f_3137_3]) ).

fof(f_3138_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_3138_2,plain,
    ! [U_11901,U_11900,U_11899,U_11898,U_11897,U_11896] :
      ( hAPP(U_11899,hAPP(U_11898,U_11901)) = U_11901
      | ~ c_Typedef_Otype__definition(U_11896,U_11897,U_11898,U_11899,U_11900) ),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

fof(f_3138_3,plain,
    ! [U_11901,U_11900,U_11899,U_11898] :
      ( ! [U_11897,U_11896] : ~ c_Typedef_Otype__definition(U_11896,U_11897,U_11898,U_11899,U_11900)
      | hAPP(U_11899,hAPP(U_11898,U_11901)) = U_11901 ),
    inference(miniscope,[status(thm)],[f_3138_2]) ).

cnf(f_3138_4,plain,
    ( ~ c_Typedef_Otype__definition(U_11896,U_11897,U_11898,U_11899,U_11900)
    | hAPP(U_11899,hAPP(U_11898,U_11901)) = U_11901 ),
    inference(clausify,[status(thm)],[f_3138_3]) ).

fof(f_3139_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_3139_2,plain,
    ! [U_11908,U_11907,U_11906,U_11905,U_11904,U_11903,U_11902] :
      ( ( ( hAPP(U_11904,U_11907) = hAPP(U_11904,U_11908)
          | U_11907 != U_11908 )
        & ( U_11907 = U_11908
          | hAPP(U_11904,U_11907) != hAPP(U_11904,U_11908) ) )
      | ~ c_Typedef_Otype__definition(U_11902,U_11903,U_11904,U_11905,U_11906) ),
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

fof(f_3139_3,plain,
    ! [U_11908,U_11907,U_11906,U_11905,U_11904] :
      ( ! [U_11903,U_11902] : ~ c_Typedef_Otype__definition(U_11902,U_11903,U_11904,U_11905,U_11906)
      | ( ( hAPP(U_11904,U_11907) = hAPP(U_11904,U_11908)
          | U_11907 != U_11908 )
        & ( U_11907 = U_11908
          | hAPP(U_11904,U_11907) != hAPP(U_11904,U_11908) ) ) ),
    inference(miniscope,[status(thm)],[f_3139_2]) ).

cnf(f_3139_4,plain,
    ( U_11907 = U_11908
    | hAPP(U_11904,U_11907) != hAPP(U_11904,U_11908)
    | ~ c_Typedef_Otype__definition(U_11902,U_11903,U_11904,U_11905,U_11906) ),
    inference(clausify,[status(thm)],[f_3139_3]) ).

cnf(f_3139_5,plain,
    ( hAPP(U_11904,U_11907) = hAPP(U_11904,U_11908)
    | U_11907 != U_11908
    | ~ c_Typedef_Otype__definition(U_11902,U_11903,U_11904,U_11905,U_11906) ),
    inference(clausify,[status(thm)],[f_3139_3]) ).

fof(f_3140_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_3140_2,plain,
    ! [U_11915,U_11914,U_11913,U_11912,U_11911,U_11910,U_11909] :
      ( ( ( hAPP(U_11912,U_11914) = hAPP(U_11912,U_11915)
          | U_11914 != U_11915 )
        & ( U_11914 = U_11915
          | hAPP(U_11912,U_11914) != hAPP(U_11912,U_11915) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11915),U_11913))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11914),U_11913))
      | ~ c_Typedef_Otype__definition(U_11909,U_11910,U_11911,U_11912,U_11913) ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

fof(f_3140_3,plain,
    ! [U_11915,U_11914,U_11913,U_11912,U_11911,U_11910] :
      ( ! [U_11909] : ~ c_Typedef_Otype__definition(U_11909,U_11910,U_11911,U_11912,U_11913)
      | ( ( hAPP(U_11912,U_11914) = hAPP(U_11912,U_11915)
          | U_11914 != U_11915 )
        & ( U_11914 = U_11915
          | hAPP(U_11912,U_11914) != hAPP(U_11912,U_11915) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11915),U_11913))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11914),U_11913)) ),
    inference(miniscope,[status(thm)],[f_3140_2]) ).

cnf(f_3140_4,plain,
    ( U_11914 = U_11915
    | hAPP(U_11912,U_11914) != hAPP(U_11912,U_11915)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11915),U_11913))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11914),U_11913))
    | ~ c_Typedef_Otype__definition(U_11909,U_11910,U_11911,U_11912,U_11913) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

cnf(f_3140_5,plain,
    ( hAPP(U_11912,U_11914) = hAPP(U_11912,U_11915)
    | U_11914 != U_11915
    | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11915),U_11913))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11910),U_11914),U_11913))
    | ~ c_Typedef_Otype__definition(U_11909,U_11910,U_11911,U_11912,U_11913) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

fof(f_3141_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_3141_2,plain,
    ! [U_11921,U_11920,U_11919,U_11918,U_11917,U_11916] :
      ( hAPP(U_11918,hAPP(U_11919,U_11921)) = U_11921
      | ~ hBOOL(hAPP(hAPP(c_member(U_11917),U_11921),U_11920))
      | ~ c_Typedef_Otype__definition(U_11916,U_11917,U_11918,U_11919,U_11920) ),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

fof(f_3141_3,plain,
    ! [U_11921,U_11920,U_11919,U_11918,U_11917] :
      ( ! [U_11916] : ~ c_Typedef_Otype__definition(U_11916,U_11917,U_11918,U_11919,U_11920)
      | hAPP(U_11918,hAPP(U_11919,U_11921)) = U_11921
      | ~ hBOOL(hAPP(hAPP(c_member(U_11917),U_11921),U_11920)) ),
    inference(miniscope,[status(thm)],[f_3141_2]) ).

cnf(f_3141_4,plain,
    ( ~ c_Typedef_Otype__definition(U_11916,U_11917,U_11918,U_11919,U_11920)
    | hAPP(U_11918,hAPP(U_11919,U_11921)) = U_11921
    | ~ hBOOL(hAPP(hAPP(c_member(U_11917),U_11921),U_11920)) ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

fof(f_3142_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_3142_2,plain,
    ! [U_11924,U_11923,U_11922] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11922,hAPP(hAPP(c_COMBC(U_11922,tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_fun(U_11922,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11922,tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_fun(U_11922,tc_HOL_Obool)),U_11922),c_COMBC(U_11922,tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11922,tc_prod(U_11922,U_11922)),tc_fun(U_11922,tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),U_11922),hAPP(c_COMBB(tc_prod(U_11922,U_11922),tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool),U_11922),c_member(tc_prod(U_11922,U_11922)))),c_Product__Type_OPair(U_11922,U_11922)))),U_11923)),U_11924))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11922),U_11924),c_Wellfounded_Oacc(U_11922,U_11923))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_11922),U_11924),c_Wellfounded_Oacc(U_11922,U_11923)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11922,hAPP(hAPP(c_COMBC(U_11922,tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_fun(U_11922,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11922,tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_fun(U_11922,tc_HOL_Obool)),U_11922),c_COMBC(U_11922,tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11922,tc_prod(U_11922,U_11922)),tc_fun(U_11922,tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool)),U_11922),hAPP(c_COMBB(tc_prod(U_11922,U_11922),tc_fun(tc_fun(tc_prod(U_11922,U_11922),tc_HOL_Obool),tc_HOL_Obool),U_11922),c_member(tc_prod(U_11922,U_11922)))),c_Product__Type_OPair(U_11922,U_11922)))),U_11923)),U_11924)) ) ),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

fof(f_3142_3,plain,
    ( ! [U_11930,U_11928,U_11926] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11926,hAPP(hAPP(c_COMBC(U_11926,tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_fun(U_11926,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11926,tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_fun(U_11926,tc_HOL_Obool)),U_11926),c_COMBC(U_11926,tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11926,tc_prod(U_11926,U_11926)),tc_fun(U_11926,tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),U_11926),hAPP(c_COMBB(tc_prod(U_11926,U_11926),tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool),U_11926),c_member(tc_prod(U_11926,U_11926)))),c_Product__Type_OPair(U_11926,U_11926)))),U_11928)),U_11930))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11926),U_11930),c_Wellfounded_Oacc(U_11926,U_11928))) )
    & ! [U_11929,U_11927,U_11925] :
        ( hBOOL(hAPP(hAPP(c_member(U_11925),U_11929),c_Wellfounded_Oacc(U_11925,U_11927)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11925,hAPP(hAPP(c_COMBC(U_11925,tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_fun(U_11925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11925,tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_fun(U_11925,tc_HOL_Obool)),U_11925),c_COMBC(U_11925,tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11925,tc_prod(U_11925,U_11925)),tc_fun(U_11925,tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),U_11925),hAPP(c_COMBB(tc_prod(U_11925,U_11925),tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool),U_11925),c_member(tc_prod(U_11925,U_11925)))),c_Product__Type_OPair(U_11925,U_11925)))),U_11927)),U_11929)) ) ),
    inference(miniscope,[status(thm)],[f_3142_2]) ).

cnf(f_3142_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11925),U_11929),c_Wellfounded_Oacc(U_11925,U_11927)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11925,hAPP(hAPP(c_COMBC(U_11925,tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_fun(U_11925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11925,tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_fun(U_11925,tc_HOL_Obool)),U_11925),c_COMBC(U_11925,tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11925,tc_prod(U_11925,U_11925)),tc_fun(U_11925,tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool)),U_11925),hAPP(c_COMBB(tc_prod(U_11925,U_11925),tc_fun(tc_fun(tc_prod(U_11925,U_11925),tc_HOL_Obool),tc_HOL_Obool),U_11925),c_member(tc_prod(U_11925,U_11925)))),c_Product__Type_OPair(U_11925,U_11925)))),U_11927)),U_11929)) ),
    inference(clausify,[status(thm)],[f_3142_3]) ).

cnf(f_3142_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11926,hAPP(hAPP(c_COMBC(U_11926,tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_fun(U_11926,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11926,tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_fun(U_11926,tc_HOL_Obool)),U_11926),c_COMBC(U_11926,tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11926,tc_prod(U_11926,U_11926)),tc_fun(U_11926,tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool)),U_11926),hAPP(c_COMBB(tc_prod(U_11926,U_11926),tc_fun(tc_fun(tc_prod(U_11926,U_11926),tc_HOL_Obool),tc_HOL_Obool),U_11926),c_member(tc_prod(U_11926,U_11926)))),c_Product__Type_OPair(U_11926,U_11926)))),U_11928)),U_11930))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11926),U_11930),c_Wellfounded_Oacc(U_11926,U_11928))) ),
    inference(clausify,[status(thm)],[f_3142_3]) ).

fof(f_3143_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_3143_2,plain,
    ! [U_11938,U_11937,U_11936,U_11935] :
      ( ( c_Wellfounded_Omax__extp(U_11935,U_11936,U_11937,U_11938)
        | ? [U_11934] :
            ( ! [U_11933] :
                ( ~ hBOOL(hAPP(hAPP(U_11936,U_11934),U_11933))
                | ~ hBOOL(hAPP(hAPP(c_member(U_11935),U_11933),U_11938)) )
            & hBOOL(hAPP(hAPP(c_member(U_11935),U_11934),U_11937)) )
        | U_11938 = c_Orderings_Obot__class_Obot(tc_fun(U_11935,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11935),U_11938))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11935),U_11937)) )
      & ( ( ! [U_11932] :
              ( ? [U_11931] :
                  ( hBOOL(hAPP(hAPP(U_11936,U_11932),U_11931))
                  & hBOOL(hAPP(hAPP(c_member(U_11935),U_11931),U_11938)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_11935),U_11932),U_11937)) )
          & U_11938 != c_Orderings_Obot__class_Obot(tc_fun(U_11935,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11935),U_11938))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11935),U_11937)) )
        | ~ c_Wellfounded_Omax__extp(U_11935,U_11936,U_11937,U_11938) ) ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

fof(f_3143_3,plain,
    ( ! [U_11946,U_11944,U_11942,U_11940] :
        ( c_Wellfounded_Omax__extp(U_11940,U_11942,U_11944,U_11946)
        | ? [U_11934] :
            ( ! [U_11933] :
                ( ~ hBOOL(hAPP(hAPP(U_11942,U_11934),U_11933))
                | ~ hBOOL(hAPP(hAPP(c_member(U_11940),U_11933),U_11946)) )
            & hBOOL(hAPP(hAPP(c_member(U_11940),U_11934),U_11944)) )
        | U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11940,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11946))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11944)) )
    & ! [U_11945,U_11943,U_11941,U_11939] :
        ( ( ! [U_11932] :
              ( ? [U_11931] :
                  ( hBOOL(hAPP(hAPP(U_11941,U_11932),U_11931))
                  & hBOOL(hAPP(hAPP(c_member(U_11939),U_11931),U_11945)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_11939),U_11932),U_11943)) )
          & U_11945 != c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11945))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11943)) )
        | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ) ),
    inference(miniscope,[status(thm)],[f_3143_2]) ).

fof(f_3143_4,plain,
    ( ! [U_11946,U_11944,U_11942,U_11940] :
        ( c_Wellfounded_Omax__extp(U_11940,U_11942,U_11944,U_11946)
        | ? [U_11934] :
            ( ! [U_11933] :
                ( ~ hBOOL(hAPP(hAPP(U_11942,U_11934),U_11933))
                | ~ hBOOL(hAPP(hAPP(c_member(U_11940),U_11933),U_11946)) )
            & hBOOL(hAPP(hAPP(c_member(U_11940),U_11934),U_11944)) )
        | U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11940,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11946))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11944)) )
    & ! [U_11945,U_11943,U_11941,U_11939] :
        ( ( ! [U_11932] :
              ( ( hBOOL(hAPP(hAPP(U_11941,U_11932),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)))
                & hBOOL(hAPP(hAPP(c_member(U_11939),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)),U_11945)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_11939),U_11932),U_11943)) )
          & U_11945 != c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11945))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11943)) )
        | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_11931,sK279(U_11945,U_11943,U_11941,U_11939,U_11932))],[f_3143_3]) ).

fof(f_3143_5,plain,
    ( ! [U_11946,U_11944,U_11942,U_11940] :
        ( c_Wellfounded_Omax__extp(U_11940,U_11942,U_11944,U_11946)
        | ( ! [U_11933] :
              ( ~ hBOOL(hAPP(hAPP(U_11942,sK280(U_11946,U_11944,U_11942,U_11940)),U_11933))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11940),U_11933),U_11946)) )
          & hBOOL(hAPP(hAPP(c_member(U_11940),sK280(U_11946,U_11944,U_11942,U_11940)),U_11944)) )
        | U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11940,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11946))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11944)) )
    & ! [U_11945,U_11943,U_11941,U_11939] :
        ( ( ! [U_11932] :
              ( ( hBOOL(hAPP(hAPP(U_11941,U_11932),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)))
                & hBOOL(hAPP(hAPP(c_member(U_11939),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)),U_11945)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_11939),U_11932),U_11943)) )
          & U_11945 != c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11945))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11943)) )
        | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_11934,sK280(U_11946,U_11944,U_11942,U_11940))],[f_3143_4]) ).

cnf(f_3143_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11943))
    | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11939),U_11945))
    | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_8,plain,
    ( U_11945 != c_Orderings_Obot__class_Obot(tc_fun(U_11939,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11939),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)),U_11945))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11939),U_11932),U_11943))
    | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_10,plain,
    ( hBOOL(hAPP(hAPP(U_11941,U_11932),sK279(U_11945,U_11943,U_11941,U_11939,U_11932)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11939),U_11932),U_11943))
    | ~ c_Wellfounded_Omax__extp(U_11939,U_11941,U_11943,U_11945) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11940),sK280(U_11946,U_11944,U_11942,U_11940)),U_11944))
    | U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11940,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11946))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11944))
    | c_Wellfounded_Omax__extp(U_11940,U_11942,U_11944,U_11946) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

cnf(f_3143_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11942,sK280(U_11946,U_11944,U_11942,U_11940)),U_11933))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11940),U_11933),U_11946))
    | U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11940,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11946))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11940),U_11944))
    | c_Wellfounded_Omax__extp(U_11940,U_11942,U_11944,U_11946) ),
    inference(clausify,[status(thm)],[f_3143_5]) ).

fof(f_3144_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_3144_2,plain,
    ! [U_11952,U_11951,U_11950,U_11949] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11949,U_11952)))
      | ? [U_11948] :
          ( ! [U_11947] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11949,U_11949)),hAPP(hAPP(c_Product__Type_OPair(U_11949,U_11949),U_11948),U_11947)),U_11952))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11949),U_11947),U_11951)) )
          & hBOOL(hAPP(hAPP(c_member(U_11949),U_11948),U_11950)) )
      | U_11951 = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11951))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11950)) ),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

fof(f_3144_3,plain,
    ! [U_11952,U_11951,U_11950,U_11949] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11949,U_11952)))
      | ( ! [U_11947] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11949,U_11949)),hAPP(hAPP(c_Product__Type_OPair(U_11949,U_11949),sK281(U_11952,U_11951,U_11950,U_11949)),U_11947)),U_11952))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11949),U_11947),U_11951)) )
        & hBOOL(hAPP(hAPP(c_member(U_11949),sK281(U_11952,U_11951,U_11950,U_11949)),U_11950)) )
      | U_11951 = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11951))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11950)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_11948,sK281(U_11952,U_11951,U_11950,U_11949))],[f_3144_2]) ).

cnf(f_3144_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11949),sK281(U_11952,U_11951,U_11950,U_11949)),U_11950))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11949,U_11952)))
    | U_11951 = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11951))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11950)) ),
    inference(clausify,[status(thm)],[f_3144_3]) ).

cnf(f_3144_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11949,U_11949)),hAPP(hAPP(c_Product__Type_OPair(U_11949,U_11949),sK281(U_11952,U_11951,U_11950,U_11949)),U_11947)),U_11952))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11949),U_11947),U_11951))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11949,tc_HOL_Obool),tc_fun(U_11949,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11949,U_11952)))
    | U_11951 = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11951))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11949),U_11950)) ),
    inference(clausify,[status(thm)],[f_3144_3]) ).

fof(f_3145_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_3145_2,plain,
    ! [U_11955,U_11954,U_11953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11953,tc_HOL_Obool)),c_Wellfounded_Oacc(U_11953,U_11955)),c_Wellfounded_Oacc(U_11953,U_11954)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool)),U_11954),U_11955)) ),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

cnf(f_3145_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11953,tc_HOL_Obool)),c_Wellfounded_Oacc(U_11953,U_11955)),c_Wellfounded_Oacc(U_11953,U_11954)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool)),U_11954),U_11955)) ),
    inference(clausify,[status(thm)],[f_3145_2]) ).

fof(f_3146_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_3146_2,plain,
    ! [U_11959,U_11958,U_11957,U_11956] :
      ( hBOOL(hAPP(hAPP(c_member(U_11956),U_11959),c_Wellfounded_Oacc(U_11956,U_11958)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11956,U_11956)),hAPP(hAPP(c_Product__Type_OPair(U_11956,U_11956),U_11959),U_11957)),U_11958))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11956),U_11957),c_Wellfounded_Oacc(U_11956,U_11958))) ),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

cnf(f_3146_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11956),U_11959),c_Wellfounded_Oacc(U_11956,U_11958)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11956,U_11956)),hAPP(hAPP(c_Product__Type_OPair(U_11956,U_11956),U_11959),U_11957)),U_11958))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11956),U_11957),c_Wellfounded_Oacc(U_11956,U_11958))) ),
    inference(clausify,[status(thm)],[f_3146_2]) ).

fof(f_3147_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_3147_2,plain,
    ! [U_11964,U_11963,U_11962] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11962),U_11963),c_Wellfounded_Oacc(U_11962,U_11964)))
        | ? [U_11961] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_11962),U_11961),c_Wellfounded_Oacc(U_11962,U_11964)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11962,U_11962)),hAPP(hAPP(c_Product__Type_OPair(U_11962,U_11962),U_11961),U_11963)),U_11964)) ) )
      & ( ! [U_11960] :
            ( hBOOL(hAPP(hAPP(c_member(U_11962),U_11960),c_Wellfounded_Oacc(U_11962,U_11964)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11962,U_11962)),hAPP(hAPP(c_Product__Type_OPair(U_11962,U_11962),U_11960),U_11963)),U_11964)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11962),U_11963),c_Wellfounded_Oacc(U_11962,U_11964))) ) ),
    inference(variable_rename,[status(thm)],[f_3147_1]) ).

fof(f_3147_3,plain,
    ( ! [U_11970,U_11968,U_11966] :
        ( hBOOL(hAPP(hAPP(c_member(U_11966),U_11968),c_Wellfounded_Oacc(U_11966,U_11970)))
        | ? [U_11961] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_11966),U_11961),c_Wellfounded_Oacc(U_11966,U_11970)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11966,U_11966)),hAPP(hAPP(c_Product__Type_OPair(U_11966,U_11966),U_11961),U_11968)),U_11970)) ) )
    & ! [U_11969,U_11967,U_11965] :
        ( ! [U_11960] :
            ( hBOOL(hAPP(hAPP(c_member(U_11965),U_11960),c_Wellfounded_Oacc(U_11965,U_11969)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11965)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11965),U_11960),U_11967)),U_11969)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11967),c_Wellfounded_Oacc(U_11965,U_11969))) ) ),
    inference(miniscope,[status(thm)],[f_3147_2]) ).

fof(f_3147_4,plain,
    ( ! [U_11970,U_11968,U_11966] :
        ( hBOOL(hAPP(hAPP(c_member(U_11966),U_11968),c_Wellfounded_Oacc(U_11966,U_11970)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_11966),sK282(U_11970,U_11968,U_11966)),c_Wellfounded_Oacc(U_11966,U_11970)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11966,U_11966)),hAPP(hAPP(c_Product__Type_OPair(U_11966,U_11966),sK282(U_11970,U_11968,U_11966)),U_11968)),U_11970)) ) )
    & ! [U_11969,U_11967,U_11965] :
        ( ! [U_11960] :
            ( hBOOL(hAPP(hAPP(c_member(U_11965),U_11960),c_Wellfounded_Oacc(U_11965,U_11969)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11965)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11965),U_11960),U_11967)),U_11969)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11967),c_Wellfounded_Oacc(U_11965,U_11969))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_11961,sK282(U_11970,U_11968,U_11966))],[f_3147_3]) ).

cnf(f_3147_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11965),U_11960),c_Wellfounded_Oacc(U_11965,U_11969)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11965,U_11965)),hAPP(hAPP(c_Product__Type_OPair(U_11965,U_11965),U_11960),U_11967)),U_11969))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11965),U_11967),c_Wellfounded_Oacc(U_11965,U_11969))) ),
    inference(clausify,[status(thm)],[f_3147_4]) ).

cnf(f_3147_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11966,U_11966)),hAPP(hAPP(c_Product__Type_OPair(U_11966,U_11966),sK282(U_11970,U_11968,U_11966)),U_11968)),U_11970))
    | hBOOL(hAPP(hAPP(c_member(U_11966),U_11968),c_Wellfounded_Oacc(U_11966,U_11970))) ),
    inference(clausify,[status(thm)],[f_3147_4]) ).

cnf(f_3147_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_11966),sK282(U_11970,U_11968,U_11966)),c_Wellfounded_Oacc(U_11966,U_11970)))
    | hBOOL(hAPP(hAPP(c_member(U_11966),U_11968),c_Wellfounded_Oacc(U_11966,U_11970))) ),
    inference(clausify,[status(thm)],[f_3147_4]) ).

fof(f_3148_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_3148_2,plain,
    ! [U_11971] : c_Nitpick_Ozero__frac(U_11971) = c_Nitpick_OAbs__Frac(U_11971,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_3148_1]) ).

cnf(f_3148_3,plain,
    c_Nitpick_Ozero__frac(U_11971) = c_Nitpick_OAbs__Frac(U_11971,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_3148_2]) ).

fof(f_3149_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_3149_2,plain,
    ! [U_11976,U_11975,U_11974,U_11973] :
      ( c_Fun_Oinj__on(U_11974,U_11975,U_11976,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_11974,tc_HOL_Obool),U_11973))
      | ? [U_11972] :
          ( ~ c_Fun_Oinj__on(U_11974,U_11975,U_11976,U_11972)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_11974,tc_HOL_Obool)),U_11972),U_11973)) )
      | U_11973 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11974,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

fof(f_3149_3,plain,
    ! [U_11976,U_11975,U_11974,U_11973] :
      ( c_Fun_Oinj__on(U_11974,U_11975,U_11976,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_11974,tc_HOL_Obool),U_11973))
      | ( ~ c_Fun_Oinj__on(U_11974,U_11975,U_11976,sK283(U_11976,U_11975,U_11974,U_11973))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_11974,tc_HOL_Obool)),sK283(U_11976,U_11975,U_11974,U_11973)),U_11973)) )
      | U_11973 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11974,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_11972,sK283(U_11976,U_11975,U_11974,U_11973))],[f_3149_2]) ).

cnf(f_3149_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11974,tc_HOL_Obool)),sK283(U_11976,U_11975,U_11974,U_11973)),U_11973))
    | c_Fun_Oinj__on(U_11974,U_11975,U_11976,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_11974,tc_HOL_Obool),U_11973))
    | U_11973 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11974,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3149_3]) ).

cnf(f_3149_5,plain,
    ( ~ c_Fun_Oinj__on(U_11974,U_11975,U_11976,sK283(U_11976,U_11975,U_11974,U_11973))
    | c_Fun_Oinj__on(U_11974,U_11975,U_11976,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_11974,tc_HOL_Obool),U_11973))
    | U_11973 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11974,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3149_3]) ).

fof(f_3150_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_3150_2,plain,
    ! [U_11978,U_11977] : c_Set_Othe__elem(U_11977,U_11978) = c_HOL_OThe(U_11977,hAPP(hAPP(c_COMBB(tc_fun(U_11977,tc_HOL_Obool),tc_HOL_Obool,U_11977),hAPP(c_fequal,U_11978)),hAPP(hAPP(c_COMBC(U_11977,tc_fun(U_11977,tc_HOL_Obool),tc_fun(U_11977,tc_HOL_Obool)),c_Set_Oinsert(U_11977)),c_Orderings_Obot__class_Obot(tc_fun(U_11977,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

cnf(f_3150_3,plain,
    c_Set_Othe__elem(U_11977,U_11978) = c_HOL_OThe(U_11977,hAPP(hAPP(c_COMBB(tc_fun(U_11977,tc_HOL_Obool),tc_HOL_Obool,U_11977),hAPP(c_fequal,U_11978)),hAPP(hAPP(c_COMBC(U_11977,tc_fun(U_11977,tc_HOL_Obool),tc_fun(U_11977,tc_HOL_Obool)),c_Set_Oinsert(U_11977)),c_Orderings_Obot__class_Obot(tc_fun(U_11977,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3150_2]) ).

fof(f_3151_1,plain,
    ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).

fof(f_3151_2,plain,
    ! [U_11981,U_11980,U_11979] : c_HOL_OThe(tc_prod(U_11979,U_11980),U_11981) = c_HOL_OThe(tc_prod(U_11979,U_11980),hAPP(c_Product__Type_Oprod_Oprod__case(U_11979,U_11980,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11980,tc_prod(U_11979,U_11980)),tc_fun(U_11980,tc_HOL_Obool),U_11979),hAPP(c_COMBB(tc_prod(U_11979,U_11980),tc_HOL_Obool,U_11980),U_11981)),c_Product__Type_OPair(U_11979,U_11980)))),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

cnf(f_3151_3,plain,
    c_HOL_OThe(tc_prod(U_11979,U_11980),U_11981) = c_HOL_OThe(tc_prod(U_11979,U_11980),hAPP(c_Product__Type_Oprod_Oprod__case(U_11979,U_11980,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11980,tc_prod(U_11979,U_11980)),tc_fun(U_11980,tc_HOL_Obool),U_11979),hAPP(c_COMBB(tc_prod(U_11979,U_11980),tc_HOL_Obool,U_11980),U_11981)),c_Product__Type_OPair(U_11979,U_11980)))),
    inference(clausify,[status(thm)],[f_3151_2]) ).

fof(f_3152_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_3152_2,plain,
    ! [U_11985,U_11984,U_11983,U_11982] : c_HOL_OThe(tc_prod(U_11982,U_11983),hAPP(c_Product__Type_Oprod_Oprod__case(U_11982,U_11983,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11982,tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),U_11982),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11983)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11982),c_fconj),hAPP(c_fequal,U_11984)))),hAPP(c_fequal,U_11985)))) = hAPP(hAPP(c_Product__Type_OPair(U_11982,U_11983),U_11984),U_11985),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

cnf(f_3152_3,plain,
    c_HOL_OThe(tc_prod(U_11982,U_11983),hAPP(c_Product__Type_Oprod_Oprod__case(U_11982,U_11983,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11982,tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),U_11982),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11983)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11982),c_fconj),hAPP(c_fequal,U_11984)))),hAPP(c_fequal,U_11985)))) = hAPP(hAPP(c_Product__Type_OPair(U_11982,U_11983),U_11984),U_11985),
    inference(clausify,[status(thm)],[f_3152_2]) ).

fof(f_3153_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_3153_2,plain,
    ! [U_11990,U_11989,U_11988,U_11987,U_11986] : hAPP(c_Fun_Othe__inv__into(U_11986,U_11987,U_11988,U_11989),U_11990) = c_HOL_OThe(U_11986,hAPP(hAPP(c_COMBS(U_11986,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11986),c_fconj),hAPP(hAPP(c_COMBC(U_11986,tc_fun(U_11986,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11986)),U_11988))),hAPP(hAPP(c_COMBC(U_11986,U_11987,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11987,tc_fun(U_11987,tc_HOL_Obool),U_11986),c_fequal),U_11989)),U_11990))),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

cnf(f_3153_3,plain,
    hAPP(c_Fun_Othe__inv__into(U_11986,U_11987,U_11988,U_11989),U_11990) = c_HOL_OThe(U_11986,hAPP(hAPP(c_COMBS(U_11986,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11986),c_fconj),hAPP(hAPP(c_COMBC(U_11986,tc_fun(U_11986,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11986)),U_11988))),hAPP(hAPP(c_COMBC(U_11986,U_11987,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11987,tc_fun(U_11987,tc_HOL_Obool),U_11986),c_fequal),U_11989)),U_11990))),
    inference(clausify,[status(thm)],[f_3153_2]) ).

fof(f_3154_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_3154_2,plain,
    ! [U_11995,U_11994,U_11993,U_11992,U_11991] : hAPP(hAPP(c_Finite__Set_Ofold(U_11991,U_11992,U_11993),U_11994),U_11995) = c_HOL_OThe(U_11992,c_Finite__Set_Ofold__graph(U_11991,U_11992,U_11993,U_11994,U_11995)),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

cnf(f_3154_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_11991,U_11992,U_11993),U_11994),U_11995) = c_HOL_OThe(U_11992,c_Finite__Set_Ofold__graph(U_11991,U_11992,U_11993,U_11994,U_11995)),
    inference(clausify,[status(thm)],[f_3154_2]) ).

fof(f_3155_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_3155_2,plain,
    ! [U_11997,U_11996] : c_Divides_Odivmod__nat(U_11996,U_11997) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11996,U_11997)),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

cnf(f_3155_3,plain,
    c_Divides_Odivmod__nat(U_11996,U_11997) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11996,U_11997)),
    inference(clausify,[status(thm)],[f_3155_2]) ).

fof(f_3156_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_3156_2,plain,
    ! [U_12000,U_11999,U_11998] : hAPP(c_Finite__Set_Ofold1(U_11998,U_11999),U_12000) = c_HOL_OThe(U_11998,c_Finite__Set_Ofold1Set(U_11998,U_11999,U_12000)),
    inference(variable_rename,[status(thm)],[f_3156_1]) ).

cnf(f_3156_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_11998,U_11999),U_12000) = c_HOL_OThe(U_11998,c_Finite__Set_Ofold1Set(U_11998,U_11999,U_12000)),
    inference(clausify,[status(thm)],[f_3156_2]) ).

fof(f_3157_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_3157_2,plain,
    ! [U_12003,U_12002,U_12001] : c_HOL_OThe(tc_prod(U_12001,U_12002),hAPP(c_Product__Type_Oprod_Oprod__case(U_12001,U_12002,tc_HOL_Obool),U_12003)) = c_HOL_OThe(tc_prod(U_12001,U_12002),hAPP(hAPP(c_COMBS(tc_prod(U_12001,U_12002),U_12002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12001,tc_fun(U_12002,tc_HOL_Obool),tc_prod(U_12001,U_12002)),U_12003),c_Product__Type_Ofst(U_12001,U_12002))),c_Product__Type_Osnd(U_12001,U_12002))),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

cnf(f_3157_3,plain,
    c_HOL_OThe(tc_prod(U_12001,U_12002),hAPP(c_Product__Type_Oprod_Oprod__case(U_12001,U_12002,tc_HOL_Obool),U_12003)) = c_HOL_OThe(tc_prod(U_12001,U_12002),hAPP(hAPP(c_COMBS(tc_prod(U_12001,U_12002),U_12002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12001,tc_fun(U_12002,tc_HOL_Obool),tc_prod(U_12001,U_12002)),U_12003),c_Product__Type_Ofst(U_12001,U_12002))),c_Product__Type_Osnd(U_12001,U_12002))),
    inference(clausify,[status(thm)],[f_3157_2]) ).

fof(f_3158_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_3158_2,plain,
    ! [U_12004] : c_Nitpick_Oone__frac(U_12004) = c_Nitpick_OAbs__Frac(U_12004,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_3158_1]) ).

cnf(f_3158_3,plain,
    c_Nitpick_Oone__frac(U_12004) = c_Nitpick_OAbs__Frac(U_12004,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_3158_2]) ).

fof(f_3159_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_3159_2,plain,
    ! [U_12006,U_12005] : c_Nitpick_Onumber__of__frac(U_12005,U_12006) = c_Nitpick_OAbs__Frac(U_12005,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12006),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

cnf(f_3159_3,plain,
    c_Nitpick_Onumber__of__frac(U_12005,U_12006) = c_Nitpick_OAbs__Frac(U_12005,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12006),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3159_2]) ).

fof(f_3160_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_3160_2,plain,
    ! [U_12009,U_12008,U_12007] : hAPP(hAPP(c_Nitpick_Ofrac(U_12007),U_12008),U_12009) = c_Nitpick_OAbs__Frac(U_12007,c_Nitpick_Onorm__frac(U_12008,U_12009)),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

cnf(f_3160_3,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_12007),U_12008),U_12009) = c_Nitpick_OAbs__Frac(U_12007,c_Nitpick_Onorm__frac(U_12008,U_12009)),
    inference(clausify,[status(thm)],[f_3160_2]) ).

fof(f_3161_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_3161_2,plain,
    ! [U_12012,U_12011,U_12010] :
      ( ( c_Partial__Function_Oflat__lub(U_12010,U_12012,U_12011) = c_HOL_OThe(U_12010,hAPP(hAPP(c_COMBC(U_12010,tc_fun(U_12010,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12010)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12010,tc_HOL_Obool)),U_12011),hAPP(hAPP(c_Set_Oinsert(U_12010),U_12012),c_Orderings_Obot__class_Obot(tc_fun(U_12010,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12010,tc_HOL_Obool)),U_12011),hAPP(hAPP(c_Set_Oinsert(U_12010),U_12012),c_Orderings_Obot__class_Obot(tc_fun(U_12010,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_12010,U_12012,U_12011) = U_12012
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12010,tc_HOL_Obool)),U_12011),hAPP(hAPP(c_Set_Oinsert(U_12010),U_12012),c_Orderings_Obot__class_Obot(tc_fun(U_12010,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ( ! [U_12018,U_12016,U_12014] :
        ( c_Partial__Function_Oflat__lub(U_12014,U_12018,U_12016) = c_HOL_OThe(U_12014,hAPP(hAPP(c_COMBC(U_12014,tc_fun(U_12014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12014)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12014,tc_HOL_Obool)),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_Orderings_Oord__class_Oless__eq(tc_fun(U_12014,tc_HOL_Obool)),U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12018),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))))) )
    & ! [U_12017,U_12015,U_12013] :
        ( c_Partial__Function_Oflat__lub(U_12013,U_12017,U_12015) = U_12017
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12013,tc_HOL_Obool)),U_12015),hAPP(hAPP(c_Set_Oinsert(U_12013),U_12017),c_Orderings_Obot__class_Obot(tc_fun(U_12013,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_3161_2]) ).

cnf(f_3161_4,plain,
    ( c_Partial__Function_Oflat__lub(U_12013,U_12017,U_12015) = U_12017
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12013,tc_HOL_Obool)),U_12015),hAPP(hAPP(c_Set_Oinsert(U_12013),U_12017),c_Orderings_Obot__class_Obot(tc_fun(U_12013,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

cnf(f_3161_5,plain,
    ( c_Partial__Function_Oflat__lub(U_12014,U_12018,U_12016) = c_HOL_OThe(U_12014,hAPP(hAPP(c_COMBC(U_12014,tc_fun(U_12014,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12014)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12014,tc_HOL_Obool)),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_Orderings_Oord__class_Oless__eq(tc_fun(U_12014,tc_HOL_Obool)),U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12018),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

fof(f_3162_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_3162_2,plain,
    ! [U_12022,U_12021,U_12020,U_12019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12019,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12019,U_12020,U_12021),hAPP(hAPP(c_Set_Oinsert(U_12020),U_12022),c_Orderings_Obot__class_Obot(tc_fun(U_12020,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12019),c_HOL_OThe(U_12019,hAPP(hAPP(c_COMBC(U_12019,U_12020,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12020,tc_fun(U_12020,tc_HOL_Obool),U_12019),c_fequal),U_12021)),U_12022))),c_Orderings_Obot__class_Obot(tc_fun(U_12019,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_12019,U_12020,U_12021,c_Orderings_Otop__class_Otop(tc_fun(U_12019,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

cnf(f_3162_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12019,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12019,U_12020,U_12021),hAPP(hAPP(c_Set_Oinsert(U_12020),U_12022),c_Orderings_Obot__class_Obot(tc_fun(U_12020,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12019),c_HOL_OThe(U_12019,hAPP(hAPP(c_COMBC(U_12019,U_12020,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12020,tc_fun(U_12020,tc_HOL_Obool),U_12019),c_fequal),U_12021)),U_12022))),c_Orderings_Obot__class_Obot(tc_fun(U_12019,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_12019,U_12020,U_12021,c_Orderings_Otop__class_Otop(tc_fun(U_12019,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3162_2]) ).

fof(f_3163_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_3163_2,plain,
    ! [U_12029,U_12028,U_12027,U_12026,U_12025] :
      ( hAPP(U_12028,hAPP(U_12027,U_12029)) = hAPP(U_12027,hAPP(c_Set_Oimage(U_12025,U_12025,U_12028),U_12029))
      | U_12029 = c_Orderings_Obot__class_Obot(tc_fun(U_12025,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12025),U_12029))
      | ? [U_12024,U_12023] : hAPP(U_12028,hAPP(hAPP(U_12026,U_12024),U_12023)) != hAPP(hAPP(U_12026,hAPP(U_12028,U_12024)),hAPP(U_12028,U_12023))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12025,U_12026,U_12027) ),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

fof(f_3163_3,plain,
    ! [U_12029,U_12028,U_12027,U_12026,U_12025] :
      ( hAPP(U_12028,hAPP(U_12027,U_12029)) = hAPP(U_12027,hAPP(c_Set_Oimage(U_12025,U_12025,U_12028),U_12029))
      | U_12029 = c_Orderings_Obot__class_Obot(tc_fun(U_12025,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12025),U_12029))
      | ? [U_12023] : hAPP(U_12028,hAPP(hAPP(U_12026,sK284(U_12029,U_12028,U_12027,U_12026,U_12025)),U_12023)) != hAPP(hAPP(U_12026,hAPP(U_12028,sK284(U_12029,U_12028,U_12027,U_12026,U_12025))),hAPP(U_12028,U_12023))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12025,U_12026,U_12027) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_12024,sK284(U_12029,U_12028,U_12027,U_12026,U_12025))],[f_3163_2]) ).

fof(f_3163_4,plain,
    ! [U_12029,U_12028,U_12027,U_12026,U_12025] :
      ( hAPP(U_12028,hAPP(U_12027,U_12029)) = hAPP(U_12027,hAPP(c_Set_Oimage(U_12025,U_12025,U_12028),U_12029))
      | U_12029 = c_Orderings_Obot__class_Obot(tc_fun(U_12025,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12025),U_12029))
      | hAPP(U_12028,hAPP(hAPP(U_12026,sK284(U_12029,U_12028,U_12027,U_12026,U_12025)),sK285(U_12029,U_12028,U_12027,U_12026,U_12025))) != hAPP(hAPP(U_12026,hAPP(U_12028,sK284(U_12029,U_12028,U_12027,U_12026,U_12025))),hAPP(U_12028,sK285(U_12029,U_12028,U_12027,U_12026,U_12025)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12025,U_12026,U_12027) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_12023,sK285(U_12029,U_12028,U_12027,U_12026,U_12025))],[f_3163_3]) ).

cnf(f_3163_5,plain,
    ( hAPP(U_12028,hAPP(U_12027,U_12029)) = hAPP(U_12027,hAPP(c_Set_Oimage(U_12025,U_12025,U_12028),U_12029))
    | U_12029 = c_Orderings_Obot__class_Obot(tc_fun(U_12025,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12025),U_12029))
    | hAPP(U_12028,hAPP(hAPP(U_12026,sK284(U_12029,U_12028,U_12027,U_12026,U_12025)),sK285(U_12029,U_12028,U_12027,U_12026,U_12025))) != hAPP(hAPP(U_12026,hAPP(U_12028,sK284(U_12029,U_12028,U_12027,U_12026,U_12025))),hAPP(U_12028,sK285(U_12029,U_12028,U_12027,U_12026,U_12025)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12025,U_12026,U_12027) ),
    inference(clausify,[status(thm)],[f_3163_4]) ).

fof(f_3164_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_3164_2,plain,
    ! [U_12035,U_12034,U_12033,U_12032,U_12031,U_12030] :
      ( hBOOL(hAPP(hAPP(c_member(U_12035),U_12031),hAPP(c_Set_Ovimage(U_12035,U_12033,U_12030),U_12034)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12032),U_12034))
      | hAPP(U_12030,U_12031) != U_12032 ),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

cnf(f_3164_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12035),U_12031),hAPP(c_Set_Ovimage(U_12035,U_12033,U_12030),U_12034)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12032),U_12034))
    | hAPP(U_12030,U_12031) != U_12032 ),
    inference(clausify,[status(thm)],[f_3164_2]) ).

fof(f_3165_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_3165_2,plain,
    ! [U_12040,U_12039,U_12038,U_12037,U_12036] :
      ( hBOOL(hAPP(hAPP(c_member(U_12040),U_12038),hAPP(c_Set_Ovimage(U_12040,U_12036,U_12037),U_12039)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),U_12039)) ),
    inference(variable_rename,[status(thm)],[f_3165_1]) ).

cnf(f_3165_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12040),U_12038),hAPP(c_Set_Ovimage(U_12040,U_12036,U_12037),U_12039)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),U_12039)) ),
    inference(clausify,[status(thm)],[f_3165_2]) ).

fof(f_3166_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_3166_2,plain,
    ! [U_12045,U_12044,U_12043,U_12042,U_12041] :
      ( hBOOL(hAPP(hAPP(c_member(U_12043),hAPP(U_12044,U_12042)),U_12045))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12041),U_12042),hAPP(c_Set_Ovimage(U_12041,U_12043,U_12044),U_12045))) ),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

fof(f_3166_3,plain,
    ! [U_12045,U_12044,U_12043,U_12042] :
      ( ! [U_12041] : ~ hBOOL(hAPP(hAPP(c_member(U_12041),U_12042),hAPP(c_Set_Ovimage(U_12041,U_12043,U_12044),U_12045)))
      | hBOOL(hAPP(hAPP(c_member(U_12043),hAPP(U_12044,U_12042)),U_12045)) ),
    inference(miniscope,[status(thm)],[f_3166_2]) ).

cnf(f_3166_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12041),U_12042),hAPP(c_Set_Ovimage(U_12041,U_12043,U_12044),U_12045)))
    | hBOOL(hAPP(hAPP(c_member(U_12043),hAPP(U_12044,U_12042)),U_12045)) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

fof(f_3167_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_3167_2,plain,
    ! [U_12050,U_12049,U_12048,U_12047,U_12046] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12046),U_12047),hAPP(c_Set_Ovimage(U_12046,U_12048,U_12049),U_12050)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12048),hAPP(U_12049,U_12047)),U_12050)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_12048),hAPP(U_12049,U_12047)),U_12050))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12046),U_12047),hAPP(c_Set_Ovimage(U_12046,U_12048,U_12049),U_12050))) ) ),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

fof(f_3167_3,plain,
    ( ! [U_12060,U_12058,U_12056,U_12054] :
        ( ! [U_12052] : hBOOL(hAPP(hAPP(c_member(U_12052),U_12054),hAPP(c_Set_Ovimage(U_12052,U_12056,U_12058),U_12060)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12056),hAPP(U_12058,U_12054)),U_12060)) )
    & ! [U_12059,U_12057,U_12055,U_12053] :
        ( ! [U_12051] : ~ hBOOL(hAPP(hAPP(c_member(U_12051),U_12053),hAPP(c_Set_Ovimage(U_12051,U_12055,U_12057),U_12059)))
        | hBOOL(hAPP(hAPP(c_member(U_12055),hAPP(U_12057,U_12053)),U_12059)) ) ),
    inference(miniscope,[status(thm)],[f_3167_2]) ).

cnf(f_3167_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12051),U_12053),hAPP(c_Set_Ovimage(U_12051,U_12055,U_12057),U_12059)))
    | hBOOL(hAPP(hAPP(c_member(U_12055),hAPP(U_12057,U_12053)),U_12059)) ),
    inference(clausify,[status(thm)],[f_3167_3]) ).

cnf(f_3167_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12052),U_12054),hAPP(c_Set_Ovimage(U_12052,U_12056,U_12058),U_12060)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12056),hAPP(U_12058,U_12054)),U_12060)) ),
    inference(clausify,[status(thm)],[f_3167_3]) ).

fof(f_3168_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_3168_2,plain,
    ! [U_12065,U_12064,U_12063,U_12062,U_12061] : hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12062,tc_HOL_Obool)),U_12064),U_12065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12061,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),U_12064)),hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),U_12065)),
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

cnf(f_3168_3,plain,
    hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12062,tc_HOL_Obool)),U_12064),U_12065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12061,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),U_12064)),hAPP(c_Set_Ovimage(U_12061,U_12062,U_12063),U_12065)),
    inference(clausify,[status(thm)],[f_3168_2]) ).

fof(f_3169_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_3169_2,plain,
    ! [U_12070,U_12069,U_12068,U_12067,U_12066] : hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12067,tc_HOL_Obool)),U_12069),U_12070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12066,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),U_12069)),hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),U_12070)),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

cnf(f_3169_3,plain,
    hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12067,tc_HOL_Obool)),U_12069),U_12070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12066,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),U_12069)),hAPP(c_Set_Ovimage(U_12066,U_12067,U_12068),U_12070)),
    inference(clausify,[status(thm)],[f_3169_2]) ).

fof(f_3170_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_3170_2,plain,
    ! [U_12076,U_12075,U_12074,U_12073,U_12072,U_12071] : hAPP(c_Set_Ovimage(U_12071,U_12072,U_12073),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12074,tc_fun(U_12072,tc_HOL_Obool)),U_12075),U_12076)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12074,tc_fun(U_12071,tc_HOL_Obool)),U_12075),hAPP(hAPP(c_COMBB(tc_fun(U_12072,tc_HOL_Obool),tc_fun(U_12071,tc_HOL_Obool),U_12074),c_Set_Ovimage(U_12071,U_12072,U_12073)),U_12076)),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

cnf(f_3170_3,plain,
    hAPP(c_Set_Ovimage(U_12071,U_12072,U_12073),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12074,tc_fun(U_12072,tc_HOL_Obool)),U_12075),U_12076)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12074,tc_fun(U_12071,tc_HOL_Obool)),U_12075),hAPP(hAPP(c_COMBB(tc_fun(U_12072,tc_HOL_Obool),tc_fun(U_12071,tc_HOL_Obool),U_12074),c_Set_Ovimage(U_12071,U_12072,U_12073)),U_12076)),
    inference(clausify,[status(thm)],[f_3170_2]) ).

fof(f_3171_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_3171_2,plain,
    ! [U_12081,U_12080,U_12079,U_12078,U_12077] : hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12078,tc_HOL_Obool)),U_12080),U_12081)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12077,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),U_12080)),hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),U_12081)),
    inference(variable_rename,[status(thm)],[f_3171_1]) ).

cnf(f_3171_3,plain,
    hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12078,tc_HOL_Obool)),U_12080),U_12081)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12077,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),U_12080)),hAPP(c_Set_Ovimage(U_12077,U_12078,U_12079),U_12081)),
    inference(clausify,[status(thm)],[f_3171_2]) ).

fof(f_3172_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_3172_2,plain,
    ! [U_12084,U_12083,U_12082] : hAPP(c_Set_Ovimage(U_12082,U_12083,U_12084),c_Orderings_Obot__class_Obot(tc_fun(U_12083,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12082,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

cnf(f_3172_3,plain,
    hAPP(c_Set_Ovimage(U_12082,U_12083,U_12084),c_Orderings_Obot__class_Obot(tc_fun(U_12083,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12082,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3172_2]) ).

fof(f_3173_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_3173_2,plain,
    ! [U_12089,U_12088,U_12087,U_12086,U_12085] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12085,U_12086,U_12087),U_12088),U_12089))
        | ~ hBOOL(hAPP(U_12088,hAPP(U_12087,U_12089))) )
      & ( hBOOL(hAPP(U_12088,hAPP(U_12087,U_12089)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12085,U_12086,U_12087),U_12088),U_12089)) ) ),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

fof(f_3173_3,plain,
    ( ! [U_12099,U_12097,U_12095] :
        ( ! [U_12093,U_12091] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12091,U_12093,U_12095),U_12097),U_12099))
        | ~ hBOOL(hAPP(U_12097,hAPP(U_12095,U_12099))) )
    & ! [U_12098,U_12096,U_12094] :
        ( ! [U_12092,U_12090] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12090,U_12092,U_12094),U_12096),U_12098))
        | hBOOL(hAPP(U_12096,hAPP(U_12094,U_12098))) ) ),
    inference(miniscope,[status(thm)],[f_3173_2]) ).

cnf(f_3173_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12090,U_12092,U_12094),U_12096),U_12098))
    | hBOOL(hAPP(U_12096,hAPP(U_12094,U_12098))) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_5,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12091,U_12093,U_12095),U_12097),U_12099))
    | ~ hBOOL(hAPP(U_12097,hAPP(U_12095,U_12099))) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

fof(f_3174_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_3174_2,plain,
    ! [U_12103,U_12102,U_12101,U_12100] : hAPP(c_Set_Ovimage(U_12100,U_12101,U_12102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12101,tc_HOL_Obool)),U_12103)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12100,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12100,U_12101,U_12102),U_12103)),
    inference(variable_rename,[status(thm)],[f_3174_1]) ).

cnf(f_3174_3,plain,
    hAPP(c_Set_Ovimage(U_12100,U_12101,U_12102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12101,tc_HOL_Obool)),U_12103)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12100,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12100,U_12101,U_12102),U_12103)),
    inference(clausify,[status(thm)],[f_3174_2]) ).

fof(f_3175_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_3175_2,plain,
    ! [U_12105,U_12104] : hAPP(c_Set_Ovimage(U_12104,U_12104,c_COMBI(U_12104)),U_12105) = U_12105,
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

cnf(f_3175_3,plain,
    hAPP(c_Set_Ovimage(U_12104,U_12104,c_COMBI(U_12104)),U_12105) = U_12105,
    inference(clausify,[status(thm)],[f_3175_2]) ).

fof(f_3176_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_3176_2,plain,
    ! [U_12110,U_12109,U_12108,U_12107,U_12106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12109,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12109,U_12106,U_12110),U_12107)),hAPP(c_Set_Ovimage(U_12109,U_12106,U_12110),U_12108)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12106,tc_HOL_Obool)),U_12107),U_12108)) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

cnf(f_3176_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12109,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12109,U_12106,U_12110),U_12107)),hAPP(c_Set_Ovimage(U_12109,U_12106,U_12110),U_12108)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12106,tc_HOL_Obool)),U_12107),U_12108)) ),
    inference(clausify,[status(thm)],[f_3176_2]) ).

fof(f_3177_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_3177_2,plain,
    ! [U_12116,U_12115,U_12114,U_12113,U_12112,U_12111] : hAPP(c_Set_Ovimage(U_12111,U_12112,U_12113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12114,tc_fun(U_12112,tc_HOL_Obool)),U_12115),U_12116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12114,tc_fun(U_12111,tc_HOL_Obool)),U_12115),hAPP(hAPP(c_COMBB(tc_fun(U_12112,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool),U_12114),c_Set_Ovimage(U_12111,U_12112,U_12113)),U_12116)),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

cnf(f_3177_3,plain,
    hAPP(c_Set_Ovimage(U_12111,U_12112,U_12113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12114,tc_fun(U_12112,tc_HOL_Obool)),U_12115),U_12116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12114,tc_fun(U_12111,tc_HOL_Obool)),U_12115),hAPP(hAPP(c_COMBB(tc_fun(U_12112,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool),U_12114),c_Set_Ovimage(U_12111,U_12112,U_12113)),U_12116)),
    inference(clausify,[status(thm)],[f_3177_2]) ).

fof(f_3178_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_3178_2,plain,
    ! [U_12119,U_12118,U_12117] : hAPP(c_Set_Ovimage(U_12117,U_12118,U_12119),c_Orderings_Otop__class_Otop(tc_fun(U_12118,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12117,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3178_1]) ).

cnf(f_3178_3,plain,
    hAPP(c_Set_Ovimage(U_12117,U_12118,U_12119),c_Orderings_Otop__class_Otop(tc_fun(U_12118,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12117,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3178_2]) ).

fof(f_3179_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_3179_2,plain,
    ! [U_12123,U_12122,U_12121,U_12120] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12120,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12121,U_12120,U_12122),hAPP(c_Set_Ovimage(U_12121,U_12120,U_12122),U_12123))),U_12123)),
    inference(variable_rename,[status(thm)],[f_3179_1]) ).

cnf(f_3179_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12120,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12121,U_12120,U_12122),hAPP(c_Set_Ovimage(U_12121,U_12120,U_12122),U_12123))),U_12123)),
    inference(clausify,[status(thm)],[f_3179_2]) ).

fof(f_3180_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_3180_2,plain,
    ! [U_12127,U_12126,U_12125,U_12124] :
      ( hAPP(c_Set_Oimage(U_12124,U_12125,U_12126),hAPP(c_Set_Ovimage(U_12124,U_12125,U_12126),U_12127)) = U_12127
      | hAPP(c_Set_Oimage(U_12124,U_12125,U_12126),c_Orderings_Otop__class_Otop(tc_fun(U_12124,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12125,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

cnf(f_3180_3,plain,
    ( hAPP(c_Set_Oimage(U_12124,U_12125,U_12126),hAPP(c_Set_Ovimage(U_12124,U_12125,U_12126),U_12127)) = U_12127
    | hAPP(c_Set_Oimage(U_12124,U_12125,U_12126),c_Orderings_Otop__class_Otop(tc_fun(U_12124,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12125,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3180_2]) ).

fof(f_3181_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_3181_2,plain,
    ! [U_12131,U_12130,U_12129,U_12128] : hAPP(c_Set_Ovimage(U_12128,U_12129,U_12130),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12129,tc_HOL_Obool),U_12131)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12129,tc_HOL_Obool),tc_fun(U_12128,tc_HOL_Obool)),U_12131),c_Set_Ovimage(U_12128,U_12129,U_12130)),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

cnf(f_3181_3,plain,
    hAPP(c_Set_Ovimage(U_12128,U_12129,U_12130),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12129,tc_HOL_Obool),U_12131)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12129,tc_HOL_Obool),tc_fun(U_12128,tc_HOL_Obool)),U_12131),c_Set_Ovimage(U_12128,U_12129,U_12130)),
    inference(clausify,[status(thm)],[f_3181_2]) ).

fof(f_3182_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_3182_2,plain,
    ! [U_12136,U_12135,U_12134,U_12133,U_12132] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12132),U_12133),hAPP(c_Set_Ovimage(U_12132,U_12134,U_12135),hAPP(hAPP(c_Set_Oinsert(U_12134),U_12136),c_Orderings_Obot__class_Obot(tc_fun(U_12134,tc_HOL_Obool))))))
        | hAPP(U_12135,U_12133) != U_12136 )
      & ( hAPP(U_12135,U_12133) = U_12136
        | ~ hBOOL(hAPP(hAPP(c_member(U_12132),U_12133),hAPP(c_Set_Ovimage(U_12132,U_12134,U_12135),hAPP(hAPP(c_Set_Oinsert(U_12134),U_12136),c_Orderings_Obot__class_Obot(tc_fun(U_12134,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

fof(f_3182_3,plain,
    ( ! [U_12146,U_12144,U_12142,U_12140] :
        ( ! [U_12138] : hBOOL(hAPP(hAPP(c_member(U_12138),U_12140),hAPP(c_Set_Ovimage(U_12138,U_12142,U_12144),hAPP(hAPP(c_Set_Oinsert(U_12142),U_12146),c_Orderings_Obot__class_Obot(tc_fun(U_12142,tc_HOL_Obool))))))
        | hAPP(U_12144,U_12140) != U_12146 )
    & ! [U_12145,U_12143,U_12141,U_12139] :
        ( ! [U_12137] : ~ hBOOL(hAPP(hAPP(c_member(U_12137),U_12139),hAPP(c_Set_Ovimage(U_12137,U_12141,U_12143),hAPP(hAPP(c_Set_Oinsert(U_12141),U_12145),c_Orderings_Obot__class_Obot(tc_fun(U_12141,tc_HOL_Obool))))))
        | hAPP(U_12143,U_12139) = U_12145 ) ),
    inference(miniscope,[status(thm)],[f_3182_2]) ).

cnf(f_3182_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12137),U_12139),hAPP(c_Set_Ovimage(U_12137,U_12141,U_12143),hAPP(hAPP(c_Set_Oinsert(U_12141),U_12145),c_Orderings_Obot__class_Obot(tc_fun(U_12141,tc_HOL_Obool))))))
    | hAPP(U_12143,U_12139) = U_12145 ),
    inference(clausify,[status(thm)],[f_3182_3]) ).

cnf(f_3182_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12138),U_12140),hAPP(c_Set_Ovimage(U_12138,U_12142,U_12144),hAPP(hAPP(c_Set_Oinsert(U_12142),U_12146),c_Orderings_Obot__class_Obot(tc_fun(U_12142,tc_HOL_Obool))))))
    | hAPP(U_12144,U_12140) != U_12146 ),
    inference(clausify,[status(thm)],[f_3182_3]) ).

fof(f_3183_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_3183_2,plain,
    ! [U_12151,U_12150,U_12149,U_12148,U_12147] : hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),hAPP(hAPP(c_Set_Oinsert(U_12148),U_12150),U_12151)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12147,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),hAPP(hAPP(c_Set_Oinsert(U_12148),U_12150),c_Orderings_Obot__class_Obot(tc_fun(U_12148,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),U_12151)),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

cnf(f_3183_3,plain,
    hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),hAPP(hAPP(c_Set_Oinsert(U_12148),U_12150),U_12151)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12147,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),hAPP(hAPP(c_Set_Oinsert(U_12148),U_12150),c_Orderings_Obot__class_Obot(tc_fun(U_12148,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12147,U_12148,U_12149),U_12151)),
    inference(clausify,[status(thm)],[f_3183_2]) ).

fof(f_3184_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_3184_2,plain,
    ! [U_12155,U_12154,U_12153,U_12152] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12153),U_12155))
      | hAPP(c_Set_Oimage(U_12152,U_12153,U_12154),c_Orderings_Otop__class_Otop(tc_fun(U_12152,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12153,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12152),hAPP(c_Set_Ovimage(U_12152,U_12153,U_12154),U_12155))) ),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

cnf(f_3184_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12153),U_12155))
    | hAPP(c_Set_Oimage(U_12152,U_12153,U_12154),c_Orderings_Otop__class_Otop(tc_fun(U_12152,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12153,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12152),hAPP(c_Set_Ovimage(U_12152,U_12153,U_12154),U_12155))) ),
    inference(clausify,[status(thm)],[f_3184_2]) ).

fof(f_3185_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_3185_2,plain,
    ! [U_12160,U_12159,U_12158,U_12157,U_12156] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12157,tc_HOL_Obool)),U_12159),hAPP(c_Set_Oimage(U_12156,U_12157,U_12158),U_12160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12156,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12156,U_12157,U_12158),U_12159)),U_12160))
      | hAPP(c_Set_Oimage(U_12156,U_12157,U_12158),c_Orderings_Otop__class_Otop(tc_fun(U_12156,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12157,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

cnf(f_3185_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12157,tc_HOL_Obool)),U_12159),hAPP(c_Set_Oimage(U_12156,U_12157,U_12158),U_12160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12156,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12156,U_12157,U_12158),U_12159)),U_12160))
    | hAPP(c_Set_Oimage(U_12156,U_12157,U_12158),c_Orderings_Otop__class_Otop(tc_fun(U_12156,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12157,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3185_2]) ).

fof(f_3186_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_3186_2,plain,
    ! [U_12164,U_12163,U_12162,U_12161] : hAPP(c_Set_Oimage(U_12161,U_12162,U_12163),hAPP(c_Set_Ovimage(U_12161,U_12162,U_12163),U_12164)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12162,tc_HOL_Obool)),U_12164),hAPP(c_Set_Oimage(U_12161,U_12162,U_12163),c_Orderings_Otop__class_Otop(tc_fun(U_12161,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

cnf(f_3186_3,plain,
    hAPP(c_Set_Oimage(U_12161,U_12162,U_12163),hAPP(c_Set_Ovimage(U_12161,U_12162,U_12163),U_12164)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12162,tc_HOL_Obool)),U_12164),hAPP(c_Set_Oimage(U_12161,U_12162,U_12163),c_Orderings_Otop__class_Otop(tc_fun(U_12161,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3186_2]) ).

fof(f_3187_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_3187_2,plain,
    ! [U_12168,U_12167,U_12166,U_12165] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12167),hAPP(c_Set_Ovimage(U_12167,U_12165,U_12168),U_12166)))
      | ~ c_Fun_Oinj__on(U_12167,U_12165,U_12168,c_Orderings_Otop__class_Otop(tc_fun(U_12167,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12165),U_12166)) ),
    inference(variable_rename,[status(thm)],[f_3187_1]) ).

cnf(f_3187_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12167),hAPP(c_Set_Ovimage(U_12167,U_12165,U_12168),U_12166)))
    | ~ c_Fun_Oinj__on(U_12167,U_12165,U_12168,c_Orderings_Otop__class_Otop(tc_fun(U_12167,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12165),U_12166)) ),
    inference(clausify,[status(thm)],[f_3187_2]) ).

fof(f_3188_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_3188_2,plain,
    ! [U_12172,U_12171,U_12170,U_12169] :
      ( hAPP(c_Set_Ovimage(U_12169,U_12170,U_12171),hAPP(c_Set_Oimage(U_12169,U_12170,U_12171),U_12172)) = U_12172
      | ~ c_Fun_Oinj__on(U_12169,U_12170,U_12171,c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

cnf(f_3188_3,plain,
    ( hAPP(c_Set_Ovimage(U_12169,U_12170,U_12171),hAPP(c_Set_Oimage(U_12169,U_12170,U_12171),U_12172)) = U_12172
    | ~ c_Fun_Oinj__on(U_12169,U_12170,U_12171,c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3188_2]) ).

fof(f_3189_1,plain,
    ! [T_c,V_A_2,V_ca_2,T_b] :
      ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
      & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).

fof(f_3189_2,plain,
    ! [U_12176,U_12175,U_12174,U_12173] :
      ( ( hAPP(c_Set_Ovimage(U_12176,U_12173,hAPP(c_COMBK(U_12173,U_12176),U_12174)),U_12175) = c_Orderings_Obot__class_Obot(tc_fun(U_12176,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_12173),U_12174),U_12175)) )
      & ( hAPP(c_Set_Ovimage(U_12176,U_12173,hAPP(c_COMBK(U_12173,U_12176),U_12174)),U_12175) = c_Orderings_Otop__class_Otop(tc_fun(U_12176,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12173),U_12174),U_12175)) ) ),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

fof(f_3189_3,plain,
    ( ! [U_12184,U_12182,U_12180,U_12178] :
        ( hAPP(c_Set_Ovimage(U_12184,U_12178,hAPP(c_COMBK(U_12178,U_12184),U_12180)),U_12182) = c_Orderings_Obot__class_Obot(tc_fun(U_12184,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_12178),U_12180),U_12182)) )
    & ! [U_12183,U_12181,U_12179,U_12177] :
        ( hAPP(c_Set_Ovimage(U_12183,U_12177,hAPP(c_COMBK(U_12177,U_12183),U_12179)),U_12181) = c_Orderings_Otop__class_Otop(tc_fun(U_12183,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12177),U_12179),U_12181)) ) ),
    inference(miniscope,[status(thm)],[f_3189_2]) ).

cnf(f_3189_4,plain,
    ( hAPP(c_Set_Ovimage(U_12183,U_12177,hAPP(c_COMBK(U_12177,U_12183),U_12179)),U_12181) = c_Orderings_Otop__class_Otop(tc_fun(U_12183,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12177),U_12179),U_12181)) ),
    inference(clausify,[status(thm)],[f_3189_3]) ).

cnf(f_3189_5,plain,
    ( hAPP(c_Set_Ovimage(U_12184,U_12178,hAPP(c_COMBK(U_12178,U_12184),U_12180)),U_12182) = c_Orderings_Obot__class_Obot(tc_fun(U_12184,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_12178),U_12180),U_12182)) ),
    inference(clausify,[status(thm)],[f_3189_3]) ).

fof(f_3190_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_3190_2,plain,
    ! [U_12188,U_12187,U_12186,U_12185] : hAPP(c_Set_Ovimage(U_12185,U_12186,U_12187),U_12188) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12186,tc_fun(U_12185,tc_HOL_Obool)),U_12188),hAPP(hAPP(c_COMBB(tc_fun(U_12186,tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool),U_12186),c_Set_Ovimage(U_12185,U_12186,U_12187)),hAPP(hAPP(c_COMBC(U_12186,tc_fun(U_12186,tc_HOL_Obool),tc_fun(U_12186,tc_HOL_Obool)),c_Set_Oinsert(U_12186)),c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

cnf(f_3190_3,plain,
    hAPP(c_Set_Ovimage(U_12185,U_12186,U_12187),U_12188) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12186,tc_fun(U_12185,tc_HOL_Obool)),U_12188),hAPP(hAPP(c_COMBB(tc_fun(U_12186,tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool),U_12186),c_Set_Ovimage(U_12185,U_12186,U_12187)),hAPP(hAPP(c_COMBC(U_12186,tc_fun(U_12186,tc_HOL_Obool),tc_fun(U_12186,tc_HOL_Obool)),c_Set_Oinsert(U_12186)),c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3190_2]) ).

fof(f_3191_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_3191_2,plain,
    ! [U_12193,U_12192,U_12191,U_12190,U_12189] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12189,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12189,U_12190,U_12191),U_12192)),U_12193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12190,tc_HOL_Obool)),U_12192),hAPP(c_Set_Oimage(U_12189,U_12190,U_12191),U_12193)))
      | ~ c_Fun_Oinj__on(U_12189,U_12190,U_12191,c_Orderings_Otop__class_Otop(tc_fun(U_12189,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

cnf(f_3191_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12189,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12189,U_12190,U_12191),U_12192)),U_12193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12190,tc_HOL_Obool)),U_12192),hAPP(c_Set_Oimage(U_12189,U_12190,U_12191),U_12193)))
    | ~ c_Fun_Oinj__on(U_12189,U_12190,U_12191,c_Orderings_Otop__class_Otop(tc_fun(U_12189,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3191_2]) ).

fof(f_3192_1,plain,
    ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).

fof(f_3192_2,plain,
    ! [U_12199,U_12198,U_12197,U_12196,U_12195,U_12194] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_12198,U_12194,hAPP(hAPP(c_COMBC(U_12198,U_12194,U_12194),hAPP(hAPP(c_COMBC(U_12198,U_12194,tc_fun(U_12194,U_12194)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12194,tc_fun(U_12194,U_12194)),U_12198),c_If(U_12194)),hAPP(hAPP(c_COMBC(U_12198,tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12198)),U_12199))),U_12195)),U_12197)),U_12196) = c_Orderings_Obot__class_Obot(tc_fun(U_12198,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_12194),U_12197),U_12196)) )
          & ( hAPP(c_Set_Ovimage(U_12198,U_12194,hAPP(hAPP(c_COMBC(U_12198,U_12194,U_12194),hAPP(hAPP(c_COMBC(U_12198,U_12194,tc_fun(U_12194,U_12194)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12194,tc_fun(U_12194,U_12194)),U_12198),c_If(U_12194)),hAPP(hAPP(c_COMBC(U_12198,tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12198)),U_12199))),U_12195)),U_12197)),U_12196) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12198,tc_HOL_Obool)),U_12199)
            | ~ hBOOL(hAPP(hAPP(c_member(U_12194),U_12197),U_12196)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_12194),U_12195),U_12196)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_12198,U_12194,hAPP(hAPP(c_COMBC(U_12198,U_12194,U_12194),hAPP(hAPP(c_COMBC(U_12198,U_12194,tc_fun(U_12194,U_12194)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12194,tc_fun(U_12194,U_12194)),U_12198),c_If(U_12194)),hAPP(hAPP(c_COMBC(U_12198,tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12198)),U_12199))),U_12195)),U_12197)),U_12196) = U_12199
            | hBOOL(hAPP(hAPP(c_member(U_12194),U_12197),U_12196)) )
          & ( hAPP(c_Set_Ovimage(U_12198,U_12194,hAPP(hAPP(c_COMBC(U_12198,U_12194,U_12194),hAPP(hAPP(c_COMBC(U_12198,U_12194,tc_fun(U_12194,U_12194)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12194,tc_fun(U_12194,U_12194)),U_12198),c_If(U_12194)),hAPP(hAPP(c_COMBC(U_12198,tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12198)),U_12199))),U_12195)),U_12197)),U_12196) = c_Orderings_Otop__class_Otop(tc_fun(U_12198,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12194),U_12197),U_12196)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12194),U_12195),U_12196)) ) ),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

fof(f_3192_3,plain,
    ( ! [U_12211,U_12209,U_12207,U_12205,U_12203,U_12201] :
        ( ( ( hAPP(c_Set_Ovimage(U_12209,U_12201,hAPP(hAPP(c_COMBC(U_12209,U_12201,U_12201),hAPP(hAPP(c_COMBC(U_12209,U_12201,tc_fun(U_12201,U_12201)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12201,tc_fun(U_12201,U_12201)),U_12209),c_If(U_12201)),hAPP(hAPP(c_COMBC(U_12209,tc_fun(U_12209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12209)),U_12211))),U_12203)),U_12207)),U_12205) = c_Orderings_Obot__class_Obot(tc_fun(U_12209,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_12201),U_12207),U_12205)) )
          & ( hAPP(c_Set_Ovimage(U_12209,U_12201,hAPP(hAPP(c_COMBC(U_12209,U_12201,U_12201),hAPP(hAPP(c_COMBC(U_12209,U_12201,tc_fun(U_12201,U_12201)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12201,tc_fun(U_12201,U_12201)),U_12209),c_If(U_12201)),hAPP(hAPP(c_COMBC(U_12209,tc_fun(U_12209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12209)),U_12211))),U_12203)),U_12207)),U_12205) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12209,tc_HOL_Obool)),U_12211)
            | ~ hBOOL(hAPP(hAPP(c_member(U_12201),U_12207),U_12205)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_12201),U_12203),U_12205)) )
    & ! [U_12210,U_12208,U_12206,U_12204,U_12202,U_12200] :
        ( ( ( hAPP(c_Set_Ovimage(U_12208,U_12200,hAPP(hAPP(c_COMBC(U_12208,U_12200,U_12200),hAPP(hAPP(c_COMBC(U_12208,U_12200,tc_fun(U_12200,U_12200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12200,tc_fun(U_12200,U_12200)),U_12208),c_If(U_12200)),hAPP(hAPP(c_COMBC(U_12208,tc_fun(U_12208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12208)),U_12210))),U_12202)),U_12206)),U_12204) = U_12210
            | hBOOL(hAPP(hAPP(c_member(U_12200),U_12206),U_12204)) )
          & ( hAPP(c_Set_Ovimage(U_12208,U_12200,hAPP(hAPP(c_COMBC(U_12208,U_12200,U_12200),hAPP(hAPP(c_COMBC(U_12208,U_12200,tc_fun(U_12200,U_12200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12200,tc_fun(U_12200,U_12200)),U_12208),c_If(U_12200)),hAPP(hAPP(c_COMBC(U_12208,tc_fun(U_12208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12208)),U_12210))),U_12202)),U_12206)),U_12204) = c_Orderings_Otop__class_Otop(tc_fun(U_12208,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12200),U_12206),U_12204)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12200),U_12202),U_12204)) ) ),
    inference(miniscope,[status(thm)],[f_3192_2]) ).

cnf(f_3192_4,plain,
    ( hAPP(c_Set_Ovimage(U_12208,U_12200,hAPP(hAPP(c_COMBC(U_12208,U_12200,U_12200),hAPP(hAPP(c_COMBC(U_12208,U_12200,tc_fun(U_12200,U_12200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12200,tc_fun(U_12200,U_12200)),U_12208),c_If(U_12200)),hAPP(hAPP(c_COMBC(U_12208,tc_fun(U_12208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12208)),U_12210))),U_12202)),U_12206)),U_12204) = c_Orderings_Otop__class_Otop(tc_fun(U_12208,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12200),U_12206),U_12204))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12200),U_12202),U_12204)) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

cnf(f_3192_5,plain,
    ( hAPP(c_Set_Ovimage(U_12208,U_12200,hAPP(hAPP(c_COMBC(U_12208,U_12200,U_12200),hAPP(hAPP(c_COMBC(U_12208,U_12200,tc_fun(U_12200,U_12200)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12200,tc_fun(U_12200,U_12200)),U_12208),c_If(U_12200)),hAPP(hAPP(c_COMBC(U_12208,tc_fun(U_12208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12208)),U_12210))),U_12202)),U_12206)),U_12204) = U_12210
    | hBOOL(hAPP(hAPP(c_member(U_12200),U_12206),U_12204))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12200),U_12202),U_12204)) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

cnf(f_3192_6,plain,
    ( hAPP(c_Set_Ovimage(U_12209,U_12201,hAPP(hAPP(c_COMBC(U_12209,U_12201,U_12201),hAPP(hAPP(c_COMBC(U_12209,U_12201,tc_fun(U_12201,U_12201)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12201,tc_fun(U_12201,U_12201)),U_12209),c_If(U_12201)),hAPP(hAPP(c_COMBC(U_12209,tc_fun(U_12209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12209)),U_12211))),U_12203)),U_12207)),U_12205) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12209,tc_HOL_Obool)),U_12211)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12201),U_12207),U_12205))
    | hBOOL(hAPP(hAPP(c_member(U_12201),U_12203),U_12205)) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

cnf(f_3192_7,plain,
    ( hAPP(c_Set_Ovimage(U_12209,U_12201,hAPP(hAPP(c_COMBC(U_12209,U_12201,U_12201),hAPP(hAPP(c_COMBC(U_12209,U_12201,tc_fun(U_12201,U_12201)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12201,tc_fun(U_12201,U_12201)),U_12209),c_If(U_12201)),hAPP(hAPP(c_COMBC(U_12209,tc_fun(U_12209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12209)),U_12211))),U_12203)),U_12207)),U_12205) = c_Orderings_Obot__class_Obot(tc_fun(U_12209,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_12201),U_12207),U_12205))
    | hBOOL(hAPP(hAPP(c_member(U_12201),U_12203),U_12205)) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

fof(f_3193_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_3193_2,plain,
    ! [U_12217,U_12216,U_12215,U_12214,U_12213,U_12212] : hAPP(c_Set_Oimage(U_12212,tc_prod(U_12213,U_12214),hAPP(hAPP(c_COMBS(U_12212,U_12214,tc_prod(U_12213,U_12214)),hAPP(hAPP(c_COMBB(U_12213,tc_fun(U_12214,tc_prod(U_12213,U_12214)),U_12212),c_Product__Type_OPair(U_12213,U_12214)),U_12215)),U_12216)),U_12217) = hAPP(hAPP(c_Product__Type_OSigma(U_12213,U_12214),hAPP(c_Set_Oimage(U_12212,U_12213,U_12215),U_12217)),hAPP(hAPP(c_COMBB(tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12214,tc_HOL_Obool),U_12213),c_Set_Oimage(U_12212,U_12214,U_12216)),hAPP(hAPP(c_COMBC(U_12213,tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12212,tc_HOL_Obool),tc_fun(tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool)),U_12213),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12212,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12213,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool),U_12213),c_Set_Ovimage(U_12212,U_12213,U_12215)),hAPP(hAPP(c_COMBC(U_12213,tc_fun(U_12213,tc_HOL_Obool),tc_fun(U_12213,tc_HOL_Obool)),c_Set_Oinsert(U_12213)),c_Orderings_Obot__class_Obot(tc_fun(U_12213,tc_HOL_Obool)))))),U_12217))),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

cnf(f_3193_3,plain,
    hAPP(c_Set_Oimage(U_12212,tc_prod(U_12213,U_12214),hAPP(hAPP(c_COMBS(U_12212,U_12214,tc_prod(U_12213,U_12214)),hAPP(hAPP(c_COMBB(U_12213,tc_fun(U_12214,tc_prod(U_12213,U_12214)),U_12212),c_Product__Type_OPair(U_12213,U_12214)),U_12215)),U_12216)),U_12217) = hAPP(hAPP(c_Product__Type_OSigma(U_12213,U_12214),hAPP(c_Set_Oimage(U_12212,U_12213,U_12215),U_12217)),hAPP(hAPP(c_COMBB(tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12214,tc_HOL_Obool),U_12213),c_Set_Oimage(U_12212,U_12214,U_12216)),hAPP(hAPP(c_COMBC(U_12213,tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12212,tc_HOL_Obool),tc_fun(tc_fun(U_12212,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool)),U_12213),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12212,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12213,tc_HOL_Obool),tc_fun(U_12212,tc_HOL_Obool),U_12213),c_Set_Ovimage(U_12212,U_12213,U_12215)),hAPP(hAPP(c_COMBC(U_12213,tc_fun(U_12213,tc_HOL_Obool),tc_fun(U_12213,tc_HOL_Obool)),c_Set_Oinsert(U_12213)),c_Orderings_Obot__class_Obot(tc_fun(U_12213,tc_HOL_Obool)))))),U_12217))),
    inference(clausify,[status(thm)],[f_3193_2]) ).

fof(f_3194_1,plain,
    ! [V_Pa_2,V_y_2] :
      ( hBOOL(hAPP(V_Pa_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_Pa_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_3194_2,plain,
    ! [U_12220,U_12219] :
      ( hBOOL(hAPP(U_12220,U_12219))
      | ? [U_12218] : ~ hBOOL(hAPP(U_12220,hAPP(c_Int_ORep__Integ,U_12218)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12219),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

fof(f_3194_3,plain,
    ! [U_12220,U_12219] :
      ( hBOOL(hAPP(U_12220,U_12219))
      | ~ hBOOL(hAPP(U_12220,hAPP(c_Int_ORep__Integ,sK286(U_12220,U_12219))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12219),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_12218,sK286(U_12220,U_12219))],[f_3194_2]) ).

cnf(f_3194_4,plain,
    ( hBOOL(hAPP(U_12220,U_12219))
    | ~ hBOOL(hAPP(U_12220,hAPP(c_Int_ORep__Integ,sK286(U_12220,U_12219))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12219),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

fof(f_3195_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_3195_2,plain,
    ! [U_12222] :
      ( ? [U_12221] : U_12222 = hAPP(c_Int_ORep__Integ,U_12221)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12222),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

fof(f_3195_3,plain,
    ! [U_12222] :
      ( U_12222 = hAPP(c_Int_ORep__Integ,sK287(U_12222))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12222),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_12221,sK287(U_12222))],[f_3195_2]) ).

cnf(f_3195_4,plain,
    ( U_12222 = hAPP(c_Int_ORep__Integ,sK287(U_12222))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12222),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3195_3]) ).

fof(f_3196_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_3196_2,plain,
    ! [U_12228,U_12227,U_12226,U_12225,U_12224,U_12223] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12223,U_12226)),hAPP(hAPP(c_Product__Type_OPair(U_12223,U_12226),U_12224),U_12227)),hAPP(hAPP(c_Product__Type_OSigma(U_12223,U_12226),U_12225),U_12228)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12226),U_12227),hAPP(U_12228,U_12224)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12223),U_12224),U_12225)) ),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

cnf(f_3196_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12223,U_12226)),hAPP(hAPP(c_Product__Type_OPair(U_12223,U_12226),U_12224),U_12227)),hAPP(hAPP(c_Product__Type_OSigma(U_12223,U_12226),U_12225),U_12228)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12226),U_12227),hAPP(U_12228,U_12224)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12223),U_12224),U_12225)) ),
    inference(clausify,[status(thm)],[f_3196_2]) ).

fof(f_3197_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_3197_2,plain,
    ! [U_12231,U_12230,U_12229] : hAPP(hAPP(c_Product__Type_OSigma(U_12229,U_12230),c_Orderings_Obot__class_Obot(tc_fun(U_12229,tc_HOL_Obool))),U_12231) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12229,U_12230),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

cnf(f_3197_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12229,U_12230),c_Orderings_Obot__class_Obot(tc_fun(U_12229,tc_HOL_Obool))),U_12231) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12229,U_12230),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3197_2]) ).

fof(f_3198_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_3198_2,plain,
    ! [U_12235,U_12234,U_12233,U_12232] : hAPP(hAPP(c_Product__Type_OSigma(U_12232,U_12233),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12232,tc_HOL_Obool),U_12234)),U_12235) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12232,tc_HOL_Obool),tc_fun(tc_prod(U_12232,U_12233),tc_HOL_Obool)),U_12234),hAPP(hAPP(c_COMBC(tc_fun(U_12232,tc_HOL_Obool),tc_fun(U_12232,tc_fun(U_12233,tc_HOL_Obool)),tc_fun(tc_prod(U_12232,U_12233),tc_HOL_Obool)),c_Product__Type_OSigma(U_12232,U_12233)),U_12235)),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

cnf(f_3198_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12232,U_12233),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12232,tc_HOL_Obool),U_12234)),U_12235) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12232,tc_HOL_Obool),tc_fun(tc_prod(U_12232,U_12233),tc_HOL_Obool)),U_12234),hAPP(hAPP(c_COMBC(tc_fun(U_12232,tc_HOL_Obool),tc_fun(U_12232,tc_fun(U_12233,tc_HOL_Obool)),tc_fun(tc_prod(U_12232,U_12233),tc_HOL_Obool)),c_Product__Type_OSigma(U_12232,U_12233)),U_12235)),
    inference(clausify,[status(thm)],[f_3198_2]) ).

fof(f_3199_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_3199_2,plain,
    ! [U_12240,U_12239,U_12238,U_12237,U_12236] : hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12236,tc_HOL_Obool)),U_12238),U_12239)),U_12240) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12236,U_12237),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),U_12238),U_12240)),hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),U_12239),U_12240)),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

cnf(f_3199_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12236,tc_HOL_Obool)),U_12238),U_12239)),U_12240) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12236,U_12237),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),U_12238),U_12240)),hAPP(hAPP(c_Product__Type_OSigma(U_12236,U_12237),U_12239),U_12240)),
    inference(clausify,[status(thm)],[f_3199_2]) ).

fof(f_3200_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_3200_2,plain,
    ! [U_12245,U_12244,U_12243,U_12242,U_12241] : hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12241,tc_HOL_Obool)),U_12243),U_12244)),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12241,U_12242),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),U_12243),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245))),hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),U_12244),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245))),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

cnf(f_3200_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12241,tc_HOL_Obool)),U_12243),U_12244)),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12241,U_12242),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),U_12243),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245))),hAPP(hAPP(c_Product__Type_OSigma(U_12241,U_12242),U_12244),hAPP(c_COMBK(tc_fun(U_12242,tc_HOL_Obool),U_12241),U_12245))),
    inference(clausify,[status(thm)],[f_3200_2]) ).

fof(f_3201_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_3201_2,plain,
    ! [U_12250,U_12249,U_12248,U_12247,U_12246] : hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),hAPP(hAPP(c_COMBS(U_12246,tc_fun(U_12247,tc_HOL_Obool),tc_fun(U_12247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12247,tc_HOL_Obool),tc_fun(tc_fun(U_12247,tc_HOL_Obool),tc_fun(U_12247,tc_HOL_Obool)),U_12246),c_Groups_Ominus__class_Ominus(tc_fun(U_12247,tc_HOL_Obool))),U_12249)),U_12250)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12246,U_12247),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),U_12249)),hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),U_12250)),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

cnf(f_3201_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),hAPP(hAPP(c_COMBS(U_12246,tc_fun(U_12247,tc_HOL_Obool),tc_fun(U_12247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12247,tc_HOL_Obool),tc_fun(tc_fun(U_12247,tc_HOL_Obool),tc_fun(U_12247,tc_HOL_Obool)),U_12246),c_Groups_Ominus__class_Ominus(tc_fun(U_12247,tc_HOL_Obool))),U_12249)),U_12250)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12246,U_12247),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),U_12249)),hAPP(hAPP(c_Product__Type_OSigma(U_12246,U_12247),U_12248),U_12250)),
    inference(clausify,[status(thm)],[f_3201_2]) ).

fof(f_3202_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_3202_2,plain,
    ! [U_12256,U_12255,U_12254,U_12253,U_12252,U_12251] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12255),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253)) = hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12256),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253))
          | U_12255 != U_12256 )
        & ( U_12255 = U_12256
          | hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12255),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253)) != hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12256),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12251),U_12252),U_12253)) ),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

cnf(f_3202_3,plain,
    ( U_12255 = U_12256
    | hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12255),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253)) != hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12256),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12251),U_12252),U_12253)) ),
    inference(clausify,[status(thm)],[f_3202_2]) ).

cnf(f_3202_4,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12255),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253)) = hAPP(hAPP(c_Product__Type_OSigma(U_12254,U_12251),U_12256),hAPP(c_COMBK(tc_fun(U_12251,tc_HOL_Obool),U_12254),U_12253))
    | U_12255 != U_12256
    | ~ hBOOL(hAPP(hAPP(c_member(U_12251),U_12252),U_12253)) ),
    inference(clausify,[status(thm)],[f_3202_2]) ).

fof(f_3203_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_3203_2,plain,
    ! [U_12260,U_12259,U_12258,U_12257] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12257,U_12258)),hAPP(hAPP(c_Product__Type_OSigma(U_12257,U_12258),U_12259),hAPP(c_COMBK(tc_fun(U_12258,tc_HOL_Obool),U_12257),U_12260))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12257),U_12259)),hAPP(c_Finite__Set_Ocard(U_12258),U_12260)),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

cnf(f_3203_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_12257,U_12258)),hAPP(hAPP(c_Product__Type_OSigma(U_12257,U_12258),U_12259),hAPP(c_COMBK(tc_fun(U_12258,tc_HOL_Obool),U_12257),U_12260))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12257),U_12259)),hAPP(c_Finite__Set_Ocard(U_12258),U_12260)),
    inference(clausify,[status(thm)],[f_3203_2]) ).

fof(f_3204_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_3204_2,plain,
    ! [U_12266,U_12265,U_12264,U_12263,U_12262,U_12261] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBC(U_12262,tc_fun(U_12263,tc_HOL_Obool),U_12261),hAPP(hAPP(c_COMBB(tc_fun(U_12263,U_12261),tc_fun(tc_fun(U_12263,tc_HOL_Obool),U_12261),U_12262),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12263,U_12261)),U_12264)),U_12265)),U_12266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12262,U_12263),U_12261),hAPP(c_Product__Type_Oprod_Oprod__case(U_12262,U_12263,U_12261),U_12264)),hAPP(hAPP(c_Product__Type_OSigma(U_12262,U_12263),U_12266),hAPP(c_COMBK(tc_fun(U_12263,tc_HOL_Obool),U_12262),U_12265)))
      | ~ class_Groups_Ocomm__monoid__add(U_12261) ),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

cnf(f_3204_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBC(U_12262,tc_fun(U_12263,tc_HOL_Obool),U_12261),hAPP(hAPP(c_COMBB(tc_fun(U_12263,U_12261),tc_fun(tc_fun(U_12263,tc_HOL_Obool),U_12261),U_12262),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12263,U_12261)),U_12264)),U_12265)),U_12266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12262,U_12263),U_12261),hAPP(c_Product__Type_Oprod_Oprod__case(U_12262,U_12263,U_12261),U_12264)),hAPP(hAPP(c_Product__Type_OSigma(U_12262,U_12263),U_12266),hAPP(c_COMBK(tc_fun(U_12263,tc_HOL_Obool),U_12262),U_12265)))
    | ~ class_Groups_Ocomm__monoid__add(U_12261) ),
    inference(clausify,[status(thm)],[f_3204_2]) ).

fof(f_3205_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_3205_2,plain,
    ! [U_12269,U_12268,U_12267] : hAPP(hAPP(c_Product__Type_OSigma(U_12267,U_12268),U_12269),hAPP(c_COMBK(tc_fun(U_12268,tc_HOL_Obool),U_12267),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12267,U_12268),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

cnf(f_3205_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12267,U_12268),U_12269),hAPP(c_COMBK(tc_fun(U_12268,tc_HOL_Obool),U_12267),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12267,U_12268),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3205_2]) ).

fof(f_3206_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_3206_2,plain,
    ! [U_12273,U_12272,U_12271,U_12270] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12270,U_12271),U_12272),hAPP(c_COMBK(tc_fun(U_12271,tc_HOL_Obool),U_12270),U_12273)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12270,U_12271),tc_HOL_Obool))
        | ( U_12273 != c_Orderings_Obot__class_Obot(tc_fun(U_12271,tc_HOL_Obool))
          & U_12272 != c_Orderings_Obot__class_Obot(tc_fun(U_12270,tc_HOL_Obool)) ) )
      & ( U_12273 = c_Orderings_Obot__class_Obot(tc_fun(U_12271,tc_HOL_Obool))
        | U_12272 = c_Orderings_Obot__class_Obot(tc_fun(U_12270,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_12270,U_12271),U_12272),hAPP(c_COMBK(tc_fun(U_12271,tc_HOL_Obool),U_12270),U_12273)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12270,U_12271),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

fof(f_3206_3,plain,
    ( ! [U_12281,U_12279,U_12277,U_12275] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_12275,U_12277),U_12279),hAPP(c_COMBK(tc_fun(U_12277,tc_HOL_Obool),U_12275),U_12281)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12275,U_12277),tc_HOL_Obool))
        | ( U_12281 != c_Orderings_Obot__class_Obot(tc_fun(U_12277,tc_HOL_Obool))
          & U_12279 != c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool)) ) )
    & ! [U_12280,U_12278,U_12276,U_12274] :
        ( U_12280 = c_Orderings_Obot__class_Obot(tc_fun(U_12276,tc_HOL_Obool))
        | U_12278 = c_Orderings_Obot__class_Obot(tc_fun(U_12274,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_12274,U_12276),U_12278),hAPP(c_COMBK(tc_fun(U_12276,tc_HOL_Obool),U_12274),U_12280)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12274,U_12276),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3206_2]) ).

cnf(f_3206_4,plain,
    ( U_12280 = c_Orderings_Obot__class_Obot(tc_fun(U_12276,tc_HOL_Obool))
    | U_12278 = c_Orderings_Obot__class_Obot(tc_fun(U_12274,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12274,U_12276),U_12278),hAPP(c_COMBK(tc_fun(U_12276,tc_HOL_Obool),U_12274),U_12280)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12274,U_12276),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

cnf(f_3206_5,plain,
    ( U_12279 != c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12275,U_12277),U_12279),hAPP(c_COMBK(tc_fun(U_12277,tc_HOL_Obool),U_12275),U_12281)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12275,U_12277),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

cnf(f_3206_6,plain,
    ( U_12281 != c_Orderings_Obot__class_Obot(tc_fun(U_12277,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12275,U_12277),U_12279),hAPP(c_COMBK(tc_fun(U_12277,tc_HOL_Obool),U_12275),U_12281)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12275,U_12277),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

fof(f_3207_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_3207_2,plain,
    ! [U_12284,U_12283,U_12282] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12282,U_12283),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12282,U_12283),c_Orderings_Otop__class_Otop(tc_fun(U_12282,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12283,tc_HOL_Obool),U_12282),U_12284))) = hAPP(hAPP(c_Product__Type_OSigma(U_12282,U_12283),c_Orderings_Otop__class_Otop(tc_fun(U_12282,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12283,tc_HOL_Obool),U_12282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12283,tc_HOL_Obool)),U_12284))),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

cnf(f_3207_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12282,U_12283),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12282,U_12283),c_Orderings_Otop__class_Otop(tc_fun(U_12282,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12283,tc_HOL_Obool),U_12282),U_12284))) = hAPP(hAPP(c_Product__Type_OSigma(U_12282,U_12283),c_Orderings_Otop__class_Otop(tc_fun(U_12282,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12283,tc_HOL_Obool),U_12282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12283,tc_HOL_Obool)),U_12284))),
    inference(clausify,[status(thm)],[f_3207_2]) ).

fof(f_3208_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_3208_2,plain,
    ! [U_12287,U_12286,U_12285] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12285,U_12286),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12285,U_12286),U_12287),hAPP(c_COMBK(tc_fun(U_12286,tc_HOL_Obool),U_12285),c_Orderings_Otop__class_Otop(tc_fun(U_12286,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12285,U_12286),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12285,tc_HOL_Obool)),U_12287)),hAPP(c_COMBK(tc_fun(U_12286,tc_HOL_Obool),U_12285),c_Orderings_Otop__class_Otop(tc_fun(U_12286,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

cnf(f_3208_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12285,U_12286),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12285,U_12286),U_12287),hAPP(c_COMBK(tc_fun(U_12286,tc_HOL_Obool),U_12285),c_Orderings_Otop__class_Otop(tc_fun(U_12286,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12285,U_12286),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12285,tc_HOL_Obool)),U_12287)),hAPP(c_COMBK(tc_fun(U_12286,tc_HOL_Obool),U_12285),c_Orderings_Otop__class_Otop(tc_fun(U_12286,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3208_2]) ).

fof(f_3209_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_3209_2,plain,
    ! [U_12293,U_12292,U_12291,U_12290,U_12289,U_12288] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12289,U_12288),hAPP(hAPP(c_COMBC(U_12289,tc_fun(U_12290,tc_HOL_Obool),U_12288),hAPP(hAPP(c_COMBB(tc_fun(U_12290,U_12288),tc_fun(tc_fun(U_12290,tc_HOL_Obool),U_12288),U_12289),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12290,U_12288)),U_12291)),U_12292)),U_12293) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12289,U_12290),U_12288),hAPP(c_Product__Type_Oprod_Oprod__case(U_12289,U_12290,U_12288),U_12291)),hAPP(hAPP(c_Product__Type_OSigma(U_12289,U_12290),U_12293),hAPP(c_COMBK(tc_fun(U_12290,tc_HOL_Obool),U_12289),U_12292)))
      | ~ class_Groups_Ocomm__monoid__mult(U_12288) ),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

cnf(f_3209_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12289,U_12288),hAPP(hAPP(c_COMBC(U_12289,tc_fun(U_12290,tc_HOL_Obool),U_12288),hAPP(hAPP(c_COMBB(tc_fun(U_12290,U_12288),tc_fun(tc_fun(U_12290,tc_HOL_Obool),U_12288),U_12289),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12290,U_12288)),U_12291)),U_12292)),U_12293) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12289,U_12290),U_12288),hAPP(c_Product__Type_Oprod_Oprod__case(U_12289,U_12290,U_12288),U_12291)),hAPP(hAPP(c_Product__Type_OSigma(U_12289,U_12290),U_12293),hAPP(c_COMBK(tc_fun(U_12290,tc_HOL_Obool),U_12289),U_12292)))
    | ~ class_Groups_Ocomm__monoid__mult(U_12288) ),
    inference(clausify,[status(thm)],[f_3209_2]) ).

fof(f_3210_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_3210_2,plain,
    ! [U_12298,U_12297,U_12296,U_12295,U_12294] : hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12294,tc_HOL_Obool)),U_12296),U_12297)),U_12298) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12294,U_12295),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),U_12296),U_12298)),hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),U_12297),U_12298)),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

cnf(f_3210_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12294,tc_HOL_Obool)),U_12296),U_12297)),U_12298) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12294,U_12295),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),U_12296),U_12298)),hAPP(hAPP(c_Product__Type_OSigma(U_12294,U_12295),U_12297),U_12298)),
    inference(clausify,[status(thm)],[f_3210_2]) ).

fof(f_3211_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_3211_2,plain,
    ! [U_12303,U_12302,U_12301,U_12300,U_12299] : hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12299,tc_HOL_Obool)),U_12301),U_12302)),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12299,U_12300),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),U_12301),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303))),hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),U_12302),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303))),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

cnf(f_3211_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12299,tc_HOL_Obool)),U_12301),U_12302)),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12299,U_12300),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),U_12301),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303))),hAPP(hAPP(c_Product__Type_OSigma(U_12299,U_12300),U_12302),hAPP(c_COMBK(tc_fun(U_12300,tc_HOL_Obool),U_12299),U_12303))),
    inference(clausify,[status(thm)],[f_3211_2]) ).

fof(f_3212_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_3212_2,plain,
    ! [U_12308,U_12307,U_12306,U_12305,U_12304] : hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),hAPP(hAPP(c_COMBS(U_12304,tc_fun(U_12305,tc_HOL_Obool),tc_fun(U_12305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12305,tc_HOL_Obool),tc_fun(tc_fun(U_12305,tc_HOL_Obool),tc_fun(U_12305,tc_HOL_Obool)),U_12304),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12305,tc_HOL_Obool))),U_12307)),U_12308)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12304,U_12305),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),U_12307)),hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),U_12308)),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

cnf(f_3212_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),hAPP(hAPP(c_COMBS(U_12304,tc_fun(U_12305,tc_HOL_Obool),tc_fun(U_12305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12305,tc_HOL_Obool),tc_fun(tc_fun(U_12305,tc_HOL_Obool),tc_fun(U_12305,tc_HOL_Obool)),U_12304),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12305,tc_HOL_Obool))),U_12307)),U_12308)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12304,U_12305),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),U_12307)),hAPP(hAPP(c_Product__Type_OSigma(U_12304,U_12305),U_12306),U_12308)),
    inference(clausify,[status(thm)],[f_3212_2]) ).

fof(f_3213_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_3213_2,plain,
    ! [U_12312,U_12311,U_12310,U_12309] : hAPP(c_Set_Oimage(tc_prod(U_12309,U_12310),tc_prod(U_12310,U_12309),hAPP(c_Product__Type_Oprod_Oprod__case(U_12309,U_12310,tc_prod(U_12310,U_12309)),hAPP(c_COMBC(U_12310,U_12309,tc_prod(U_12310,U_12309)),c_Product__Type_OPair(U_12310,U_12309)))),hAPP(hAPP(c_Product__Type_OSigma(U_12309,U_12310),U_12311),hAPP(c_COMBK(tc_fun(U_12310,tc_HOL_Obool),U_12309),U_12312))) = hAPP(hAPP(c_Product__Type_OSigma(U_12310,U_12309),U_12312),hAPP(c_COMBK(tc_fun(U_12309,tc_HOL_Obool),U_12310),U_12311)),
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

cnf(f_3213_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_12309,U_12310),tc_prod(U_12310,U_12309),hAPP(c_Product__Type_Oprod_Oprod__case(U_12309,U_12310,tc_prod(U_12310,U_12309)),hAPP(c_COMBC(U_12310,U_12309,tc_prod(U_12310,U_12309)),c_Product__Type_OPair(U_12310,U_12309)))),hAPP(hAPP(c_Product__Type_OSigma(U_12309,U_12310),U_12311),hAPP(c_COMBK(tc_fun(U_12310,tc_HOL_Obool),U_12309),U_12312))) = hAPP(hAPP(c_Product__Type_OSigma(U_12310,U_12309),U_12312),hAPP(c_COMBK(tc_fun(U_12309,tc_HOL_Obool),U_12310),U_12311)),
    inference(clausify,[status(thm)],[f_3213_2]) ).

fof(f_3214_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_3214_2,plain,
    ! [U_12316,U_12315,U_12314,U_12313] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12313,U_12315)),hAPP(hAPP(c_Product__Type_OSigma(U_12313,U_12315),U_12314),hAPP(c_COMBK(tc_fun(U_12315,tc_HOL_Obool),U_12313),U_12316))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12315),U_12316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

cnf(f_3214_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12313,U_12315)),hAPP(hAPP(c_Product__Type_OSigma(U_12313,U_12315),U_12314),hAPP(c_COMBK(tc_fun(U_12315,tc_HOL_Obool),U_12313),U_12316))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12315),U_12316))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(clausify,[status(thm)],[f_3214_2]) ).

fof(f_3215_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_3215_2,plain,
    ! [U_12319,U_12318,U_12317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12317,U_12317),tc_HOL_Obool)),U_12319),hAPP(hAPP(c_Product__Type_OSigma(U_12317,U_12317),U_12318),hAPP(c_COMBK(tc_fun(U_12317,tc_HOL_Obool),U_12317),U_12318))))
      | ~ c_Equiv__Relations_Oequiv(U_12317,U_12318,U_12319) ),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

cnf(f_3215_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12317,U_12317),tc_HOL_Obool)),U_12319),hAPP(hAPP(c_Product__Type_OSigma(U_12317,U_12317),U_12318),hAPP(c_COMBK(tc_fun(U_12317,tc_HOL_Obool),U_12317),U_12318))))
    | ~ c_Equiv__Relations_Oequiv(U_12317,U_12318,U_12319) ),
    inference(clausify,[status(thm)],[f_3215_2]) ).

fof(f_3216_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_3216_2,plain,
    ! [U_12324,U_12323,U_12322,U_12321,U_12320] : hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),hAPP(hAPP(c_COMBS(U_12320,tc_fun(U_12321,tc_HOL_Obool),tc_fun(U_12321,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12321,tc_HOL_Obool),tc_fun(tc_fun(U_12321,tc_HOL_Obool),tc_fun(U_12321,tc_HOL_Obool)),U_12320),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12321,tc_HOL_Obool))),U_12323)),U_12324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12320,U_12321),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),U_12323)),hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),U_12324)),
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

cnf(f_3216_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),hAPP(hAPP(c_COMBS(U_12320,tc_fun(U_12321,tc_HOL_Obool),tc_fun(U_12321,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12321,tc_HOL_Obool),tc_fun(tc_fun(U_12321,tc_HOL_Obool),tc_fun(U_12321,tc_HOL_Obool)),U_12320),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12321,tc_HOL_Obool))),U_12323)),U_12324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12320,U_12321),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),U_12323)),hAPP(hAPP(c_Product__Type_OSigma(U_12320,U_12321),U_12322),U_12324)),
    inference(clausify,[status(thm)],[f_3216_2]) ).

fof(f_3217_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_3217_2,plain,
    ! [U_12329,U_12328,U_12327,U_12326,U_12325] : hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12325,tc_HOL_Obool)),U_12327),U_12328)),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12325,U_12326),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),U_12327),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329))),hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),U_12328),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329))),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

cnf(f_3217_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12325,tc_HOL_Obool)),U_12327),U_12328)),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12325,U_12326),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),U_12327),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329))),hAPP(hAPP(c_Product__Type_OSigma(U_12325,U_12326),U_12328),hAPP(c_COMBK(tc_fun(U_12326,tc_HOL_Obool),U_12325),U_12329))),
    inference(clausify,[status(thm)],[f_3217_2]) ).

fof(f_3218_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_3218_2,plain,
    ! [U_12334,U_12333,U_12332,U_12331,U_12330] : hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12330,tc_HOL_Obool)),U_12332),U_12333)),U_12334) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12330,U_12331),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),U_12332),U_12334)),hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),U_12333),U_12334)),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

cnf(f_3218_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12330,tc_HOL_Obool)),U_12332),U_12333)),U_12334) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12330,U_12331),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),U_12332),U_12334)),hAPP(hAPP(c_Product__Type_OSigma(U_12330,U_12331),U_12333),U_12334)),
    inference(clausify,[status(thm)],[f_3218_2]) ).

fof(f_3219_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_3219_2,plain,
    ! [U_12336,U_12335] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12335,U_12335),tc_HOL_Obool)),c_Relation_OId__on(U_12335,U_12336)),hAPP(hAPP(c_Product__Type_OSigma(U_12335,U_12335),U_12336),hAPP(c_COMBK(tc_fun(U_12335,tc_HOL_Obool),U_12335),U_12336)))),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

cnf(f_3219_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12335,U_12335),tc_HOL_Obool)),c_Relation_OId__on(U_12335,U_12336)),hAPP(hAPP(c_Product__Type_OSigma(U_12335,U_12335),U_12336),hAPP(c_COMBK(tc_fun(U_12335,tc_HOL_Obool),U_12335),U_12336)))),
    inference(clausify,[status(thm)],[f_3219_2]) ).

fof(f_3220_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_3220_2,plain,
    ! [U_12338,U_12337] : hAPP(hAPP(c_Product__Type_OSigma(U_12337,U_12338),c_Orderings_Otop__class_Otop(tc_fun(U_12337,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12338,tc_HOL_Obool),U_12337),c_Orderings_Otop__class_Otop(tc_fun(U_12338,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12337,U_12338),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

cnf(f_3220_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12337,U_12338),c_Orderings_Otop__class_Otop(tc_fun(U_12337,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12338,tc_HOL_Obool),U_12337),c_Orderings_Otop__class_Otop(tc_fun(U_12338,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12337,U_12338),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3220_2]) ).

fof(f_3221_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_3221_2,plain,
    ! [U_12344,U_12343,U_12342,U_12341,U_12340,U_12339] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12339,U_12340)),hAPP(hAPP(c_Product__Type_OPair(U_12339,U_12340),U_12341),U_12342)),hAPP(hAPP(c_Product__Type_OSigma(U_12339,U_12340),U_12343),U_12344)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12340),U_12342),hAPP(U_12344,U_12341)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12339),U_12341),U_12343)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_12340),U_12342),hAPP(U_12344,U_12341)))
          & hBOOL(hAPP(hAPP(c_member(U_12339),U_12341),U_12343)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12339,U_12340)),hAPP(hAPP(c_Product__Type_OPair(U_12339,U_12340),U_12341),U_12342)),hAPP(hAPP(c_Product__Type_OSigma(U_12339,U_12340),U_12343),U_12344))) ) ),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

fof(f_3221_3,plain,
    ( ! [U_12356,U_12354,U_12352,U_12350,U_12348,U_12346] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12346,U_12348)),hAPP(hAPP(c_Product__Type_OPair(U_12346,U_12348),U_12350),U_12352)),hAPP(hAPP(c_Product__Type_OSigma(U_12346,U_12348),U_12354),U_12356)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12348),U_12352),hAPP(U_12356,U_12350)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12346),U_12350),U_12354)) )
    & ! [U_12355,U_12353,U_12351,U_12349,U_12347,U_12345] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_12347),U_12351),hAPP(U_12355,U_12349)))
          & hBOOL(hAPP(hAPP(c_member(U_12345),U_12349),U_12353)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12345,U_12347)),hAPP(hAPP(c_Product__Type_OPair(U_12345,U_12347),U_12349),U_12351)),hAPP(hAPP(c_Product__Type_OSigma(U_12345,U_12347),U_12353),U_12355))) ) ),
    inference(miniscope,[status(thm)],[f_3221_2]) ).

cnf(f_3221_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12345),U_12349),U_12353))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12345,U_12347)),hAPP(hAPP(c_Product__Type_OPair(U_12345,U_12347),U_12349),U_12351)),hAPP(hAPP(c_Product__Type_OSigma(U_12345,U_12347),U_12353),U_12355))) ),
    inference(clausify,[status(thm)],[f_3221_3]) ).

cnf(f_3221_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12347),U_12351),hAPP(U_12355,U_12349)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12345,U_12347)),hAPP(hAPP(c_Product__Type_OPair(U_12345,U_12347),U_12349),U_12351)),hAPP(hAPP(c_Product__Type_OSigma(U_12345,U_12347),U_12353),U_12355))) ),
    inference(clausify,[status(thm)],[f_3221_3]) ).

cnf(f_3221_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12346,U_12348)),hAPP(hAPP(c_Product__Type_OPair(U_12346,U_12348),U_12350),U_12352)),hAPP(hAPP(c_Product__Type_OSigma(U_12346,U_12348),U_12354),U_12356)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12348),U_12352),hAPP(U_12356,U_12350)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12346),U_12350),U_12354)) ),
    inference(clausify,[status(thm)],[f_3221_3]) ).

fof(f_3222_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_3222_2,plain,
    ! [U_12362,U_12361,U_12360,U_12359,U_12358,U_12357] :
      ( hBOOL(hAPP(hAPP(c_member(U_12357),U_12359),U_12361))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12357,U_12358)),hAPP(hAPP(c_Product__Type_OPair(U_12357,U_12358),U_12359),U_12360)),hAPP(hAPP(c_Product__Type_OSigma(U_12357,U_12358),U_12361),U_12362))) ),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

cnf(f_3222_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12357),U_12359),U_12361))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12357,U_12358)),hAPP(hAPP(c_Product__Type_OPair(U_12357,U_12358),U_12359),U_12360)),hAPP(hAPP(c_Product__Type_OSigma(U_12357,U_12358),U_12361),U_12362))) ),
    inference(clausify,[status(thm)],[f_3222_2]) ).

fof(f_3223_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_3223_2,plain,
    ! [U_12368,U_12367,U_12366,U_12365,U_12364,U_12363] :
      ( hBOOL(hAPP(hAPP(c_member(U_12364),U_12366),hAPP(U_12368,U_12365)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12363,U_12364)),hAPP(hAPP(c_Product__Type_OPair(U_12363,U_12364),U_12365),U_12366)),hAPP(hAPP(c_Product__Type_OSigma(U_12363,U_12364),U_12367),U_12368))) ),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

fof(f_3223_3,plain,
    ! [U_12368,U_12367,U_12366,U_12365,U_12364] :
      ( ! [U_12363] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12363,U_12364)),hAPP(hAPP(c_Product__Type_OPair(U_12363,U_12364),U_12365),U_12366)),hAPP(hAPP(c_Product__Type_OSigma(U_12363,U_12364),U_12367),U_12368)))
      | hBOOL(hAPP(hAPP(c_member(U_12364),U_12366),hAPP(U_12368,U_12365))) ),
    inference(miniscope,[status(thm)],[f_3223_2]) ).

cnf(f_3223_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12363,U_12364)),hAPP(hAPP(c_Product__Type_OPair(U_12363,U_12364),U_12365),U_12366)),hAPP(hAPP(c_Product__Type_OSigma(U_12363,U_12364),U_12367),U_12368)))
    | hBOOL(hAPP(hAPP(c_member(U_12364),U_12366),hAPP(U_12368,U_12365))) ),
    inference(clausify,[status(thm)],[f_3223_3]) ).

fof(f_3224_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_3224_2,plain,
    ! [U_12374,U_12373,U_12372,U_12371,U_12370,U_12369] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12370),U_12372),hAPP(U_12374,U_12371)))
        & hBOOL(hAPP(hAPP(c_member(U_12369),U_12371),U_12373)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12369,U_12370)),hAPP(hAPP(c_Product__Type_OPair(U_12369,U_12370),U_12371),U_12372)),hAPP(hAPP(c_Product__Type_OSigma(U_12369,U_12370),U_12373),U_12374))) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

cnf(f_3224_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12369),U_12371),U_12373))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12369,U_12370)),hAPP(hAPP(c_Product__Type_OPair(U_12369,U_12370),U_12371),U_12372)),hAPP(hAPP(c_Product__Type_OSigma(U_12369,U_12370),U_12373),U_12374))) ),
    inference(clausify,[status(thm)],[f_3224_2]) ).

cnf(f_3224_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12370),U_12372),hAPP(U_12374,U_12371)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12369,U_12370)),hAPP(hAPP(c_Product__Type_OPair(U_12369,U_12370),U_12371),U_12372)),hAPP(hAPP(c_Product__Type_OSigma(U_12369,U_12370),U_12373),U_12374))) ),
    inference(clausify,[status(thm)],[f_3224_2]) ).

fof(f_3225_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_3225_2,plain,
    ! [U_12378,U_12377,U_12376,U_12375] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12375,U_12376)),hAPP(hAPP(c_Product__Type_OSigma(U_12375,U_12376),hAPP(hAPP(c_Set_Oinsert(U_12375),U_12377),c_Orderings_Obot__class_Obot(tc_fun(U_12375,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12376,tc_HOL_Obool),U_12375),U_12378))) = hAPP(c_Finite__Set_Ocard(U_12376),U_12378),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

cnf(f_3225_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_12375,U_12376)),hAPP(hAPP(c_Product__Type_OSigma(U_12375,U_12376),hAPP(hAPP(c_Set_Oinsert(U_12375),U_12377),c_Orderings_Obot__class_Obot(tc_fun(U_12375,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12376,tc_HOL_Obool),U_12375),U_12378))) = hAPP(c_Finite__Set_Ocard(U_12376),U_12378),
    inference(clausify,[status(thm)],[f_3225_2]) ).

fof(f_3226_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_3226_2,plain,
    ! [U_12384,U_12383,U_12382,U_12381,U_12380,U_12379] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12382,U_12379),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12383),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12384),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12382,U_12379),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12383),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12384),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12379),U_12380),U_12381)) ),
    inference(variable_rename,[status(thm)],[f_3226_1]) ).

cnf(f_3226_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12382,U_12379),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12383),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12384),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12379),U_12380),U_12381)) ),
    inference(clausify,[status(thm)],[f_3226_2]) ).

cnf(f_3226_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12382,U_12379),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12383),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))),hAPP(hAPP(c_Product__Type_OSigma(U_12382,U_12379),U_12384),hAPP(c_COMBK(tc_fun(U_12379,tc_HOL_Obool),U_12382),U_12381))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12382,tc_HOL_Obool)),U_12383),U_12384))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12379),U_12380),U_12381)) ),
    inference(clausify,[status(thm)],[f_3226_2]) ).

fof(f_3227_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_3227_2,plain,
    ! [U_12390,U_12389,U_12388,U_12387,U_12386,U_12385] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12386,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12385,U_12386,U_12387),U_12390)),U_12389))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12385,U_12386),tc_HOL_Obool)),U_12387),hAPP(hAPP(c_Product__Type_OSigma(U_12385,U_12386),U_12388),hAPP(c_COMBK(tc_fun(U_12386,tc_HOL_Obool),U_12385),U_12389)))) ),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

cnf(f_3227_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12386,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12385,U_12386,U_12387),U_12390)),U_12389))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12385,U_12386),tc_HOL_Obool)),U_12387),hAPP(hAPP(c_Product__Type_OSigma(U_12385,U_12386),U_12388),hAPP(c_COMBK(tc_fun(U_12386,tc_HOL_Obool),U_12385),U_12389)))) ),
    inference(clausify,[status(thm)],[f_3227_2]) ).

fof(f_3228_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_3228_2,plain,
    ! [U_12394,U_12393,U_12392,U_12391] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12391),U_12393))
      | U_12394 = c_Orderings_Obot__class_Obot(tc_fun(U_12392,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12391,U_12392)),hAPP(hAPP(c_Product__Type_OSigma(U_12391,U_12392),U_12393),hAPP(c_COMBK(tc_fun(U_12392,tc_HOL_Obool),U_12391),U_12394)))) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

cnf(f_3228_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12391),U_12393))
    | U_12394 = c_Orderings_Obot__class_Obot(tc_fun(U_12392,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12391,U_12392)),hAPP(hAPP(c_Product__Type_OSigma(U_12391,U_12392),U_12393),hAPP(c_COMBK(tc_fun(U_12392,tc_HOL_Obool),U_12391),U_12394)))) ),
    inference(clausify,[status(thm)],[f_3228_2]) ).

fof(f_3229_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_3229_2,plain,
    ! [U_12398,U_12397,U_12396,U_12395] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12396),U_12398))
      | U_12397 = c_Orderings_Obot__class_Obot(tc_fun(U_12395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12395,U_12396)),hAPP(hAPP(c_Product__Type_OSigma(U_12395,U_12396),U_12397),hAPP(c_COMBK(tc_fun(U_12396,tc_HOL_Obool),U_12395),U_12398)))) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

cnf(f_3229_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12396),U_12398))
    | U_12397 = c_Orderings_Obot__class_Obot(tc_fun(U_12395,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12395,U_12396)),hAPP(hAPP(c_Product__Type_OSigma(U_12395,U_12396),U_12397),hAPP(c_COMBK(tc_fun(U_12396,tc_HOL_Obool),U_12395),U_12398)))) ),
    inference(clausify,[status(thm)],[f_3229_2]) ).

fof(f_3230_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_3230_2,plain,
    ! [U_12402,U_12401,U_12400,U_12399] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_12401,U_12400),U_12401,c_Product__Type_Ofst(U_12401,U_12400)),hAPP(hAPP(c_Product__Type_OSigma(U_12401,U_12400),U_12402),hAPP(c_COMBK(tc_fun(U_12400,tc_HOL_Obool),U_12401),U_12399))) = U_12402
        | U_12399 = c_Orderings_Obot__class_Obot(tc_fun(U_12400,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_12401,U_12400),U_12401,c_Product__Type_Ofst(U_12401,U_12400)),hAPP(hAPP(c_Product__Type_OSigma(U_12401,U_12400),U_12402),hAPP(c_COMBK(tc_fun(U_12400,tc_HOL_Obool),U_12401),U_12399))) = c_Orderings_Obot__class_Obot(tc_fun(U_12401,tc_HOL_Obool))
        | U_12399 != c_Orderings_Obot__class_Obot(tc_fun(U_12400,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

fof(f_3230_3,plain,
    ( ! [U_12410,U_12408,U_12406,U_12404] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12408,U_12406),U_12408,c_Product__Type_Ofst(U_12408,U_12406)),hAPP(hAPP(c_Product__Type_OSigma(U_12408,U_12406),U_12410),hAPP(c_COMBK(tc_fun(U_12406,tc_HOL_Obool),U_12408),U_12404))) = U_12410
        | U_12404 = c_Orderings_Obot__class_Obot(tc_fun(U_12406,tc_HOL_Obool)) )
    & ! [U_12409,U_12407,U_12405,U_12403] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12407,U_12405),U_12407,c_Product__Type_Ofst(U_12407,U_12405)),hAPP(hAPP(c_Product__Type_OSigma(U_12407,U_12405),U_12409),hAPP(c_COMBK(tc_fun(U_12405,tc_HOL_Obool),U_12407),U_12403))) = c_Orderings_Obot__class_Obot(tc_fun(U_12407,tc_HOL_Obool))
        | U_12403 != c_Orderings_Obot__class_Obot(tc_fun(U_12405,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3230_2]) ).

cnf(f_3230_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12407,U_12405),U_12407,c_Product__Type_Ofst(U_12407,U_12405)),hAPP(hAPP(c_Product__Type_OSigma(U_12407,U_12405),U_12409),hAPP(c_COMBK(tc_fun(U_12405,tc_HOL_Obool),U_12407),U_12403))) = c_Orderings_Obot__class_Obot(tc_fun(U_12407,tc_HOL_Obool))
    | U_12403 != c_Orderings_Obot__class_Obot(tc_fun(U_12405,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

cnf(f_3230_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12408,U_12406),U_12408,c_Product__Type_Ofst(U_12408,U_12406)),hAPP(hAPP(c_Product__Type_OSigma(U_12408,U_12406),U_12410),hAPP(c_COMBK(tc_fun(U_12406,tc_HOL_Obool),U_12408),U_12404))) = U_12410
    | U_12404 = c_Orderings_Obot__class_Obot(tc_fun(U_12406,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

fof(f_3231_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_3231_2,plain,
    ! [U_12414,U_12413,U_12412,U_12411] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_12412,U_12413),U_12413,c_Product__Type_Osnd(U_12412,U_12413)),hAPP(hAPP(c_Product__Type_OSigma(U_12412,U_12413),U_12411),hAPP(c_COMBK(tc_fun(U_12413,tc_HOL_Obool),U_12412),U_12414))) = U_12414
        | U_12411 = c_Orderings_Obot__class_Obot(tc_fun(U_12412,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_12412,U_12413),U_12413,c_Product__Type_Osnd(U_12412,U_12413)),hAPP(hAPP(c_Product__Type_OSigma(U_12412,U_12413),U_12411),hAPP(c_COMBK(tc_fun(U_12413,tc_HOL_Obool),U_12412),U_12414))) = c_Orderings_Obot__class_Obot(tc_fun(U_12413,tc_HOL_Obool))
        | U_12411 != c_Orderings_Obot__class_Obot(tc_fun(U_12412,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

fof(f_3231_3,plain,
    ( ! [U_12422,U_12420,U_12418,U_12416] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12418,U_12420),U_12420,c_Product__Type_Osnd(U_12418,U_12420)),hAPP(hAPP(c_Product__Type_OSigma(U_12418,U_12420),U_12416),hAPP(c_COMBK(tc_fun(U_12420,tc_HOL_Obool),U_12418),U_12422))) = U_12422
        | U_12416 = c_Orderings_Obot__class_Obot(tc_fun(U_12418,tc_HOL_Obool)) )
    & ! [U_12421,U_12419,U_12417,U_12415] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12417,U_12419),U_12419,c_Product__Type_Osnd(U_12417,U_12419)),hAPP(hAPP(c_Product__Type_OSigma(U_12417,U_12419),U_12415),hAPP(c_COMBK(tc_fun(U_12419,tc_HOL_Obool),U_12417),U_12421))) = c_Orderings_Obot__class_Obot(tc_fun(U_12419,tc_HOL_Obool))
        | U_12415 != c_Orderings_Obot__class_Obot(tc_fun(U_12417,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3231_2]) ).

cnf(f_3231_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12417,U_12419),U_12419,c_Product__Type_Osnd(U_12417,U_12419)),hAPP(hAPP(c_Product__Type_OSigma(U_12417,U_12419),U_12415),hAPP(c_COMBK(tc_fun(U_12419,tc_HOL_Obool),U_12417),U_12421))) = c_Orderings_Obot__class_Obot(tc_fun(U_12419,tc_HOL_Obool))
    | U_12415 != c_Orderings_Obot__class_Obot(tc_fun(U_12417,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

cnf(f_3231_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12418,U_12420),U_12420,c_Product__Type_Osnd(U_12418,U_12420)),hAPP(hAPP(c_Product__Type_OSigma(U_12418,U_12420),U_12416),hAPP(c_COMBK(tc_fun(U_12420,tc_HOL_Obool),U_12418),U_12422))) = U_12422
    | U_12416 = c_Orderings_Obot__class_Obot(tc_fun(U_12418,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

fof(f_3232_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_3232_2,plain,
    ! [U_12428,U_12427,U_12426,U_12425,U_12424,U_12423] : hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),hAPP(hAPP(c_Set_Oinsert(U_12423),U_12425),U_12426)),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12424),U_12427),U_12428))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12423,U_12424)),hAPP(hAPP(c_Product__Type_OPair(U_12423,U_12424),U_12425),U_12427)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12423,U_12424),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),U_12426),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12424),U_12427),U_12428)))),hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),hAPP(hAPP(c_Set_Oinsert(U_12423),U_12425),U_12426)),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),U_12428)))),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

cnf(f_3232_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),hAPP(hAPP(c_Set_Oinsert(U_12423),U_12425),U_12426)),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12424),U_12427),U_12428))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12423,U_12424)),hAPP(hAPP(c_Product__Type_OPair(U_12423,U_12424),U_12425),U_12427)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12423,U_12424),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),U_12426),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12424),U_12427),U_12428)))),hAPP(hAPP(c_Product__Type_OSigma(U_12423,U_12424),hAPP(hAPP(c_Set_Oinsert(U_12423),U_12425),U_12426)),hAPP(c_COMBK(tc_fun(U_12424,tc_HOL_Obool),U_12423),U_12428)))),
    inference(clausify,[status(thm)],[f_3232_2]) ).

fof(f_3233_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_3233_2,plain,
    ! [U_12432,U_12431,U_12430,U_12429] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12429),U_12432))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12429),U_12430),U_12431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12429,U_12429),tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Product__Type_OSigma(U_12429,U_12429),U_12430),hAPP(c_COMBK(tc_fun(U_12429,tc_HOL_Obool),U_12429),U_12430))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12429),U_12430)) ),
    inference(variable_rename,[status(thm)],[f_3233_1]) ).

cnf(f_3233_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12429),U_12432))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12429),U_12430),U_12431)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12429,U_12429),tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Product__Type_OSigma(U_12429,U_12429),U_12430),hAPP(c_COMBK(tc_fun(U_12429,tc_HOL_Obool),U_12429),U_12430))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12429),U_12430)) ),
    inference(clausify,[status(thm)],[f_3233_2]) ).

fof(f_3234_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_3234_2,plain,
    ! [U_12440,U_12439,U_12438,U_12437,U_12436,U_12435,U_12434,U_12433] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12433,U_12434),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12433,U_12434),U_12437),hAPP(c_COMBK(tc_fun(U_12434,tc_HOL_Obool),U_12433),U_12438))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12433,U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12433,tc_fun(U_12434,tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool))),tc_fun(U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),tc_fun(tc_fun(U_12434,tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool))),tc_fun(U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool))),U_12433),c_COMBB(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool),U_12434)),hAPP(hAPP(c_COMBB(tc_fun(U_12435,tc_HOL_Obool),tc_fun(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),U_12433),c_Product__Type_OSigma(U_12435,U_12436)),U_12439))),hAPP(hAPP(c_COMBB(tc_fun(U_12436,tc_HOL_Obool),tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),U_12434),c_COMBK(tc_fun(U_12436,tc_HOL_Obool),U_12435)),U_12440)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12435,U_12436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12433,tc_fun(U_12435,tc_HOL_Obool)),U_12437),U_12439)),hAPP(c_COMBK(tc_fun(U_12436,tc_HOL_Obool),U_12435),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12434,tc_fun(U_12436,tc_HOL_Obool)),U_12438),U_12440))),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

cnf(f_3234_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12433,U_12434),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12433,U_12434),U_12437),hAPP(c_COMBK(tc_fun(U_12434,tc_HOL_Obool),U_12433),U_12438))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12433,U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12433,tc_fun(U_12434,tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool))),tc_fun(U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),tc_fun(tc_fun(U_12434,tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool))),tc_fun(U_12434,tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool))),U_12433),c_COMBB(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool),U_12434)),hAPP(hAPP(c_COMBB(tc_fun(U_12435,tc_HOL_Obool),tc_fun(tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),tc_fun(tc_prod(U_12435,U_12436),tc_HOL_Obool)),U_12433),c_Product__Type_OSigma(U_12435,U_12436)),U_12439))),hAPP(hAPP(c_COMBB(tc_fun(U_12436,tc_HOL_Obool),tc_fun(U_12435,tc_fun(U_12436,tc_HOL_Obool)),U_12434),c_COMBK(tc_fun(U_12436,tc_HOL_Obool),U_12435)),U_12440)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12435,U_12436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12433,tc_fun(U_12435,tc_HOL_Obool)),U_12437),U_12439)),hAPP(c_COMBK(tc_fun(U_12436,tc_HOL_Obool),U_12435),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12434,tc_fun(U_12436,tc_HOL_Obool)),U_12438),U_12440))),
    inference(clausify,[status(thm)],[f_3234_2]) ).

fof(f_3235_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_3235_2,plain,
    ! [U_12444,U_12443,U_12442,U_12441] : hAPP(hAPP(c_Product__Type_OSigma(U_12441,U_12442),U_12443),U_12444) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12441,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12443),hAPP(hAPP(c_COMBS(U_12441,tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_HOL_Obool),tc_fun(tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12441),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12444)),hAPP(hAPP(c_COMBC(U_12441,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12441),c_COMBC(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_prod(U_12441,U_12442)),tc_fun(U_12442,tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12441),hAPP(c_COMBB(tc_prod(U_12441,U_12442),tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12442),c_Set_Oinsert(tc_prod(U_12441,U_12442)))),c_Product__Type_OPair(U_12441,U_12442)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

cnf(f_3235_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12441,U_12442),U_12443),U_12444) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12441,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12443),hAPP(hAPP(c_COMBS(U_12441,tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_HOL_Obool),tc_fun(tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12441),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12444)),hAPP(hAPP(c_COMBC(U_12441,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12441),c_COMBC(U_12442,tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12442,tc_prod(U_12441,U_12442)),tc_fun(U_12442,tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))),U_12441),hAPP(c_COMBB(tc_prod(U_12441,U_12442),tc_fun(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool),tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool)),U_12442),c_Set_Oinsert(tc_prod(U_12441,U_12442)))),c_Product__Type_OPair(U_12441,U_12442)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12441,U_12442),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3235_2]) ).

fof(f_3236_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_3236_2,plain,
    ! [U_12447,U_12446,U_12445] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12445,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12445),U_12446),U_12447)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12445,U_12445),tc_HOL_Obool)),U_12447),hAPP(hAPP(c_Product__Type_OSigma(U_12445,U_12445),U_12446),hAPP(c_COMBK(tc_fun(U_12445,tc_HOL_Obool),U_12445),U_12446))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12445),U_12446)) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

cnf(f_3236_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12445,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12445),U_12446),U_12447)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12445,U_12445),tc_HOL_Obool)),U_12447),hAPP(hAPP(c_Product__Type_OSigma(U_12445,U_12445),U_12446),hAPP(c_COMBK(tc_fun(U_12445,tc_HOL_Obool),U_12445),U_12446))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12445),U_12446)) ),
    inference(clausify,[status(thm)],[f_3236_2]) ).

fof(f_3237_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_3237_2,plain,
    ! [U_12452,U_12451,U_12450,U_12449] :
    ? [U_12448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12450,U_12449),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12449,tc_prod(U_12450,U_12449),U_12448),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452))),hAPP(hAPP(c_Product__Type_OSigma(U_12450,U_12449),U_12451),U_12452)))
      & c_Fun_Oinj__on(U_12449,tc_prod(U_12450,U_12449),U_12448,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452)) ),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

fof(f_3237_3,plain,
    ! [U_12452,U_12451,U_12450,U_12449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12450,U_12449),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12449,tc_prod(U_12450,U_12449),sK288(U_12452,U_12451,U_12450,U_12449)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452))),hAPP(hAPP(c_Product__Type_OSigma(U_12450,U_12449),U_12451),U_12452)))
      & c_Fun_Oinj__on(U_12449,tc_prod(U_12450,U_12449),sK288(U_12452,U_12451,U_12450,U_12449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_12448,sK288(U_12452,U_12451,U_12450,U_12449))],[f_3237_2]) ).

cnf(f_3237_4,plain,
    c_Fun_Oinj__on(U_12449,tc_prod(U_12450,U_12449),sK288(U_12452,U_12451,U_12450,U_12449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452)),
    inference(clausify,[status(thm)],[f_3237_3]) ).

cnf(f_3237_5,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12450,U_12449),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12449,tc_prod(U_12450,U_12449),sK288(U_12452,U_12451,U_12450,U_12449)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12450,tc_fun(U_12449,tc_HOL_Obool)),U_12451),U_12452))),hAPP(hAPP(c_Product__Type_OSigma(U_12450,U_12449),U_12451),U_12452))),
    inference(clausify,[status(thm)],[f_3237_3]) ).

fof(f_3238_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_3238_2,plain,
    ! [U_12459,U_12458,U_12457,U_12456,U_12455,U_12454] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,U_12455,c_Groups_Otimes__class_Otimes(U_12454)),hAPP(hAPP(c_COMBS(U_12455,tc_fun(U_12457,tc_HOL_Obool),U_12454),hAPP(hAPP(c_COMBC(U_12455,U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),hAPP(hAPP(c_COMBB(tc_fun(U_12457,U_12454),tc_fun(U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),U_12455),c_Finite__Set_Ofold__image(U_12454,U_12457,c_Groups_Otimes__class_Otimes(U_12454))),U_12459)),c_Groups_Oone__class_Oone(U_12454))),U_12458)),c_Groups_Oone__class_Oone(U_12454)),U_12456) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,tc_prod(U_12455,U_12457),c_Groups_Otimes__class_Otimes(U_12454)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12455,U_12457,U_12454),U_12459)),c_Groups_Oone__class_Oone(U_12454)),hAPP(hAPP(c_Product__Type_OSigma(U_12455,U_12457),U_12456),U_12458))
      | ? [U_12453] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12457),hAPP(U_12458,U_12453)))
          & hBOOL(hAPP(hAPP(c_member(U_12455),U_12453),U_12456)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12455),U_12456))
      | ~ class_Groups_Ocomm__monoid__mult(U_12454) ),
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

fof(f_3238_3,plain,
    ! [U_12459,U_12458,U_12457,U_12456,U_12455,U_12454] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,U_12455,c_Groups_Otimes__class_Otimes(U_12454)),hAPP(hAPP(c_COMBS(U_12455,tc_fun(U_12457,tc_HOL_Obool),U_12454),hAPP(hAPP(c_COMBC(U_12455,U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),hAPP(hAPP(c_COMBB(tc_fun(U_12457,U_12454),tc_fun(U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),U_12455),c_Finite__Set_Ofold__image(U_12454,U_12457,c_Groups_Otimes__class_Otimes(U_12454))),U_12459)),c_Groups_Oone__class_Oone(U_12454))),U_12458)),c_Groups_Oone__class_Oone(U_12454)),U_12456) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,tc_prod(U_12455,U_12457),c_Groups_Otimes__class_Otimes(U_12454)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12455,U_12457,U_12454),U_12459)),c_Groups_Oone__class_Oone(U_12454)),hAPP(hAPP(c_Product__Type_OSigma(U_12455,U_12457),U_12456),U_12458))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12457),hAPP(U_12458,sK289(U_12459,U_12458,U_12457,U_12456,U_12455,U_12454))))
        & hBOOL(hAPP(hAPP(c_member(U_12455),sK289(U_12459,U_12458,U_12457,U_12456,U_12455,U_12454)),U_12456)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12455),U_12456))
      | ~ class_Groups_Ocomm__monoid__mult(U_12454) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_12453,sK289(U_12459,U_12458,U_12457,U_12456,U_12455,U_12454))],[f_3238_2]) ).

cnf(f_3238_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12455),sK289(U_12459,U_12458,U_12457,U_12456,U_12455,U_12454)),U_12456))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,U_12455,c_Groups_Otimes__class_Otimes(U_12454)),hAPP(hAPP(c_COMBS(U_12455,tc_fun(U_12457,tc_HOL_Obool),U_12454),hAPP(hAPP(c_COMBC(U_12455,U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),hAPP(hAPP(c_COMBB(tc_fun(U_12457,U_12454),tc_fun(U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),U_12455),c_Finite__Set_Ofold__image(U_12454,U_12457,c_Groups_Otimes__class_Otimes(U_12454))),U_12459)),c_Groups_Oone__class_Oone(U_12454))),U_12458)),c_Groups_Oone__class_Oone(U_12454)),U_12456) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,tc_prod(U_12455,U_12457),c_Groups_Otimes__class_Otimes(U_12454)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12455,U_12457,U_12454),U_12459)),c_Groups_Oone__class_Oone(U_12454)),hAPP(hAPP(c_Product__Type_OSigma(U_12455,U_12457),U_12456),U_12458))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12455),U_12456))
    | ~ class_Groups_Ocomm__monoid__mult(U_12454) ),
    inference(clausify,[status(thm)],[f_3238_3]) ).

cnf(f_3238_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12457),hAPP(U_12458,sK289(U_12459,U_12458,U_12457,U_12456,U_12455,U_12454))))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,U_12455,c_Groups_Otimes__class_Otimes(U_12454)),hAPP(hAPP(c_COMBS(U_12455,tc_fun(U_12457,tc_HOL_Obool),U_12454),hAPP(hAPP(c_COMBC(U_12455,U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),hAPP(hAPP(c_COMBB(tc_fun(U_12457,U_12454),tc_fun(U_12454,tc_fun(tc_fun(U_12457,tc_HOL_Obool),U_12454)),U_12455),c_Finite__Set_Ofold__image(U_12454,U_12457,c_Groups_Otimes__class_Otimes(U_12454))),U_12459)),c_Groups_Oone__class_Oone(U_12454))),U_12458)),c_Groups_Oone__class_Oone(U_12454)),U_12456) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12454,tc_prod(U_12455,U_12457),c_Groups_Otimes__class_Otimes(U_12454)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12455,U_12457,U_12454),U_12459)),c_Groups_Oone__class_Oone(U_12454)),hAPP(hAPP(c_Product__Type_OSigma(U_12455,U_12457),U_12456),U_12458))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12455),U_12456))
    | ~ class_Groups_Ocomm__monoid__mult(U_12454) ),
    inference(clausify,[status(thm)],[f_3238_3]) ).

fof(f_3239_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_3239_2,plain,
    ! [U_12464,U_12463,U_12462,U_12461] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12461,U_12463)),hAPP(hAPP(c_Product__Type_OSigma(U_12461,U_12463),U_12462),U_12464)))
      | ? [U_12460] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12463),hAPP(U_12464,U_12460)))
          & hBOOL(hAPP(hAPP(c_member(U_12461),U_12460),U_12462)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12461),U_12462)) ),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12464,U_12463,U_12462,U_12461] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12461,U_12463)),hAPP(hAPP(c_Product__Type_OSigma(U_12461,U_12463),U_12462),U_12464)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12463),hAPP(U_12464,sK290(U_12464,U_12463,U_12462,U_12461))))
        & hBOOL(hAPP(hAPP(c_member(U_12461),sK290(U_12464,U_12463,U_12462,U_12461)),U_12462)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12461),U_12462)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_12460,sK290(U_12464,U_12463,U_12462,U_12461))],[f_3239_2]) ).

cnf(f_3239_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12461),sK290(U_12464,U_12463,U_12462,U_12461)),U_12462))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12461,U_12463)),hAPP(hAPP(c_Product__Type_OSigma(U_12461,U_12463),U_12462),U_12464)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12461),U_12462)) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

cnf(f_3239_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12463),hAPP(U_12464,sK290(U_12464,U_12463,U_12462,U_12461))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12461,U_12463)),hAPP(hAPP(c_Product__Type_OSigma(U_12461,U_12463),U_12462),U_12464)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12461),U_12462)) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_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_3240_2,plain,
    ! [U_12471,U_12470,U_12469,U_12468,U_12467,U_12466] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12467,U_12466),hAPP(hAPP(c_COMBS(U_12467,tc_fun(U_12469,tc_HOL_Obool),U_12466),hAPP(hAPP(c_COMBB(tc_fun(U_12469,U_12466),tc_fun(tc_fun(U_12469,tc_HOL_Obool),U_12466),U_12467),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12469,U_12466)),U_12471)),U_12470)),U_12468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12467,U_12469),U_12466),hAPP(c_Product__Type_Oprod_Oprod__case(U_12467,U_12469,U_12466),U_12471)),hAPP(hAPP(c_Product__Type_OSigma(U_12467,U_12469),U_12468),U_12470))
      | ? [U_12465] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12469),hAPP(U_12470,U_12465)))
          & hBOOL(hAPP(hAPP(c_member(U_12467),U_12465),U_12468)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12467),U_12468))
      | ~ class_Groups_Ocomm__monoid__mult(U_12466) ),
    inference(variable_rename,[status(thm)],[f_3240_1]) ).

fof(f_3240_3,plain,
    ! [U_12471,U_12470,U_12469,U_12468,U_12467,U_12466] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12467,U_12466),hAPP(hAPP(c_COMBS(U_12467,tc_fun(U_12469,tc_HOL_Obool),U_12466),hAPP(hAPP(c_COMBB(tc_fun(U_12469,U_12466),tc_fun(tc_fun(U_12469,tc_HOL_Obool),U_12466),U_12467),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12469,U_12466)),U_12471)),U_12470)),U_12468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12467,U_12469),U_12466),hAPP(c_Product__Type_Oprod_Oprod__case(U_12467,U_12469,U_12466),U_12471)),hAPP(hAPP(c_Product__Type_OSigma(U_12467,U_12469),U_12468),U_12470))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12469),hAPP(U_12470,sK291(U_12471,U_12470,U_12469,U_12468,U_12467,U_12466))))
        & hBOOL(hAPP(hAPP(c_member(U_12467),sK291(U_12471,U_12470,U_12469,U_12468,U_12467,U_12466)),U_12468)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12467),U_12468))
      | ~ class_Groups_Ocomm__monoid__mult(U_12466) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_12465,sK291(U_12471,U_12470,U_12469,U_12468,U_12467,U_12466))],[f_3240_2]) ).

cnf(f_3240_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12467),sK291(U_12471,U_12470,U_12469,U_12468,U_12467,U_12466)),U_12468))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12467,U_12466),hAPP(hAPP(c_COMBS(U_12467,tc_fun(U_12469,tc_HOL_Obool),U_12466),hAPP(hAPP(c_COMBB(tc_fun(U_12469,U_12466),tc_fun(tc_fun(U_12469,tc_HOL_Obool),U_12466),U_12467),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12469,U_12466)),U_12471)),U_12470)),U_12468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12467,U_12469),U_12466),hAPP(c_Product__Type_Oprod_Oprod__case(U_12467,U_12469,U_12466),U_12471)),hAPP(hAPP(c_Product__Type_OSigma(U_12467,U_12469),U_12468),U_12470))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12467),U_12468))
    | ~ class_Groups_Ocomm__monoid__mult(U_12466) ),
    inference(clausify,[status(thm)],[f_3240_3]) ).

cnf(f_3240_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12469),hAPP(U_12470,sK291(U_12471,U_12470,U_12469,U_12468,U_12467,U_12466))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12467,U_12466),hAPP(hAPP(c_COMBS(U_12467,tc_fun(U_12469,tc_HOL_Obool),U_12466),hAPP(hAPP(c_COMBB(tc_fun(U_12469,U_12466),tc_fun(tc_fun(U_12469,tc_HOL_Obool),U_12466),U_12467),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12469,U_12466)),U_12471)),U_12470)),U_12468) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12467,U_12469),U_12466),hAPP(c_Product__Type_Oprod_Oprod__case(U_12467,U_12469,U_12466),U_12471)),hAPP(hAPP(c_Product__Type_OSigma(U_12467,U_12469),U_12468),U_12470))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12467),U_12468))
    | ~ class_Groups_Ocomm__monoid__mult(U_12466) ),
    inference(clausify,[status(thm)],[f_3240_3]) ).

fof(f_3241_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_3241_2,plain,
    ! [U_12478,U_12477,U_12476,U_12475,U_12474,U_12473] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12474,U_12473),hAPP(hAPP(c_COMBS(U_12474,tc_fun(U_12476,tc_HOL_Obool),U_12473),hAPP(hAPP(c_COMBB(tc_fun(U_12476,U_12473),tc_fun(tc_fun(U_12476,tc_HOL_Obool),U_12473),U_12474),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12473)),U_12478)),U_12477)),U_12475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12474,U_12476),U_12473),hAPP(c_Product__Type_Oprod_Oprod__case(U_12474,U_12476,U_12473),U_12478)),hAPP(hAPP(c_Product__Type_OSigma(U_12474,U_12476),U_12475),U_12477))
      | ? [U_12472] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),hAPP(U_12477,U_12472)))
          & hBOOL(hAPP(hAPP(c_member(U_12474),U_12472),U_12475)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12474),U_12475))
      | ~ class_Groups_Ocomm__monoid__add(U_12473) ),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

fof(f_3241_3,plain,
    ! [U_12478,U_12477,U_12476,U_12475,U_12474,U_12473] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12474,U_12473),hAPP(hAPP(c_COMBS(U_12474,tc_fun(U_12476,tc_HOL_Obool),U_12473),hAPP(hAPP(c_COMBB(tc_fun(U_12476,U_12473),tc_fun(tc_fun(U_12476,tc_HOL_Obool),U_12473),U_12474),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12473)),U_12478)),U_12477)),U_12475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12474,U_12476),U_12473),hAPP(c_Product__Type_Oprod_Oprod__case(U_12474,U_12476,U_12473),U_12478)),hAPP(hAPP(c_Product__Type_OSigma(U_12474,U_12476),U_12475),U_12477))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),hAPP(U_12477,sK292(U_12478,U_12477,U_12476,U_12475,U_12474,U_12473))))
        & hBOOL(hAPP(hAPP(c_member(U_12474),sK292(U_12478,U_12477,U_12476,U_12475,U_12474,U_12473)),U_12475)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12474),U_12475))
      | ~ class_Groups_Ocomm__monoid__add(U_12473) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_12472,sK292(U_12478,U_12477,U_12476,U_12475,U_12474,U_12473))],[f_3241_2]) ).

cnf(f_3241_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12474),sK292(U_12478,U_12477,U_12476,U_12475,U_12474,U_12473)),U_12475))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12474,U_12473),hAPP(hAPP(c_COMBS(U_12474,tc_fun(U_12476,tc_HOL_Obool),U_12473),hAPP(hAPP(c_COMBB(tc_fun(U_12476,U_12473),tc_fun(tc_fun(U_12476,tc_HOL_Obool),U_12473),U_12474),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12473)),U_12478)),U_12477)),U_12475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12474,U_12476),U_12473),hAPP(c_Product__Type_Oprod_Oprod__case(U_12474,U_12476,U_12473),U_12478)),hAPP(hAPP(c_Product__Type_OSigma(U_12474,U_12476),U_12475),U_12477))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12474),U_12475))
    | ~ class_Groups_Ocomm__monoid__add(U_12473) ),
    inference(clausify,[status(thm)],[f_3241_3]) ).

cnf(f_3241_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),hAPP(U_12477,sK292(U_12478,U_12477,U_12476,U_12475,U_12474,U_12473))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12474,U_12473),hAPP(hAPP(c_COMBS(U_12474,tc_fun(U_12476,tc_HOL_Obool),U_12473),hAPP(hAPP(c_COMBB(tc_fun(U_12476,U_12473),tc_fun(tc_fun(U_12476,tc_HOL_Obool),U_12473),U_12474),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12473)),U_12478)),U_12477)),U_12475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12474,U_12476),U_12473),hAPP(c_Product__Type_Oprod_Oprod__case(U_12474,U_12476,U_12473),U_12478)),hAPP(hAPP(c_Product__Type_OSigma(U_12474,U_12476),U_12475),U_12477))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12474),U_12475))
    | ~ class_Groups_Ocomm__monoid__add(U_12473) ),
    inference(clausify,[status(thm)],[f_3241_3]) ).

fof(f_3242_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_3242_2,plain,
    ! [U_12483,U_12482,U_12481,U_12480] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_12480,U_12482)),hAPP(hAPP(c_Product__Type_OSigma(U_12480,U_12482),U_12481),U_12483)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12480,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12482,tc_HOL_Obool),tc_Nat_Onat,U_12480),c_Finite__Set_Ocard(U_12482)),U_12483)),U_12481)
      | ? [U_12479] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),hAPP(U_12483,U_12479)))
          & hBOOL(hAPP(hAPP(c_member(U_12480),U_12479),U_12481)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12480),U_12481)) ),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

fof(f_3242_3,plain,
    ! [U_12483,U_12482,U_12481,U_12480] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_12480,U_12482)),hAPP(hAPP(c_Product__Type_OSigma(U_12480,U_12482),U_12481),U_12483)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12480,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12482,tc_HOL_Obool),tc_Nat_Onat,U_12480),c_Finite__Set_Ocard(U_12482)),U_12483)),U_12481)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),hAPP(U_12483,sK293(U_12483,U_12482,U_12481,U_12480))))
        & hBOOL(hAPP(hAPP(c_member(U_12480),sK293(U_12483,U_12482,U_12481,U_12480)),U_12481)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12480),U_12481)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_12479,sK293(U_12483,U_12482,U_12481,U_12480))],[f_3242_2]) ).

cnf(f_3242_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12480),sK293(U_12483,U_12482,U_12481,U_12480)),U_12481))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_12480,U_12482)),hAPP(hAPP(c_Product__Type_OSigma(U_12480,U_12482),U_12481),U_12483)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12480,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12482,tc_HOL_Obool),tc_Nat_Onat,U_12480),c_Finite__Set_Ocard(U_12482)),U_12483)),U_12481)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12480),U_12481)) ),
    inference(clausify,[status(thm)],[f_3242_3]) ).

cnf(f_3242_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),hAPP(U_12483,sK293(U_12483,U_12482,U_12481,U_12480))))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_12480,U_12482)),hAPP(hAPP(c_Product__Type_OSigma(U_12480,U_12482),U_12481),U_12483)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12480,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12482,tc_HOL_Obool),tc_Nat_Onat,U_12480),c_Finite__Set_Ocard(U_12482)),U_12483)),U_12481)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12480),U_12481)) ),
    inference(clausify,[status(thm)],[f_3242_3]) ).

fof(f_3243_1,plain,
    ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
      ( ? [B_x] :
          ( ? [B_y] :
              ( V_ca_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_ca_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_3243_2,plain,
    ! [U_12490,U_12489,U_12488,U_12487,U_12486] :
      ( ? [U_12485] :
          ( ? [U_12484] :
              ( U_12488 = hAPP(hAPP(c_Product__Type_OPair(U_12486,U_12487),U_12485),U_12484)
              & hBOOL(hAPP(hAPP(c_member(U_12487),U_12484),hAPP(U_12490,U_12485))) )
          & hBOOL(hAPP(hAPP(c_member(U_12486),U_12485),U_12489)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

fof(f_3243_3,plain,
    ! [U_12490,U_12489,U_12488,U_12487,U_12486] :
      ( ( ? [U_12484] :
            ( U_12488 = hAPP(hAPP(c_Product__Type_OPair(U_12486,U_12487),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),U_12484)
            & hBOOL(hAPP(hAPP(c_member(U_12487),U_12484),hAPP(U_12490,sK294(U_12490,U_12489,U_12488,U_12487,U_12486)))) )
        & hBOOL(hAPP(hAPP(c_member(U_12486),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),U_12489)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_12485,sK294(U_12490,U_12489,U_12488,U_12487,U_12486))],[f_3243_2]) ).

fof(f_3243_4,plain,
    ! [U_12490,U_12489,U_12488,U_12487,U_12486] :
      ( ( U_12488 = hAPP(hAPP(c_Product__Type_OPair(U_12486,U_12487),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),sK295(U_12490,U_12489,U_12488,U_12487,U_12486))
        & hBOOL(hAPP(hAPP(c_member(U_12487),sK295(U_12490,U_12489,U_12488,U_12487,U_12486)),hAPP(U_12490,sK294(U_12490,U_12489,U_12488,U_12487,U_12486))))
        & hBOOL(hAPP(hAPP(c_member(U_12486),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),U_12489)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_12484,sK295(U_12490,U_12489,U_12488,U_12487,U_12486))],[f_3243_3]) ).

cnf(f_3243_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12486),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),U_12489))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(clausify,[status(thm)],[f_3243_4]) ).

cnf(f_3243_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12487),sK295(U_12490,U_12489,U_12488,U_12487,U_12486)),hAPP(U_12490,sK294(U_12490,U_12489,U_12488,U_12487,U_12486))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(clausify,[status(thm)],[f_3243_4]) ).

cnf(f_3243_7,plain,
    ( U_12488 = hAPP(hAPP(c_Product__Type_OPair(U_12486,U_12487),sK294(U_12490,U_12489,U_12488,U_12487,U_12486)),sK295(U_12490,U_12489,U_12488,U_12487,U_12486))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12486,U_12487)),U_12488),hAPP(hAPP(c_Product__Type_OSigma(U_12486,U_12487),U_12489),U_12490))) ),
    inference(clausify,[status(thm)],[f_3243_4]) ).

fof(f_3244_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_3244_2,plain,
    ! [U_12496,U_12495,U_12494,U_12493,U_12492,U_12491] :
      ( hAPP(c_Set_Oimage(tc_prod(U_12491,U_12494),tc_prod(U_12492,U_12495),c_Product__Type_Omap__pair(U_12491,U_12492,U_12494,U_12495,U_12493,U_12496)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12491,U_12494),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12492,U_12495),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_12494,U_12495,U_12496),c_Orderings_Otop__class_Otop(tc_fun(U_12494,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12495,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_12491,U_12492,U_12493),c_Orderings_Otop__class_Otop(tc_fun(U_12491,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12492,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

cnf(f_3244_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12491,U_12494),tc_prod(U_12492,U_12495),c_Product__Type_Omap__pair(U_12491,U_12492,U_12494,U_12495,U_12493,U_12496)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12491,U_12494),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12492,U_12495),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_12494,U_12495,U_12496),c_Orderings_Otop__class_Otop(tc_fun(U_12494,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12495,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_12491,U_12492,U_12493),c_Orderings_Otop__class_Otop(tc_fun(U_12491,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12492,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3244_2]) ).

fof(f_3245_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_3245_2,plain,
    ! [U_12504,U_12503,U_12502,U_12501,U_12500,U_12499,U_12498,U_12497] :
      ( c_Fun_Oinj__on(tc_prod(U_12497,U_12501),tc_prod(U_12498,U_12502),c_Product__Type_Omap__pair(U_12497,U_12498,U_12501,U_12502,U_12499,U_12503),hAPP(hAPP(c_Product__Type_OSigma(U_12497,U_12501),U_12500),hAPP(c_COMBK(tc_fun(U_12501,tc_HOL_Obool),U_12497),U_12504)))
      | ~ c_Fun_Oinj__on(U_12501,U_12502,U_12503,U_12504)
      | ~ c_Fun_Oinj__on(U_12497,U_12498,U_12499,U_12500) ),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

cnf(f_3245_3,plain,
    ( c_Fun_Oinj__on(tc_prod(U_12497,U_12501),tc_prod(U_12498,U_12502),c_Product__Type_Omap__pair(U_12497,U_12498,U_12501,U_12502,U_12499,U_12503),hAPP(hAPP(c_Product__Type_OSigma(U_12497,U_12501),U_12500),hAPP(c_COMBK(tc_fun(U_12501,tc_HOL_Obool),U_12497),U_12504)))
    | ~ c_Fun_Oinj__on(U_12501,U_12502,U_12503,U_12504)
    | ~ c_Fun_Oinj__on(U_12497,U_12498,U_12499,U_12500) ),
    inference(clausify,[status(thm)],[f_3245_2]) ).

fof(f_3246_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_3246_2,plain,
    ! [U_12513,U_12512,U_12511,U_12510,U_12509,U_12508,U_12507,U_12506,U_12505] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12510,U_12511)),hAPP(hAPP(c_Product__Type_OPair(U_12510,U_12511),hAPP(U_12512,U_12507)),hAPP(U_12513,U_12508))),hAPP(c_Set_Oimage(tc_prod(U_12505,U_12506),tc_prod(U_12510,U_12511),c_Product__Type_Omap__pair(U_12505,U_12510,U_12506,U_12511,U_12512,U_12513)),U_12509)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12505,U_12506)),hAPP(hAPP(c_Product__Type_OPair(U_12505,U_12506),U_12507),U_12508)),U_12509)) ),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

cnf(f_3246_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12510,U_12511)),hAPP(hAPP(c_Product__Type_OPair(U_12510,U_12511),hAPP(U_12512,U_12507)),hAPP(U_12513,U_12508))),hAPP(c_Set_Oimage(tc_prod(U_12505,U_12506),tc_prod(U_12510,U_12511),c_Product__Type_Omap__pair(U_12505,U_12510,U_12506,U_12511,U_12512,U_12513)),U_12509)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12505,U_12506)),hAPP(hAPP(c_Product__Type_OPair(U_12505,U_12506),U_12507),U_12508)),U_12509)) ),
    inference(clausify,[status(thm)],[f_3246_2]) ).

fof(f_3247_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_3247_2,plain,
    ! [U_12521,U_12520,U_12519,U_12518,U_12517,U_12516,U_12515,U_12514] : hAPP(c_Product__Type_Omap__pair(U_12514,U_12515,U_12516,U_12517,U_12518,U_12519),hAPP(hAPP(c_Product__Type_OPair(U_12514,U_12516),U_12520),U_12521)) = hAPP(hAPP(c_Product__Type_OPair(U_12515,U_12517),hAPP(U_12518,U_12520)),hAPP(U_12519,U_12521)),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

cnf(f_3247_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_12514,U_12515,U_12516,U_12517,U_12518,U_12519),hAPP(hAPP(c_Product__Type_OPair(U_12514,U_12516),U_12520),U_12521)) = hAPP(hAPP(c_Product__Type_OPair(U_12515,U_12517),hAPP(U_12518,U_12520)),hAPP(U_12519,U_12521)),
    inference(clausify,[status(thm)],[f_3247_2]) ).

fof(f_3248_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_3248_2,plain,
    ! [U_12528,U_12527,U_12526,U_12525,U_12524,U_12523,U_12522] : hAPP(c_Product__Type_Ofst(U_12522,U_12523),hAPP(c_Product__Type_Omap__pair(U_12524,U_12522,U_12525,U_12523,U_12526,U_12527),U_12528)) = hAPP(U_12526,hAPP(c_Product__Type_Ofst(U_12524,U_12525),U_12528)),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

cnf(f_3248_3,plain,
    hAPP(c_Product__Type_Ofst(U_12522,U_12523),hAPP(c_Product__Type_Omap__pair(U_12524,U_12522,U_12525,U_12523,U_12526,U_12527),U_12528)) = hAPP(U_12526,hAPP(c_Product__Type_Ofst(U_12524,U_12525),U_12528)),
    inference(clausify,[status(thm)],[f_3248_2]) ).

fof(f_3249_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_3249_2,plain,
    ! [U_12535,U_12534,U_12533,U_12532,U_12531,U_12530,U_12529] : hAPP(c_Product__Type_Osnd(U_12529,U_12530),hAPP(c_Product__Type_Omap__pair(U_12531,U_12529,U_12532,U_12530,U_12533,U_12534),U_12535)) = hAPP(U_12534,hAPP(c_Product__Type_Osnd(U_12531,U_12532),U_12535)),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

cnf(f_3249_3,plain,
    hAPP(c_Product__Type_Osnd(U_12529,U_12530),hAPP(c_Product__Type_Omap__pair(U_12531,U_12529,U_12532,U_12530,U_12533,U_12534),U_12535)) = hAPP(U_12534,hAPP(c_Product__Type_Osnd(U_12531,U_12532),U_12535)),
    inference(clausify,[status(thm)],[f_3249_2]) ).

fof(f_3250_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_3250_2,plain,
    ! [U_12538,U_12537,U_12536] : hAPP(c_Product__Type_Omap__pair(U_12536,U_12536,U_12537,U_12537,c_COMBI(U_12536),c_COMBI(U_12537)),U_12538) = U_12538,
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

cnf(f_3250_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_12536,U_12536,U_12537,U_12537,c_COMBI(U_12536),c_COMBI(U_12537)),U_12538) = U_12538,
    inference(clausify,[status(thm)],[f_3250_2]) ).

fof(f_3251_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_3251_2,plain,
    ! [U_12544,U_12543,U_12542,U_12541,U_12540,U_12539] : c_Product__Type_Omap__pair(U_12539,U_12540,U_12541,U_12542,U_12543,U_12544) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12539,U_12541,tc_prod(U_12540,U_12542)),hAPP(hAPP(c_COMBC(U_12539,tc_fun(U_12541,U_12542),tc_fun(U_12541,tc_prod(U_12540,U_12542))),hAPP(hAPP(c_COMBB(tc_fun(U_12542,tc_prod(U_12540,U_12542)),tc_fun(tc_fun(U_12541,U_12542),tc_fun(U_12541,tc_prod(U_12540,U_12542))),U_12539),c_COMBB(U_12542,tc_prod(U_12540,U_12542),U_12541)),hAPP(hAPP(c_COMBB(U_12540,tc_fun(U_12542,tc_prod(U_12540,U_12542)),U_12539),c_Product__Type_OPair(U_12540,U_12542)),U_12543))),U_12544)),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

cnf(f_3251_3,plain,
    c_Product__Type_Omap__pair(U_12539,U_12540,U_12541,U_12542,U_12543,U_12544) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12539,U_12541,tc_prod(U_12540,U_12542)),hAPP(hAPP(c_COMBC(U_12539,tc_fun(U_12541,U_12542),tc_fun(U_12541,tc_prod(U_12540,U_12542))),hAPP(hAPP(c_COMBB(tc_fun(U_12542,tc_prod(U_12540,U_12542)),tc_fun(tc_fun(U_12541,U_12542),tc_fun(U_12541,tc_prod(U_12540,U_12542))),U_12539),c_COMBB(U_12542,tc_prod(U_12540,U_12542),U_12541)),hAPP(hAPP(c_COMBB(U_12540,tc_fun(U_12542,tc_prod(U_12540,U_12542)),U_12539),c_Product__Type_OPair(U_12540,U_12542)),U_12543))),U_12544)),
    inference(clausify,[status(thm)],[f_3251_2]) ).

fof(f_3252_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_3252_2,plain,
    ! [U_12554,U_12553,U_12552,U_12551,U_12550,U_12549,U_12548,U_12547,U_12546,U_12545] :
      ( hAPP(c_Set_Oimage(tc_prod(U_12545,U_12550),tc_prod(U_12546,U_12551),c_Product__Type_Omap__pair(U_12545,U_12546,U_12550,U_12551,U_12547,U_12552)),hAPP(hAPP(c_Product__Type_OSigma(U_12545,U_12550),U_12548),hAPP(c_COMBK(tc_fun(U_12550,tc_HOL_Obool),U_12545),U_12553))) = hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12551),U_12549),hAPP(c_COMBK(tc_fun(U_12551,tc_HOL_Obool),U_12546),U_12554))
      | hAPP(c_Set_Oimage(U_12550,U_12551,U_12552),U_12553) != U_12554
      | hAPP(c_Set_Oimage(U_12545,U_12546,U_12547),U_12548) != U_12549 ),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

cnf(f_3252_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12545,U_12550),tc_prod(U_12546,U_12551),c_Product__Type_Omap__pair(U_12545,U_12546,U_12550,U_12551,U_12547,U_12552)),hAPP(hAPP(c_Product__Type_OSigma(U_12545,U_12550),U_12548),hAPP(c_COMBK(tc_fun(U_12550,tc_HOL_Obool),U_12545),U_12553))) = hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12551),U_12549),hAPP(c_COMBK(tc_fun(U_12551,tc_HOL_Obool),U_12546),U_12554))
    | hAPP(c_Set_Oimage(U_12550,U_12551,U_12552),U_12553) != U_12554
    | hAPP(c_Set_Oimage(U_12545,U_12546,U_12547),U_12548) != U_12549 ),
    inference(clausify,[status(thm)],[f_3252_2]) ).

fof(f_3253_1,plain,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_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_ca_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_ca_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_3253_2,plain,
    ! [U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557] :
      ( ? [U_12556,U_12555] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12560,U_12561)),hAPP(hAPP(c_Product__Type_OPair(U_12560,U_12561),U_12556),U_12555)),U_12564))
          & U_12559 = hAPP(hAPP(c_Product__Type_OPair(U_12557,U_12558),hAPP(U_12562,U_12556)),hAPP(U_12563,U_12555)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12557,U_12558)),U_12559),hAPP(c_Set_Oimage(tc_prod(U_12560,U_12561),tc_prod(U_12557,U_12558),c_Product__Type_Omap__pair(U_12560,U_12557,U_12561,U_12558,U_12562,U_12563)),U_12564))) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

fof(f_3253_3,plain,
    ! [U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557] :
      ( ? [U_12555] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12560,U_12561)),hAPP(hAPP(c_Product__Type_OPair(U_12560,U_12561),sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557)),U_12555)),U_12564))
          & U_12559 = hAPP(hAPP(c_Product__Type_OPair(U_12557,U_12558),hAPP(U_12562,sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))),hAPP(U_12563,U_12555)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12557,U_12558)),U_12559),hAPP(c_Set_Oimage(tc_prod(U_12560,U_12561),tc_prod(U_12557,U_12558),c_Product__Type_Omap__pair(U_12560,U_12557,U_12561,U_12558,U_12562,U_12563)),U_12564))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_12556,sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))],[f_3253_2]) ).

fof(f_3253_4,plain,
    ! [U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12560,U_12561)),hAPP(hAPP(c_Product__Type_OPair(U_12560,U_12561),sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557)),sK297(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))),U_12564))
        & U_12559 = hAPP(hAPP(c_Product__Type_OPair(U_12557,U_12558),hAPP(U_12562,sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))),hAPP(U_12563,sK297(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12557,U_12558)),U_12559),hAPP(c_Set_Oimage(tc_prod(U_12560,U_12561),tc_prod(U_12557,U_12558),c_Product__Type_Omap__pair(U_12560,U_12557,U_12561,U_12558,U_12562,U_12563)),U_12564))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_12555,sK297(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))],[f_3253_3]) ).

cnf(f_3253_5,plain,
    ( U_12559 = hAPP(hAPP(c_Product__Type_OPair(U_12557,U_12558),hAPP(U_12562,sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))),hAPP(U_12563,sK297(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12557,U_12558)),U_12559),hAPP(c_Set_Oimage(tc_prod(U_12560,U_12561),tc_prod(U_12557,U_12558),c_Product__Type_Omap__pair(U_12560,U_12557,U_12561,U_12558,U_12562,U_12563)),U_12564))) ),
    inference(clausify,[status(thm)],[f_3253_4]) ).

cnf(f_3253_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12560,U_12561)),hAPP(hAPP(c_Product__Type_OPair(U_12560,U_12561),sK296(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557)),sK297(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559,U_12558,U_12557))),U_12564))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12557,U_12558)),U_12559),hAPP(c_Set_Oimage(tc_prod(U_12560,U_12561),tc_prod(U_12557,U_12558),c_Product__Type_Omap__pair(U_12560,U_12557,U_12561,U_12558,U_12562,U_12563)),U_12564))) ),
    inference(clausify,[status(thm)],[f_3253_4]) ).

fof(f_3254_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_3254_2,plain,
    ! [U_12569,U_12568,U_12567] :
      ( ( c_Relation_Orefl__on(U_12567,U_12568,U_12569)
        | ? [U_12566] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12567,U_12567)),hAPP(hAPP(c_Product__Type_OPair(U_12567,U_12567),U_12566),U_12566)),U_12569))
            & hBOOL(hAPP(hAPP(c_member(U_12567),U_12566),U_12568)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12567,U_12567),tc_HOL_Obool)),U_12569),hAPP(hAPP(c_Product__Type_OSigma(U_12567,U_12567),U_12568),hAPP(c_COMBK(tc_fun(U_12567,tc_HOL_Obool),U_12567),U_12568)))) )
      & ( ( ! [U_12565] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12567,U_12567)),hAPP(hAPP(c_Product__Type_OPair(U_12567,U_12567),U_12565),U_12565)),U_12569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12567),U_12565),U_12568)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12567,U_12567),tc_HOL_Obool)),U_12569),hAPP(hAPP(c_Product__Type_OSigma(U_12567,U_12567),U_12568),hAPP(c_COMBK(tc_fun(U_12567,tc_HOL_Obool),U_12567),U_12568)))) )
        | ~ c_Relation_Orefl__on(U_12567,U_12568,U_12569) ) ),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

fof(f_3254_3,plain,
    ( ! [U_12575,U_12573,U_12571] :
        ( c_Relation_Orefl__on(U_12571,U_12573,U_12575)
        | ? [U_12566] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12571,U_12571)),hAPP(hAPP(c_Product__Type_OPair(U_12571,U_12571),U_12566),U_12566)),U_12575))
            & hBOOL(hAPP(hAPP(c_member(U_12571),U_12566),U_12573)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12571,U_12571),tc_HOL_Obool)),U_12575),hAPP(hAPP(c_Product__Type_OSigma(U_12571,U_12571),U_12573),hAPP(c_COMBK(tc_fun(U_12571,tc_HOL_Obool),U_12571),U_12573)))) )
    & ! [U_12574,U_12572,U_12570] :
        ( ( ! [U_12565] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12570,U_12570)),hAPP(hAPP(c_Product__Type_OPair(U_12570,U_12570),U_12565),U_12565)),U_12574))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12565),U_12572)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12570,U_12570),tc_HOL_Obool)),U_12574),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12570),U_12572),hAPP(c_COMBK(tc_fun(U_12570,tc_HOL_Obool),U_12570),U_12572)))) )
        | ~ c_Relation_Orefl__on(U_12570,U_12572,U_12574) ) ),
    inference(miniscope,[status(thm)],[f_3254_2]) ).

fof(f_3254_4,plain,
    ( ! [U_12575,U_12573,U_12571] :
        ( c_Relation_Orefl__on(U_12571,U_12573,U_12575)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12571,U_12571)),hAPP(hAPP(c_Product__Type_OPair(U_12571,U_12571),sK298(U_12575,U_12573,U_12571)),sK298(U_12575,U_12573,U_12571))),U_12575))
          & hBOOL(hAPP(hAPP(c_member(U_12571),sK298(U_12575,U_12573,U_12571)),U_12573)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12571,U_12571),tc_HOL_Obool)),U_12575),hAPP(hAPP(c_Product__Type_OSigma(U_12571,U_12571),U_12573),hAPP(c_COMBK(tc_fun(U_12571,tc_HOL_Obool),U_12571),U_12573)))) )
    & ! [U_12574,U_12572,U_12570] :
        ( ( ! [U_12565] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12570,U_12570)),hAPP(hAPP(c_Product__Type_OPair(U_12570,U_12570),U_12565),U_12565)),U_12574))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12565),U_12572)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12570,U_12570),tc_HOL_Obool)),U_12574),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12570),U_12572),hAPP(c_COMBK(tc_fun(U_12570,tc_HOL_Obool),U_12570),U_12572)))) )
        | ~ c_Relation_Orefl__on(U_12570,U_12572,U_12574) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_12566,sK298(U_12575,U_12573,U_12571))],[f_3254_3]) ).

cnf(f_3254_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12570,U_12570),tc_HOL_Obool)),U_12574),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12570),U_12572),hAPP(c_COMBK(tc_fun(U_12570,tc_HOL_Obool),U_12570),U_12572))))
    | ~ c_Relation_Orefl__on(U_12570,U_12572,U_12574) ),
    inference(clausify,[status(thm)],[f_3254_4]) ).

cnf(f_3254_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12570,U_12570)),hAPP(hAPP(c_Product__Type_OPair(U_12570,U_12570),U_12565),U_12565)),U_12574))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12565),U_12572))
    | ~ c_Relation_Orefl__on(U_12570,U_12572,U_12574) ),
    inference(clausify,[status(thm)],[f_3254_4]) ).

cnf(f_3254_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12571),sK298(U_12575,U_12573,U_12571)),U_12573))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12571,U_12571),tc_HOL_Obool)),U_12575),hAPP(hAPP(c_Product__Type_OSigma(U_12571,U_12571),U_12573),hAPP(c_COMBK(tc_fun(U_12571,tc_HOL_Obool),U_12571),U_12573))))
    | c_Relation_Orefl__on(U_12571,U_12573,U_12575) ),
    inference(clausify,[status(thm)],[f_3254_4]) ).

cnf(f_3254_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12571,U_12571)),hAPP(hAPP(c_Product__Type_OPair(U_12571,U_12571),sK298(U_12575,U_12573,U_12571)),sK298(U_12575,U_12573,U_12571))),U_12575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12571,U_12571),tc_HOL_Obool)),U_12575),hAPP(hAPP(c_Product__Type_OSigma(U_12571,U_12571),U_12573),hAPP(c_COMBK(tc_fun(U_12571,tc_HOL_Obool),U_12571),U_12573))))
    | c_Relation_Orefl__on(U_12571,U_12573,U_12575) ),
    inference(clausify,[status(thm)],[f_3254_4]) ).

fof(f_3255_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_3255_2,plain,
    ! [U_12582,U_12581,U_12580,U_12579,U_12578,U_12577] :
      ( c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12578,tc_fun(U_12579,tc_HOL_Obool)),U_12577),U_12582))
      | ? [U_12576] :
          ( ~ c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(U_12582,U_12576))
          & hBOOL(hAPP(hAPP(c_member(U_12578),U_12576),U_12577)) )
      | U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

fof(f_3255_3,plain,
    ! [U_12582,U_12581,U_12580,U_12579,U_12578,U_12577] :
      ( c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12578,tc_fun(U_12579,tc_HOL_Obool)),U_12577),U_12582))
      | ( ~ c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(U_12582,sK299(U_12582,U_12581,U_12580,U_12579,U_12578,U_12577)))
        & hBOOL(hAPP(hAPP(c_member(U_12578),sK299(U_12582,U_12581,U_12580,U_12579,U_12578,U_12577)),U_12577)) )
      | U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_12576,sK299(U_12582,U_12581,U_12580,U_12579,U_12578,U_12577))],[f_3255_2]) ).

cnf(f_3255_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12578),sK299(U_12582,U_12581,U_12580,U_12579,U_12578,U_12577)),U_12577))
    | c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12578,tc_fun(U_12579,tc_HOL_Obool)),U_12577),U_12582))
    | U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

cnf(f_3255_5,plain,
    ( ~ c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(U_12582,sK299(U_12582,U_12581,U_12580,U_12579,U_12578,U_12577)))
    | c_Fun_Oinj__on(U_12579,U_12580,U_12581,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12578,tc_fun(U_12579,tc_HOL_Obool)),U_12577),U_12582))
    | U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

fof(f_3256_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_3256_2,plain,
    ! [U_12584,U_12583] : c_Relation_Orefl__on(U_12583,U_12584,c_Relation_OId__on(U_12583,U_12584)),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

cnf(f_3256_3,plain,
    c_Relation_Orefl__on(U_12583,U_12584,c_Relation_OId__on(U_12583,U_12584)),
    inference(clausify,[status(thm)],[f_3256_2]) ).

fof(f_3257_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_3257_2,plain,
    ! [U_12585] : c_Relation_Orefl__on(U_12585,c_Orderings_Obot__class_Obot(tc_fun(U_12585,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12585,U_12585),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

cnf(f_3257_3,plain,
    c_Relation_Orefl__on(U_12585,c_Orderings_Obot__class_Obot(tc_fun(U_12585,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12585,U_12585),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3257_2]) ).

fof(f_3258_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_3258_2,plain,
    ! [U_12590,U_12589,U_12588,U_12587,U_12586] :
      ( c_Relation_Orefl__on(U_12586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12586,tc_HOL_Obool)),U_12587),U_12589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12586,U_12586),tc_HOL_Obool)),U_12588),U_12590))
      | ~ c_Relation_Orefl__on(U_12586,U_12589,U_12590)
      | ~ c_Relation_Orefl__on(U_12586,U_12587,U_12588) ),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

cnf(f_3258_3,plain,
    ( c_Relation_Orefl__on(U_12586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12586,tc_HOL_Obool)),U_12587),U_12589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12586,U_12586),tc_HOL_Obool)),U_12588),U_12590))
    | ~ c_Relation_Orefl__on(U_12586,U_12589,U_12590)
    | ~ c_Relation_Orefl__on(U_12586,U_12587,U_12588) ),
    inference(clausify,[status(thm)],[f_3258_2]) ).

fof(f_3259_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_3259_2,plain,
    ! [U_12595,U_12594,U_12593,U_12592,U_12591] :
      ( c_Relation_Orefl__on(U_12591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12591,tc_HOL_Obool)),U_12592),U_12594),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12591,U_12591),tc_HOL_Obool)),U_12593),U_12595))
      | ~ c_Relation_Orefl__on(U_12591,U_12594,U_12595)
      | ~ c_Relation_Orefl__on(U_12591,U_12592,U_12593) ),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

cnf(f_3259_3,plain,
    ( c_Relation_Orefl__on(U_12591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12591,tc_HOL_Obool)),U_12592),U_12594),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12591,U_12591),tc_HOL_Obool)),U_12593),U_12595))
    | ~ c_Relation_Orefl__on(U_12591,U_12594,U_12595)
    | ~ c_Relation_Orefl__on(U_12591,U_12592,U_12593) ),
    inference(clausify,[status(thm)],[f_3259_2]) ).

fof(f_3260_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_3260_2,plain,
    ! [U_12600,U_12599,U_12598,U_12597,U_12596] :
      ( hBOOL(hAPP(hAPP(c_member(U_12596),U_12600),U_12597))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12596,U_12596)),hAPP(hAPP(c_Product__Type_OPair(U_12596,U_12596),U_12599),U_12600)),U_12598))
      | ~ c_Relation_Orefl__on(U_12596,U_12597,U_12598) ),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

cnf(f_3260_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12596),U_12600),U_12597))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12596,U_12596)),hAPP(hAPP(c_Product__Type_OPair(U_12596,U_12596),U_12599),U_12600)),U_12598))
    | ~ c_Relation_Orefl__on(U_12596,U_12597,U_12598) ),
    inference(clausify,[status(thm)],[f_3260_2]) ).

fof(f_3261_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_3261_2,plain,
    ! [U_12605,U_12604,U_12603,U_12602,U_12601] :
      ( hBOOL(hAPP(hAPP(c_member(U_12601),U_12604),U_12602))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12601,U_12601)),hAPP(hAPP(c_Product__Type_OPair(U_12601,U_12601),U_12604),U_12605)),U_12603))
      | ~ c_Relation_Orefl__on(U_12601,U_12602,U_12603) ),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

cnf(f_3261_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12601),U_12604),U_12602))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12601,U_12601)),hAPP(hAPP(c_Product__Type_OPair(U_12601,U_12601),U_12604),U_12605)),U_12603))
    | ~ c_Relation_Orefl__on(U_12601,U_12602,U_12603) ),
    inference(clausify,[status(thm)],[f_3261_2]) ).

fof(f_3262_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_3262_2,plain,
    ! [U_12609,U_12608,U_12607,U_12606] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12606,U_12606)),hAPP(hAPP(c_Product__Type_OPair(U_12606,U_12606),U_12609),U_12609)),U_12608))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12606),U_12609),U_12607))
      | ~ c_Relation_Orefl__on(U_12606,U_12607,U_12608) ),
    inference(variable_rename,[status(thm)],[f_3262_1]) ).

cnf(f_3262_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12606,U_12606)),hAPP(hAPP(c_Product__Type_OPair(U_12606,U_12606),U_12609),U_12609)),U_12608))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12606),U_12609),U_12607))
    | ~ c_Relation_Orefl__on(U_12606,U_12607,U_12608) ),
    inference(clausify,[status(thm)],[f_3262_2]) ).

fof(f_3263_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_3263_2,plain,
    ! [U_12613,U_12612,U_12611] :
      ( c_Relation_Orefl__on(U_12611,U_12613,U_12612)
      | ? [U_12610] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12611,U_12611)),hAPP(hAPP(c_Product__Type_OPair(U_12611,U_12611),U_12610),U_12610)),U_12612))
          & hBOOL(hAPP(hAPP(c_member(U_12611),U_12610),U_12613)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12611,U_12611),tc_HOL_Obool)),U_12612),hAPP(hAPP(c_Product__Type_OSigma(U_12611,U_12611),U_12613),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12611),U_12613)))) ),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

fof(f_3263_3,plain,
    ! [U_12613,U_12612,U_12611] :
      ( c_Relation_Orefl__on(U_12611,U_12613,U_12612)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12611,U_12611)),hAPP(hAPP(c_Product__Type_OPair(U_12611,U_12611),sK300(U_12613,U_12612,U_12611)),sK300(U_12613,U_12612,U_12611))),U_12612))
        & hBOOL(hAPP(hAPP(c_member(U_12611),sK300(U_12613,U_12612,U_12611)),U_12613)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12611,U_12611),tc_HOL_Obool)),U_12612),hAPP(hAPP(c_Product__Type_OSigma(U_12611,U_12611),U_12613),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12611),U_12613)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_12610,sK300(U_12613,U_12612,U_12611))],[f_3263_2]) ).

cnf(f_3263_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12611),sK300(U_12613,U_12612,U_12611)),U_12613))
    | c_Relation_Orefl__on(U_12611,U_12613,U_12612)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12611,U_12611),tc_HOL_Obool)),U_12612),hAPP(hAPP(c_Product__Type_OSigma(U_12611,U_12611),U_12613),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12611),U_12613)))) ),
    inference(clausify,[status(thm)],[f_3263_3]) ).

cnf(f_3263_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12611,U_12611)),hAPP(hAPP(c_Product__Type_OPair(U_12611,U_12611),sK300(U_12613,U_12612,U_12611)),sK300(U_12613,U_12612,U_12611))),U_12612))
    | c_Relation_Orefl__on(U_12611,U_12613,U_12612)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12611,U_12611),tc_HOL_Obool)),U_12612),hAPP(hAPP(c_Product__Type_OSigma(U_12611,U_12611),U_12613),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12611),U_12613)))) ),
    inference(clausify,[status(thm)],[f_3263_3]) ).

fof(f_3264_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_3264_2,plain,
    ! [U_12615,U_12614] :
      ( 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_12614))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12615)))) = 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_12614))),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_12615)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12614)) ),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

cnf(f_3264_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_12614))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12615)))) = 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_12614))),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_12615)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12614)) ),
    inference(clausify,[status(thm)],[f_3264_2]) ).

fof(f_3265_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_3265_2,plain,
    ! [U_12617,U_12616] :
      ( 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_12616))),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_12617))))) != 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_12616)) ),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

cnf(f_3265_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_12616))),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_12617))))) != 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_12616)) ),
    inference(clausify,[status(thm)],[f_3265_2]) ).

fof(f_3266_1,plain,
    ! [T_b,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
      | ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_CollectI]) ).

fof(f_3266_2,plain,
    ! [U_12620,U_12619,U_12618] :
      ( hBOOL(hAPP(hAPP(c_member(U_12620),U_12619),hAPP(c_Set_OCollect(U_12620),U_12618)))
      | ~ hBOOL(hAPP(U_12618,U_12619)) ),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

cnf(f_3266_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12620),U_12619),hAPP(c_Set_OCollect(U_12620),U_12618)))
    | ~ hBOOL(hAPP(U_12618,U_12619)) ),
    inference(clausify,[status(thm)],[f_3266_2]) ).

fof(f_3267_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).

fof(f_3267_2,plain,
    ! [U_12623,U_12622,U_12621] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),hAPP(hAPP(c_COMBS(U_12621,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12621),c_fconj),U_12622)),U_12623))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),U_12623)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),U_12622))) ) ),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

cnf(f_3267_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),U_12622)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),hAPP(hAPP(c_COMBS(U_12621,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12621),c_fconj),U_12622)),U_12623)))) ),
    inference(clausify,[status(thm)],[f_3267_2]) ).

cnf(f_3267_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),U_12623)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),hAPP(c_Set_OCollect(U_12621),hAPP(hAPP(c_COMBS(U_12621,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12621),c_fconj),U_12622)),U_12623)))) ),
    inference(clausify,[status(thm)],[f_3267_2]) ).

fof(f_3268_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_3268_2,plain,
    ! [U_12624] : 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_12624)))),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

cnf(f_3268_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_12624)))),
    inference(clausify,[status(thm)],[f_3268_2]) ).

fof(f_3269_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_3269_2,plain,
    ! [U_12625] : 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_12625)))),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

cnf(f_3269_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_12625)))),
    inference(clausify,[status(thm)],[f_3269_2]) ).

fof(f_3270_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectE]) ).

fof(f_3270_2,plain,
    ! [U_12628,U_12627,U_12626] :
      ( hBOOL(hAPP(U_12628,U_12627))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12626),U_12627),hAPP(c_Set_OCollect(U_12626),U_12628))) ),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

fof(f_3270_3,plain,
    ! [U_12628,U_12627] :
      ( ! [U_12626] : ~ hBOOL(hAPP(hAPP(c_member(U_12626),U_12627),hAPP(c_Set_OCollect(U_12626),U_12628)))
      | hBOOL(hAPP(U_12628,U_12627)) ),
    inference(miniscope,[status(thm)],[f_3270_2]) ).

cnf(f_3270_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12626),U_12627),hAPP(c_Set_OCollect(U_12626),U_12628)))
    | hBOOL(hAPP(U_12628,U_12627)) ),
    inference(clausify,[status(thm)],[f_3270_3]) ).

fof(f_3271_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectD]) ).

fof(f_3271_2,plain,
    ! [U_12631,U_12630,U_12629] :
      ( hBOOL(hAPP(U_12631,U_12630))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12629),U_12630),hAPP(c_Set_OCollect(U_12629),U_12631))) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

fof(f_3271_3,plain,
    ! [U_12631,U_12630] :
      ( ! [U_12629] : ~ hBOOL(hAPP(hAPP(c_member(U_12629),U_12630),hAPP(c_Set_OCollect(U_12629),U_12631)))
      | hBOOL(hAPP(U_12631,U_12630)) ),
    inference(miniscope,[status(thm)],[f_3271_2]) ).

cnf(f_3271_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12629),U_12630),hAPP(c_Set_OCollect(U_12629),U_12631)))
    | hBOOL(hAPP(U_12631,U_12630)) ),
    inference(clausify,[status(thm)],[f_3271_3]) ).

fof(f_3272_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
        | ~ hBOOL(hAPP(V_Pa_2,V_a_2)) )
      & ( hBOOL(hAPP(V_Pa_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).

fof(f_3272_2,plain,
    ! [U_12634,U_12633,U_12632] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12632),U_12633),hAPP(c_Set_OCollect(U_12632),U_12634)))
        | ~ hBOOL(hAPP(U_12634,U_12633)) )
      & ( hBOOL(hAPP(U_12634,U_12633))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12632),U_12633),hAPP(c_Set_OCollect(U_12632),U_12634))) ) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

fof(f_3272_3,plain,
    ( ! [U_12640,U_12638] :
        ( ! [U_12636] : hBOOL(hAPP(hAPP(c_member(U_12636),U_12638),hAPP(c_Set_OCollect(U_12636),U_12640)))
        | ~ hBOOL(hAPP(U_12640,U_12638)) )
    & ! [U_12639,U_12637] :
        ( ! [U_12635] : ~ hBOOL(hAPP(hAPP(c_member(U_12635),U_12637),hAPP(c_Set_OCollect(U_12635),U_12639)))
        | hBOOL(hAPP(U_12639,U_12637)) ) ),
    inference(miniscope,[status(thm)],[f_3272_2]) ).

cnf(f_3272_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12635),U_12637),hAPP(c_Set_OCollect(U_12635),U_12639)))
    | hBOOL(hAPP(U_12639,U_12637)) ),
    inference(clausify,[status(thm)],[f_3272_3]) ).

cnf(f_3272_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12636),U_12638),hAPP(c_Set_OCollect(U_12636),U_12640)))
    | ~ hBOOL(hAPP(U_12640,U_12638)) ),
    inference(clausify,[status(thm)],[f_3272_3]) ).

fof(f_3273_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_3273_2,plain,
    ! [U_12642,U_12641] : hAPP(c_Set_OCollect(U_12641),hAPP(hAPP(c_COMBC(U_12641,tc_fun(U_12641,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12641)),U_12642)) = U_12642,
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

cnf(f_3273_3,plain,
    hAPP(c_Set_OCollect(U_12641),hAPP(hAPP(c_COMBC(U_12641,tc_fun(U_12641,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12641)),U_12642)) = U_12642,
    inference(clausify,[status(thm)],[f_3273_2]) ).

fof(f_3274_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).

fof(f_3274_2,plain,
    ! [U_12645,U_12644,U_12643] : hAPP(c_Set_OCollect(U_12643),hAPP(hAPP(c_COMBS(U_12643,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12643),c_fconj),U_12644)),U_12645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12643,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12643),U_12644)),hAPP(c_Set_OCollect(U_12643),U_12645)),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

cnf(f_3274_3,plain,
    hAPP(c_Set_OCollect(U_12643),hAPP(hAPP(c_COMBS(U_12643,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12643),c_fconj),U_12644)),U_12645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12643,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12643),U_12644)),hAPP(c_Set_OCollect(U_12643),U_12645)),
    inference(clausify,[status(thm)],[f_3274_2]) ).

fof(f_3275_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).

fof(f_3275_2,plain,
    ! [U_12648,U_12647,U_12646] : hAPP(c_Set_OCollect(U_12646),hAPP(hAPP(c_COMBS(U_12646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12646),c_fdisj),U_12647)),U_12648)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12646,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12646),U_12647)),hAPP(c_Set_OCollect(U_12646),U_12648)),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

cnf(f_3275_3,plain,
    hAPP(c_Set_OCollect(U_12646),hAPP(hAPP(c_COMBS(U_12646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12646),c_fdisj),U_12647)),U_12648)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12646,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12646),U_12647)),hAPP(c_Set_OCollect(U_12646),U_12648)),
    inference(clausify,[status(thm)],[f_3275_2]) ).

fof(f_3276_1,plain,
    ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).

fof(f_3276_2,plain,
    ! [U_12651,U_12650,U_12649] : hAPP(hAPP(c_Set_Oinsert(U_12649),U_12650),hAPP(c_Set_OCollect(U_12649),U_12651)) = hAPP(c_Set_OCollect(U_12649),hAPP(hAPP(c_COMBS(U_12649,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12649),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12649),c_fNot),hAPP(hAPP(c_COMBC(U_12649,U_12649,tc_HOL_Obool),c_fequal),U_12650)))),U_12651)),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

cnf(f_3276_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_12649),U_12650),hAPP(c_Set_OCollect(U_12649),U_12651)) = hAPP(c_Set_OCollect(U_12649),hAPP(hAPP(c_COMBS(U_12649,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12649),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12649),c_fNot),hAPP(hAPP(c_COMBC(U_12649,U_12649,tc_HOL_Obool),c_fequal),U_12650)))),U_12651)),
    inference(clausify,[status(thm)],[f_3276_2]) ).

fof(f_3277_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_3277_2,plain,
    ! [U_12652] : c_Orderings_Obot__class_Obot(tc_fun(U_12652,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12652),hAPP(c_COMBK(tc_HOL_Obool,U_12652),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

cnf(f_3277_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_12652,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12652),hAPP(c_COMBK(tc_HOL_Obool,U_12652),c_fFalse)),
    inference(clausify,[status(thm)],[f_3277_2]) ).

fof(f_3278_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),V_Qa_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).

fof(f_3278_2,plain,
    ! [U_12655,U_12654,U_12653] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),hAPP(hAPP(c_COMBS(U_12653,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12653),c_fdisj),U_12654)),U_12655))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),U_12655)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),U_12654))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),U_12655)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),U_12654))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12653),hAPP(c_Set_OCollect(U_12653),hAPP(hAPP(c_COMBS(U_12653,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12653),c_fdisj),U_12654)),U_12655)))) ) ),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

fof(f_3278_3,plain,
    ( ! [U_12661,U_12659,U_12657] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),hAPP(hAPP(c_COMBS(U_12657,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12657),c_fdisj),U_12659)),U_12661))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),U_12661)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),U_12659))) )
    & ! [U_12660,U_12658,U_12656] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),U_12660)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),U_12658))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),hAPP(hAPP(c_COMBS(U_12656,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12656),c_fdisj),U_12658)),U_12660)))) ) ),
    inference(miniscope,[status(thm)],[f_3278_2]) ).

cnf(f_3278_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),U_12658)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),hAPP(hAPP(c_COMBS(U_12656,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12656),c_fdisj),U_12658)),U_12660)))) ),
    inference(clausify,[status(thm)],[f_3278_3]) ).

cnf(f_3278_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),U_12660)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12656),hAPP(c_Set_OCollect(U_12656),hAPP(hAPP(c_COMBS(U_12656,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12656),c_fdisj),U_12658)),U_12660)))) ),
    inference(clausify,[status(thm)],[f_3278_3]) ).

cnf(f_3278_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),hAPP(hAPP(c_COMBS(U_12657,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12657),c_fdisj),U_12659)),U_12661))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),U_12661)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12657),hAPP(c_Set_OCollect(U_12657),U_12659))) ),
    inference(clausify,[status(thm)],[f_3278_3]) ).

fof(f_3279_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
        | ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).

fof(f_3279_2,plain,
    ! [U_12665,U_12664] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_12664,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12664),U_12665)
        | ? [U_12663] : hBOOL(hAPP(U_12665,U_12663)) )
      & ( ! [U_12662] : ~ hBOOL(hAPP(U_12665,U_12662))
        | c_Orderings_Obot__class_Obot(tc_fun(U_12664,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12664),U_12665) ) ),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

fof(f_3279_3,plain,
    ( ! [U_12669] :
        ( ! [U_12667] : c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12667),U_12669)
        | ? [U_12663] : hBOOL(hAPP(U_12669,U_12663)) )
    & ! [U_12668] :
        ( ! [U_12666] : c_Orderings_Obot__class_Obot(tc_fun(U_12666,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12666),U_12668)
        | ! [U_12662] : ~ hBOOL(hAPP(U_12668,U_12662)) ) ),
    inference(miniscope,[status(thm)],[f_3279_2]) ).

fof(f_3279_4,plain,
    ( ! [U_12669] :
        ( ! [U_12667] : c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12667),U_12669)
        | hBOOL(hAPP(U_12669,sK301(U_12669))) )
    & ! [U_12668] :
        ( ! [U_12666] : c_Orderings_Obot__class_Obot(tc_fun(U_12666,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12666),U_12668)
        | ! [U_12662] : ~ hBOOL(hAPP(U_12668,U_12662)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_12663,sK301(U_12669))],[f_3279_3]) ).

cnf(f_3279_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_12666,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12666),U_12668)
    | ~ hBOOL(hAPP(U_12668,U_12662)) ),
    inference(clausify,[status(thm)],[f_3279_4]) ).

cnf(f_3279_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12667),U_12669)
    | hBOOL(hAPP(U_12669,sK301(U_12669))) ),
    inference(clausify,[status(thm)],[f_3279_4]) ).

fof(f_3280_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
        | hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).

fof(f_3280_2,plain,
    ! [U_12673,U_12672] :
      ( ( hAPP(c_Set_OCollect(U_12672),U_12673) = c_Orderings_Obot__class_Obot(tc_fun(U_12672,tc_HOL_Obool))
        | ? [U_12671] : hBOOL(hAPP(U_12673,U_12671)) )
      & ( ! [U_12670] : ~ hBOOL(hAPP(U_12673,U_12670))
        | hAPP(c_Set_OCollect(U_12672),U_12673) != c_Orderings_Obot__class_Obot(tc_fun(U_12672,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

fof(f_3280_3,plain,
    ( ! [U_12677] :
        ( ! [U_12675] : hAPP(c_Set_OCollect(U_12675),U_12677) = c_Orderings_Obot__class_Obot(tc_fun(U_12675,tc_HOL_Obool))
        | ? [U_12671] : hBOOL(hAPP(U_12677,U_12671)) )
    & ! [U_12676] :
        ( ! [U_12674] : hAPP(c_Set_OCollect(U_12674),U_12676) != c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool))
        | ! [U_12670] : ~ hBOOL(hAPP(U_12676,U_12670)) ) ),
    inference(miniscope,[status(thm)],[f_3280_2]) ).

fof(f_3280_4,plain,
    ( ! [U_12677] :
        ( ! [U_12675] : hAPP(c_Set_OCollect(U_12675),U_12677) = c_Orderings_Obot__class_Obot(tc_fun(U_12675,tc_HOL_Obool))
        | hBOOL(hAPP(U_12677,sK302(U_12677))) )
    & ! [U_12676] :
        ( ! [U_12674] : hAPP(c_Set_OCollect(U_12674),U_12676) != c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool))
        | ! [U_12670] : ~ hBOOL(hAPP(U_12676,U_12670)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_12671,sK302(U_12677))],[f_3280_3]) ).

cnf(f_3280_5,plain,
    ( hAPP(c_Set_OCollect(U_12674),U_12676) != c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_12676,U_12670)) ),
    inference(clausify,[status(thm)],[f_3280_4]) ).

cnf(f_3280_6,plain,
    ( hAPP(c_Set_OCollect(U_12675),U_12677) = c_Orderings_Obot__class_Obot(tc_fun(U_12675,tc_HOL_Obool))
    | hBOOL(hAPP(U_12677,sK302(U_12677))) ),
    inference(clausify,[status(thm)],[f_3280_4]) ).

fof(f_3281_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).

fof(f_3281_2,plain,
    ! [U_12679,U_12678] : hAPP(c_Set_OCollect(U_12678),U_12679) = U_12679,
    inference(variable_rename,[status(thm)],[f_3281_1]) ).

cnf(f_3281_3,plain,
    hAPP(c_Set_OCollect(U_12678),U_12679) = U_12679,
    inference(clausify,[status(thm)],[f_3281_2]) ).

fof(f_3282_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_3282_2,plain,
    ! [U_12680] : c_Orderings_Otop__class_Otop(tc_fun(U_12680,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12680),hAPP(c_COMBK(tc_HOL_Obool,U_12680),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_3282_1]) ).

cnf(f_3282_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_12680,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12680),hAPP(c_COMBK(tc_HOL_Obool,U_12680),c_fTrue)),
    inference(clausify,[status(thm)],[f_3282_2]) ).

fof(f_3283_1,plain,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(f_3283_2,plain,
    ! [U_12684,U_12683,U_12682,U_12681] : hAPP(c_Set_Ovimage(U_12681,U_12682,U_12683),hAPP(c_Set_OCollect(U_12682),U_12684)) = hAPP(c_Set_OCollect(U_12681),hAPP(hAPP(c_COMBB(U_12682,tc_HOL_Obool,U_12681),U_12684),U_12683)),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

cnf(f_3283_3,plain,
    hAPP(c_Set_Ovimage(U_12681,U_12682,U_12683),hAPP(c_Set_OCollect(U_12682),U_12684)) = hAPP(c_Set_OCollect(U_12681),hAPP(hAPP(c_COMBB(U_12682,tc_HOL_Obool,U_12681),U_12684),U_12683)),
    inference(clausify,[status(thm)],[f_3283_2]) ).

fof(f_3284_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).

fof(f_3284_2,plain,
    ! [U_12686,U_12685] : hAPP(c_Set_OCollect(U_12685),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12685),c_fNot),U_12686)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12685,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12685),U_12686)),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

cnf(f_3284_3,plain,
    hAPP(c_Set_OCollect(U_12685),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12685),c_fNot),U_12686)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12685,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12685),U_12686)),
    inference(clausify,[status(thm)],[f_3284_2]) ).

fof(f_3285_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).

fof(f_3285_2,plain,
    ! [U_12690,U_12689,U_12688,U_12687] : hAPP(c_Set_OCollect(tc_prod(U_12687,U_12688)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12687,U_12688,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12687,tc_fun(U_12688,tc_HOL_Obool),tc_fun(U_12688,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12688,tc_HOL_Obool),tc_fun(U_12688,tc_HOL_Obool)),U_12687),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12688)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12687),c_fconj),U_12689))),U_12690))) = hAPP(hAPP(c_Product__Type_OSigma(U_12687,U_12688),hAPP(c_Set_OCollect(U_12687),U_12689)),hAPP(c_COMBK(tc_fun(U_12688,tc_HOL_Obool),U_12687),hAPP(c_Set_OCollect(U_12688),U_12690))),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

cnf(f_3285_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_12687,U_12688)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12687,U_12688,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12687,tc_fun(U_12688,tc_HOL_Obool),tc_fun(U_12688,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12688,tc_HOL_Obool),tc_fun(U_12688,tc_HOL_Obool)),U_12687),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12688)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12687),c_fconj),U_12689))),U_12690))) = hAPP(hAPP(c_Product__Type_OSigma(U_12687,U_12688),hAPP(c_Set_OCollect(U_12687),U_12689)),hAPP(c_COMBK(tc_fun(U_12688,tc_HOL_Obool),U_12687),hAPP(c_Set_OCollect(U_12688),U_12690))),
    inference(clausify,[status(thm)],[f_3285_2]) ).

fof(f_3286_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_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_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(f_3286_2,plain,
    ! [U_12694,U_12693,U_12692,U_12691] : hAPP(c_Set_OCollect(tc_prod(U_12691,U_12692)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12691,U_12692,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12691,tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool)),U_12691),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12692)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12691),c_fconj),U_12693))),U_12694))) = hAPP(hAPP(c_Product__Type_OSigma(U_12691,U_12692),hAPP(c_Set_OCollect(U_12691),U_12693)),hAPP(hAPP(c_COMBB(tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool),U_12691),c_Set_OCollect(U_12692)),U_12694)),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

cnf(f_3286_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_12691,U_12692)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12691,U_12692,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12691,tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool)),U_12691),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12692)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12691),c_fconj),U_12693))),U_12694))) = hAPP(hAPP(c_Product__Type_OSigma(U_12691,U_12692),hAPP(c_Set_OCollect(U_12691),U_12693)),hAPP(hAPP(c_COMBB(tc_fun(U_12692,tc_HOL_Obool),tc_fun(U_12692,tc_HOL_Obool),U_12691),c_Set_OCollect(U_12692)),U_12694)),
    inference(clausify,[status(thm)],[f_3286_2]) ).

fof(f_3287_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_3287_2,plain,
    ! [U_12697,U_12696,U_12695] : hAPP(hAPP(c_Set_Oinsert(U_12695),U_12696),U_12697) = hAPP(c_Set_OCollect(U_12695),hAPP(hAPP(c_COMBS(U_12695,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12695),c_fdisj),hAPP(hAPP(c_COMBC(U_12695,U_12695,tc_HOL_Obool),c_fequal),U_12696))),hAPP(hAPP(c_COMBC(U_12695,tc_fun(U_12695,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12695)),U_12697))),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

cnf(f_3287_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_12695),U_12696),U_12697) = hAPP(c_Set_OCollect(U_12695),hAPP(hAPP(c_COMBS(U_12695,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12695),c_fdisj),hAPP(hAPP(c_COMBC(U_12695,U_12695,tc_HOL_Obool),c_fequal),U_12696))),hAPP(hAPP(c_COMBC(U_12695,tc_fun(U_12695,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12695)),U_12697))),
    inference(clausify,[status(thm)],[f_3287_2]) ).

fof(f_3288_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_3288_2,plain,
    ! [U_12700,U_12699,U_12698] : hAPP(hAPP(c_Set_Oinsert(U_12698),U_12699),U_12700) = hAPP(c_Set_OCollect(U_12698),hAPP(hAPP(c_COMBS(U_12698,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12698),c_fdisj),hAPP(hAPP(c_COMBC(U_12698,U_12698,tc_HOL_Obool),c_fequal),U_12699))),hAPP(hAPP(c_COMBC(U_12698,tc_fun(U_12698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12698)),U_12700))),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

cnf(f_3288_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_12698),U_12699),U_12700) = hAPP(c_Set_OCollect(U_12698),hAPP(hAPP(c_COMBS(U_12698,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12698),c_fdisj),hAPP(hAPP(c_COMBC(U_12698,U_12698,tc_HOL_Obool),c_fequal),U_12699))),hAPP(hAPP(c_COMBC(U_12698,tc_fun(U_12698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12698)),U_12700))),
    inference(clausify,[status(thm)],[f_3288_2]) ).

fof(f_3289_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_3289_2,plain,
    ! [U_12703,U_12702,U_12701] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12701,tc_HOL_Obool)),U_12702),U_12703) = hAPP(c_Set_OCollect(U_12701),hAPP(hAPP(c_COMBS(U_12701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12701),c_fdisj),hAPP(hAPP(c_COMBC(U_12701,tc_fun(U_12701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12701)),U_12702))),hAPP(hAPP(c_COMBC(U_12701,tc_fun(U_12701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12701)),U_12703))),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

cnf(f_3289_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12701,tc_HOL_Obool)),U_12702),U_12703) = hAPP(c_Set_OCollect(U_12701),hAPP(hAPP(c_COMBS(U_12701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12701),c_fdisj),hAPP(hAPP(c_COMBC(U_12701,tc_fun(U_12701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12701)),U_12702))),hAPP(hAPP(c_COMBC(U_12701,tc_fun(U_12701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12701)),U_12703))),
    inference(clausify,[status(thm)],[f_3289_2]) ).

fof(f_3290_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_3290_2,plain,
    ! [U_12706,U_12705,U_12704] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12704,tc_HOL_Obool)),U_12705),U_12706) = hAPP(c_Set_OCollect(U_12704),hAPP(hAPP(c_COMBS(U_12704,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12704),c_fconj),hAPP(hAPP(c_COMBC(U_12704,tc_fun(U_12704,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12704)),U_12705))),hAPP(hAPP(c_COMBC(U_12704,tc_fun(U_12704,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12704)),U_12706))),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

cnf(f_3290_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12704,tc_HOL_Obool)),U_12705),U_12706) = hAPP(c_Set_OCollect(U_12704),hAPP(hAPP(c_COMBS(U_12704,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12704),c_fconj),hAPP(hAPP(c_COMBC(U_12704,tc_fun(U_12704,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12704)),U_12705))),hAPP(hAPP(c_COMBC(U_12704,tc_fun(U_12704,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12704)),U_12706))),
    inference(clausify,[status(thm)],[f_3290_2]) ).

fof(f_3291_1,plain,
    ! [V_Pa_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_Pa_2))))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(V_Pa_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_Pa_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).

fof(f_3291_2,plain,
    ! [U_12710,U_12709,U_12708,U_12707] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12707),U_12708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12707,tc_HOL_Obool)),U_12709),hAPP(c_Set_OCollect(U_12707),U_12710))))
        | ~ hBOOL(hAPP(U_12710,U_12708))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12707),U_12708),U_12709)) )
      & ( ( hBOOL(hAPP(U_12710,U_12708))
          & hBOOL(hAPP(hAPP(c_member(U_12707),U_12708),U_12709)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12707),U_12708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12707,tc_HOL_Obool)),U_12709),hAPP(c_Set_OCollect(U_12707),U_12710)))) ) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

fof(f_3291_3,plain,
    ( ! [U_12718,U_12716,U_12714,U_12712] :
        ( hBOOL(hAPP(hAPP(c_member(U_12712),U_12714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12712,tc_HOL_Obool)),U_12716),hAPP(c_Set_OCollect(U_12712),U_12718))))
        | ~ hBOOL(hAPP(U_12718,U_12714))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12712),U_12714),U_12716)) )
    & ! [U_12717,U_12715,U_12713,U_12711] :
        ( ( hBOOL(hAPP(U_12717,U_12713))
          & hBOOL(hAPP(hAPP(c_member(U_12711),U_12713),U_12715)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12711),U_12713),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12711,tc_HOL_Obool)),U_12715),hAPP(c_Set_OCollect(U_12711),U_12717)))) ) ),
    inference(miniscope,[status(thm)],[f_3291_2]) ).

cnf(f_3291_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12711),U_12713),U_12715))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12711),U_12713),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12711,tc_HOL_Obool)),U_12715),hAPP(c_Set_OCollect(U_12711),U_12717)))) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

cnf(f_3291_5,plain,
    ( hBOOL(hAPP(U_12717,U_12713))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12711),U_12713),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12711,tc_HOL_Obool)),U_12715),hAPP(c_Set_OCollect(U_12711),U_12717)))) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

cnf(f_3291_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12712),U_12714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12712,tc_HOL_Obool)),U_12716),hAPP(c_Set_OCollect(U_12712),U_12718))))
    | ~ hBOOL(hAPP(U_12718,U_12714))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12712),U_12714),U_12716)) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

fof(f_3292_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_3292_2,plain,
    ! [U_12720,U_12719] : hAPP(c_Set_OCollect(U_12719),hAPP(c_fequal,U_12720)) = hAPP(hAPP(c_Set_Oinsert(U_12719),U_12720),c_Orderings_Obot__class_Obot(tc_fun(U_12719,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3292_1]) ).

cnf(f_3292_3,plain,
    hAPP(c_Set_OCollect(U_12719),hAPP(c_fequal,U_12720)) = hAPP(hAPP(c_Set_Oinsert(U_12719),U_12720),c_Orderings_Obot__class_Obot(tc_fun(U_12719,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3292_2]) ).

fof(f_3293_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_3293_2,plain,
    ! [U_12722,U_12721] : hAPP(c_Set_OCollect(U_12721),hAPP(hAPP(c_COMBC(U_12721,U_12721,tc_HOL_Obool),c_fequal),U_12722)) = hAPP(hAPP(c_Set_Oinsert(U_12721),U_12722),c_Orderings_Obot__class_Obot(tc_fun(U_12721,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

cnf(f_3293_3,plain,
    hAPP(c_Set_OCollect(U_12721),hAPP(hAPP(c_COMBC(U_12721,U_12721,tc_HOL_Obool),c_fequal),U_12722)) = hAPP(hAPP(c_Set_Oinsert(U_12721),U_12722),c_Orderings_Obot__class_Obot(tc_fun(U_12721,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3293_2]) ).

fof(f_3294_1,plain,
    ! [T_b,V_a_2,V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).

fof(f_3294_2,plain,
    ! [U_12725,U_12724,U_12723] :
      ( ( hAPP(c_Set_OCollect(U_12725),hAPP(hAPP(c_COMBS(U_12725,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12725),c_fconj),hAPP(c_fequal,U_12724))),U_12723)) = c_Orderings_Obot__class_Obot(tc_fun(U_12725,tc_HOL_Obool))
        | hBOOL(hAPP(U_12723,U_12724)) )
      & ( hAPP(c_Set_OCollect(U_12725),hAPP(hAPP(c_COMBS(U_12725,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12725),c_fconj),hAPP(c_fequal,U_12724))),U_12723)) = hAPP(hAPP(c_Set_Oinsert(U_12725),U_12724),c_Orderings_Obot__class_Obot(tc_fun(U_12725,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_12723,U_12724)) ) ),
    inference(variable_rename,[status(thm)],[f_3294_1]) ).

fof(f_3294_3,plain,
    ( ! [U_12731,U_12729,U_12727] :
        ( hAPP(c_Set_OCollect(U_12731),hAPP(hAPP(c_COMBS(U_12731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12731),c_fconj),hAPP(c_fequal,U_12729))),U_12727)) = c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))
        | hBOOL(hAPP(U_12727,U_12729)) )
    & ! [U_12730,U_12728,U_12726] :
        ( hAPP(c_Set_OCollect(U_12730),hAPP(hAPP(c_COMBS(U_12730,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12730),c_fconj),hAPP(c_fequal,U_12728))),U_12726)) = hAPP(hAPP(c_Set_Oinsert(U_12730),U_12728),c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_12726,U_12728)) ) ),
    inference(miniscope,[status(thm)],[f_3294_2]) ).

cnf(f_3294_4,plain,
    ( hAPP(c_Set_OCollect(U_12730),hAPP(hAPP(c_COMBS(U_12730,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12730),c_fconj),hAPP(c_fequal,U_12728))),U_12726)) = hAPP(hAPP(c_Set_Oinsert(U_12730),U_12728),c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_12726,U_12728)) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

cnf(f_3294_5,plain,
    ( hAPP(c_Set_OCollect(U_12731),hAPP(hAPP(c_COMBS(U_12731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12731),c_fconj),hAPP(c_fequal,U_12729))),U_12727)) = c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))
    | hBOOL(hAPP(U_12727,U_12729)) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

fof(f_3295_1,plain,
    ! [T_b,V_a_2,V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).

fof(f_3295_2,plain,
    ! [U_12734,U_12733,U_12732] :
      ( ( hAPP(c_Set_OCollect(U_12734),hAPP(hAPP(c_COMBS(U_12734,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12734),c_fconj),hAPP(hAPP(c_COMBC(U_12734,U_12734,tc_HOL_Obool),c_fequal),U_12733))),U_12732)) = c_Orderings_Obot__class_Obot(tc_fun(U_12734,tc_HOL_Obool))
        | hBOOL(hAPP(U_12732,U_12733)) )
      & ( hAPP(c_Set_OCollect(U_12734),hAPP(hAPP(c_COMBS(U_12734,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12734),c_fconj),hAPP(hAPP(c_COMBC(U_12734,U_12734,tc_HOL_Obool),c_fequal),U_12733))),U_12732)) = hAPP(hAPP(c_Set_Oinsert(U_12734),U_12733),c_Orderings_Obot__class_Obot(tc_fun(U_12734,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_12732,U_12733)) ) ),
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

fof(f_3295_3,plain,
    ( ! [U_12740,U_12738,U_12736] :
        ( hAPP(c_Set_OCollect(U_12740),hAPP(hAPP(c_COMBS(U_12740,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12740),c_fconj),hAPP(hAPP(c_COMBC(U_12740,U_12740,tc_HOL_Obool),c_fequal),U_12738))),U_12736)) = c_Orderings_Obot__class_Obot(tc_fun(U_12740,tc_HOL_Obool))
        | hBOOL(hAPP(U_12736,U_12738)) )
    & ! [U_12739,U_12737,U_12735] :
        ( hAPP(c_Set_OCollect(U_12739),hAPP(hAPP(c_COMBS(U_12739,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12739),c_fconj),hAPP(hAPP(c_COMBC(U_12739,U_12739,tc_HOL_Obool),c_fequal),U_12737))),U_12735)) = hAPP(hAPP(c_Set_Oinsert(U_12739),U_12737),c_Orderings_Obot__class_Obot(tc_fun(U_12739,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_12735,U_12737)) ) ),
    inference(miniscope,[status(thm)],[f_3295_2]) ).

cnf(f_3295_4,plain,
    ( hAPP(c_Set_OCollect(U_12739),hAPP(hAPP(c_COMBS(U_12739,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12739),c_fconj),hAPP(hAPP(c_COMBC(U_12739,U_12739,tc_HOL_Obool),c_fequal),U_12737))),U_12735)) = hAPP(hAPP(c_Set_Oinsert(U_12739),U_12737),c_Orderings_Obot__class_Obot(tc_fun(U_12739,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_12735,U_12737)) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

cnf(f_3295_5,plain,
    ( hAPP(c_Set_OCollect(U_12740),hAPP(hAPP(c_COMBS(U_12740,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12740),c_fconj),hAPP(hAPP(c_COMBC(U_12740,U_12740,tc_HOL_Obool),c_fequal),U_12738))),U_12736)) = c_Orderings_Obot__class_Obot(tc_fun(U_12740,tc_HOL_Obool))
    | hBOOL(hAPP(U_12736,U_12738)) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

fof(f_3296_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_3296_2,plain,
    ! [U_12743,U_12742,U_12741] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12741,tc_HOL_Obool)),U_12742),U_12743) = hAPP(c_Set_OCollect(U_12741),hAPP(hAPP(c_COMBS(U_12741,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12741),c_fconj),hAPP(hAPP(c_COMBC(U_12741,tc_fun(U_12741,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12741)),U_12742))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12741),c_fNot),hAPP(hAPP(c_COMBC(U_12741,tc_fun(U_12741,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12741)),U_12743)))),
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

cnf(f_3296_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12741,tc_HOL_Obool)),U_12742),U_12743) = hAPP(c_Set_OCollect(U_12741),hAPP(hAPP(c_COMBS(U_12741,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12741),c_fconj),hAPP(hAPP(c_COMBC(U_12741,tc_fun(U_12741,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12741)),U_12742))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12741),c_fNot),hAPP(hAPP(c_COMBC(U_12741,tc_fun(U_12741,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12741)),U_12743)))),
    inference(clausify,[status(thm)],[f_3296_2]) ).

fof(f_3297_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).

fof(f_3297_2,plain,
    ! [U_12745,U_12744] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12744),c_fNot),U_12745))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12744),c_fNot),U_12745)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),U_12745))) ),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

cnf(f_3297_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12744),c_fNot),U_12745))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),U_12745))) ),
    inference(clausify,[status(thm)],[f_3297_2]) ).

cnf(f_3297_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12744),c_fNot),U_12745))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),c_Orderings_Otop__class_Otop(tc_fun(U_12744,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12744),hAPP(c_Set_OCollect(U_12744),U_12745))) ),
    inference(clausify,[status(thm)],[f_3297_2]) ).

fof(f_3298_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_3298_2,plain,
    ! [U_12748,U_12747,U_12746] : hAPP(hAPP(c_Set_Oinsert(U_12746),U_12747),U_12748) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12746,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12746),hAPP(hAPP(c_COMBC(U_12746,U_12746,tc_HOL_Obool),c_fequal),U_12747))),U_12748),
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

cnf(f_3298_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_12746),U_12747),U_12748) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12746,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12746),hAPP(hAPP(c_COMBC(U_12746,U_12746,tc_HOL_Obool),c_fequal),U_12747))),U_12748),
    inference(clausify,[status(thm)],[f_3298_2]) ).

fof(f_3299_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_3299_2,plain,
    ! [U_12750,U_12749] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12749,tc_HOL_Obool)),U_12750) = hAPP(c_Set_OCollect(U_12749),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12749),c_fNot),hAPP(hAPP(c_COMBC(U_12749,tc_fun(U_12749,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12749)),U_12750))),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

cnf(f_3299_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12749,tc_HOL_Obool)),U_12750) = hAPP(c_Set_OCollect(U_12749),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12749),c_fNot),hAPP(hAPP(c_COMBC(U_12749,tc_fun(U_12749,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12749)),U_12750))),
    inference(clausify,[status(thm)],[f_3299_2]) ).

fof(f_3300_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_3300_2,plain,
    ! [U_12754,U_12753,U_12752,U_12751] : hAPP(c_Set_Ovimage(U_12751,U_12752,U_12753),U_12754) = hAPP(c_Set_OCollect(U_12751),hAPP(hAPP(c_COMBC(U_12751,tc_fun(U_12752,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12752,tc_fun(tc_fun(U_12752,tc_HOL_Obool),tc_HOL_Obool),U_12751),c_member(U_12752)),U_12753)),U_12754)),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

cnf(f_3300_3,plain,
    hAPP(c_Set_Ovimage(U_12751,U_12752,U_12753),U_12754) = hAPP(c_Set_OCollect(U_12751),hAPP(hAPP(c_COMBC(U_12751,tc_fun(U_12752,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12752,tc_fun(tc_fun(U_12752,tc_HOL_Obool),tc_HOL_Obool),U_12751),c_member(U_12752)),U_12753)),U_12754)),
    inference(clausify,[status(thm)],[f_3300_2]) ).

fof(f_3301_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_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_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).

fof(f_3301_2,plain,
    ! [U_12757,U_12756,U_12755] : hAPP(c_Set_OCollect(U_12755),hAPP(hAPP(c_COMBS(U_12755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12755),c_fimplies),U_12756)),U_12757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12755),U_12756))),hAPP(c_Set_OCollect(U_12755),U_12757)),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

cnf(f_3301_3,plain,
    hAPP(c_Set_OCollect(U_12755),hAPP(hAPP(c_COMBS(U_12755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12755),c_fimplies),U_12756)),U_12757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12755,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12755),U_12756))),hAPP(c_Set_OCollect(U_12755),U_12757)),
    inference(clausify,[status(thm)],[f_3301_2]) ).

fof(f_3302_1,plain,
    ! [V_i_2,V_Pa_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_Pa_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_3302_2,plain,
    ! [U_12759,U_12758] : 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_12758)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12759))))),
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

cnf(f_3302_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_12758)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12759))))),
    inference(clausify,[status(thm)],[f_3302_2]) ).

fof(f_3303_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_3303_2,plain,
    ! [U_12766,U_12765,U_12764,U_12763,U_12762,U_12761,U_12760] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,U_12760),hAPP(hAPP(c_COMBS(U_12761,tc_fun(U_12763,tc_HOL_Obool),U_12760),hAPP(hAPP(c_COMBB(tc_fun(U_12763,U_12760),tc_fun(tc_fun(U_12763,tc_HOL_Obool),U_12760),U_12761),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12763,U_12760)),U_12765)),hAPP(hAPP(c_COMBB(tc_fun(U_12763,tc_HOL_Obool),tc_fun(U_12763,tc_HOL_Obool),U_12761),c_Set_OCollect(U_12763)),hAPP(hAPP(c_COMBB(tc_fun(U_12763,tc_HOL_Obool),tc_fun(U_12763,tc_HOL_Obool),U_12761),hAPP(c_COMBS(U_12763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12763),c_fconj),hAPP(hAPP(c_COMBC(U_12763,tc_fun(U_12763,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12763)),U_12764)))),U_12766)))),U_12762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12763,U_12760),hAPP(hAPP(c_COMBS(U_12763,tc_fun(U_12761,tc_HOL_Obool),U_12760),hAPP(hAPP(c_COMBB(tc_fun(U_12761,U_12760),tc_fun(tc_fun(U_12761,tc_HOL_Obool),U_12760),U_12763),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,U_12760)),hAPP(c_COMBC(U_12761,U_12763,U_12760),U_12765))),hAPP(hAPP(c_COMBB(tc_fun(U_12761,tc_HOL_Obool),tc_fun(U_12761,tc_HOL_Obool),U_12763),c_Set_OCollect(U_12761)),hAPP(hAPP(c_COMBB(tc_fun(U_12761,tc_HOL_Obool),tc_fun(U_12761,tc_HOL_Obool),U_12763),hAPP(c_COMBS(U_12761,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12761),c_fconj),hAPP(hAPP(c_COMBC(U_12761,tc_fun(U_12761,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12761)),U_12762)))),hAPP(c_COMBC(U_12761,U_12763,tc_HOL_Obool),U_12766))))),U_12764)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12763),U_12764))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762))
      | ~ class_Groups_Ocomm__monoid__add(U_12760) ),
    inference(variable_rename,[status(thm)],[f_3303_1]) ).

cnf(f_3303_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,U_12760),hAPP(hAPP(c_COMBS(U_12761,tc_fun(U_12763,tc_HOL_Obool),U_12760),hAPP(hAPP(c_COMBB(tc_fun(U_12763,U_12760),tc_fun(tc_fun(U_12763,tc_HOL_Obool),U_12760),U_12761),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12763,U_12760)),U_12765)),hAPP(hAPP(c_COMBB(tc_fun(U_12763,tc_HOL_Obool),tc_fun(U_12763,tc_HOL_Obool),U_12761),c_Set_OCollect(U_12763)),hAPP(hAPP(c_COMBB(tc_fun(U_12763,tc_HOL_Obool),tc_fun(U_12763,tc_HOL_Obool),U_12761),hAPP(c_COMBS(U_12763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12763),c_fconj),hAPP(hAPP(c_COMBC(U_12763,tc_fun(U_12763,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12763)),U_12764)))),U_12766)))),U_12762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12763,U_12760),hAPP(hAPP(c_COMBS(U_12763,tc_fun(U_12761,tc_HOL_Obool),U_12760),hAPP(hAPP(c_COMBB(tc_fun(U_12761,U_12760),tc_fun(tc_fun(U_12761,tc_HOL_Obool),U_12760),U_12763),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,U_12760)),hAPP(c_COMBC(U_12761,U_12763,U_12760),U_12765))),hAPP(hAPP(c_COMBB(tc_fun(U_12761,tc_HOL_Obool),tc_fun(U_12761,tc_HOL_Obool),U_12763),c_Set_OCollect(U_12761)),hAPP(hAPP(c_COMBB(tc_fun(U_12761,tc_HOL_Obool),tc_fun(U_12761,tc_HOL_Obool),U_12763),hAPP(c_COMBS(U_12761,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12761),c_fconj),hAPP(hAPP(c_COMBC(U_12761,tc_fun(U_12761,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12761)),U_12762)))),hAPP(c_COMBC(U_12761,U_12763,tc_HOL_Obool),U_12766))))),U_12764)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12763),U_12764))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762))
    | ~ class_Groups_Ocomm__monoid__add(U_12760) ),
    inference(clausify,[status(thm)],[f_3303_2]) ).

fof(f_3304_1,plain,
    ! [V_S_2,V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2))))),
    inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).

fof(f_3304_2,plain,
    ! [U_12772,U_12771,U_12770,U_12769,U_12768,U_12767] : hAPP(c_Set_Oimage(U_12767,U_12768,hAPP(hAPP(c_COMBS(U_12767,U_12768,U_12768),hAPP(hAPP(c_COMBS(U_12767,U_12768,tc_fun(U_12768,U_12768)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12768,tc_fun(U_12768,U_12768)),U_12767),c_If(U_12768)),U_12769)),U_12770)),U_12771)),U_12772) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12768,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12767,U_12768,U_12770),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12767,tc_HOL_Obool)),U_12772),hAPP(c_Set_OCollect(U_12767),U_12769)))),hAPP(c_Set_Oimage(U_12767,U_12768,U_12771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12767,tc_HOL_Obool)),U_12772),hAPP(c_Set_OCollect(U_12767),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12767),c_fNot),U_12769))))),
    inference(variable_rename,[status(thm)],[f_3304_1]) ).

cnf(f_3304_3,plain,
    hAPP(c_Set_Oimage(U_12767,U_12768,hAPP(hAPP(c_COMBS(U_12767,U_12768,U_12768),hAPP(hAPP(c_COMBS(U_12767,U_12768,tc_fun(U_12768,U_12768)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12768,tc_fun(U_12768,U_12768)),U_12767),c_If(U_12768)),U_12769)),U_12770)),U_12771)),U_12772) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12768,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12767,U_12768,U_12770),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12767,tc_HOL_Obool)),U_12772),hAPP(c_Set_OCollect(U_12767),U_12769)))),hAPP(c_Set_Oimage(U_12767,U_12768,U_12771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12767,tc_HOL_Obool)),U_12772),hAPP(c_Set_OCollect(U_12767),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12767),c_fNot),U_12769))))),
    inference(clausify,[status(thm)],[f_3304_2]) ).

fof(f_3305_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_3305_2,plain,
    ! [U_12776,U_12775,U_12774,U_12773] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12774),U_12773))
      | U_12773 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12774,U_12775),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_12776))) ),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

cnf(f_3305_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12774),U_12773))
    | U_12773 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12774,U_12775),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_12776))) ),
    inference(clausify,[status(thm)],[f_3305_2]) ).

fof(f_3306_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_3306_2,plain,
    ! [U_12781,U_12780,U_12779,U_12778,U_12777] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12778,U_12777),U_12780),hAPP(c_Set_OCollect(U_12778),hAPP(hAPP(c_COMBS(U_12778,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12778),c_fconj),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12779))),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12781)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12778,U_12777),hAPP(hAPP(c_COMBC(U_12778,U_12777,U_12777),hAPP(hAPP(c_COMBS(U_12778,U_12777,tc_fun(U_12777,U_12777)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12777,tc_fun(U_12777,U_12777)),U_12778),c_If(U_12777)),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12781))),U_12780)),c_Groups_Ozero__class_Ozero(U_12777))),U_12779)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12778),U_12779))
      | ~ class_Groups_Ocomm__monoid__add(U_12777) ),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

cnf(f_3306_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12778,U_12777),U_12780),hAPP(c_Set_OCollect(U_12778),hAPP(hAPP(c_COMBS(U_12778,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12778),c_fconj),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12779))),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12781)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12778,U_12777),hAPP(hAPP(c_COMBC(U_12778,U_12777,U_12777),hAPP(hAPP(c_COMBS(U_12778,U_12777,tc_fun(U_12777,U_12777)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12777,tc_fun(U_12777,U_12777)),U_12778),c_If(U_12777)),hAPP(hAPP(c_COMBC(U_12778,tc_fun(U_12778,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12778)),U_12781))),U_12780)),c_Groups_Ozero__class_Ozero(U_12777))),U_12779)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12778),U_12779))
    | ~ class_Groups_Ocomm__monoid__add(U_12777) ),
    inference(clausify,[status(thm)],[f_3306_2]) ).

fof(f_3307_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_3307_2,plain,
    ! [U_12787,U_12786,U_12785,U_12784,U_12783,U_12782] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12783,U_12782),U_12785),U_12784) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12782),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),U_12782,U_12786),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12783,U_12782),U_12785)),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),tc_fun(U_12783,tc_HOL_Obool),U_12786),c_Set_OCollect(U_12783)),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),tc_fun(U_12783,tc_HOL_Obool),U_12786),hAPP(c_COMBS(U_12783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12783),c_fconj),hAPP(hAPP(c_COMBC(U_12783,tc_fun(U_12783,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12783)),U_12784)))),hAPP(c_COMBC(U_12783,U_12786,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12786,tc_fun(U_12786,tc_HOL_Obool),U_12783),c_fequal),U_12787)))))),hAPP(c_Set_Oimage(U_12783,U_12786,U_12787),U_12784))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12783),U_12784))
      | ~ class_Groups_Ocomm__monoid__add(U_12782) ),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

cnf(f_3307_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12783,U_12782),U_12785),U_12784) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12782),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),U_12782,U_12786),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12783,U_12782),U_12785)),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),tc_fun(U_12783,tc_HOL_Obool),U_12786),c_Set_OCollect(U_12783)),hAPP(hAPP(c_COMBB(tc_fun(U_12783,tc_HOL_Obool),tc_fun(U_12783,tc_HOL_Obool),U_12786),hAPP(c_COMBS(U_12783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12783),c_fconj),hAPP(hAPP(c_COMBC(U_12783,tc_fun(U_12783,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12783)),U_12784)))),hAPP(c_COMBC(U_12783,U_12786,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12786,tc_fun(U_12786,tc_HOL_Obool),U_12783),c_fequal),U_12787)))))),hAPP(c_Set_Oimage(U_12783,U_12786,U_12787),U_12784))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12783),U_12784))
    | ~ class_Groups_Ocomm__monoid__add(U_12782) ),
    inference(clausify,[status(thm)],[f_3307_2]) ).

fof(f_3308_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_3308_2,plain,
    ! [U_12791,U_12790,U_12789,U_12788] : hAPP(c_Relation_OImage(U_12788,U_12789,U_12790),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12791),c_Orderings_Obot__class_Obot(tc_fun(U_12788,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12789),hAPP(hAPP(c_COMBC(U_12789,tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12788,U_12789),tc_fun(tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool),tc_HOL_Obool),U_12789),c_member(tc_prod(U_12788,U_12789))),hAPP(c_Product__Type_OPair(U_12788,U_12789),U_12791))),U_12790)),
    inference(variable_rename,[status(thm)],[f_3308_1]) ).

cnf(f_3308_3,plain,
    hAPP(c_Relation_OImage(U_12788,U_12789,U_12790),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12791),c_Orderings_Obot__class_Obot(tc_fun(U_12788,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12789),hAPP(hAPP(c_COMBC(U_12789,tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12788,U_12789),tc_fun(tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool),tc_HOL_Obool),U_12789),c_member(tc_prod(U_12788,U_12789))),hAPP(c_Product__Type_OPair(U_12788,U_12789),U_12791))),U_12790)),
    inference(clausify,[status(thm)],[f_3308_2]) ).

fof(f_3309_1,plain,
    ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_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_3309_2,plain,
    ! [U_12797,U_12796,U_12795,U_12794,U_12793,U_12792] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),hAPP(hAPP(c_COMBS(U_12793,U_12792,U_12792),hAPP(hAPP(c_COMBS(U_12793,U_12792,tc_fun(U_12792,U_12792)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12792,tc_fun(U_12792,U_12792)),U_12793),c_If(U_12792)),U_12795)),U_12796)),U_12797)),U_12794) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12792),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),U_12796),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12793,tc_HOL_Obool)),U_12794),hAPP(c_Set_OCollect(U_12793),U_12795)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),U_12797),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12793,tc_HOL_Obool)),U_12794),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12793),U_12795)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12793),U_12794))
      | ~ class_Groups_Ocomm__monoid__add(U_12792) ),
    inference(variable_rename,[status(thm)],[f_3309_1]) ).

cnf(f_3309_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),hAPP(hAPP(c_COMBS(U_12793,U_12792,U_12792),hAPP(hAPP(c_COMBS(U_12793,U_12792,tc_fun(U_12792,U_12792)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12792,tc_fun(U_12792,U_12792)),U_12793),c_If(U_12792)),U_12795)),U_12796)),U_12797)),U_12794) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12792),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),U_12796),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12793,tc_HOL_Obool)),U_12794),hAPP(c_Set_OCollect(U_12793),U_12795)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12793,U_12792),U_12797),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12793,tc_HOL_Obool)),U_12794),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12793),U_12795)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12793),U_12794))
    | ~ class_Groups_Ocomm__monoid__add(U_12792) ),
    inference(clausify,[status(thm)],[f_3309_2]) ).

fof(f_3310_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_3310_2,plain,
    ! [U_12799,U_12798] :
      ( 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_12798))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12799))))) = 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_12798))),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_12799)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12798)) ),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

cnf(f_3310_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_12798))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12799))))) = 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_12798))),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_12799)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12798)) ),
    inference(clausify,[status(thm)],[f_3310_2]) ).

fof(f_3311_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_3311_2,plain,
    ! [U_12806,U_12805,U_12804,U_12803,U_12802,U_12801] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12801,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_Nat_Onat,U_12801),c_Finite__Set_Ocard(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),c_Set_OCollect(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),hAPP(c_COMBS(U_12803,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12803),c_fconj),hAPP(hAPP(c_COMBC(U_12803,tc_fun(U_12803,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12803)),U_12804)))),U_12805)))),U_12802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12806),hAPP(c_Finite__Set_Ocard(U_12803),U_12804))
      | ? [U_12800] :
          ( hAPP(c_Finite__Set_Ocard(U_12801),hAPP(c_Set_OCollect(U_12801),hAPP(hAPP(c_COMBS(U_12801,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12801),c_fconj),hAPP(hAPP(c_COMBC(U_12801,tc_fun(U_12801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12801)),U_12802))),hAPP(hAPP(c_COMBC(U_12801,U_12803,tc_HOL_Obool),U_12805),U_12800)))) != U_12806
          & hBOOL(hAPP(hAPP(c_member(U_12803),U_12800),U_12804)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12803),U_12804))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12801),U_12802)) ),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

fof(f_3311_3,plain,
    ! [U_12806,U_12805,U_12804,U_12803,U_12802,U_12801] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12801,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_Nat_Onat,U_12801),c_Finite__Set_Ocard(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),c_Set_OCollect(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),hAPP(c_COMBS(U_12803,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12803),c_fconj),hAPP(hAPP(c_COMBC(U_12803,tc_fun(U_12803,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12803)),U_12804)))),U_12805)))),U_12802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12806),hAPP(c_Finite__Set_Ocard(U_12803),U_12804))
      | ( hAPP(c_Finite__Set_Ocard(U_12801),hAPP(c_Set_OCollect(U_12801),hAPP(hAPP(c_COMBS(U_12801,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12801),c_fconj),hAPP(hAPP(c_COMBC(U_12801,tc_fun(U_12801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12801)),U_12802))),hAPP(hAPP(c_COMBC(U_12801,U_12803,tc_HOL_Obool),U_12805),sK303(U_12806,U_12805,U_12804,U_12803,U_12802,U_12801))))) != U_12806
        & hBOOL(hAPP(hAPP(c_member(U_12803),sK303(U_12806,U_12805,U_12804,U_12803,U_12802,U_12801)),U_12804)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12803),U_12804))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12801),U_12802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_12800,sK303(U_12806,U_12805,U_12804,U_12803,U_12802,U_12801))],[f_3311_2]) ).

cnf(f_3311_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12803),sK303(U_12806,U_12805,U_12804,U_12803,U_12802,U_12801)),U_12804))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12801,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_Nat_Onat,U_12801),c_Finite__Set_Ocard(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),c_Set_OCollect(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),hAPP(c_COMBS(U_12803,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12803),c_fconj),hAPP(hAPP(c_COMBC(U_12803,tc_fun(U_12803,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12803)),U_12804)))),U_12805)))),U_12802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12806),hAPP(c_Finite__Set_Ocard(U_12803),U_12804))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12803),U_12804))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12801),U_12802)) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

cnf(f_3311_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_12801),hAPP(c_Set_OCollect(U_12801),hAPP(hAPP(c_COMBS(U_12801,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12801),c_fconj),hAPP(hAPP(c_COMBC(U_12801,tc_fun(U_12801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12801)),U_12802))),hAPP(hAPP(c_COMBC(U_12801,U_12803,tc_HOL_Obool),U_12805),sK303(U_12806,U_12805,U_12804,U_12803,U_12802,U_12801))))) != U_12806
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12801,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_Nat_Onat,U_12801),c_Finite__Set_Ocard(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),c_Set_OCollect(U_12803)),hAPP(hAPP(c_COMBB(tc_fun(U_12803,tc_HOL_Obool),tc_fun(U_12803,tc_HOL_Obool),U_12801),hAPP(c_COMBS(U_12803,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12803),c_fconj),hAPP(hAPP(c_COMBC(U_12803,tc_fun(U_12803,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12803)),U_12804)))),U_12805)))),U_12802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12806),hAPP(c_Finite__Set_Ocard(U_12803),U_12804))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12803),U_12804))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12801),U_12802)) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

fof(f_3312_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_3312_2,plain,
    ! [U_12809,U_12808,U_12807] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12807),c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),U_12808)),c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),U_12809)) = c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),hAPP(c_Set_OCollect(U_12807),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool,U_12807),c_HOL_OEx(U_12807)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_HOL_Obool),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool,U_12807),c_HOL_OEx(U_12807))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),tc_fun(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),U_12807),c_COMBS(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12807,tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBS(U_12807,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12807),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12807),c_fconj))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_fun(U_12807,U_12807)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool)),tc_fun(tc_fun(U_12807,tc_fun(U_12807,U_12807)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),U_12807),c_COMBB(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool),U_12807)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBB(U_12807,tc_HOL_Obool,U_12807)),c_fequal))),c_Orderings_Oord__class_Omin(U_12807)))))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12807)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12807),c_fconj),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12807)),U_12808)))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12807)),U_12809)))))))
      | U_12809 = c_Orderings_Obot__class_Obot(tc_fun(U_12807,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12809))
      | U_12808 = c_Orderings_Obot__class_Obot(tc_fun(U_12807,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12808))
      | ~ class_Orderings_Olinorder(U_12807) ),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

cnf(f_3312_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12807),c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),U_12808)),c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),U_12809)) = c_Big__Operators_Olattice_OSup__fin(U_12807,c_Orderings_Oord__class_Omax(U_12807),hAPP(c_Set_OCollect(U_12807),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool,U_12807),c_HOL_OEx(U_12807)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_HOL_Obool),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool,U_12807),c_HOL_OEx(U_12807))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),tc_fun(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),U_12807),c_COMBS(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12807,tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool))),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBS(U_12807,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool)),tc_fun(U_12807,tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12807),hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12807),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12807),c_fconj))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_fun(U_12807,U_12807)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool)),tc_fun(tc_fun(U_12807,tc_fun(U_12807,U_12807)),tc_fun(U_12807,tc_fun(U_12807,tc_HOL_Obool))),U_12807),c_COMBB(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool),U_12807)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(tc_fun(U_12807,U_12807),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBB(U_12807,tc_HOL_Obool,U_12807)),c_fequal))),c_Orderings_Oord__class_Omin(U_12807)))))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12807,tc_HOL_Obool),tc_fun(U_12807,tc_HOL_Obool)),U_12807),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12807)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12807),c_fconj),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12807)),U_12808)))),hAPP(hAPP(c_COMBC(U_12807,tc_fun(U_12807,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12807)),U_12809)))))))
    | U_12809 = c_Orderings_Obot__class_Obot(tc_fun(U_12807,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12809))
    | U_12808 = c_Orderings_Obot__class_Obot(tc_fun(U_12807,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12808))
    | ~ class_Orderings_Olinorder(U_12807) ),
    inference(clausify,[status(thm)],[f_3312_2]) ).

fof(f_3313_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_3313_2,plain,
    ! [U_12812,U_12811,U_12810] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12810),U_12812),c_Big__Operators_Olattice_OSup__fin(U_12810,c_Orderings_Oord__class_Omax(U_12810),U_12811)) = c_Big__Operators_Olattice_OSup__fin(U_12810,c_Orderings_Oord__class_Omax(U_12810),hAPP(c_Set_OCollect(U_12810),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_HOL_Obool,U_12810),c_HOL_OEx(U_12810)),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_HOL_Obool)),U_12810),c_COMBS(U_12810,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12810),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12810),c_fconj)),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,U_12810),tc_fun(U_12810,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_fun(tc_fun(U_12810,U_12810),tc_fun(U_12810,tc_HOL_Obool)),U_12810),c_COMBB(U_12810,tc_HOL_Obool,U_12810)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_12810),U_12812))))),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12810)),U_12811)))))
      | U_12811 = c_Orderings_Obot__class_Obot(tc_fun(U_12810,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12810),U_12811))
      | ~ class_Orderings_Olinorder(U_12810) ),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

cnf(f_3313_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12810),U_12812),c_Big__Operators_Olattice_OSup__fin(U_12810,c_Orderings_Oord__class_Omax(U_12810),U_12811)) = c_Big__Operators_Olattice_OSup__fin(U_12810,c_Orderings_Oord__class_Omax(U_12810),hAPP(c_Set_OCollect(U_12810),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_HOL_Obool,U_12810),c_HOL_OEx(U_12810)),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_HOL_Obool)),U_12810),c_COMBS(U_12810,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_fun(U_12810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12810),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12810),c_fconj)),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,U_12810),tc_fun(U_12810,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12810,tc_HOL_Obool),tc_fun(tc_fun(U_12810,U_12810),tc_fun(U_12810,tc_HOL_Obool)),U_12810),c_COMBB(U_12810,tc_HOL_Obool,U_12810)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_12810),U_12812))))),hAPP(hAPP(c_COMBC(U_12810,tc_fun(U_12810,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12810)),U_12811)))))
    | U_12811 = c_Orderings_Obot__class_Obot(tc_fun(U_12810,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12810),U_12811))
    | ~ class_Orderings_Olinorder(U_12810) ),
    inference(clausify,[status(thm)],[f_3313_2]) ).

fof(f_3314_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_3314_2,plain,
    ! [U_12814,U_12813] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12813,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_12813,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_12813,tc_HOL_Obool),tc_fun(U_12813,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_12813,tc_HOL_Obool))),U_12814))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12813),U_12814)) ),
    inference(variable_rename,[status(thm)],[f_3314_1]) ).

cnf(f_3314_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12813,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_12813,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_12813,tc_HOL_Obool),tc_fun(U_12813,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_12813,tc_HOL_Obool))),U_12814))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12813),U_12814)) ),
    inference(clausify,[status(thm)],[f_3314_2]) ).

fof(f_3315_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_3315_2,plain,
    ! [U_12816,U_12815] : hAPP(c_Set_OPow(U_12815),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12815,tc_HOL_Obool)),U_12816)) = hAPP(c_Set_OCollect(tc_fun(U_12815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_12815,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),c_COMBS(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),c_COMBB(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_12815,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_12815,tc_HOL_Obool)),U_12816)),c_Set_OPow(U_12815))))),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

cnf(f_3315_3,plain,
    hAPP(c_Set_OPow(U_12815),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12815,tc_HOL_Obool)),U_12816)) = hAPP(c_Set_OCollect(tc_fun(U_12815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_12815,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),c_COMBS(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_12815,tc_HOL_Obool),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_fun(U_12815,tc_HOL_Obool)),tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12815,tc_HOL_Obool)),c_COMBB(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_12815,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12815,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_12815,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_12815,tc_HOL_Obool)),U_12816)),c_Set_OPow(U_12815))))),
    inference(clausify,[status(thm)],[f_3315_2]) ).

fof(f_3316_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_3316_2,plain,
    ! [U_12818,U_12817] : hAPP(c_Set_OPow(U_12817),U_12818) = hAPP(c_Set_OCollect(tc_fun(U_12817,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_12817,tc_HOL_Obool),tc_fun(U_12817,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_12817,tc_HOL_Obool))),U_12818)),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

cnf(f_3316_3,plain,
    hAPP(c_Set_OPow(U_12817),U_12818) = hAPP(c_Set_OCollect(tc_fun(U_12817,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_12817,tc_HOL_Obool),tc_fun(U_12817,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_12817,tc_HOL_Obool))),U_12818)),
    inference(clausify,[status(thm)],[f_3316_2]) ).

fof(f_3317_1,plain,
    ! [V_Qa_2,T_c,V_Pa_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_Pa_2))),V_Qa_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_Qa_2),B_y))))
              & hBOOL(hAPP(V_Pa_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_Qa_2),B_y))))
              | ~ hBOOL(hAPP(V_Pa_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_Pa_2))),V_Qa_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).

fof(f_3317_2,plain,
    ! [U_12824,U_12823,U_12822,U_12821] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824)))))
          | ? [U_12820] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),U_12820))))
              & hBOOL(hAPP(U_12822,U_12820)) ) )
        & ( ! [U_12819] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),U_12819))))
              | ~ hBOOL(hAPP(U_12822,U_12819)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),hAPP(c_Set_OCollect(U_12821),U_12822))) ),
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

fof(f_3317_3,plain,
    ! [U_12824,U_12823,U_12822,U_12821] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),sK304(U_12824,U_12823,U_12822,U_12821)))))
            & hBOOL(hAPP(U_12822,sK304(U_12824,U_12823,U_12822,U_12821))) ) )
        & ( ! [U_12819] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),U_12819))))
              | ~ hBOOL(hAPP(U_12822,U_12819)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),hAPP(c_Set_OCollect(U_12821),U_12822))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_12820,sK304(U_12824,U_12823,U_12822,U_12821))],[f_3317_2]) ).

cnf(f_3317_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),U_12819))))
    | ~ hBOOL(hAPP(U_12822,U_12819))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),hAPP(c_Set_OCollect(U_12821),U_12822))) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

cnf(f_3317_5,plain,
    ( hBOOL(hAPP(U_12822,sK304(U_12824,U_12823,U_12822,U_12821)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),hAPP(c_Set_OCollect(U_12821),U_12822))) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

cnf(f_3317_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBC(U_12823,U_12821,tc_HOL_Obool),U_12824),sK304(U_12824,U_12823,U_12822,U_12821)))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),hAPP(c_Set_OCollect(U_12823),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_HOL_Obool,U_12823),c_HOL_OEx(U_12821)),hAPP(hAPP(c_COMBB(tc_fun(U_12821,tc_HOL_Obool),tc_fun(U_12821,tc_HOL_Obool),U_12823),hAPP(c_COMBS(U_12821,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12821),c_fconj),U_12822))),U_12824)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),hAPP(c_Set_OCollect(U_12821),U_12822))) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

fof(f_3318_1,plain,
    ! [V_f_2,T_c,V_Pa_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_Pa_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).

fof(f_3318_2,plain,
    ! [U_12828,U_12827,U_12826,U_12825] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12827),hAPP(c_Set_OCollect(U_12827),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_HOL_Obool),tc_HOL_Obool,U_12827),c_HOL_OEx(U_12825)),hAPP(hAPP(c_COMBC(U_12827,tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_HOL_Obool)),U_12827),c_COMBS(U_12825,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12827),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12825),c_fconj)),hAPP(hAPP(c_COMBC(U_12827,tc_fun(U_12825,U_12827),tc_fun(U_12825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12827,tc_HOL_Obool),tc_fun(tc_fun(U_12825,U_12827),tc_fun(U_12825,tc_HOL_Obool)),U_12827),c_COMBB(U_12827,tc_HOL_Obool,U_12825)),c_fequal)),U_12828)))),U_12826)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12825),hAPP(c_Set_OCollect(U_12825),U_12826))) ),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

cnf(f_3318_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12827),hAPP(c_Set_OCollect(U_12827),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_HOL_Obool),tc_HOL_Obool,U_12827),c_HOL_OEx(U_12825)),hAPP(hAPP(c_COMBC(U_12827,tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_HOL_Obool)),U_12827),c_COMBS(U_12825,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12825,tc_HOL_Obool),tc_fun(U_12825,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12827),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12825),c_fconj)),hAPP(hAPP(c_COMBC(U_12827,tc_fun(U_12825,U_12827),tc_fun(U_12825,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12827,tc_HOL_Obool),tc_fun(tc_fun(U_12825,U_12827),tc_fun(U_12825,tc_HOL_Obool)),U_12827),c_COMBB(U_12827,tc_HOL_Obool,U_12825)),c_fequal)),U_12828)))),U_12826)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12825),hAPP(c_Set_OCollect(U_12825),U_12826))) ),
    inference(clausify,[status(thm)],[f_3318_2]) ).

fof(f_3319_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_3319_2,plain,
    ! [U_12830,U_12829] : c_Fun_Oinj__on(tc_fun(U_12829,U_12830),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(U_12829,U_12830)),c_Set_OCollect(tc_prod(U_12829,U_12830))),hAPP(hAPP(c_COMBB(tc_fun(U_12829,tc_fun(U_12830,tc_HOL_Obool)),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(U_12829,U_12830)),c_Product__Type_Oprod_Oprod__case(U_12829,U_12830,tc_HOL_Obool)),hAPP(c_COMBB(U_12830,tc_fun(U_12830,tc_HOL_Obool),U_12829),hAPP(c_COMBC(U_12830,U_12830,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12829,U_12830),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

cnf(f_3319_3,plain,
    c_Fun_Oinj__on(tc_fun(U_12829,U_12830),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(U_12829,U_12830)),c_Set_OCollect(tc_prod(U_12829,U_12830))),hAPP(hAPP(c_COMBB(tc_fun(U_12829,tc_fun(U_12830,tc_HOL_Obool)),tc_fun(tc_prod(U_12829,U_12830),tc_HOL_Obool),tc_fun(U_12829,U_12830)),c_Product__Type_Oprod_Oprod__case(U_12829,U_12830,tc_HOL_Obool)),hAPP(c_COMBB(U_12830,tc_fun(U_12830,tc_HOL_Obool),U_12829),hAPP(c_COMBC(U_12830,U_12830,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12829,U_12830),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3319_2]) ).

fof(f_3320_1,plain,
    ! [V_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(f_3320_2,plain,
    ! [U_12831] : 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_12831))),
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

cnf(f_3320_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_12831))),
    inference(clausify,[status(thm)],[f_3320_2]) ).

fof(f_3321_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_3321_2,plain,
    ! [U_12832] : c_Wellfounded_Ofinite__psubset(U_12832) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12832,tc_HOL_Obool)),c_COMBS(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12832,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_12832,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_12832)))),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

cnf(f_3321_3,plain,
    c_Wellfounded_Ofinite__psubset(U_12832) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_12832,tc_HOL_Obool)),c_COMBS(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12832,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_12832,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_12832,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_12832,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_12832)))),
    inference(clausify,[status(thm)],[f_3321_2]) ).

fof(f_3322_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_3322_2,plain,
    ! [U_12836,U_12835,U_12834,U_12833] : hAPP(hAPP(c_Relation_Oinv__image(U_12833,U_12834),U_12835),U_12836) = hAPP(c_Set_OCollect(tc_prod(U_12834,U_12834)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12834,U_12834,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12834,tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_fun(U_12834,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_fun(U_12834,tc_HOL_Obool)),U_12834),c_COMBC(U_12834,tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_prod(U_12833,U_12833)),tc_fun(U_12834,tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),U_12834),hAPP(c_COMBB(tc_prod(U_12833,U_12833),tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool),U_12834),c_member(tc_prod(U_12833,U_12833)))),hAPP(hAPP(c_COMBC(U_12834,tc_fun(U_12834,U_12833),tc_fun(U_12834,tc_prod(U_12833,U_12833))),hAPP(hAPP(c_COMBB(tc_fun(U_12833,tc_prod(U_12833,U_12833)),tc_fun(tc_fun(U_12834,U_12833),tc_fun(U_12834,tc_prod(U_12833,U_12833))),U_12834),c_COMBB(U_12833,tc_prod(U_12833,U_12833),U_12834)),hAPP(hAPP(c_COMBB(U_12833,tc_fun(U_12833,tc_prod(U_12833,U_12833)),U_12834),c_Product__Type_OPair(U_12833,U_12833)),U_12836))),U_12836)))),U_12835))),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

cnf(f_3322_3,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_12833,U_12834),U_12835),U_12836) = hAPP(c_Set_OCollect(tc_prod(U_12834,U_12834)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12834,U_12834,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12834,tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_fun(U_12834,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_fun(U_12834,tc_HOL_Obool)),U_12834),c_COMBC(U_12834,tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12834,tc_prod(U_12833,U_12833)),tc_fun(U_12834,tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool)),U_12834),hAPP(c_COMBB(tc_prod(U_12833,U_12833),tc_fun(tc_fun(tc_prod(U_12833,U_12833),tc_HOL_Obool),tc_HOL_Obool),U_12834),c_member(tc_prod(U_12833,U_12833)))),hAPP(hAPP(c_COMBC(U_12834,tc_fun(U_12834,U_12833),tc_fun(U_12834,tc_prod(U_12833,U_12833))),hAPP(hAPP(c_COMBB(tc_fun(U_12833,tc_prod(U_12833,U_12833)),tc_fun(tc_fun(U_12834,U_12833),tc_fun(U_12834,tc_prod(U_12833,U_12833))),U_12834),c_COMBB(U_12833,tc_prod(U_12833,U_12833),U_12834)),hAPP(hAPP(c_COMBB(U_12833,tc_fun(U_12833,tc_prod(U_12833,U_12833)),U_12834),c_Product__Type_OPair(U_12833,U_12833)),U_12836))),U_12836)))),U_12835))),
    inference(clausify,[status(thm)],[f_3322_2]) ).

fof(f_3323_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_3323_2,plain,
    ! [U_12837] : 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_12837)) = 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_12837),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

cnf(f_3323_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_12837)) = 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_12837),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3323_2]) ).

fof(f_3324_1,plain,
    ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_2),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(f_3324_2,plain,
    ! [U_12838] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_12838) = 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_12838),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

cnf(f_3324_3,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_12838) = 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_12838),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_3324_2]) ).

fof(f_3325_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_3325_2,plain,
    ! [U_12841,U_12840,U_12839] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12839),U_12841),c_Big__Operators_Olinorder__class_OMin(U_12839,U_12840)) = c_Big__Operators_Olinorder__class_OMin(U_12839,hAPP(c_Set_OCollect(U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_HOL_Obool,U_12839),c_HOL_OEx(U_12839)),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_HOL_Obool)),U_12839),c_COMBS(U_12839,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12839),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12839),c_fconj)),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,U_12839),tc_fun(U_12839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_fun(tc_fun(U_12839,U_12839),tc_fun(U_12839,tc_HOL_Obool)),U_12839),c_COMBB(U_12839,tc_HOL_Obool,U_12839)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_12839),U_12841))))),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12839)),U_12840)))))
      | U_12840 = c_Orderings_Obot__class_Obot(tc_fun(U_12839,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12839),U_12840))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_12839) ),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

cnf(f_3325_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12839),U_12841),c_Big__Operators_Olinorder__class_OMin(U_12839,U_12840)) = c_Big__Operators_Olinorder__class_OMin(U_12839,hAPP(c_Set_OCollect(U_12839),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_HOL_Obool,U_12839),c_HOL_OEx(U_12839)),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_HOL_Obool)),U_12839),c_COMBS(U_12839,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_fun(U_12839,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12839),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12839),c_fconj)),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,U_12839),tc_fun(U_12839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12839,tc_HOL_Obool),tc_fun(tc_fun(U_12839,U_12839),tc_fun(U_12839,tc_HOL_Obool)),U_12839),c_COMBB(U_12839,tc_HOL_Obool,U_12839)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_12839),U_12841))))),hAPP(hAPP(c_COMBC(U_12839,tc_fun(U_12839,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12839)),U_12840)))))
    | U_12840 = c_Orderings_Obot__class_Obot(tc_fun(U_12839,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12839),U_12840))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_12839) ),
    inference(clausify,[status(thm)],[f_3325_2]) ).

fof(f_3326_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_3326_2,plain,
    ! [U_12844,U_12843,U_12842] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12842),U_12844),c_Big__Operators_Olinorder__class_OMax(U_12842,U_12843)) = c_Big__Operators_Olinorder__class_OMax(U_12842,hAPP(c_Set_OCollect(U_12842),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_HOL_Obool,U_12842),c_HOL_OEx(U_12842)),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_HOL_Obool)),U_12842),c_COMBS(U_12842,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12842),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12842),c_fconj)),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,U_12842),tc_fun(U_12842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_fun(tc_fun(U_12842,U_12842),tc_fun(U_12842,tc_HOL_Obool)),U_12842),c_COMBB(U_12842,tc_HOL_Obool,U_12842)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_12842),U_12844))))),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12842)),U_12843)))))
      | U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_12842) ),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

cnf(f_3326_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12842),U_12844),c_Big__Operators_Olinorder__class_OMax(U_12842,U_12843)) = c_Big__Operators_Olinorder__class_OMax(U_12842,hAPP(c_Set_OCollect(U_12842),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_HOL_Obool,U_12842),c_HOL_OEx(U_12842)),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_HOL_Obool)),U_12842),c_COMBS(U_12842,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_fun(U_12842,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12842),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12842),c_fconj)),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,U_12842),tc_fun(U_12842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12842,tc_HOL_Obool),tc_fun(tc_fun(U_12842,U_12842),tc_fun(U_12842,tc_HOL_Obool)),U_12842),c_COMBB(U_12842,tc_HOL_Obool,U_12842)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_12842),U_12844))))),hAPP(hAPP(c_COMBC(U_12842,tc_fun(U_12842,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12842)),U_12843)))))
    | U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_12842) ),
    inference(clausify,[status(thm)],[f_3326_2]) ).

fof(f_3327_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_3327_2,plain,
    ! [U_12847,U_12846,U_12845] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12845),U_12847),c_Big__Operators_Olattice__class_OInf__fin(U_12845,U_12846)) = c_Big__Operators_Olattice__class_OInf__fin(U_12845,hAPP(c_Set_OCollect(U_12845),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_HOL_Obool,U_12845),c_HOL_OEx(U_12845)),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_HOL_Obool)),U_12845),c_COMBS(U_12845,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12845),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12845),c_fconj)),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,U_12845),tc_fun(U_12845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_fun(tc_fun(U_12845,U_12845),tc_fun(U_12845,tc_HOL_Obool)),U_12845),c_COMBB(U_12845,tc_HOL_Obool,U_12845)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12845),U_12847))))),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12845)),U_12846)))))
      | U_12846 = c_Orderings_Obot__class_Obot(tc_fun(U_12845,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12845),U_12846))
      | ~ class_Lattices_Odistrib__lattice(U_12845) ),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

cnf(f_3327_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12845),U_12847),c_Big__Operators_Olattice__class_OInf__fin(U_12845,U_12846)) = c_Big__Operators_Olattice__class_OInf__fin(U_12845,hAPP(c_Set_OCollect(U_12845),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_HOL_Obool,U_12845),c_HOL_OEx(U_12845)),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_HOL_Obool)),U_12845),c_COMBS(U_12845,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_fun(U_12845,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12845),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12845),c_fconj)),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,U_12845),tc_fun(U_12845,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12845,tc_HOL_Obool),tc_fun(tc_fun(U_12845,U_12845),tc_fun(U_12845,tc_HOL_Obool)),U_12845),c_COMBB(U_12845,tc_HOL_Obool,U_12845)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12845),U_12847))))),hAPP(hAPP(c_COMBC(U_12845,tc_fun(U_12845,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12845)),U_12846)))))
    | U_12846 = c_Orderings_Obot__class_Obot(tc_fun(U_12845,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12845),U_12846))
    | ~ class_Lattices_Odistrib__lattice(U_12845) ),
    inference(clausify,[status(thm)],[f_3327_2]) ).

fof(f_3328_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_3328_2,plain,
    ! [U_12850,U_12849,U_12848] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12848),c_Big__Operators_Olattice__class_OInf__fin(U_12848,U_12849)),c_Big__Operators_Olattice__class_OInf__fin(U_12848,U_12850)) = c_Big__Operators_Olattice__class_OInf__fin(U_12848,hAPP(c_Set_OCollect(U_12848),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool,U_12848),c_HOL_OEx(U_12848)),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_HOL_Obool),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool,U_12848),c_HOL_OEx(U_12848))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),tc_fun(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),U_12848),c_COMBS(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12848,tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBS(U_12848,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12848),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12848),c_fconj))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_fun(U_12848,U_12848)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool)),tc_fun(tc_fun(U_12848,tc_fun(U_12848,U_12848)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),U_12848),c_COMBB(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool),U_12848)),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_fun(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBB(U_12848,tc_HOL_Obool,U_12848)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_12848)))))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12848)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12848),c_fconj),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12848)),U_12849)))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12848)),U_12850)))))))
      | U_12850 = c_Orderings_Obot__class_Obot(tc_fun(U_12848,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12848),U_12850))
      | U_12849 = c_Orderings_Obot__class_Obot(tc_fun(U_12848,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12848),U_12849))
      | ~ class_Lattices_Odistrib__lattice(U_12848) ),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

cnf(f_3328_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12848),c_Big__Operators_Olattice__class_OInf__fin(U_12848,U_12849)),c_Big__Operators_Olattice__class_OInf__fin(U_12848,U_12850)) = c_Big__Operators_Olattice__class_OInf__fin(U_12848,hAPP(c_Set_OCollect(U_12848),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool,U_12848),c_HOL_OEx(U_12848)),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_HOL_Obool),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool,U_12848),c_HOL_OEx(U_12848))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),tc_fun(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),U_12848),c_COMBS(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12848,tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool))),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBS(U_12848,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool)),tc_fun(U_12848,tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12848),hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12848),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12848),c_fconj))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_fun(U_12848,U_12848)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool)),tc_fun(tc_fun(U_12848,tc_fun(U_12848,U_12848)),tc_fun(U_12848,tc_fun(U_12848,tc_HOL_Obool))),U_12848),c_COMBB(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool),U_12848)),hAPP(hAPP(c_COMBB(tc_fun(U_12848,tc_HOL_Obool),tc_fun(tc_fun(U_12848,U_12848),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBB(U_12848,tc_HOL_Obool,U_12848)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_12848)))))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12848,tc_HOL_Obool),tc_fun(U_12848,tc_HOL_Obool)),U_12848),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12848)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12848),c_fconj),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12848)),U_12849)))),hAPP(hAPP(c_COMBC(U_12848,tc_fun(U_12848,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12848)),U_12850)))))))
    | U_12850 = c_Orderings_Obot__class_Obot(tc_fun(U_12848,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12848),U_12850))
    | U_12849 = c_Orderings_Obot__class_Obot(tc_fun(U_12848,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12848),U_12849))
    | ~ class_Lattices_Odistrib__lattice(U_12848) ),
    inference(clausify,[status(thm)],[f_3328_2]) ).

fof(f_3329_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_3329_2,plain,
    ! [U_12853,U_12852,U_12851] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12851),U_12853),c_Big__Operators_Olattice__class_OSup__fin(U_12851,U_12852)) = c_Big__Operators_Olattice__class_OSup__fin(U_12851,hAPP(c_Set_OCollect(U_12851),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_HOL_Obool,U_12851),c_HOL_OEx(U_12851)),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_HOL_Obool)),U_12851),c_COMBS(U_12851,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12851),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12851),c_fconj)),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,U_12851),tc_fun(U_12851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_fun(tc_fun(U_12851,U_12851),tc_fun(U_12851,tc_HOL_Obool)),U_12851),c_COMBB(U_12851,tc_HOL_Obool,U_12851)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12851),U_12853))))),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12851)),U_12852)))))
      | U_12852 = c_Orderings_Obot__class_Obot(tc_fun(U_12851,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12851),U_12852))
      | ~ class_Lattices_Odistrib__lattice(U_12851) ),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

cnf(f_3329_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12851),U_12853),c_Big__Operators_Olattice__class_OSup__fin(U_12851,U_12852)) = c_Big__Operators_Olattice__class_OSup__fin(U_12851,hAPP(c_Set_OCollect(U_12851),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_HOL_Obool,U_12851),c_HOL_OEx(U_12851)),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_HOL_Obool)),U_12851),c_COMBS(U_12851,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_fun(U_12851,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12851),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12851),c_fconj)),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,U_12851),tc_fun(U_12851,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12851,tc_HOL_Obool),tc_fun(tc_fun(U_12851,U_12851),tc_fun(U_12851,tc_HOL_Obool)),U_12851),c_COMBB(U_12851,tc_HOL_Obool,U_12851)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12851),U_12853))))),hAPP(hAPP(c_COMBC(U_12851,tc_fun(U_12851,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12851)),U_12852)))))
    | U_12852 = c_Orderings_Obot__class_Obot(tc_fun(U_12851,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12851),U_12852))
    | ~ class_Lattices_Odistrib__lattice(U_12851) ),
    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__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_3330_2,plain,
    ! [U_12856,U_12855,U_12854] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12854),c_Big__Operators_Olattice__class_OSup__fin(U_12854,U_12855)),c_Big__Operators_Olattice__class_OSup__fin(U_12854,U_12856)) = c_Big__Operators_Olattice__class_OSup__fin(U_12854,hAPP(c_Set_OCollect(U_12854),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool,U_12854),c_HOL_OEx(U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_HOL_Obool),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool,U_12854),c_HOL_OEx(U_12854))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),tc_fun(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),U_12854),c_COMBS(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12854,tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBS(U_12854,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12854),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12854),c_fconj))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_fun(U_12854,U_12854)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool)),tc_fun(tc_fun(U_12854,tc_fun(U_12854,U_12854)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),U_12854),c_COMBB(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_fun(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBB(U_12854,tc_HOL_Obool,U_12854)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_12854)))))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12854)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12854),c_fconj),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12854)),U_12855)))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12854)),U_12856)))))))
      | U_12856 = c_Orderings_Obot__class_Obot(tc_fun(U_12854,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12854),U_12856))
      | U_12855 = c_Orderings_Obot__class_Obot(tc_fun(U_12854,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12854),U_12855))
      | ~ class_Lattices_Odistrib__lattice(U_12854) ),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

cnf(f_3330_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_12854),c_Big__Operators_Olattice__class_OSup__fin(U_12854,U_12855)),c_Big__Operators_Olattice__class_OSup__fin(U_12854,U_12856)) = c_Big__Operators_Olattice__class_OSup__fin(U_12854,hAPP(c_Set_OCollect(U_12854),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool,U_12854),c_HOL_OEx(U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_HOL_Obool),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool,U_12854),c_HOL_OEx(U_12854))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),tc_fun(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),U_12854),c_COMBS(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12854,tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool))),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBS(U_12854,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool)),tc_fun(U_12854,tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12854),hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12854),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12854),c_fconj))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_fun(U_12854,U_12854)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool)),tc_fun(tc_fun(U_12854,tc_fun(U_12854,U_12854)),tc_fun(U_12854,tc_fun(U_12854,tc_HOL_Obool))),U_12854),c_COMBB(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12854,tc_HOL_Obool),tc_fun(tc_fun(U_12854,U_12854),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBB(U_12854,tc_HOL_Obool,U_12854)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_12854)))))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12854,tc_HOL_Obool),tc_fun(U_12854,tc_HOL_Obool)),U_12854),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12854)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12854),c_fconj),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12854)),U_12855)))),hAPP(hAPP(c_COMBC(U_12854,tc_fun(U_12854,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12854)),U_12856)))))))
    | U_12856 = c_Orderings_Obot__class_Obot(tc_fun(U_12854,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12854),U_12856))
    | U_12855 = c_Orderings_Obot__class_Obot(tc_fun(U_12854,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12854),U_12855))
    | ~ class_Lattices_Odistrib__lattice(U_12854) ),
    inference(clausify,[status(thm)],[f_3330_2]) ).

fof(f_3331_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_3331_2,plain,
    ! [U_12859,U_12858,U_12857] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12857),U_12859),c_Big__Operators_Olattice_OInf__fin(U_12857,c_Orderings_Oord__class_Omin(U_12857),U_12858)) = c_Big__Operators_Olattice_OInf__fin(U_12857,c_Orderings_Oord__class_Omin(U_12857),hAPP(c_Set_OCollect(U_12857),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_HOL_Obool,U_12857),c_HOL_OEx(U_12857)),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),U_12857),c_COMBS(U_12857,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12857),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12857),c_fconj)),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,U_12857),tc_fun(U_12857,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_fun(tc_fun(U_12857,U_12857),tc_fun(U_12857,tc_HOL_Obool)),U_12857),c_COMBB(U_12857,tc_HOL_Obool,U_12857)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_12857),U_12859))))),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12857)),U_12858)))))
      | U_12858 = c_Orderings_Obot__class_Obot(tc_fun(U_12857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12857),U_12858))
      | ~ class_Orderings_Olinorder(U_12857) ),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

cnf(f_3331_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12857),U_12859),c_Big__Operators_Olattice_OInf__fin(U_12857,c_Orderings_Oord__class_Omin(U_12857),U_12858)) = c_Big__Operators_Olattice_OInf__fin(U_12857,c_Orderings_Oord__class_Omin(U_12857),hAPP(c_Set_OCollect(U_12857),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_HOL_Obool,U_12857),c_HOL_OEx(U_12857)),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_HOL_Obool)),U_12857),c_COMBS(U_12857,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_fun(U_12857,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12857),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12857),c_fconj)),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,U_12857),tc_fun(U_12857,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,tc_HOL_Obool),tc_fun(tc_fun(U_12857,U_12857),tc_fun(U_12857,tc_HOL_Obool)),U_12857),c_COMBB(U_12857,tc_HOL_Obool,U_12857)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_12857),U_12859))))),hAPP(hAPP(c_COMBC(U_12857,tc_fun(U_12857,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12857)),U_12858)))))
    | U_12858 = c_Orderings_Obot__class_Obot(tc_fun(U_12857,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12857),U_12858))
    | ~ class_Orderings_Olinorder(U_12857) ),
    inference(clausify,[status(thm)],[f_3331_2]) ).

fof(f_3332_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_3332_2,plain,
    ! [U_12862,U_12861,U_12860] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12860),c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),U_12861)),c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),U_12862)) = c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),hAPP(c_Set_OCollect(U_12860),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool,U_12860),c_HOL_OEx(U_12860)),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_HOL_Obool),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool,U_12860),c_HOL_OEx(U_12860))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),tc_fun(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),U_12860),c_COMBS(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12860,tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBS(U_12860,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12860),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12860),c_fconj))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_fun(U_12860,U_12860)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool)),tc_fun(tc_fun(U_12860,tc_fun(U_12860,U_12860)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),U_12860),c_COMBB(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool),U_12860)),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_fun(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBB(U_12860,tc_HOL_Obool,U_12860)),c_fequal))),c_Orderings_Oord__class_Omax(U_12860)))))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12860)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12860),c_fconj),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12860)),U_12861)))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12860)),U_12862)))))))
      | U_12862 = c_Orderings_Obot__class_Obot(tc_fun(U_12860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12860),U_12862))
      | U_12861 = c_Orderings_Obot__class_Obot(tc_fun(U_12860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12860),U_12861))
      | ~ class_Orderings_Olinorder(U_12860) ),
    inference(variable_rename,[status(thm)],[f_3332_1]) ).

cnf(f_3332_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12860),c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),U_12861)),c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),U_12862)) = c_Big__Operators_Olattice_OInf__fin(U_12860,c_Orderings_Oord__class_Omin(U_12860),hAPP(c_Set_OCollect(U_12860),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool,U_12860),c_HOL_OEx(U_12860)),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_HOL_Obool),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool,U_12860),c_HOL_OEx(U_12860))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),tc_fun(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),U_12860),c_COMBS(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12860,tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool))),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBS(U_12860,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool)),tc_fun(U_12860,tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12860),hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12860),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12860),c_fconj))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_fun(U_12860,U_12860)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool)),tc_fun(tc_fun(U_12860,tc_fun(U_12860,U_12860)),tc_fun(U_12860,tc_fun(U_12860,tc_HOL_Obool))),U_12860),c_COMBB(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool),U_12860)),hAPP(hAPP(c_COMBB(tc_fun(U_12860,tc_HOL_Obool),tc_fun(tc_fun(U_12860,U_12860),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBB(U_12860,tc_HOL_Obool,U_12860)),c_fequal))),c_Orderings_Oord__class_Omax(U_12860)))))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12860,tc_HOL_Obool),tc_fun(U_12860,tc_HOL_Obool)),U_12860),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12860)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12860),c_fconj),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12860)),U_12861)))),hAPP(hAPP(c_COMBC(U_12860,tc_fun(U_12860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12860)),U_12862)))))))
    | U_12862 = c_Orderings_Obot__class_Obot(tc_fun(U_12860,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12860),U_12862))
    | U_12861 = c_Orderings_Obot__class_Obot(tc_fun(U_12860,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12860),U_12861))
    | ~ class_Orderings_Olinorder(U_12860) ),
    inference(clausify,[status(thm)],[f_3332_2]) ).

fof(f_3333_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_3333_2,plain,
    ! [U_12866,U_12865,U_12864,U_12863] : c_Nitpick_Oprod(U_12863,U_12864,U_12865,U_12866) = hAPP(c_Set_OCollect(tc_prod(U_12863,U_12864)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12863,U_12864,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12863,tc_fun(U_12864,tc_HOL_Obool),tc_fun(U_12864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12864,tc_HOL_Obool),tc_fun(U_12864,tc_HOL_Obool)),U_12863),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12864)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12863),c_fconj),hAPP(hAPP(c_COMBC(U_12863,tc_fun(U_12863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12863)),U_12865)))),hAPP(hAPP(c_COMBC(U_12864,tc_fun(U_12864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12864)),U_12866)))),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

cnf(f_3333_3,plain,
    c_Nitpick_Oprod(U_12863,U_12864,U_12865,U_12866) = hAPP(c_Set_OCollect(tc_prod(U_12863,U_12864)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12863,U_12864,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12863,tc_fun(U_12864,tc_HOL_Obool),tc_fun(U_12864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12864,tc_HOL_Obool),tc_fun(U_12864,tc_HOL_Obool)),U_12863),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12864)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12863),c_fconj),hAPP(hAPP(c_COMBC(U_12863,tc_fun(U_12863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12863)),U_12865)))),hAPP(hAPP(c_COMBC(U_12864,tc_fun(U_12864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12864)),U_12866)))),
    inference(clausify,[status(thm)],[f_3333_2]) ).

fof(f_3334_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_3334_2,plain,
    ! [U_12867] : c_Int_Oint__ge__less__than(U_12867) = 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_12867)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

cnf(f_3334_3,plain,
    c_Int_Oint__ge__less__than(U_12867) = 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_12867)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3334_2]) ).

fof(f_3335_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_3335_2,plain,
    ! [U_12868] : c_Int_Oint__ge__less__than2(U_12868) = 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_12868)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3335_1]) ).

cnf(f_3335_3,plain,
    c_Int_Oint__ge__less__than2(U_12868) = 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_12868)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3335_2]) ).

fof(f_3336_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_3336_2,plain,
    ! [U_12870,U_12869] :
      ( ( c_Predicate_Oreflp(U_12869,U_12870)
        | ~ c_Relation_Orefl__on(U_12869,c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12869,U_12869)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12869,tc_HOL_Obool),U_12870))) )
      & ( c_Relation_Orefl__on(U_12869,c_Orderings_Otop__class_Otop(tc_fun(U_12869,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12869,U_12869)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12869,tc_HOL_Obool),U_12870)))
        | ~ c_Predicate_Oreflp(U_12869,U_12870) ) ),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

fof(f_3336_3,plain,
    ( ! [U_12874,U_12872] :
        ( c_Predicate_Oreflp(U_12872,U_12874)
        | ~ c_Relation_Orefl__on(U_12872,c_Orderings_Otop__class_Otop(tc_fun(U_12872,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12872,U_12872)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12872,U_12872,tc_HOL_Obool),U_12874))) )
    & ! [U_12873,U_12871] :
        ( c_Relation_Orefl__on(U_12871,c_Orderings_Otop__class_Otop(tc_fun(U_12871,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12871,U_12871)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12871,tc_HOL_Obool),U_12873)))
        | ~ c_Predicate_Oreflp(U_12871,U_12873) ) ),
    inference(miniscope,[status(thm)],[f_3336_2]) ).

cnf(f_3336_4,plain,
    ( c_Relation_Orefl__on(U_12871,c_Orderings_Otop__class_Otop(tc_fun(U_12871,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12871,U_12871)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12871,tc_HOL_Obool),U_12873)))
    | ~ c_Predicate_Oreflp(U_12871,U_12873) ),
    inference(clausify,[status(thm)],[f_3336_3]) ).

cnf(f_3336_5,plain,
    ( c_Predicate_Oreflp(U_12872,U_12874)
    | ~ c_Relation_Orefl__on(U_12872,c_Orderings_Otop__class_Otop(tc_fun(U_12872,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_12872,U_12872)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12872,U_12872,tc_HOL_Obool),U_12874))) ),
    inference(clausify,[status(thm)],[f_3336_3]) ).

fof(f_3337_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_3337_2,plain,
    ! [U_12881,U_12880,U_12879,U_12878,U_12877,U_12876,U_12875] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12876,U_12875),U_12878),U_12880)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12877,U_12875),U_12879),U_12881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,U_12875),c_Fun_Oid(U_12875)),hAPP(c_Set_OCollect(U_12875),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_HOL_Obool),tc_HOL_Obool,U_12875),c_HOL_OEx(U_12876)),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_HOL_Obool),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_HOL_Obool,U_12876),c_HOL_OEx(U_12877))),hAPP(hAPP(c_COMBC(U_12875,tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),tc_fun(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),U_12875),c_COMBS(U_12876,tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12876,tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),U_12876),c_COMBS(U_12877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12877),c_fconj))),hAPP(hAPP(c_COMBC(U_12875,tc_fun(U_12876,tc_fun(U_12877,U_12875)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool)),tc_fun(tc_fun(U_12876,tc_fun(U_12877,U_12875)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),U_12875),c_COMBB(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool),U_12876)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,tc_HOL_Obool),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool)),U_12875),c_COMBB(U_12875,tc_HOL_Obool,U_12877)),c_fequal))),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,U_12875),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),U_12876),c_COMBB(U_12875,U_12875,U_12877)),hAPP(hAPP(c_COMBB(U_12875,tc_fun(U_12875,U_12875),U_12876),c_Groups_Otimes__class_Otimes(U_12875)),U_12878))),U_12879)))))),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),U_12876),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12877)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12876),c_fconj),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12876)),U_12880)))),hAPP(hAPP(c_COMBC(U_12877,tc_fun(U_12877,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12877)),U_12881)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_12876,U_12877),U_12875,hAPP(c_Product__Type_Oprod_Oprod__case(U_12876,U_12877,U_12875),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,U_12875),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),U_12876),c_COMBB(U_12875,U_12875,U_12877)),hAPP(hAPP(c_COMBB(U_12875,tc_fun(U_12875,U_12875),U_12876),c_Groups_Otimes__class_Otimes(U_12875)),U_12878))),U_12879)),hAPP(hAPP(c_Product__Type_OSigma(U_12876,U_12877),U_12880),hAPP(c_COMBK(tc_fun(U_12877,tc_HOL_Obool),U_12876),U_12881)))
      | ~ class_Rings_Osemiring__0(U_12875) ),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

cnf(f_3337_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12876,U_12875),U_12878),U_12880)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12877,U_12875),U_12879),U_12881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,U_12875),c_Fun_Oid(U_12875)),hAPP(c_Set_OCollect(U_12875),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_HOL_Obool),tc_HOL_Obool,U_12875),c_HOL_OEx(U_12876)),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_HOL_Obool),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_HOL_Obool,U_12876),c_HOL_OEx(U_12877))),hAPP(hAPP(c_COMBC(U_12875,tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),tc_fun(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),U_12875),c_COMBS(U_12876,tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_12876,tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool))),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),U_12876),c_COMBS(U_12877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool)),tc_fun(U_12876,tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_12875),hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12877),c_fconj))),hAPP(hAPP(c_COMBC(U_12875,tc_fun(U_12876,tc_fun(U_12877,U_12875)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool)),tc_fun(tc_fun(U_12876,tc_fun(U_12877,U_12875)),tc_fun(U_12876,tc_fun(U_12877,tc_HOL_Obool))),U_12875),c_COMBB(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool),U_12876)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,tc_HOL_Obool),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,tc_HOL_Obool)),U_12875),c_COMBB(U_12875,tc_HOL_Obool,U_12877)),c_fequal))),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,U_12875),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),U_12876),c_COMBB(U_12875,U_12875,U_12877)),hAPP(hAPP(c_COMBB(U_12875,tc_fun(U_12875,U_12875),U_12876),c_Groups_Otimes__class_Otimes(U_12875)),U_12878))),U_12879)))))),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12877,tc_HOL_Obool),tc_fun(U_12877,tc_HOL_Obool)),U_12876),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12877)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12876),c_fconj),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12876)),U_12880)))),hAPP(hAPP(c_COMBC(U_12877,tc_fun(U_12877,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12877)),U_12881)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_12876,U_12877),U_12875,hAPP(c_Product__Type_Oprod_Oprod__case(U_12876,U_12877,U_12875),hAPP(hAPP(c_COMBC(U_12876,tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),hAPP(hAPP(c_COMBB(tc_fun(U_12875,U_12875),tc_fun(tc_fun(U_12877,U_12875),tc_fun(U_12877,U_12875)),U_12876),c_COMBB(U_12875,U_12875,U_12877)),hAPP(hAPP(c_COMBB(U_12875,tc_fun(U_12875,U_12875),U_12876),c_Groups_Otimes__class_Otimes(U_12875)),U_12878))),U_12879)),hAPP(hAPP(c_Product__Type_OSigma(U_12876,U_12877),U_12880),hAPP(c_COMBK(tc_fun(U_12877,tc_HOL_Obool),U_12876),U_12881)))
    | ~ class_Rings_Osemiring__0(U_12875) ),
    inference(clausify,[status(thm)],[f_3337_2]) ).

fof(f_3338_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_3338_2,plain,
    ! [U_12888,U_12887,U_12886,U_12885,U_12884,U_12883] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12883,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_Nat_Onat,U_12883),c_Finite__Set_Ocard(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),c_Set_OCollect(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),hAPP(c_COMBS(U_12885,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12885),c_fconj),hAPP(hAPP(c_COMBC(U_12885,tc_fun(U_12885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12885)),U_12886)))),U_12887)))),U_12884) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12885,tc_Nat_Onat),U_12888),U_12886)
      | ? [U_12882] :
          ( hAPP(c_Finite__Set_Ocard(U_12883),hAPP(c_Set_OCollect(U_12883),hAPP(hAPP(c_COMBS(U_12883,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12883),c_fconj),hAPP(hAPP(c_COMBC(U_12883,tc_fun(U_12883,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12883)),U_12884))),hAPP(hAPP(c_COMBC(U_12883,U_12885,tc_HOL_Obool),U_12887),U_12882)))) != hAPP(U_12888,U_12882)
          & hBOOL(hAPP(hAPP(c_member(U_12885),U_12882),U_12886)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12883),U_12884)) ),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

fof(f_3338_3,plain,
    ! [U_12888,U_12887,U_12886,U_12885,U_12884,U_12883] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12883,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_Nat_Onat,U_12883),c_Finite__Set_Ocard(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),c_Set_OCollect(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),hAPP(c_COMBS(U_12885,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12885),c_fconj),hAPP(hAPP(c_COMBC(U_12885,tc_fun(U_12885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12885)),U_12886)))),U_12887)))),U_12884) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12885,tc_Nat_Onat),U_12888),U_12886)
      | ( hAPP(c_Finite__Set_Ocard(U_12883),hAPP(c_Set_OCollect(U_12883),hAPP(hAPP(c_COMBS(U_12883,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12883),c_fconj),hAPP(hAPP(c_COMBC(U_12883,tc_fun(U_12883,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12883)),U_12884))),hAPP(hAPP(c_COMBC(U_12883,U_12885,tc_HOL_Obool),U_12887),sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883))))) != hAPP(U_12888,sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883))
        & hBOOL(hAPP(hAPP(c_member(U_12885),sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883)),U_12886)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12883),U_12884)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_12882,sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883))],[f_3338_2]) ).

cnf(f_3338_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12885),sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883)),U_12886))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12883,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_Nat_Onat,U_12883),c_Finite__Set_Ocard(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),c_Set_OCollect(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),hAPP(c_COMBS(U_12885,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12885),c_fconj),hAPP(hAPP(c_COMBC(U_12885,tc_fun(U_12885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12885)),U_12886)))),U_12887)))),U_12884) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12885,tc_Nat_Onat),U_12888),U_12886)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12883),U_12884)) ),
    inference(clausify,[status(thm)],[f_3338_3]) ).

cnf(f_3338_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_12883),hAPP(c_Set_OCollect(U_12883),hAPP(hAPP(c_COMBS(U_12883,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12883),c_fconj),hAPP(hAPP(c_COMBC(U_12883,tc_fun(U_12883,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12883)),U_12884))),hAPP(hAPP(c_COMBC(U_12883,U_12885,tc_HOL_Obool),U_12887),sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883))))) != hAPP(U_12888,sK305(U_12888,U_12887,U_12886,U_12885,U_12884,U_12883))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12883,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_Nat_Onat,U_12883),c_Finite__Set_Ocard(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),c_Set_OCollect(U_12885)),hAPP(hAPP(c_COMBB(tc_fun(U_12885,tc_HOL_Obool),tc_fun(U_12885,tc_HOL_Obool),U_12883),hAPP(c_COMBS(U_12885,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12885),c_fconj),hAPP(hAPP(c_COMBC(U_12885,tc_fun(U_12885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12885)),U_12886)))),U_12887)))),U_12884) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12885,tc_Nat_Onat),U_12888),U_12886)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12883),U_12884)) ),
    inference(clausify,[status(thm)],[f_3338_3]) ).

fof(f_3339_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_3339_2,plain,
    ! [U_12890,U_12889] : c_Fun_Oinj__on(U_12889,U_12889,c_Fun_Oid(U_12889),U_12890),
    inference(variable_rename,[status(thm)],[f_3339_1]) ).

cnf(f_3339_3,plain,
    c_Fun_Oinj__on(U_12889,U_12889,c_Fun_Oid(U_12889),U_12890),
    inference(clausify,[status(thm)],[f_3339_2]) ).

fof(f_3340_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_3340_2,plain,
    ! [U_12892,U_12891] : c_Product__Type_Omap__pair(U_12891,U_12891,U_12892,U_12892,c_Fun_Oid(U_12891),c_Fun_Oid(U_12892)) = c_Fun_Oid(tc_prod(U_12891,U_12892)),
    inference(variable_rename,[status(thm)],[f_3340_1]) ).

cnf(f_3340_3,plain,
    c_Product__Type_Omap__pair(U_12891,U_12891,U_12892,U_12892,c_Fun_Oid(U_12891),c_Fun_Oid(U_12892)) = c_Fun_Oid(tc_prod(U_12891,U_12892)),
    inference(clausify,[status(thm)],[f_3340_2]) ).

fof(f_3341_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_3341_2,plain,
    ! [U_12894,U_12893] : c_Product__Type_Omap__pair(U_12893,U_12893,U_12894,U_12894,c_COMBI(U_12893),c_COMBI(U_12894)) = c_Fun_Oid(tc_prod(U_12893,U_12894)),
    inference(variable_rename,[status(thm)],[f_3341_1]) ).

cnf(f_3341_3,plain,
    c_Product__Type_Omap__pair(U_12893,U_12893,U_12894,U_12894,c_COMBI(U_12893),c_COMBI(U_12894)) = c_Fun_Oid(tc_prod(U_12893,U_12894)),
    inference(clausify,[status(thm)],[f_3341_2]) ).

fof(f_3342_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_3342_2,plain,
    ! [U_12896,U_12895] : hAPP(c_Set_Ovimage(U_12895,U_12895,c_Fun_Oid(U_12895)),U_12896) = U_12896,
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

cnf(f_3342_3,plain,
    hAPP(c_Set_Ovimage(U_12895,U_12895,c_Fun_Oid(U_12895)),U_12896) = U_12896,
    inference(clausify,[status(thm)],[f_3342_2]) ).

fof(f_3343_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_3343_2,plain,
    ! [U_12898,U_12897] : hAPP(c_Fun_Oid(U_12897),U_12898) = U_12898,
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

cnf(f_3343_3,plain,
    hAPP(c_Fun_Oid(U_12897),U_12898) = U_12898,
    inference(clausify,[status(thm)],[f_3343_2]) ).

fof(f_3344_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_3344_2,plain,
    ! [U_12900,U_12899] : hAPP(c_Fun_Oid(U_12899),U_12900) = U_12900,
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

cnf(f_3344_3,plain,
    hAPP(c_Fun_Oid(U_12899),U_12900) = U_12900,
    inference(clausify,[status(thm)],[f_3344_2]) ).

fof(f_3345_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_3345_2,plain,
    ! [U_12903,U_12902,U_12901] :
      ( hBOOL(hAPP(hAPP(U_12902,U_12903),U_12903))
      | ~ c_Predicate_Oreflp(U_12901,U_12902) ),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

fof(f_3345_3,plain,
    ! [U_12903,U_12902] :
      ( ! [U_12901] : ~ c_Predicate_Oreflp(U_12901,U_12902)
      | hBOOL(hAPP(hAPP(U_12902,U_12903),U_12903)) ),
    inference(miniscope,[status(thm)],[f_3345_2]) ).

cnf(f_3345_4,plain,
    ( ~ c_Predicate_Oreflp(U_12901,U_12902)
    | hBOOL(hAPP(hAPP(U_12902,U_12903),U_12903)) ),
    inference(clausify,[status(thm)],[f_3345_3]) ).

fof(f_3346_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_3346_2,plain,
    ! [U_12905,U_12904] : c_Product__Type_Oapsnd(U_12904,U_12904,U_12905,c_Fun_Oid(U_12904)) = c_Fun_Oid(tc_prod(U_12905,U_12904)),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

cnf(f_3346_3,plain,
    c_Product__Type_Oapsnd(U_12904,U_12904,U_12905,c_Fun_Oid(U_12904)) = c_Fun_Oid(tc_prod(U_12905,U_12904)),
    inference(clausify,[status(thm)],[f_3346_2]) ).

fof(f_3347_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_3347_2,plain,
    ! [U_12907,U_12906] : c_Product__Type_Oapfst(U_12906,U_12906,U_12907,c_Fun_Oid(U_12906)) = c_Fun_Oid(tc_prod(U_12906,U_12907)),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

cnf(f_3347_3,plain,
    c_Product__Type_Oapfst(U_12906,U_12906,U_12907,c_Fun_Oid(U_12906)) = c_Fun_Oid(tc_prod(U_12906,U_12907)),
    inference(clausify,[status(thm)],[f_3347_2]) ).

fof(f_3348_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_3348_2,plain,
    ! [U_12909,U_12908] : hAPP(c_Set_Oimage(U_12908,U_12908,c_Fun_Oid(U_12908)),U_12909) = U_12909,
    inference(variable_rename,[status(thm)],[f_3348_1]) ).

cnf(f_3348_3,plain,
    hAPP(c_Set_Oimage(U_12908,U_12908,c_Fun_Oid(U_12908)),U_12909) = U_12909,
    inference(clausify,[status(thm)],[f_3348_2]) ).

fof(f_3349_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_3349_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3349_1]) ).

fof(f_3350_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_3350_2,plain,
    ! [U_12910] : hAPP(c_Set_Oimage(U_12910,U_12910,c_Fun_Oid(U_12910)),c_Orderings_Otop__class_Otop(tc_fun(U_12910,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12910,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3350_1]) ).

cnf(f_3350_3,plain,
    hAPP(c_Set_Oimage(U_12910,U_12910,c_Fun_Oid(U_12910)),c_Orderings_Otop__class_Otop(tc_fun(U_12910,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12910,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3350_2]) ).

fof(f_3351_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_3351_2,plain,
    ! [U_12914,U_12913,U_12912,U_12911] : c_Product__Type_Oapsnd(U_12911,U_12912,U_12913,U_12914) = c_Product__Type_Omap__pair(U_12913,U_12913,U_12911,U_12912,c_Fun_Oid(U_12913),U_12914),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

cnf(f_3351_3,plain,
    c_Product__Type_Oapsnd(U_12911,U_12912,U_12913,U_12914) = c_Product__Type_Omap__pair(U_12913,U_12913,U_12911,U_12912,c_Fun_Oid(U_12913),U_12914),
    inference(clausify,[status(thm)],[f_3351_2]) ).

fof(f_3352_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_3352_2,plain,
    ! [U_12918,U_12917,U_12916,U_12915] : c_Product__Type_Oapfst(U_12915,U_12916,U_12917,U_12918) = c_Product__Type_Omap__pair(U_12915,U_12916,U_12917,U_12917,U_12918,c_Fun_Oid(U_12917)),
    inference(variable_rename,[status(thm)],[f_3352_1]) ).

cnf(f_3352_3,plain,
    c_Product__Type_Oapfst(U_12915,U_12916,U_12917,U_12918) = c_Product__Type_Omap__pair(U_12915,U_12916,U_12917,U_12917,U_12918,c_Fun_Oid(U_12917)),
    inference(clausify,[status(thm)],[f_3352_2]) ).

fof(f_3353_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_3353_2,plain,
    ! [U_12920,U_12919] : hAPP(c_Product__Type_Oprod_Oprod__case(U_12919,U_12920,tc_prod(U_12919,U_12920)),c_Product__Type_OPair(U_12919,U_12920)) = c_Fun_Oid(tc_prod(U_12919,U_12920)),
    inference(variable_rename,[status(thm)],[f_3353_1]) ).

cnf(f_3353_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_12919,U_12920,tc_prod(U_12919,U_12920)),c_Product__Type_OPair(U_12919,U_12920)) = c_Fun_Oid(tc_prod(U_12919,U_12920)),
    inference(clausify,[status(thm)],[f_3353_2]) ).

fof(f_3354_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_3354_2,plain,
    ! [U_12924,U_12923,U_12922,U_12921] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12922,U_12921),U_12923),U_12924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12921,U_12921),c_Fun_Oid(U_12921)),hAPP(c_Set_Oimage(U_12922,U_12921,U_12923),U_12924))
      | ~ c_Fun_Oinj__on(U_12922,U_12921,U_12923,U_12924)
      | ~ class_Groups_Ocomm__monoid__add(U_12921) ),
    inference(variable_rename,[status(thm)],[f_3354_1]) ).

cnf(f_3354_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12922,U_12921),U_12923),U_12924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12921,U_12921),c_Fun_Oid(U_12921)),hAPP(c_Set_Oimage(U_12922,U_12921,U_12923),U_12924))
    | ~ c_Fun_Oinj__on(U_12922,U_12921,U_12923,U_12924)
    | ~ class_Groups_Ocomm__monoid__add(U_12921) ),
    inference(clausify,[status(thm)],[f_3354_2]) ).

fof(f_3355_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_3355_2,plain,
    ! [U_12928,U_12927,U_12926,U_12925] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12926,U_12925),U_12927),U_12928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12925,U_12925),c_Fun_Oid(U_12925)),hAPP(c_Set_Oimage(U_12926,U_12925,U_12927),U_12928))
      | ~ c_Fun_Oinj__on(U_12926,U_12925,U_12927,U_12928)
      | ~ class_Groups_Ocomm__monoid__mult(U_12925) ),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

cnf(f_3355_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12926,U_12925),U_12927),U_12928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12925,U_12925),c_Fun_Oid(U_12925)),hAPP(c_Set_Oimage(U_12926,U_12925,U_12927),U_12928))
    | ~ c_Fun_Oinj__on(U_12926,U_12925,U_12927,U_12928)
    | ~ class_Groups_Ocomm__monoid__mult(U_12925) ),
    inference(clausify,[status(thm)],[f_3355_2]) ).

fof(f_3356_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_3356_2,plain,
    ! [U_12934,U_12933] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12933),U_12934))
        | ! [U_12932,U_12931] : U_12934 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12933,U_12931),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_12932))) )
      & ( ? [U_12930,U_12929] : U_12934 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12933,U_12929),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_12930)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12933),U_12934)) ) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

fof(f_3356_3,plain,
    ( ! [U_12938,U_12936] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),U_12938))
        | ! [U_12932,U_12931] : U_12938 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12936,U_12931),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_12932))) )
    & ! [U_12937,U_12935] :
        ( ? [U_12930,U_12929] : U_12937 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12935,U_12929),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_12930)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12935),U_12937)) ) ),
    inference(miniscope,[status(thm)],[f_3356_2]) ).

fof(f_3356_4,plain,
    ( ! [U_12938,U_12936] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),U_12938))
        | ! [U_12932,U_12931] : U_12938 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12936,U_12931),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_12932))) )
    & ! [U_12937,U_12935] :
        ( ? [U_12929] : U_12937 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12935,U_12929),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)),sK306(U_12937,U_12935))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12935),U_12937)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_12930,sK306(U_12937,U_12935))],[f_3356_3]) ).

fof(f_3356_5,plain,
    ( ! [U_12938,U_12936] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),U_12938))
        | ! [U_12932,U_12931] : U_12938 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12936,U_12931),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_12932))) )
    & ! [U_12937,U_12935] :
        ( U_12937 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12935,sK307(U_12937,U_12935)),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)),sK306(U_12937,U_12935))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12935),U_12937)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_12929,sK307(U_12937,U_12935))],[f_3356_4]) ).

cnf(f_3356_6,plain,
    ( U_12937 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12935,sK307(U_12937,U_12935)),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)),sK306(U_12937,U_12935))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12935),U_12937)) ),
    inference(clausify,[status(thm)],[f_3356_5]) ).

cnf(f_3356_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),U_12938))
    | U_12938 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12936,U_12931),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_12932))) ),
    inference(clausify,[status(thm)],[f_3356_5]) ).

fof(f_3357_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_3357_2,plain,
    ! [U_12943,U_12942,U_12941,U_12940,U_12939] : hAPP(hAPP(c_Relation_Orel__comp(U_12939,U_12940,U_12941),U_12942),U_12943) = hAPP(c_Set_OCollect(tc_prod(U_12939,U_12941)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12939,U_12941,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_HOL_Obool),U_12939),hAPP(c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_HOL_Obool,U_12941),c_HOL_OEx(U_12940))),hAPP(hAPP(c_COMBC(U_12939,tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),tc_fun(tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool))),U_12939),c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool),U_12941)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12939),c_COMBS(U_12940,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12940),c_fconj)),hAPP(hAPP(c_COMBC(U_12939,tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12939),c_COMBC(U_12940,tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_prod(U_12939,U_12940)),tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),U_12939),hAPP(c_COMBB(tc_prod(U_12939,U_12940),tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool),U_12940),c_member(tc_prod(U_12939,U_12940)))),c_Product__Type_OPair(U_12939,U_12940)))),U_12942))))),hAPP(hAPP(c_COMBC(U_12941,tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12941),c_COMBC(U_12940,tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_prod(U_12940,U_12941)),tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),U_12941),hAPP(c_COMBB(tc_prod(U_12940,U_12941),tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool),U_12940),c_member(tc_prod(U_12940,U_12941)))),hAPP(c_COMBC(U_12940,U_12941,tc_prod(U_12940,U_12941)),c_Product__Type_OPair(U_12940,U_12941))))),U_12943))))),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

cnf(f_3357_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12939,U_12940,U_12941),U_12942),U_12943) = hAPP(c_Set_OCollect(tc_prod(U_12939,U_12941)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12939,U_12941,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_HOL_Obool),U_12939),hAPP(c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_HOL_Obool,U_12941),c_HOL_OEx(U_12940))),hAPP(hAPP(c_COMBC(U_12939,tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),tc_fun(tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool)),tc_fun(U_12941,tc_fun(U_12940,tc_HOL_Obool))),U_12939),c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool),U_12941)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12939),c_COMBS(U_12940,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_HOL_Obool),tc_fun(U_12940,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12939),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12940),c_fconj)),hAPP(hAPP(c_COMBC(U_12939,tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12939),c_COMBC(U_12940,tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_prod(U_12939,U_12940)),tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool)),U_12939),hAPP(c_COMBB(tc_prod(U_12939,U_12940),tc_fun(tc_fun(tc_prod(U_12939,U_12940),tc_HOL_Obool),tc_HOL_Obool),U_12940),c_member(tc_prod(U_12939,U_12940)))),c_Product__Type_OPair(U_12939,U_12940)))),U_12942))))),hAPP(hAPP(c_COMBC(U_12941,tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_fun(U_12940,tc_HOL_Obool)),U_12941),c_COMBC(U_12940,tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12940,tc_prod(U_12940,U_12941)),tc_fun(U_12940,tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool)),U_12941),hAPP(c_COMBB(tc_prod(U_12940,U_12941),tc_fun(tc_fun(tc_prod(U_12940,U_12941),tc_HOL_Obool),tc_HOL_Obool),U_12940),c_member(tc_prod(U_12940,U_12941)))),hAPP(c_COMBC(U_12940,U_12941,tc_prod(U_12940,U_12941)),c_Product__Type_OPair(U_12940,U_12941))))),U_12943))))),
    inference(clausify,[status(thm)],[f_3357_2]) ).

fof(f_3358_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).

fof(f_3358_2,plain,
    ! [U_12946,U_12945,U_12944] : hAPP(c_Relation_ORange(U_12944,U_12945),hAPP(c_Set_OCollect(tc_prod(U_12944,U_12945)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12944,U_12945,tc_HOL_Obool),U_12946))) = hAPP(c_Set_OCollect(U_12945),hAPP(hAPP(c_COMBB(tc_fun(U_12944,tc_HOL_Obool),tc_HOL_Obool,U_12945),c_HOL_OEx(U_12944)),hAPP(c_COMBC(U_12944,U_12945,tc_HOL_Obool),U_12946))),
    inference(variable_rename,[status(thm)],[f_3358_1]) ).

cnf(f_3358_3,plain,
    hAPP(c_Relation_ORange(U_12944,U_12945),hAPP(c_Set_OCollect(tc_prod(U_12944,U_12945)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12944,U_12945,tc_HOL_Obool),U_12946))) = hAPP(c_Set_OCollect(U_12945),hAPP(hAPP(c_COMBB(tc_fun(U_12944,tc_HOL_Obool),tc_HOL_Obool,U_12945),c_HOL_OEx(U_12944)),hAPP(c_COMBC(U_12944,U_12945,tc_HOL_Obool),U_12946))),
    inference(clausify,[status(thm)],[f_3358_2]) ).

fof(f_3359_1,plain,
    ! [V_s_2,V_ca_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_ca_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_ca_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_3359_2,plain,
    ! [U_12954,U_12953,U_12952,U_12951,U_12950,U_12949,U_12948,U_12947] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12947,U_12952)),hAPP(hAPP(c_Product__Type_OPair(U_12947,U_12952),U_12949),U_12953)),hAPP(hAPP(c_Relation_Orel__comp(U_12947,U_12948,U_12952),U_12951),U_12954)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12948,U_12952)),hAPP(hAPP(c_Product__Type_OPair(U_12948,U_12952),U_12950),U_12953)),U_12954))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12947,U_12948)),hAPP(hAPP(c_Product__Type_OPair(U_12947,U_12948),U_12949),U_12950)),U_12951)) ),
    inference(variable_rename,[status(thm)],[f_3359_1]) ).

cnf(f_3359_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12947,U_12952)),hAPP(hAPP(c_Product__Type_OPair(U_12947,U_12952),U_12949),U_12953)),hAPP(hAPP(c_Relation_Orel__comp(U_12947,U_12948,U_12952),U_12951),U_12954)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12948,U_12952)),hAPP(hAPP(c_Product__Type_OPair(U_12948,U_12952),U_12950),U_12953)),U_12954))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12947,U_12948)),hAPP(hAPP(c_Product__Type_OPair(U_12947,U_12948),U_12949),U_12950)),U_12951)) ),
    inference(clausify,[status(thm)],[f_3359_2]) ).

fof(f_3360_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_3360_2,plain,
    ! [U_12959,U_12958,U_12957,U_12956,U_12955] :
      ( hBOOL(hAPP(hAPP(c_member(U_12956),U_12958),hAPP(c_Relation_ORange(U_12955,U_12956),U_12959)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12955,U_12956)),hAPP(hAPP(c_Product__Type_OPair(U_12955,U_12956),U_12957),U_12958)),U_12959)) ),
    inference(variable_rename,[status(thm)],[f_3360_1]) ).

cnf(f_3360_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12956),U_12958),hAPP(c_Relation_ORange(U_12955,U_12956),U_12959)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12955,U_12956)),hAPP(hAPP(c_Product__Type_OPair(U_12955,U_12956),U_12957),U_12958)),U_12959)) ),
    inference(clausify,[status(thm)],[f_3360_2]) ).

fof(f_3361_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_3361_2,plain,
    ! [U_12965,U_12964,U_12963,U_12962,U_12961,U_12960] : hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12960,U_12961),tc_HOL_Obool)),U_12963),U_12964)),U_12965) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12960,U_12962),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),U_12963),U_12965)),hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),U_12964),U_12965)),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

cnf(f_3361_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12960,U_12961),tc_HOL_Obool)),U_12963),U_12964)),U_12965) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12960,U_12962),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),U_12963),U_12965)),hAPP(hAPP(c_Relation_Orel__comp(U_12960,U_12961,U_12962),U_12964),U_12965)),
    inference(clausify,[status(thm)],[f_3361_2]) ).

fof(f_3362_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_3362_2,plain,
    ! [U_12971,U_12970,U_12969,U_12968,U_12967,U_12966] : hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12967,U_12968),tc_HOL_Obool)),U_12970),U_12971)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12966,U_12968),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),U_12970)),hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),U_12971)),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

cnf(f_3362_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12967,U_12968),tc_HOL_Obool)),U_12970),U_12971)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12966,U_12968),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),U_12970)),hAPP(hAPP(c_Relation_Orel__comp(U_12966,U_12967,U_12968),U_12969),U_12971)),
    inference(clausify,[status(thm)],[f_3362_2]) ).

fof(f_3363_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_3363_2,plain,
    ! [U_12973,U_12972] : hAPP(c_Relation_ORange(U_12972,U_12972),c_Relation_OId__on(U_12972,U_12973)) = U_12973,
    inference(variable_rename,[status(thm)],[f_3363_1]) ).

cnf(f_3363_3,plain,
    hAPP(c_Relation_ORange(U_12972,U_12972),c_Relation_OId__on(U_12972,U_12973)) = U_12973,
    inference(clausify,[status(thm)],[f_3363_2]) ).

fof(f_3364_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_3364_2,plain,
    ! [U_12980,U_12979,U_12978,U_12977,U_12976,U_12975,U_12974] : hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12975,U_12976),hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12977,U_12975),U_12978),U_12979)),U_12980) = hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12977,U_12976),U_12978),hAPP(hAPP(c_Relation_Orel__comp(U_12977,U_12975,U_12976),U_12979),U_12980)),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

cnf(f_3364_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12975,U_12976),hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12977,U_12975),U_12978),U_12979)),U_12980) = hAPP(hAPP(c_Relation_Orel__comp(U_12974,U_12977,U_12976),U_12978),hAPP(hAPP(c_Relation_Orel__comp(U_12977,U_12975,U_12976),U_12979),U_12980)),
    inference(clausify,[status(thm)],[f_3364_2]) ).

fof(f_3365_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_3365_2,plain,
    ! [U_12984,U_12983,U_12982,U_12981] : hAPP(hAPP(c_Relation_Orel__comp(U_12981,U_12982,U_12983),U_12984),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12982,U_12983),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12981,U_12983),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

cnf(f_3365_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12981,U_12982,U_12983),U_12984),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12982,U_12983),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12981,U_12983),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3365_2]) ).

fof(f_3366_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_3366_2,plain,
    ! [U_12988,U_12987,U_12986,U_12985] : hAPP(hAPP(c_Relation_Orel__comp(U_12985,U_12986,U_12987),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12985,U_12986),tc_HOL_Obool))),U_12988) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12985,U_12987),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

cnf(f_3366_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12985,U_12986,U_12987),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12985,U_12986),tc_HOL_Obool))),U_12988) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12985,U_12987),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3366_2]) ).

fof(f_3367_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_3367_2,plain,
    ! [U_12995,U_12994,U_12993,U_12992,U_12991,U_12990,U_12989] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12989,U_12993),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12989,U_12990,U_12993),U_12991),U_12994)),hAPP(hAPP(c_Relation_Orel__comp(U_12989,U_12990,U_12993),U_12992),U_12995)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12990,U_12993),tc_HOL_Obool)),U_12994),U_12995))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12989,U_12990),tc_HOL_Obool)),U_12991),U_12992)) ),
    inference(variable_rename,[status(thm)],[f_3367_1]) ).

cnf(f_3367_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12989,U_12993),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_12989,U_12990,U_12993),U_12991),U_12994)),hAPP(hAPP(c_Relation_Orel__comp(U_12989,U_12990,U_12993),U_12992),U_12995)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12990,U_12993),tc_HOL_Obool)),U_12994),U_12995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12989,U_12990),tc_HOL_Obool)),U_12991),U_12992)) ),
    inference(clausify,[status(thm)],[f_3367_2]) ).

fof(f_3368_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_3368_2,plain,
    ! [U_13002,U_13001,U_13000,U_12999,U_12998,U_12997,U_12996] : hAPP(hAPP(c_Relation_Orel__comp(U_12996,U_12997,U_12998),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12999,tc_fun(tc_prod(U_12996,U_12997),tc_HOL_Obool)),U_13000),U_13001)),U_13002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12999,tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),U_13000),hAPP(hAPP(c_COMBC(U_12999,tc_fun(tc_prod(U_12997,U_12998),tc_HOL_Obool),tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12996,U_12997),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12997,U_12998),tc_HOL_Obool),tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),U_12999),c_Relation_Orel__comp(U_12996,U_12997,U_12998)),U_13001)),U_13002)),
    inference(variable_rename,[status(thm)],[f_3368_1]) ).

cnf(f_3368_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_12996,U_12997,U_12998),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12999,tc_fun(tc_prod(U_12996,U_12997),tc_HOL_Obool)),U_13000),U_13001)),U_13002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12999,tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),U_13000),hAPP(hAPP(c_COMBC(U_12999,tc_fun(tc_prod(U_12997,U_12998),tc_HOL_Obool),tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12996,U_12997),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12997,U_12998),tc_HOL_Obool),tc_fun(tc_prod(U_12996,U_12998),tc_HOL_Obool)),U_12999),c_Relation_Orel__comp(U_12996,U_12997,U_12998)),U_13001)),U_13002)),
    inference(clausify,[status(thm)],[f_3368_2]) ).

fof(f_3369_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_3369_2,plain,
    ! [U_13009,U_13008,U_13007,U_13006,U_13005,U_13004,U_13003] : hAPP(hAPP(c_Relation_Orel__comp(U_13003,U_13004,U_13005),U_13006),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13007,tc_fun(tc_prod(U_13004,U_13005),tc_HOL_Obool)),U_13008),U_13009)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13007,tc_fun(tc_prod(U_13003,U_13005),tc_HOL_Obool)),U_13008),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13004,U_13005),tc_HOL_Obool),tc_fun(tc_prod(U_13003,U_13005),tc_HOL_Obool),U_13007),hAPP(c_Relation_Orel__comp(U_13003,U_13004,U_13005),U_13006)),U_13009)),
    inference(variable_rename,[status(thm)],[f_3369_1]) ).

cnf(f_3369_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13003,U_13004,U_13005),U_13006),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13007,tc_fun(tc_prod(U_13004,U_13005),tc_HOL_Obool)),U_13008),U_13009)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13007,tc_fun(tc_prod(U_13003,U_13005),tc_HOL_Obool)),U_13008),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13004,U_13005),tc_HOL_Obool),tc_fun(tc_prod(U_13003,U_13005),tc_HOL_Obool),U_13007),hAPP(c_Relation_Orel__comp(U_13003,U_13004,U_13005),U_13006)),U_13009)),
    inference(clausify,[status(thm)],[f_3369_2]) ).

fof(f_3370_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_3370_2,plain,
    ! [U_13013,U_13012,U_13011,U_13010] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool)),U_13011),U_13013)),U_13012) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),U_13013),U_13012) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),U_13011),U_13012) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

cnf(f_3370_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool)),U_13011),U_13013)),U_13012) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),U_13013),U_13012) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13010,U_13010,U_13010),U_13011),U_13012) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13010,U_13010),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3370_2]) ).

fof(f_3371_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_3371_2,plain,
    ! [U_13017,U_13016,U_13015,U_13014] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool)),U_13016),U_13017)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),U_13017) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),U_13016) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3371_1]) ).

cnf(f_3371_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool)),U_13016),U_13017)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),U_13017) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13014,U_13014,U_13014),U_13015),U_13016) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13014,U_13014),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3371_2]) ).

fof(f_3372_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_3372_2,plain,
    ! [U_13020,U_13019,U_13018] : hAPP(c_Relation_ORange(U_13018,U_13019),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13018,U_13019),tc_HOL_Obool),U_13020)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13018,U_13019),tc_HOL_Obool),tc_fun(U_13019,tc_HOL_Obool)),U_13020),c_Relation_ORange(U_13018,U_13019)),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

cnf(f_3372_3,plain,
    hAPP(c_Relation_ORange(U_13018,U_13019),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13018,U_13019),tc_HOL_Obool),U_13020)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13018,U_13019),tc_HOL_Obool),tc_fun(U_13019,tc_HOL_Obool)),U_13020),c_Relation_ORange(U_13018,U_13019)),
    inference(clausify,[status(thm)],[f_3372_2]) ).

fof(f_3373_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_3373_2,plain,
    ! [U_13022,U_13021] : hAPP(c_Relation_ORange(U_13021,U_13022),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13021,U_13022),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13022,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

cnf(f_3373_3,plain,
    hAPP(c_Relation_ORange(U_13021,U_13022),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13021,U_13022),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13022,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3373_2]) ).

fof(f_3374_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_3374_2,plain,
    ! [U_13025,U_13024,U_13023] :
      ( ( hAPP(c_Relation_ORange(U_13023,U_13024),U_13025) = c_Orderings_Obot__class_Obot(tc_fun(U_13024,tc_HOL_Obool))
        | U_13025 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13023,U_13024),tc_HOL_Obool)) )
      & ( U_13025 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13023,U_13024),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13023,U_13024),U_13025) != c_Orderings_Obot__class_Obot(tc_fun(U_13024,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

fof(f_3374_3,plain,
    ( ! [U_13031,U_13029,U_13027] :
        ( hAPP(c_Relation_ORange(U_13027,U_13029),U_13031) = c_Orderings_Obot__class_Obot(tc_fun(U_13029,tc_HOL_Obool))
        | U_13031 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13027,U_13029),tc_HOL_Obool)) )
    & ! [U_13030,U_13028,U_13026] :
        ( U_13030 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13026,U_13028),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13026,U_13028),U_13030) != c_Orderings_Obot__class_Obot(tc_fun(U_13028,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3374_2]) ).

cnf(f_3374_4,plain,
    ( U_13030 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13026,U_13028),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_13026,U_13028),U_13030) != c_Orderings_Obot__class_Obot(tc_fun(U_13028,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3374_3]) ).

cnf(f_3374_5,plain,
    ( hAPP(c_Relation_ORange(U_13027,U_13029),U_13031) = c_Orderings_Obot__class_Obot(tc_fun(U_13029,tc_HOL_Obool))
    | U_13031 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13027,U_13029),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3374_3]) ).

fof(f_3375_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_3375_2,plain,
    ! [U_13039,U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13032,U_13037),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13032,U_13033,U_13037),U_13034),U_13038)),hAPP(hAPP(c_Product__Type_OSigma(U_13032,U_13037),U_13035),hAPP(c_COMBK(tc_fun(U_13037,tc_HOL_Obool),U_13032),U_13039))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13033,U_13037),tc_HOL_Obool)),U_13038),hAPP(hAPP(c_Product__Type_OSigma(U_13033,U_13037),U_13036),hAPP(c_COMBK(tc_fun(U_13037,tc_HOL_Obool),U_13033),U_13039))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13032,U_13033),tc_HOL_Obool)),U_13034),hAPP(hAPP(c_Product__Type_OSigma(U_13032,U_13033),U_13035),hAPP(c_COMBK(tc_fun(U_13033,tc_HOL_Obool),U_13032),U_13036)))) ),
    inference(variable_rename,[status(thm)],[f_3375_1]) ).

cnf(f_3375_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13032,U_13037),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13032,U_13033,U_13037),U_13034),U_13038)),hAPP(hAPP(c_Product__Type_OSigma(U_13032,U_13037),U_13035),hAPP(c_COMBK(tc_fun(U_13037,tc_HOL_Obool),U_13032),U_13039))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13033,U_13037),tc_HOL_Obool)),U_13038),hAPP(hAPP(c_Product__Type_OSigma(U_13033,U_13037),U_13036),hAPP(c_COMBK(tc_fun(U_13037,tc_HOL_Obool),U_13033),U_13039))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13032,U_13033),tc_HOL_Obool)),U_13034),hAPP(hAPP(c_Product__Type_OSigma(U_13032,U_13033),U_13035),hAPP(c_COMBK(tc_fun(U_13033,tc_HOL_Obool),U_13032),U_13036)))) ),
    inference(clausify,[status(thm)],[f_3375_2]) ).

fof(f_3376_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_3376_2,plain,
    ! [U_13043,U_13042,U_13041,U_13040] : hAPP(c_Relation_ORange(U_13040,U_13041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13040,U_13041),tc_HOL_Obool)),U_13042),U_13043)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13041,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13040,U_13041),U_13042)),hAPP(c_Relation_ORange(U_13040,U_13041),U_13043)),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

cnf(f_3376_3,plain,
    hAPP(c_Relation_ORange(U_13040,U_13041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13040,U_13041),tc_HOL_Obool)),U_13042),U_13043)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13041,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13040,U_13041),U_13042)),hAPP(c_Relation_ORange(U_13040,U_13041),U_13043)),
    inference(clausify,[status(thm)],[f_3376_2]) ).

fof(f_3377_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_3377_2,plain,
    ! [U_13046,U_13045,U_13044] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13045),hAPP(c_Relation_ORange(U_13044,U_13045),U_13046)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13044,U_13045)),U_13046)) ),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

cnf(f_3377_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13045),hAPP(c_Relation_ORange(U_13044,U_13045),U_13046)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13044,U_13045)),U_13046)) ),
    inference(clausify,[status(thm)],[f_3377_2]) ).

fof(f_3378_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_3378_2,plain,
    ! [U_13049,U_13048,U_13047] : hAPP(c_Set_Oimage(tc_prod(U_13047,U_13048),U_13048,c_Product__Type_Osnd(U_13047,U_13048)),U_13049) = hAPP(c_Relation_ORange(U_13047,U_13048),U_13049),
    inference(variable_rename,[status(thm)],[f_3378_1]) ).

cnf(f_3378_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13047,U_13048),U_13048,c_Product__Type_Osnd(U_13047,U_13048)),U_13049) = hAPP(c_Relation_ORange(U_13047,U_13048),U_13049),
    inference(clausify,[status(thm)],[f_3378_2]) ).

fof(f_3379_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_3379_2,plain,
    ! [U_13055,U_13054,U_13053,U_13052] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13052),U_13053),hAPP(c_Relation_ORange(U_13054,U_13052),U_13055)))
        | ! [U_13051] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13054,U_13052)),hAPP(hAPP(c_Product__Type_OPair(U_13054,U_13052),U_13051),U_13053)),U_13055)) )
      & ( ? [U_13050] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13054,U_13052)),hAPP(hAPP(c_Product__Type_OPair(U_13054,U_13052),U_13050),U_13053)),U_13055))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13052),U_13053),hAPP(c_Relation_ORange(U_13054,U_13052),U_13055))) ) ),
    inference(variable_rename,[status(thm)],[f_3379_1]) ).

fof(f_3379_3,plain,
    ( ! [U_13063,U_13061,U_13059,U_13057] :
        ( hBOOL(hAPP(hAPP(c_member(U_13057),U_13059),hAPP(c_Relation_ORange(U_13061,U_13057),U_13063)))
        | ! [U_13051] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13061,U_13057)),hAPP(hAPP(c_Product__Type_OPair(U_13061,U_13057),U_13051),U_13059)),U_13063)) )
    & ! [U_13062,U_13060,U_13058,U_13056] :
        ( ? [U_13050] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13060,U_13056)),hAPP(hAPP(c_Product__Type_OPair(U_13060,U_13056),U_13050),U_13058)),U_13062))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13056),U_13058),hAPP(c_Relation_ORange(U_13060,U_13056),U_13062))) ) ),
    inference(miniscope,[status(thm)],[f_3379_2]) ).

fof(f_3379_4,plain,
    ( ! [U_13063,U_13061,U_13059,U_13057] :
        ( hBOOL(hAPP(hAPP(c_member(U_13057),U_13059),hAPP(c_Relation_ORange(U_13061,U_13057),U_13063)))
        | ! [U_13051] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13061,U_13057)),hAPP(hAPP(c_Product__Type_OPair(U_13061,U_13057),U_13051),U_13059)),U_13063)) )
    & ! [U_13062,U_13060,U_13058,U_13056] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13060,U_13056)),hAPP(hAPP(c_Product__Type_OPair(U_13060,U_13056),sK308(U_13062,U_13060,U_13058,U_13056)),U_13058)),U_13062))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13056),U_13058),hAPP(c_Relation_ORange(U_13060,U_13056),U_13062))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_13050,sK308(U_13062,U_13060,U_13058,U_13056))],[f_3379_3]) ).

cnf(f_3379_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13060,U_13056)),hAPP(hAPP(c_Product__Type_OPair(U_13060,U_13056),sK308(U_13062,U_13060,U_13058,U_13056)),U_13058)),U_13062))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13056),U_13058),hAPP(c_Relation_ORange(U_13060,U_13056),U_13062))) ),
    inference(clausify,[status(thm)],[f_3379_4]) ).

cnf(f_3379_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13057),U_13059),hAPP(c_Relation_ORange(U_13061,U_13057),U_13063)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13061,U_13057)),hAPP(hAPP(c_Product__Type_OPair(U_13061,U_13057),U_13051),U_13059)),U_13063)) ),
    inference(clausify,[status(thm)],[f_3379_4]) ).

fof(f_3380_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_3380_2,plain,
    ! [U_13068,U_13067,U_13066,U_13065,U_13064] : hAPP(c_Relation_ORange(U_13064,U_13065),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13064,U_13065)),hAPP(hAPP(c_Product__Type_OPair(U_13064,U_13065),U_13066),U_13067)),U_13068)) = hAPP(hAPP(c_Set_Oinsert(U_13065),U_13067),hAPP(c_Relation_ORange(U_13064,U_13065),U_13068)),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

cnf(f_3380_3,plain,
    hAPP(c_Relation_ORange(U_13064,U_13065),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13064,U_13065)),hAPP(hAPP(c_Product__Type_OPair(U_13064,U_13065),U_13066),U_13067)),U_13068)) = hAPP(hAPP(c_Set_Oinsert(U_13065),U_13067),hAPP(c_Relation_ORange(U_13064,U_13065),U_13068)),
    inference(clausify,[status(thm)],[f_3380_2]) ).

fof(f_3381_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_3381_2,plain,
    ! [U_13072,U_13071,U_13070,U_13069] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13069,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13070,U_13069),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13070,U_13069),tc_HOL_Obool)),U_13071),U_13072))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13069,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13070,U_13069),U_13071)),hAPP(c_Relation_ORange(U_13070,U_13069),U_13072)))),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

cnf(f_3381_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13069,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13070,U_13069),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13070,U_13069),tc_HOL_Obool)),U_13071),U_13072))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13069,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13070,U_13069),U_13071)),hAPP(c_Relation_ORange(U_13070,U_13069),U_13072)))),
    inference(clausify,[status(thm)],[f_3381_2]) ).

fof(f_3382_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_3382_2,plain,
    ! [U_13076,U_13075,U_13074,U_13073] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13073,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13073,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13074,U_13073),U_13075)),hAPP(c_Relation_ORange(U_13074,U_13073),U_13076))),hAPP(c_Relation_ORange(U_13074,U_13073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13074,U_13073),tc_HOL_Obool)),U_13075),U_13076)))),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

cnf(f_3382_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13073,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13073,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13074,U_13073),U_13075)),hAPP(c_Relation_ORange(U_13074,U_13073),U_13076))),hAPP(c_Relation_ORange(U_13074,U_13073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13074,U_13073),tc_HOL_Obool)),U_13075),U_13076)))),
    inference(clausify,[status(thm)],[f_3382_2]) ).

fof(f_3383_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_3383_2,plain,
    ! [U_13079,U_13078,U_13077] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13077,U_13078)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13077,U_13079)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13077,U_13078)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13077,U_13077),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13077,U_13077,U_13077),U_13078),U_13079)),U_13078)) ),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

cnf(f_3383_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13077,U_13078)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13077,U_13079)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13077,tc_HOL_Obool),tc_fun(U_13077,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13077,U_13078)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13077,U_13077),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13077,U_13077,U_13077),U_13078),U_13079)),U_13078)) ),
    inference(clausify,[status(thm)],[f_3383_2]) ).

fof(f_3384_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_3384_2,plain,
    ! [U_13082,U_13081,U_13080] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13080,U_13081)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13080,U_13082)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13080,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13080,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13080,U_13081)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13080,U_13080),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13080,U_13080,U_13080),U_13081),U_13082)),U_13081)) ),
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

cnf(f_3384_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13080,U_13081)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13080,U_13082)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13080,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13080,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13080,tc_HOL_Obool),tc_fun(U_13080,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13080,U_13081)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13080,U_13080),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13080,U_13080,U_13080),U_13081),U_13082)),U_13081)) ),
    inference(clausify,[status(thm)],[f_3384_2]) ).

fof(f_3385_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_3385_2,plain,
    ! [U_13086,U_13085,U_13084,U_13083] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13083,U_13084,hAPP(hAPP(c_COMBC(U_13083,tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_fun(U_13084,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13084,tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_fun(U_13084,tc_HOL_Obool)),U_13083),c_COMBC(U_13084,tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13084,tc_prod(U_13083,U_13084)),tc_fun(U_13084,tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),U_13083),hAPP(c_COMBB(tc_prod(U_13083,U_13084),tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool),U_13084),c_member(tc_prod(U_13083,U_13084)))),c_Product__Type_OPair(U_13083,U_13084)))),U_13085)),U_13086))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13086),hAPP(c_Relation_ORange(U_13083,U_13084),U_13085))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13084),U_13086),hAPP(c_Relation_ORange(U_13083,U_13084),U_13085)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13083,U_13084,hAPP(hAPP(c_COMBC(U_13083,tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_fun(U_13084,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13084,tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_fun(U_13084,tc_HOL_Obool)),U_13083),c_COMBC(U_13084,tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13084,tc_prod(U_13083,U_13084)),tc_fun(U_13084,tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool)),U_13083),hAPP(c_COMBB(tc_prod(U_13083,U_13084),tc_fun(tc_fun(tc_prod(U_13083,U_13084),tc_HOL_Obool),tc_HOL_Obool),U_13084),c_member(tc_prod(U_13083,U_13084)))),c_Product__Type_OPair(U_13083,U_13084)))),U_13085)),U_13086)) ) ),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

fof(f_3385_3,plain,
    ( ! [U_13094,U_13092,U_13090,U_13088] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_13088,U_13090,hAPP(hAPP(c_COMBC(U_13088,tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13090,tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13088),c_COMBC(U_13090,tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13090,tc_prod(U_13088,U_13090)),tc_fun(U_13090,tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),U_13088),hAPP(c_COMBB(tc_prod(U_13088,U_13090),tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool),U_13090),c_member(tc_prod(U_13088,U_13090)))),c_Product__Type_OPair(U_13088,U_13090)))),U_13092)),U_13094))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13090),U_13094),hAPP(c_Relation_ORange(U_13088,U_13090),U_13092))) )
    & ! [U_13093,U_13091,U_13089,U_13087] :
        ( hBOOL(hAPP(hAPP(c_member(U_13089),U_13093),hAPP(c_Relation_ORange(U_13087,U_13089),U_13091)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13087,U_13089,hAPP(hAPP(c_COMBC(U_13087,tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool)),U_13087),c_COMBC(U_13089,tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_prod(U_13087,U_13089)),tc_fun(U_13089,tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),U_13087),hAPP(c_COMBB(tc_prod(U_13087,U_13089),tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool),U_13089),c_member(tc_prod(U_13087,U_13089)))),c_Product__Type_OPair(U_13087,U_13089)))),U_13091)),U_13093)) ) ),
    inference(miniscope,[status(thm)],[f_3385_2]) ).

cnf(f_3385_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13089),U_13093),hAPP(c_Relation_ORange(U_13087,U_13089),U_13091)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13087,U_13089,hAPP(hAPP(c_COMBC(U_13087,tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool)),U_13087),c_COMBC(U_13089,tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_prod(U_13087,U_13089)),tc_fun(U_13089,tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool)),U_13087),hAPP(c_COMBB(tc_prod(U_13087,U_13089),tc_fun(tc_fun(tc_prod(U_13087,U_13089),tc_HOL_Obool),tc_HOL_Obool),U_13089),c_member(tc_prod(U_13087,U_13089)))),c_Product__Type_OPair(U_13087,U_13089)))),U_13091)),U_13093)) ),
    inference(clausify,[status(thm)],[f_3385_3]) ).

cnf(f_3385_5,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13088,U_13090,hAPP(hAPP(c_COMBC(U_13088,tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13090,tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_fun(U_13090,tc_HOL_Obool)),U_13088),c_COMBC(U_13090,tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13090,tc_prod(U_13088,U_13090)),tc_fun(U_13090,tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool)),U_13088),hAPP(c_COMBB(tc_prod(U_13088,U_13090),tc_fun(tc_fun(tc_prod(U_13088,U_13090),tc_HOL_Obool),tc_HOL_Obool),U_13090),c_member(tc_prod(U_13088,U_13090)))),c_Product__Type_OPair(U_13088,U_13090)))),U_13092)),U_13094))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13090),U_13094),hAPP(c_Relation_ORange(U_13088,U_13090),U_13092))) ),
    inference(clausify,[status(thm)],[f_3385_3]) ).

fof(f_3386_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_3386_2,plain,
    ! [U_13099,U_13098,U_13097,U_13096] :
      ( ? [U_13095] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13098,U_13096)),hAPP(hAPP(c_Product__Type_OPair(U_13098,U_13096),U_13095),U_13097)),U_13099))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13097),hAPP(c_Relation_ORange(U_13098,U_13096),U_13099))) ),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

fof(f_3386_3,plain,
    ! [U_13099,U_13098,U_13097,U_13096] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13098,U_13096)),hAPP(hAPP(c_Product__Type_OPair(U_13098,U_13096),sK309(U_13099,U_13098,U_13097,U_13096)),U_13097)),U_13099))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13097),hAPP(c_Relation_ORange(U_13098,U_13096),U_13099))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_13095,sK309(U_13099,U_13098,U_13097,U_13096))],[f_3386_2]) ).

cnf(f_3386_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13098,U_13096)),hAPP(hAPP(c_Product__Type_OPair(U_13098,U_13096),sK309(U_13099,U_13098,U_13097,U_13096)),U_13097)),U_13099))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13097),hAPP(c_Relation_ORange(U_13098,U_13096),U_13099))) ),
    inference(clausify,[status(thm)],[f_3386_3]) ).

fof(f_3387_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_3387_2,plain,
    ! [U_13106,U_13105,U_13104,U_13103,U_13102,U_13101,U_13100] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13100,U_13101,U_13102,hAPP(hAPP(c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13100),c_COMBC(U_13101,tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_prod(U_13100,U_13101)),tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),U_13100),hAPP(c_COMBB(tc_prod(U_13100,U_13101),tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool),U_13101),c_member(tc_prod(U_13100,U_13101)))),c_Product__Type_OPair(U_13100,U_13101)))),U_13103),hAPP(hAPP(c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_fun(U_13102,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13102,tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_fun(U_13102,tc_HOL_Obool)),U_13101),c_COMBC(U_13102,tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13102,tc_prod(U_13101,U_13102)),tc_fun(U_13102,tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),U_13101),hAPP(c_COMBB(tc_prod(U_13101,U_13102),tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool),U_13102),c_member(tc_prod(U_13101,U_13102)))),c_Product__Type_OPair(U_13101,U_13102)))),U_13104)),U_13105),U_13106))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13100,U_13102)),hAPP(hAPP(c_Product__Type_OPair(U_13100,U_13102),U_13105),U_13106)),hAPP(hAPP(c_Relation_Orel__comp(U_13100,U_13101,U_13102),U_13103),U_13104))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13100,U_13102)),hAPP(hAPP(c_Product__Type_OPair(U_13100,U_13102),U_13105),U_13106)),hAPP(hAPP(c_Relation_Orel__comp(U_13100,U_13101,U_13102),U_13103),U_13104)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13100,U_13101,U_13102,hAPP(hAPP(c_COMBC(U_13100,tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_fun(U_13101,tc_HOL_Obool)),U_13100),c_COMBC(U_13101,tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13101,tc_prod(U_13100,U_13101)),tc_fun(U_13101,tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool)),U_13100),hAPP(c_COMBB(tc_prod(U_13100,U_13101),tc_fun(tc_fun(tc_prod(U_13100,U_13101),tc_HOL_Obool),tc_HOL_Obool),U_13101),c_member(tc_prod(U_13100,U_13101)))),c_Product__Type_OPair(U_13100,U_13101)))),U_13103),hAPP(hAPP(c_COMBC(U_13101,tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_fun(U_13102,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13102,tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_fun(U_13102,tc_HOL_Obool)),U_13101),c_COMBC(U_13102,tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13102,tc_prod(U_13101,U_13102)),tc_fun(U_13102,tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool)),U_13101),hAPP(c_COMBB(tc_prod(U_13101,U_13102),tc_fun(tc_fun(tc_prod(U_13101,U_13102),tc_HOL_Obool),tc_HOL_Obool),U_13102),c_member(tc_prod(U_13101,U_13102)))),c_Product__Type_OPair(U_13101,U_13102)))),U_13104)),U_13105),U_13106)) ) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ( ! [U_13120,U_13118,U_13116,U_13114,U_13112,U_13110,U_13108] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13108,U_13110,U_13112,hAPP(hAPP(c_COMBC(U_13108,tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_fun(U_13110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13110,tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_fun(U_13110,tc_HOL_Obool)),U_13108),c_COMBC(U_13110,tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13110,tc_prod(U_13108,U_13110)),tc_fun(U_13110,tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),U_13108),hAPP(c_COMBB(tc_prod(U_13108,U_13110),tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool),U_13110),c_member(tc_prod(U_13108,U_13110)))),c_Product__Type_OPair(U_13108,U_13110)))),U_13114),hAPP(hAPP(c_COMBC(U_13110,tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_fun(U_13112,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13112,tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_fun(U_13112,tc_HOL_Obool)),U_13110),c_COMBC(U_13112,tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13112,tc_prod(U_13110,U_13112)),tc_fun(U_13112,tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),U_13110),hAPP(c_COMBB(tc_prod(U_13110,U_13112),tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool),U_13112),c_member(tc_prod(U_13110,U_13112)))),c_Product__Type_OPair(U_13110,U_13112)))),U_13116)),U_13118),U_13120))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13108,U_13112)),hAPP(hAPP(c_Product__Type_OPair(U_13108,U_13112),U_13118),U_13120)),hAPP(hAPP(c_Relation_Orel__comp(U_13108,U_13110,U_13112),U_13114),U_13116))) )
    & ! [U_13119,U_13117,U_13115,U_13113,U_13111,U_13109,U_13107] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13107,U_13111)),hAPP(hAPP(c_Product__Type_OPair(U_13107,U_13111),U_13117),U_13119)),hAPP(hAPP(c_Relation_Orel__comp(U_13107,U_13109,U_13111),U_13113),U_13115)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13107,U_13109,U_13111,hAPP(hAPP(c_COMBC(U_13107,tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_fun(U_13109,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13109,tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_fun(U_13109,tc_HOL_Obool)),U_13107),c_COMBC(U_13109,tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13109,tc_prod(U_13107,U_13109)),tc_fun(U_13109,tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),U_13107),hAPP(c_COMBB(tc_prod(U_13107,U_13109),tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool),U_13109),c_member(tc_prod(U_13107,U_13109)))),c_Product__Type_OPair(U_13107,U_13109)))),U_13113),hAPP(hAPP(c_COMBC(U_13109,tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),U_13109),c_COMBC(U_13111,tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_prod(U_13109,U_13111)),tc_fun(U_13111,tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),U_13109),hAPP(c_COMBB(tc_prod(U_13109,U_13111),tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool),U_13111),c_member(tc_prod(U_13109,U_13111)))),c_Product__Type_OPair(U_13109,U_13111)))),U_13115)),U_13117),U_13119)) ) ),
    inference(miniscope,[status(thm)],[f_3387_2]) ).

cnf(f_3387_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13107,U_13111)),hAPP(hAPP(c_Product__Type_OPair(U_13107,U_13111),U_13117),U_13119)),hAPP(hAPP(c_Relation_Orel__comp(U_13107,U_13109,U_13111),U_13113),U_13115)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13107,U_13109,U_13111,hAPP(hAPP(c_COMBC(U_13107,tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_fun(U_13109,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13109,tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_fun(U_13109,tc_HOL_Obool)),U_13107),c_COMBC(U_13109,tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13109,tc_prod(U_13107,U_13109)),tc_fun(U_13109,tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool)),U_13107),hAPP(c_COMBB(tc_prod(U_13107,U_13109),tc_fun(tc_fun(tc_prod(U_13107,U_13109),tc_HOL_Obool),tc_HOL_Obool),U_13109),c_member(tc_prod(U_13107,U_13109)))),c_Product__Type_OPair(U_13107,U_13109)))),U_13113),hAPP(hAPP(c_COMBC(U_13109,tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),U_13109),c_COMBC(U_13111,tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_prod(U_13109,U_13111)),tc_fun(U_13111,tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool)),U_13109),hAPP(c_COMBB(tc_prod(U_13109,U_13111),tc_fun(tc_fun(tc_prod(U_13109,U_13111),tc_HOL_Obool),tc_HOL_Obool),U_13111),c_member(tc_prod(U_13109,U_13111)))),c_Product__Type_OPair(U_13109,U_13111)))),U_13115)),U_13117),U_13119)) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

cnf(f_3387_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13108,U_13110,U_13112,hAPP(hAPP(c_COMBC(U_13108,tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_fun(U_13110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13110,tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_fun(U_13110,tc_HOL_Obool)),U_13108),c_COMBC(U_13110,tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13110,tc_prod(U_13108,U_13110)),tc_fun(U_13110,tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool)),U_13108),hAPP(c_COMBB(tc_prod(U_13108,U_13110),tc_fun(tc_fun(tc_prod(U_13108,U_13110),tc_HOL_Obool),tc_HOL_Obool),U_13110),c_member(tc_prod(U_13108,U_13110)))),c_Product__Type_OPair(U_13108,U_13110)))),U_13114),hAPP(hAPP(c_COMBC(U_13110,tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_fun(U_13112,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13112,tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_fun(U_13112,tc_HOL_Obool)),U_13110),c_COMBC(U_13112,tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13112,tc_prod(U_13110,U_13112)),tc_fun(U_13112,tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool)),U_13110),hAPP(c_COMBB(tc_prod(U_13110,U_13112),tc_fun(tc_fun(tc_prod(U_13110,U_13112),tc_HOL_Obool),tc_HOL_Obool),U_13112),c_member(tc_prod(U_13110,U_13112)))),c_Product__Type_OPair(U_13110,U_13112)))),U_13116)),U_13118),U_13120))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13108,U_13112)),hAPP(hAPP(c_Product__Type_OPair(U_13108,U_13112),U_13118),U_13120)),hAPP(hAPP(c_Relation_Orel__comp(U_13108,U_13110,U_13112),U_13114),U_13116))) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

fof(f_3388_1,plain,
    ! [T_d,T_c,T_b,V_ca_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_ca_2))
      | ~ hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros]) ).

fof(f_3388_2,plain,
    ! [U_13128,U_13127,U_13126,U_13125,U_13124,U_13123,U_13122,U_13121] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13126,U_13127,U_13128,U_13121,U_13124),U_13122),U_13125))
      | ~ hBOOL(hAPP(hAPP(U_13124,U_13123),U_13125))
      | ~ hBOOL(hAPP(hAPP(U_13121,U_13122),U_13123)) ),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

cnf(f_3388_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13126,U_13127,U_13128,U_13121,U_13124),U_13122),U_13125))
    | ~ hBOOL(hAPP(hAPP(U_13124,U_13123),U_13125))
    | ~ hBOOL(hAPP(hAPP(U_13121,U_13122),U_13123)) ),
    inference(clausify,[status(thm)],[f_3388_2]) ).

fof(f_3389_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_3389_2,plain,
    ! [U_13133,U_13132,U_13131,U_13130,U_13129] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_13132,U_13133,U_13129),U_13131))
      | ~ hBOOL(hAPP(hAPP(U_13129,U_13130),U_13131)) ),
    inference(variable_rename,[status(thm)],[f_3389_1]) ).

cnf(f_3389_3,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13132,U_13133,U_13129),U_13131))
    | ~ hBOOL(hAPP(hAPP(U_13129,U_13130),U_13131)) ),
    inference(clausify,[status(thm)],[f_3389_2]) ).

fof(f_3390_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_3390_2,plain,
    ! [U_13139,U_13138,U_13137,U_13136] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13136,U_13137,U_13138),U_13139))
        | ! [U_13135] : ~ hBOOL(hAPP(hAPP(U_13138,U_13135),U_13139)) )
      & ( ? [U_13134] : hBOOL(hAPP(hAPP(U_13138,U_13134),U_13139))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13136,U_13137,U_13138),U_13139)) ) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ( ! [U_13147,U_13145] :
        ( ! [U_13143,U_13141] : hBOOL(hAPP(c_Predicate_ORangeP(U_13141,U_13143,U_13145),U_13147))
        | ! [U_13135] : ~ hBOOL(hAPP(hAPP(U_13145,U_13135),U_13147)) )
    & ! [U_13146,U_13144] :
        ( ! [U_13142,U_13140] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13140,U_13142,U_13144),U_13146))
        | ? [U_13134] : hBOOL(hAPP(hAPP(U_13144,U_13134),U_13146)) ) ),
    inference(miniscope,[status(thm)],[f_3390_2]) ).

fof(f_3390_4,plain,
    ( ! [U_13147,U_13145] :
        ( ! [U_13143,U_13141] : hBOOL(hAPP(c_Predicate_ORangeP(U_13141,U_13143,U_13145),U_13147))
        | ! [U_13135] : ~ hBOOL(hAPP(hAPP(U_13145,U_13135),U_13147)) )
    & ! [U_13146,U_13144] :
        ( ! [U_13142,U_13140] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13140,U_13142,U_13144),U_13146))
        | hBOOL(hAPP(hAPP(U_13144,sK310(U_13146,U_13144)),U_13146)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_13134,sK310(U_13146,U_13144))],[f_3390_3]) ).

cnf(f_3390_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13140,U_13142,U_13144),U_13146))
    | hBOOL(hAPP(hAPP(U_13144,sK310(U_13146,U_13144)),U_13146)) ),
    inference(clausify,[status(thm)],[f_3390_4]) ).

cnf(f_3390_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13141,U_13143,U_13145),U_13147))
    | ~ hBOOL(hAPP(hAPP(U_13145,U_13135),U_13147)) ),
    inference(clausify,[status(thm)],[f_3390_4]) ).

fof(f_3391_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_3391_2,plain,
    ! [U_13156,U_13155,U_13154,U_13153,U_13152,U_13151,U_13150] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13150,U_13151,U_13152,U_13153,U_13154),U_13155),U_13156))
        | ! [U_13149] :
            ( ~ hBOOL(hAPP(hAPP(U_13154,U_13149),U_13156))
            | ~ hBOOL(hAPP(hAPP(U_13153,U_13155),U_13149)) ) )
      & ( ? [U_13148] :
            ( hBOOL(hAPP(hAPP(U_13154,U_13148),U_13156))
            & hBOOL(hAPP(hAPP(U_13153,U_13155),U_13148)) )
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13150,U_13151,U_13152,U_13153,U_13154),U_13155),U_13156)) ) ),
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

fof(f_3391_3,plain,
    ( ! [U_13170,U_13168,U_13166,U_13164] :
        ( ! [U_13162,U_13160,U_13158] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13158,U_13160,U_13162,U_13164,U_13166),U_13168),U_13170))
        | ! [U_13149] :
            ( ~ hBOOL(hAPP(hAPP(U_13166,U_13149),U_13170))
            | ~ hBOOL(hAPP(hAPP(U_13164,U_13168),U_13149)) ) )
    & ! [U_13169,U_13167,U_13165,U_13163] :
        ( ! [U_13161,U_13159,U_13157] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13157,U_13159,U_13161,U_13163,U_13165),U_13167),U_13169))
        | ? [U_13148] :
            ( hBOOL(hAPP(hAPP(U_13165,U_13148),U_13169))
            & hBOOL(hAPP(hAPP(U_13163,U_13167),U_13148)) ) ) ),
    inference(miniscope,[status(thm)],[f_3391_2]) ).

fof(f_3391_4,plain,
    ( ! [U_13170,U_13168,U_13166,U_13164] :
        ( ! [U_13162,U_13160,U_13158] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13158,U_13160,U_13162,U_13164,U_13166),U_13168),U_13170))
        | ! [U_13149] :
            ( ~ hBOOL(hAPP(hAPP(U_13166,U_13149),U_13170))
            | ~ hBOOL(hAPP(hAPP(U_13164,U_13168),U_13149)) ) )
    & ! [U_13169,U_13167,U_13165,U_13163] :
        ( ! [U_13161,U_13159,U_13157] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13157,U_13159,U_13161,U_13163,U_13165),U_13167),U_13169))
        | ( hBOOL(hAPP(hAPP(U_13165,sK311(U_13169,U_13167,U_13165,U_13163)),U_13169))
          & hBOOL(hAPP(hAPP(U_13163,U_13167),sK311(U_13169,U_13167,U_13165,U_13163))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_13148,sK311(U_13169,U_13167,U_13165,U_13163))],[f_3391_3]) ).

cnf(f_3391_5,plain,
    ( hBOOL(hAPP(hAPP(U_13163,U_13167),sK311(U_13169,U_13167,U_13165,U_13163)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13157,U_13159,U_13161,U_13163,U_13165),U_13167),U_13169)) ),
    inference(clausify,[status(thm)],[f_3391_4]) ).

cnf(f_3391_6,plain,
    ( hBOOL(hAPP(hAPP(U_13165,sK311(U_13169,U_13167,U_13165,U_13163)),U_13169))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13157,U_13159,U_13161,U_13163,U_13165),U_13167),U_13169)) ),
    inference(clausify,[status(thm)],[f_3391_4]) ).

cnf(f_3391_7,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13158,U_13160,U_13162,U_13164,U_13166),U_13168),U_13170))
    | ~ hBOOL(hAPP(hAPP(U_13166,U_13149),U_13170))
    | ~ hBOOL(hAPP(hAPP(U_13164,U_13168),U_13149)) ),
    inference(clausify,[status(thm)],[f_3391_4]) ).

fof(f_3392_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_3392_2,plain,
    ! [U_13173,U_13172,U_13171] :
      ( c_FunDef_Oreduction__pair(U_13171,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool),tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool)),U_13172),U_13173))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13171,U_13171,U_13171),U_13172),U_13173)),U_13172))
      | ~ c_Wellfounded_Owf(U_13171,U_13172) ),
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

cnf(f_3392_3,plain,
    ( c_FunDef_Oreduction__pair(U_13171,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool),tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool)),U_13172),U_13173))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13171,U_13171),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13171,U_13171,U_13171),U_13172),U_13173)),U_13172))
    | ~ c_Wellfounded_Owf(U_13171,U_13172) ),
    inference(clausify,[status(thm)],[f_3392_2]) ).

fof(f_3393_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).

fof(f_3393_2,plain,
    ! [U_13176,U_13175,U_13174] : hAPP(c_Relation_ODomain(U_13174,U_13175),hAPP(c_Set_OCollect(tc_prod(U_13174,U_13175)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13174,U_13175,tc_HOL_Obool),U_13176))) = hAPP(c_Set_OCollect(U_13174),hAPP(hAPP(c_COMBB(tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool,U_13174),c_HOL_OEx(U_13175)),U_13176)),
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

cnf(f_3393_3,plain,
    hAPP(c_Relation_ODomain(U_13174,U_13175),hAPP(c_Set_OCollect(tc_prod(U_13174,U_13175)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13174,U_13175,tc_HOL_Obool),U_13176))) = hAPP(c_Set_OCollect(U_13174),hAPP(hAPP(c_COMBB(tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool,U_13174),c_HOL_OEx(U_13175)),U_13176)),
    inference(clausify,[status(thm)],[f_3393_2]) ).

fof(f_3394_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_3394_2,plain,
    ! [U_13178,U_13177] : c_HOL_OThe(U_13177,hAPP(hAPP(c_COMBC(U_13177,U_13177,tc_HOL_Obool),c_fequal),U_13178)) = U_13178,
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

cnf(f_3394_3,plain,
    c_HOL_OThe(U_13177,hAPP(hAPP(c_COMBC(U_13177,U_13177,tc_HOL_Obool),c_fequal),U_13178)) = U_13178,
    inference(clausify,[status(thm)],[f_3394_2]) ).

fof(f_3395_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

cnf(f_3395_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3395_1]) ).

fof(f_3396_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_3396_2,plain,
    ! [U_13179] : c_Wellfounded_Owf(U_13179,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13179,U_13179),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

cnf(f_3396_3,plain,
    c_Wellfounded_Owf(U_13179,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13179,U_13179),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3396_2]) ).

fof(f_3397_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_3397_2,plain,
    ! [U_13183,U_13182,U_13181,U_13180] :
      ( c_Wellfounded_Owf(U_13182,hAPP(hAPP(c_Relation_Oinv__image(U_13180,U_13182),U_13181),U_13183))
      | ~ c_Wellfounded_Owf(U_13180,U_13181) ),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

cnf(f_3397_3,plain,
    ( c_Wellfounded_Owf(U_13182,hAPP(hAPP(c_Relation_Oinv__image(U_13180,U_13182),U_13181),U_13183))
    | ~ c_Wellfounded_Owf(U_13180,U_13181) ),
    inference(clausify,[status(thm)],[f_3397_2]) ).

fof(f_3398_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_3398_2,plain,
    ! [U_13187,U_13186,U_13185,U_13184] :
      ( c_Wellfounded_Owf(tc_prod(U_13184,U_13186),c_Wellfounded_Olex__prod(U_13184,U_13186,U_13185,U_13187))
      | ~ c_Wellfounded_Owf(U_13186,U_13187)
      | ~ c_Wellfounded_Owf(U_13184,U_13185) ),
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

cnf(f_3398_3,plain,
    ( c_Wellfounded_Owf(tc_prod(U_13184,U_13186),c_Wellfounded_Olex__prod(U_13184,U_13186,U_13185,U_13187))
    | ~ c_Wellfounded_Owf(U_13186,U_13187)
    | ~ c_Wellfounded_Owf(U_13184,U_13185) ),
    inference(clausify,[status(thm)],[f_3398_2]) ).

fof(f_3399_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_3399_2,plain,
    ! [U_13189,U_13188] : c_Wellfounded_Owf(U_13188,hAPP(c_Wellfounded_Omeasure(U_13188),U_13189)),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

cnf(f_3399_3,plain,
    c_Wellfounded_Owf(U_13188,hAPP(c_Wellfounded_Omeasure(U_13188),U_13189)),
    inference(clausify,[status(thm)],[f_3399_2]) ).

fof(f_3400_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_3400_2,plain,
    ! [U_13194,U_13193,U_13192,U_13191,U_13190] :
      ( hBOOL(hAPP(hAPP(c_member(U_13190),U_13192),hAPP(c_Relation_ODomain(U_13190,U_13191),U_13194)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13190,U_13191)),hAPP(hAPP(c_Product__Type_OPair(U_13190,U_13191),U_13192),U_13193)),U_13194)) ),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

cnf(f_3400_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13190),U_13192),hAPP(c_Relation_ODomain(U_13190,U_13191),U_13194)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13190,U_13191)),hAPP(hAPP(c_Product__Type_OPair(U_13190,U_13191),U_13192),U_13193)),U_13194)) ),
    inference(clausify,[status(thm)],[f_3400_2]) ).

fof(f_3401_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_3401_2,plain,
    ! [U_13196,U_13195] :
      ( ( c_Wellfounded_Owf(U_13195,U_13196)
        | ~ c_Wellfounded_Owf(U_13195,hAPP(hAPP(c_Relation_Orel__comp(U_13195,U_13195,U_13195),U_13196),U_13196)) )
      & ( c_Wellfounded_Owf(U_13195,hAPP(hAPP(c_Relation_Orel__comp(U_13195,U_13195,U_13195),U_13196),U_13196))
        | ~ c_Wellfounded_Owf(U_13195,U_13196) ) ),
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

fof(f_3401_3,plain,
    ( ! [U_13200,U_13198] :
        ( c_Wellfounded_Owf(U_13198,U_13200)
        | ~ c_Wellfounded_Owf(U_13198,hAPP(hAPP(c_Relation_Orel__comp(U_13198,U_13198,U_13198),U_13200),U_13200)) )
    & ! [U_13199,U_13197] :
        ( c_Wellfounded_Owf(U_13197,hAPP(hAPP(c_Relation_Orel__comp(U_13197,U_13197,U_13197),U_13199),U_13199))
        | ~ c_Wellfounded_Owf(U_13197,U_13199) ) ),
    inference(miniscope,[status(thm)],[f_3401_2]) ).

cnf(f_3401_4,plain,
    ( c_Wellfounded_Owf(U_13197,hAPP(hAPP(c_Relation_Orel__comp(U_13197,U_13197,U_13197),U_13199),U_13199))
    | ~ c_Wellfounded_Owf(U_13197,U_13199) ),
    inference(clausify,[status(thm)],[f_3401_3]) ).

cnf(f_3401_5,plain,
    ( c_Wellfounded_Owf(U_13198,U_13200)
    | ~ c_Wellfounded_Owf(U_13198,hAPP(hAPP(c_Relation_Orel__comp(U_13198,U_13198,U_13198),U_13200),U_13200)) ),
    inference(clausify,[status(thm)],[f_3401_3]) ).

fof(f_3402_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_3402_2,plain,
    ! [U_13203,U_13202,U_13201] :
      ( c_Wellfounded_Owf(U_13201,U_13203)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13201,U_13201),tc_HOL_Obool)),U_13203),U_13202))
      | ~ c_Wellfounded_Owf(U_13201,U_13202) ),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

cnf(f_3402_3,plain,
    ( c_Wellfounded_Owf(U_13201,U_13203)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13201,U_13201),tc_HOL_Obool)),U_13203),U_13202))
    | ~ c_Wellfounded_Owf(U_13201,U_13202) ),
    inference(clausify,[status(thm)],[f_3402_2]) ).

fof(f_3403_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_3403_2,plain,
    ! [U_13205,U_13204] :
      ( c_Wellfounded_Owf(tc_fun(U_13204,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13204,U_13205))
      | ~ c_Wellfounded_Owf(U_13204,U_13205) ),
    inference(variable_rename,[status(thm)],[f_3403_1]) ).

cnf(f_3403_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13204,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13204,U_13205))
    | ~ c_Wellfounded_Owf(U_13204,U_13205) ),
    inference(clausify,[status(thm)],[f_3403_2]) ).

fof(f_3404_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_3404_2,plain,
    ! [U_13208,U_13207,U_13206] :
      ( c_Wellfounded_Owf(U_13206,c_Wellfounded_Omlex__prod(U_13206,U_13208,U_13207))
      | ~ c_Wellfounded_Owf(U_13206,U_13207) ),
    inference(variable_rename,[status(thm)],[f_3404_1]) ).

cnf(f_3404_3,plain,
    ( c_Wellfounded_Owf(U_13206,c_Wellfounded_Omlex__prod(U_13206,U_13208,U_13207))
    | ~ c_Wellfounded_Owf(U_13206,U_13207) ),
    inference(clausify,[status(thm)],[f_3404_2]) ).

fof(f_3405_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_3405_2,plain,
    ! [U_13211,U_13210,U_13209] :
      ( c_Wellfounded_Owf(U_13209,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13209,U_13209),tc_HOL_Obool)),U_13211),U_13210))
      | ~ c_Wellfounded_Owf(U_13209,U_13210) ),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

cnf(f_3405_3,plain,
    ( c_Wellfounded_Owf(U_13209,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13209,U_13209),tc_HOL_Obool)),U_13211),U_13210))
    | ~ c_Wellfounded_Owf(U_13209,U_13210) ),
    inference(clausify,[status(thm)],[f_3405_2]) ).

fof(f_3406_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_3406_2,plain,
    ! [U_13214,U_13213,U_13212] :
      ( c_Wellfounded_Owf(U_13212,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13212,U_13212),tc_HOL_Obool)),U_13213),U_13214))
      | ~ c_Wellfounded_Owf(U_13212,U_13213) ),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

cnf(f_3406_3,plain,
    ( c_Wellfounded_Owf(U_13212,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13212,U_13212),tc_HOL_Obool)),U_13213),U_13214))
    | ~ c_Wellfounded_Owf(U_13212,U_13213) ),
    inference(clausify,[status(thm)],[f_3406_2]) ).

fof(f_3407_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_3407_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3407_1]) ).

fof(f_3408_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_3408_2,plain,
    ! [U_13216,U_13215] :
      ( c_Wellfounded_Owf(tc_fun(U_13215,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13215,U_13216))
      | ~ c_Wellfounded_Owf(U_13215,U_13216) ),
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

cnf(f_3408_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13215,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13215,U_13216))
    | ~ c_Wellfounded_Owf(U_13215,U_13216) ),
    inference(clausify,[status(thm)],[f_3408_2]) ).

fof(f_3409_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_3409_2,plain,
    ! [U_13218,U_13217] : hAPP(c_Relation_ODomain(U_13217,U_13217),c_Relation_OId__on(U_13217,U_13218)) = U_13218,
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

cnf(f_3409_3,plain,
    hAPP(c_Relation_ODomain(U_13217,U_13217),c_Relation_OId__on(U_13217,U_13218)) = U_13218,
    inference(clausify,[status(thm)],[f_3409_2]) ).

fof(f_3410_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_3410_2,plain,
    ! [U_13219] : c_Wellfounded_Owf(tc_fun(U_13219,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13219)),
    inference(variable_rename,[status(thm)],[f_3410_1]) ).

cnf(f_3410_3,plain,
    c_Wellfounded_Owf(tc_fun(U_13219,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13219)),
    inference(clausify,[status(thm)],[f_3410_2]) ).

fof(f_3411_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_3411_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_3411_1]) ).

fof(f_3412_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_3412_2,plain,
    ! [U_13222,U_13221,U_13220] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13220,U_13220)),hAPP(hAPP(c_Product__Type_OPair(U_13220,U_13220),U_13222),U_13222)),U_13221))
      | ~ c_Wellfounded_Owf(U_13220,U_13221) ),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

cnf(f_3412_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13220,U_13220)),hAPP(hAPP(c_Product__Type_OPair(U_13220,U_13220),U_13222),U_13222)),U_13221))
    | ~ c_Wellfounded_Owf(U_13220,U_13221) ),
    inference(clausify,[status(thm)],[f_3412_2]) ).

fof(f_3413_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_3413_2,plain,
    ! [U_13226,U_13225,U_13224,U_13223] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13223,U_13223)),hAPP(hAPP(c_Product__Type_OPair(U_13223,U_13223),U_13226),U_13225)),U_13224))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13223,U_13223)),hAPP(hAPP(c_Product__Type_OPair(U_13223,U_13223),U_13225),U_13226)),U_13224))
      | ~ c_Wellfounded_Owf(U_13223,U_13224) ),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

cnf(f_3413_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13223,U_13223)),hAPP(hAPP(c_Product__Type_OPair(U_13223,U_13223),U_13226),U_13225)),U_13224))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13223,U_13223)),hAPP(hAPP(c_Product__Type_OPair(U_13223,U_13223),U_13225),U_13226)),U_13224))
    | ~ c_Wellfounded_Owf(U_13223,U_13224) ),
    inference(clausify,[status(thm)],[f_3413_2]) ).

fof(f_3414_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_3414_2,plain,
    ! [U_13230,U_13229,U_13228,U_13227] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13227,U_13227)),hAPP(hAPP(c_Product__Type_OPair(U_13227,U_13227),U_13230),U_13229)),U_13228))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13227,U_13227)),hAPP(hAPP(c_Product__Type_OPair(U_13227,U_13227),U_13229),U_13230)),U_13228))
      | ~ c_Wellfounded_Owf(U_13227,U_13228) ),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

cnf(f_3414_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13227,U_13227)),hAPP(hAPP(c_Product__Type_OPair(U_13227,U_13227),U_13230),U_13229)),U_13228))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13227,U_13227)),hAPP(hAPP(c_Product__Type_OPair(U_13227,U_13227),U_13229),U_13230)),U_13228))
    | ~ c_Wellfounded_Owf(U_13227,U_13228) ),
    inference(clausify,[status(thm)],[f_3414_2]) ).

fof(f_3415_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_3415_2,plain,
    ! [U_13233,U_13232,U_13231] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13231,U_13231)),hAPP(hAPP(c_Product__Type_OPair(U_13231,U_13231),U_13233),U_13233)),U_13232))
      | ~ c_Wellfounded_Owf(U_13231,U_13232) ),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

cnf(f_3415_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13231,U_13231)),hAPP(hAPP(c_Product__Type_OPair(U_13231,U_13231),U_13233),U_13233)),U_13232))
    | ~ c_Wellfounded_Owf(U_13231,U_13232) ),
    inference(clausify,[status(thm)],[f_3415_2]) ).

fof(f_3416_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_3416_2,plain,
    ! [U_13234] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13234)),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

cnf(f_3416_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13234)),
    inference(clausify,[status(thm)],[f_3416_2]) ).

fof(f_3417_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_3417_2,plain,
    ! [U_13235] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13235)),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

cnf(f_3417_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13235)),
    inference(clausify,[status(thm)],[f_3417_2]) ).

fof(f_3418_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_3418_2,plain,
    ! [U_13238,U_13237,U_13236] :
      ( c_Wellfounded_Owf(U_13236,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13236,U_13236),tc_HOL_Obool)),U_13237),U_13238))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13236,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13236,U_13236),U_13237)),hAPP(c_Relation_ORange(U_13236,U_13236),U_13238)) != c_Orderings_Obot__class_Obot(tc_fun(U_13236,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_13236,U_13238)
      | ~ c_Wellfounded_Owf(U_13236,U_13237) ),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

cnf(f_3418_3,plain,
    ( c_Wellfounded_Owf(U_13236,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13236,U_13236),tc_HOL_Obool)),U_13237),U_13238))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13236,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13236,U_13236),U_13237)),hAPP(c_Relation_ORange(U_13236,U_13236),U_13238)) != c_Orderings_Obot__class_Obot(tc_fun(U_13236,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_13236,U_13238)
    | ~ c_Wellfounded_Owf(U_13236,U_13237) ),
    inference(clausify,[status(thm)],[f_3418_2]) ).

fof(f_3419_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_3419_2,plain,
    ! [U_13242,U_13241] :
      ( ( c_Wellfounded_Owf(U_13241,U_13242)
        | ? [U_13240] : ~ hBOOL(hAPP(hAPP(c_member(U_13241),U_13240),c_Wellfounded_Oacc(U_13241,U_13242))) )
      & ( ! [U_13239] : hBOOL(hAPP(hAPP(c_member(U_13241),U_13239),c_Wellfounded_Oacc(U_13241,U_13242)))
        | ~ c_Wellfounded_Owf(U_13241,U_13242) ) ),
    inference(variable_rename,[status(thm)],[f_3419_1]) ).

fof(f_3419_3,plain,
    ( ! [U_13246,U_13244] :
        ( c_Wellfounded_Owf(U_13244,U_13246)
        | ? [U_13240] : ~ hBOOL(hAPP(hAPP(c_member(U_13244),U_13240),c_Wellfounded_Oacc(U_13244,U_13246))) )
    & ! [U_13245,U_13243] :
        ( ! [U_13239] : hBOOL(hAPP(hAPP(c_member(U_13243),U_13239),c_Wellfounded_Oacc(U_13243,U_13245)))
        | ~ c_Wellfounded_Owf(U_13243,U_13245) ) ),
    inference(miniscope,[status(thm)],[f_3419_2]) ).

fof(f_3419_4,plain,
    ( ! [U_13246,U_13244] :
        ( c_Wellfounded_Owf(U_13244,U_13246)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13244),sK312(U_13246,U_13244)),c_Wellfounded_Oacc(U_13244,U_13246))) )
    & ! [U_13245,U_13243] :
        ( ! [U_13239] : hBOOL(hAPP(hAPP(c_member(U_13243),U_13239),c_Wellfounded_Oacc(U_13243,U_13245)))
        | ~ c_Wellfounded_Owf(U_13243,U_13245) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_13240,sK312(U_13246,U_13244))],[f_3419_3]) ).

cnf(f_3419_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13243),U_13239),c_Wellfounded_Oacc(U_13243,U_13245)))
    | ~ c_Wellfounded_Owf(U_13243,U_13245) ),
    inference(clausify,[status(thm)],[f_3419_4]) ).

cnf(f_3419_6,plain,
    ( c_Wellfounded_Owf(U_13244,U_13246)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13244),sK312(U_13246,U_13244)),c_Wellfounded_Oacc(U_13244,U_13246))) ),
    inference(clausify,[status(thm)],[f_3419_4]) ).

fof(f_3420_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_3420_2,plain,
    ! [U_13249,U_13248,U_13247] :
      ( hBOOL(hAPP(hAPP(c_member(U_13247),U_13249),c_Wellfounded_Oacc(U_13247,U_13248)))
      | ~ c_Wellfounded_Owf(U_13247,U_13248) ),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

cnf(f_3420_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13247),U_13249),c_Wellfounded_Oacc(U_13247,U_13248)))
    | ~ c_Wellfounded_Owf(U_13247,U_13248) ),
    inference(clausify,[status(thm)],[f_3420_2]) ).

fof(f_3421_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_3421_2,plain,
    ! [U_13251,U_13250] :
      ( c_Wellfounded_Owf(U_13250,U_13251)
      | hAPP(hAPP(c_Relation_Orel__comp(U_13250,U_13250,U_13250),U_13251),U_13251) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13250,U_13250),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

cnf(f_3421_3,plain,
    ( c_Wellfounded_Owf(U_13250,U_13251)
    | hAPP(hAPP(c_Relation_Orel__comp(U_13250,U_13250,U_13250),U_13251),U_13251) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13250,U_13250),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3421_2]) ).

fof(f_3422_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_3422_2,plain,
    ! [U_13254,U_13253,U_13252] :
      ( ( c_Wellfounded_Owf(U_13252,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),U_13253),U_13254))
        | ~ c_Wellfounded_Owf(U_13252,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13252,U_13252,U_13252),U_13253),U_13253)),hAPP(hAPP(c_Relation_Orel__comp(U_13252,U_13252,U_13252),U_13254),U_13253))),U_13254)) )
      & ( c_Wellfounded_Owf(U_13252,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13252,U_13252,U_13252),U_13253),U_13253)),hAPP(hAPP(c_Relation_Orel__comp(U_13252,U_13252,U_13252),U_13254),U_13253))),U_13254))
        | ~ c_Wellfounded_Owf(U_13252,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13252,U_13252),tc_HOL_Obool)),U_13253),U_13254)) ) ),
    inference(variable_rename,[status(thm)],[f_3422_1]) ).

fof(f_3422_3,plain,
    ( ! [U_13260,U_13258,U_13256] :
        ( c_Wellfounded_Owf(U_13256,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),U_13258),U_13260))
        | ~ c_Wellfounded_Owf(U_13256,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13256,U_13256,U_13256),U_13258),U_13258)),hAPP(hAPP(c_Relation_Orel__comp(U_13256,U_13256,U_13256),U_13260),U_13258))),U_13260)) )
    & ! [U_13259,U_13257,U_13255] :
        ( c_Wellfounded_Owf(U_13255,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13255,U_13255,U_13255),U_13257),U_13257)),hAPP(hAPP(c_Relation_Orel__comp(U_13255,U_13255,U_13255),U_13259),U_13257))),U_13259))
        | ~ c_Wellfounded_Owf(U_13255,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),U_13257),U_13259)) ) ),
    inference(miniscope,[status(thm)],[f_3422_2]) ).

cnf(f_3422_4,plain,
    ( c_Wellfounded_Owf(U_13255,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13255,U_13255,U_13255),U_13257),U_13257)),hAPP(hAPP(c_Relation_Orel__comp(U_13255,U_13255,U_13255),U_13259),U_13257))),U_13259))
    | ~ c_Wellfounded_Owf(U_13255,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13255,U_13255),tc_HOL_Obool)),U_13257),U_13259)) ),
    inference(clausify,[status(thm)],[f_3422_3]) ).

cnf(f_3422_5,plain,
    ( c_Wellfounded_Owf(U_13256,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),U_13258),U_13260))
    | ~ c_Wellfounded_Owf(U_13256,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13256,U_13256),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13256,U_13256,U_13256),U_13258),U_13258)),hAPP(hAPP(c_Relation_Orel__comp(U_13256,U_13256,U_13256),U_13260),U_13258))),U_13260)) ),
    inference(clausify,[status(thm)],[f_3422_3]) ).

fof(f_3423_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_3423_2,plain,
    ! [U_13262,U_13261] : hAPP(c_Relation_ODomain(U_13261,U_13262),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13261,U_13262),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13261,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3423_1]) ).

cnf(f_3423_3,plain,
    hAPP(c_Relation_ODomain(U_13261,U_13262),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13261,U_13262),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13261,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3423_2]) ).

fof(f_3424_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_3424_2,plain,
    ! [U_13265,U_13264,U_13263] :
      ( ( hAPP(c_Relation_ODomain(U_13263,U_13264),U_13265) = c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool))
        | U_13265 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13263,U_13264),tc_HOL_Obool)) )
      & ( U_13265 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13263,U_13264),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_13263,U_13264),U_13265) != c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3424_1]) ).

fof(f_3424_3,plain,
    ( ! [U_13271,U_13269,U_13267] :
        ( hAPP(c_Relation_ODomain(U_13267,U_13269),U_13271) = c_Orderings_Obot__class_Obot(tc_fun(U_13267,tc_HOL_Obool))
        | U_13271 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13267,U_13269),tc_HOL_Obool)) )
    & ! [U_13270,U_13268,U_13266] :
        ( U_13270 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13266,U_13268),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_13266,U_13268),U_13270) != c_Orderings_Obot__class_Obot(tc_fun(U_13266,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3424_2]) ).

cnf(f_3424_4,plain,
    ( U_13270 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13266,U_13268),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_13266,U_13268),U_13270) != c_Orderings_Obot__class_Obot(tc_fun(U_13266,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3424_3]) ).

cnf(f_3424_5,plain,
    ( hAPP(c_Relation_ODomain(U_13267,U_13269),U_13271) = c_Orderings_Obot__class_Obot(tc_fun(U_13267,tc_HOL_Obool))
    | U_13271 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13267,U_13269),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3424_3]) ).

fof(f_3425_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_3425_2,plain,
    ! [U_13275,U_13274,U_13273,U_13272] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13272,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13272,U_13273),U_13274)),hAPP(c_Relation_ODomain(U_13272,U_13273),U_13275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13272,U_13273),tc_HOL_Obool)),U_13274),U_13275)) ),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

cnf(f_3425_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13272,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13272,U_13273),U_13274)),hAPP(c_Relation_ODomain(U_13272,U_13273),U_13275)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13272,U_13273),tc_HOL_Obool)),U_13274),U_13275)) ),
    inference(clausify,[status(thm)],[f_3425_2]) ).

fof(f_3426_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_3426_2,plain,
    ! [U_13279,U_13278,U_13277,U_13276] : hAPP(c_Relation_ODomain(U_13276,U_13277),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13276,U_13277),tc_HOL_Obool)),U_13278),U_13279)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13276,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13276,U_13277),U_13278)),hAPP(c_Relation_ODomain(U_13276,U_13277),U_13279)),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

cnf(f_3426_3,plain,
    hAPP(c_Relation_ODomain(U_13276,U_13277),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13276,U_13277),tc_HOL_Obool)),U_13278),U_13279)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13276,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13276,U_13277),U_13278)),hAPP(c_Relation_ODomain(U_13276,U_13277),U_13279)),
    inference(clausify,[status(thm)],[f_3426_2]) ).

fof(f_3427_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_3427_2,plain,
    ! [U_13282,U_13281,U_13280] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),hAPP(c_Relation_ODomain(U_13280,U_13281),U_13282)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13280,U_13281)),U_13282)) ),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

cnf(f_3427_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13280),hAPP(c_Relation_ODomain(U_13280,U_13281),U_13282)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13280,U_13281)),U_13282)) ),
    inference(clausify,[status(thm)],[f_3427_2]) ).

fof(f_3428_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_3428_2,plain,
    ! [U_13285,U_13284,U_13283] : hAPP(c_Set_Oimage(tc_prod(U_13283,U_13284),U_13283,c_Product__Type_Ofst(U_13283,U_13284)),U_13285) = hAPP(c_Relation_ODomain(U_13283,U_13284),U_13285),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

cnf(f_3428_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13283,U_13284),U_13283,c_Product__Type_Ofst(U_13283,U_13284)),U_13285) = hAPP(c_Relation_ODomain(U_13283,U_13284),U_13285),
    inference(clausify,[status(thm)],[f_3428_2]) ).

fof(f_3429_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_3429_2,plain,
    ! [U_13291,U_13290] :
      ( ( c_Wellfounded_Owf(U_13290,U_13291)
        | ? [U_13289] :
          ! [U_13288] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13290,U_13290)),hAPP(hAPP(c_Product__Type_OPair(U_13290,U_13290),hAPP(U_13289,hAPP(c_Nat_OSuc,U_13288))),hAPP(U_13289,U_13288))),U_13291)) )
      & ( ! [U_13287] :
          ? [U_13286] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13290,U_13290)),hAPP(hAPP(c_Product__Type_OPair(U_13290,U_13290),hAPP(U_13287,hAPP(c_Nat_OSuc,U_13286))),hAPP(U_13287,U_13286))),U_13291))
        | ~ c_Wellfounded_Owf(U_13290,U_13291) ) ),
    inference(variable_rename,[status(thm)],[f_3429_1]) ).

fof(f_3429_3,plain,
    ( ! [U_13295,U_13293] :
        ( c_Wellfounded_Owf(U_13293,U_13295)
        | ? [U_13289] :
          ! [U_13288] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13293)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13293),hAPP(U_13289,hAPP(c_Nat_OSuc,U_13288))),hAPP(U_13289,U_13288))),U_13295)) )
    & ! [U_13294,U_13292] :
        ( ! [U_13287] :
          ? [U_13286] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13292,U_13292)),hAPP(hAPP(c_Product__Type_OPair(U_13292,U_13292),hAPP(U_13287,hAPP(c_Nat_OSuc,U_13286))),hAPP(U_13287,U_13286))),U_13294))
        | ~ c_Wellfounded_Owf(U_13292,U_13294) ) ),
    inference(miniscope,[status(thm)],[f_3429_2]) ).

fof(f_3429_4,plain,
    ( ! [U_13295,U_13293] :
        ( c_Wellfounded_Owf(U_13293,U_13295)
        | ? [U_13289] :
          ! [U_13288] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13293)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13293),hAPP(U_13289,hAPP(c_Nat_OSuc,U_13288))),hAPP(U_13289,U_13288))),U_13295)) )
    & ! [U_13294,U_13292] :
        ( ! [U_13287] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13292,U_13292)),hAPP(hAPP(c_Product__Type_OPair(U_13292,U_13292),hAPP(U_13287,hAPP(c_Nat_OSuc,sK313(U_13294,U_13292,U_13287)))),hAPP(U_13287,sK313(U_13294,U_13292,U_13287)))),U_13294))
        | ~ c_Wellfounded_Owf(U_13292,U_13294) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_13286,sK313(U_13294,U_13292,U_13287))],[f_3429_3]) ).

fof(f_3429_5,plain,
    ( ! [U_13295,U_13293] :
        ( c_Wellfounded_Owf(U_13293,U_13295)
        | ! [U_13288] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13293)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13293),hAPP(sK314(U_13295,U_13293),hAPP(c_Nat_OSuc,U_13288))),hAPP(sK314(U_13295,U_13293),U_13288))),U_13295)) )
    & ! [U_13294,U_13292] :
        ( ! [U_13287] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13292,U_13292)),hAPP(hAPP(c_Product__Type_OPair(U_13292,U_13292),hAPP(U_13287,hAPP(c_Nat_OSuc,sK313(U_13294,U_13292,U_13287)))),hAPP(U_13287,sK313(U_13294,U_13292,U_13287)))),U_13294))
        | ~ c_Wellfounded_Owf(U_13292,U_13294) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_13289,sK314(U_13295,U_13293))],[f_3429_4]) ).

cnf(f_3429_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13292,U_13292)),hAPP(hAPP(c_Product__Type_OPair(U_13292,U_13292),hAPP(U_13287,hAPP(c_Nat_OSuc,sK313(U_13294,U_13292,U_13287)))),hAPP(U_13287,sK313(U_13294,U_13292,U_13287)))),U_13294))
    | ~ c_Wellfounded_Owf(U_13292,U_13294) ),
    inference(clausify,[status(thm)],[f_3429_5]) ).

cnf(f_3429_7,plain,
    ( c_Wellfounded_Owf(U_13293,U_13295)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13293,U_13293)),hAPP(hAPP(c_Product__Type_OPair(U_13293,U_13293),hAPP(sK314(U_13295,U_13293),hAPP(c_Nat_OSuc,U_13288))),hAPP(sK314(U_13295,U_13293),U_13288))),U_13295)) ),
    inference(clausify,[status(thm)],[f_3429_5]) ).

fof(f_3430_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_3430_2,plain,
    ! [U_13298,U_13297,U_13296] :
      ( U_13298 = c_Orderings_Obot__class_Obot(tc_fun(U_13296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13296,tc_HOL_Obool)),U_13298),hAPP(c_Relation_OImage(U_13296,U_13296,U_13297),U_13298)))
      | ~ c_Wellfounded_Owf(U_13296,U_13297) ),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

cnf(f_3430_3,plain,
    ( U_13298 = c_Orderings_Obot__class_Obot(tc_fun(U_13296,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13296,tc_HOL_Obool)),U_13298),hAPP(c_Relation_OImage(U_13296,U_13296,U_13297),U_13298)))
    | ~ c_Wellfounded_Owf(U_13296,U_13297) ),
    inference(clausify,[status(thm)],[f_3430_2]) ).

fof(f_3431_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_3431_2,plain,
    ! [U_13301,U_13300,U_13299] :
      ( c_Wellfounded_Owf(U_13299,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13299,U_13299),tc_HOL_Obool)),U_13300),U_13301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13299,U_13299),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13299,U_13299,U_13299),U_13300),U_13301)),U_13300))
      | ~ c_Wellfounded_Owf(U_13299,U_13301)
      | ~ c_Wellfounded_Owf(U_13299,U_13300) ),
    inference(variable_rename,[status(thm)],[f_3431_1]) ).

cnf(f_3431_3,plain,
    ( c_Wellfounded_Owf(U_13299,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13299,U_13299),tc_HOL_Obool)),U_13300),U_13301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13299,U_13299),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13299,U_13299,U_13299),U_13300),U_13301)),U_13300))
    | ~ c_Wellfounded_Owf(U_13299,U_13301)
    | ~ c_Wellfounded_Owf(U_13299,U_13300) ),
    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_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_3432_2,plain,
    ! [U_13307,U_13306,U_13305,U_13304] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13304),U_13305),hAPP(c_Relation_ODomain(U_13304,U_13306),U_13307)))
        | ! [U_13303] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13304,U_13306)),hAPP(hAPP(c_Product__Type_OPair(U_13304,U_13306),U_13305),U_13303)),U_13307)) )
      & ( ? [U_13302] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13304,U_13306)),hAPP(hAPP(c_Product__Type_OPair(U_13304,U_13306),U_13305),U_13302)),U_13307))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13304),U_13305),hAPP(c_Relation_ODomain(U_13304,U_13306),U_13307))) ) ),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

fof(f_3432_3,plain,
    ( ! [U_13315,U_13313,U_13311,U_13309] :
        ( hBOOL(hAPP(hAPP(c_member(U_13309),U_13311),hAPP(c_Relation_ODomain(U_13309,U_13313),U_13315)))
        | ! [U_13303] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13309,U_13313)),hAPP(hAPP(c_Product__Type_OPair(U_13309,U_13313),U_13311),U_13303)),U_13315)) )
    & ! [U_13314,U_13312,U_13310,U_13308] :
        ( ? [U_13302] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13308,U_13312)),hAPP(hAPP(c_Product__Type_OPair(U_13308,U_13312),U_13310),U_13302)),U_13314))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13308),U_13310),hAPP(c_Relation_ODomain(U_13308,U_13312),U_13314))) ) ),
    inference(miniscope,[status(thm)],[f_3432_2]) ).

fof(f_3432_4,plain,
    ( ! [U_13315,U_13313,U_13311,U_13309] :
        ( hBOOL(hAPP(hAPP(c_member(U_13309),U_13311),hAPP(c_Relation_ODomain(U_13309,U_13313),U_13315)))
        | ! [U_13303] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13309,U_13313)),hAPP(hAPP(c_Product__Type_OPair(U_13309,U_13313),U_13311),U_13303)),U_13315)) )
    & ! [U_13314,U_13312,U_13310,U_13308] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13308,U_13312)),hAPP(hAPP(c_Product__Type_OPair(U_13308,U_13312),U_13310),sK315(U_13314,U_13312,U_13310,U_13308))),U_13314))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13308),U_13310),hAPP(c_Relation_ODomain(U_13308,U_13312),U_13314))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_13302,sK315(U_13314,U_13312,U_13310,U_13308))],[f_3432_3]) ).

cnf(f_3432_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13308,U_13312)),hAPP(hAPP(c_Product__Type_OPair(U_13308,U_13312),U_13310),sK315(U_13314,U_13312,U_13310,U_13308))),U_13314))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13308),U_13310),hAPP(c_Relation_ODomain(U_13308,U_13312),U_13314))) ),
    inference(clausify,[status(thm)],[f_3432_4]) ).

cnf(f_3432_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13309),U_13311),hAPP(c_Relation_ODomain(U_13309,U_13313),U_13315)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13309,U_13313)),hAPP(hAPP(c_Product__Type_OPair(U_13309,U_13313),U_13311),U_13303)),U_13315)) ),
    inference(clausify,[status(thm)],[f_3432_4]) ).

fof(f_3433_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_3433_2,plain,
    ! [U_13316] :
      ( c_Wellfounded_Owf(U_13316,hAPP(c_Set_OCollect(tc_prod(U_13316,U_13316)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13316,U_13316,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13316))))
      | ~ class_Orderings_Owellorder(U_13316) ),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

cnf(f_3433_3,plain,
    ( c_Wellfounded_Owf(U_13316,hAPP(c_Set_OCollect(tc_prod(U_13316,U_13316)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13316,U_13316,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13316))))
    | ~ class_Orderings_Owellorder(U_13316) ),
    inference(clausify,[status(thm)],[f_3433_2]) ).

fof(f_3434_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_3434_2,plain,
    ! [U_13321,U_13320,U_13319,U_13318,U_13317] : hAPP(c_Relation_ODomain(U_13317,U_13318),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13317,U_13318)),hAPP(hAPP(c_Product__Type_OPair(U_13317,U_13318),U_13319),U_13320)),U_13321)) = hAPP(hAPP(c_Set_Oinsert(U_13317),U_13319),hAPP(c_Relation_ODomain(U_13317,U_13318),U_13321)),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

cnf(f_3434_3,plain,
    hAPP(c_Relation_ODomain(U_13317,U_13318),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13317,U_13318)),hAPP(hAPP(c_Product__Type_OPair(U_13317,U_13318),U_13319),U_13320)),U_13321)) = hAPP(hAPP(c_Set_Oinsert(U_13317),U_13319),hAPP(c_Relation_ODomain(U_13317,U_13318),U_13321)),
    inference(clausify,[status(thm)],[f_3434_2]) ).

fof(f_3435_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2)) )
        | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).

fof(f_3435_2,plain,
    ! [U_13323,U_13322] :
      ( ( c_FunDef_Oreduction__pair(U_13322,U_13323)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13322,U_13322,U_13322),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)))
        | ~ c_Wellfounded_Owf(U_13322,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13322,U_13322,U_13322),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)))
          & c_Wellfounded_Owf(U_13322,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool),tc_fun(tc_prod(U_13322,U_13322),tc_HOL_Obool)),U_13323)) )
        | ~ c_FunDef_Oreduction__pair(U_13322,U_13323) ) ),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

fof(f_3435_3,plain,
    ( ! [U_13327,U_13325] :
        ( c_FunDef_Oreduction__pair(U_13325,U_13327)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13325,U_13325,U_13325),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)))
        | ~ c_Wellfounded_Owf(U_13325,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)) )
    & ! [U_13326,U_13324] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13324,U_13324,U_13324),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326)))
          & c_Wellfounded_Owf(U_13324,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326)) )
        | ~ c_FunDef_Oreduction__pair(U_13324,U_13326) ) ),
    inference(miniscope,[status(thm)],[f_3435_2]) ).

cnf(f_3435_4,plain,
    ( c_Wellfounded_Owf(U_13324,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326))
    | ~ c_FunDef_Oreduction__pair(U_13324,U_13326) ),
    inference(clausify,[status(thm)],[f_3435_3]) ).

cnf(f_3435_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13324,U_13324,U_13324),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool),tc_fun(tc_prod(U_13324,U_13324),tc_HOL_Obool)),U_13326)))
    | ~ c_FunDef_Oreduction__pair(U_13324,U_13326) ),
    inference(clausify,[status(thm)],[f_3435_3]) ).

cnf(f_3435_6,plain,
    ( c_FunDef_Oreduction__pair(U_13325,U_13327)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13325,U_13325,U_13325),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)))
    | ~ c_Wellfounded_Owf(U_13325,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13325),tc_HOL_Obool)),U_13327)) ),
    inference(clausify,[status(thm)],[f_3435_3]) ).

fof(f_3436_1,plain,
    ! [V_S_2,V_R_2,V_Pa_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_Pa_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_Pa_2)))
      | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).

fof(f_3436_2,plain,
    ! [U_13331,U_13330,U_13329,U_13328] :
      ( c_Wellfounded_Owf(U_13328,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13330),U_13331))
      | ~ c_Wellfounded_Owf(U_13328,U_13331)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13331),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool),tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13329)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13330),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool),tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13329)))
      | ~ c_FunDef_Oreduction__pair(U_13328,U_13329) ),
    inference(variable_rename,[status(thm)],[f_3436_1]) ).

cnf(f_3436_3,plain,
    ( c_Wellfounded_Owf(U_13328,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13330),U_13331))
    | ~ c_Wellfounded_Owf(U_13328,U_13331)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13331),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool),tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13330),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool),tc_fun(tc_prod(U_13328,U_13328),tc_HOL_Obool)),U_13329)))
    | ~ c_FunDef_Oreduction__pair(U_13328,U_13329) ),
    inference(clausify,[status(thm)],[f_3436_2]) ).

fof(f_3437_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_3437_2,plain,
    ! [U_13335,U_13334,U_13333,U_13332] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13332,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13332,U_13333),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13332,U_13333),tc_HOL_Obool)),U_13334),U_13335))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13332,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13332,U_13333),U_13334)),hAPP(c_Relation_ODomain(U_13332,U_13333),U_13335)))),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

cnf(f_3437_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13332,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13332,U_13333),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13332,U_13333),tc_HOL_Obool)),U_13334),U_13335))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13332,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13332,U_13333),U_13334)),hAPP(c_Relation_ODomain(U_13332,U_13333),U_13335)))),
    inference(clausify,[status(thm)],[f_3437_2]) ).

fof(f_3438_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_3438_2,plain,
    ! [U_13339,U_13338,U_13337,U_13336] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13336,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13336,U_13337),U_13338)),hAPP(c_Relation_ODomain(U_13336,U_13337),U_13339))),hAPP(c_Relation_ODomain(U_13336,U_13337),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13336,U_13337),tc_HOL_Obool)),U_13338),U_13339)))),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

cnf(f_3438_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13336,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13336,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13336,U_13337),U_13338)),hAPP(c_Relation_ODomain(U_13336,U_13337),U_13339))),hAPP(c_Relation_ODomain(U_13336,U_13337),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13336,U_13337),tc_HOL_Obool)),U_13338),U_13339)))),
    inference(clausify,[status(thm)],[f_3438_2]) ).

fof(f_3439_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_3439_2,plain,
    ! [U_13341,U_13340] : hAPP(c_Relation_OField(U_13340),U_13341) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13340,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13340,U_13340),U_13341)),hAPP(c_Relation_ORange(U_13340,U_13340),U_13341)),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

cnf(f_3439_3,plain,
    hAPP(c_Relation_OField(U_13340),U_13341) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13340,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13340,U_13340),U_13341)),hAPP(c_Relation_ORange(U_13340,U_13340),U_13341)),
    inference(clausify,[status(thm)],[f_3439_2]) ).

fof(f_3440_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_3440_2,plain,
    ! [U_13345,U_13344,U_13343,U_13342] :
      ( c_Wellfounded_Owf(U_13344,hAPP(c_Set_Oimage(tc_prod(U_13342,U_13342),tc_prod(U_13344,U_13344),c_Product__Type_Omap__pair(U_13342,U_13344,U_13342,U_13344,U_13345,U_13345)),U_13343))
      | ~ c_Fun_Oinj__on(U_13342,U_13344,U_13345,c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_13342,U_13343) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

cnf(f_3440_3,plain,
    ( c_Wellfounded_Owf(U_13344,hAPP(c_Set_Oimage(tc_prod(U_13342,U_13342),tc_prod(U_13344,U_13344),c_Product__Type_Omap__pair(U_13342,U_13344,U_13342,U_13344,U_13345,U_13345)),U_13343))
    | ~ c_Fun_Oinj__on(U_13342,U_13344,U_13345,c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_13342,U_13343) ),
    inference(clausify,[status(thm)],[f_3440_2]) ).

fof(f_3441_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_3441_2,plain,
    ! [U_13348,U_13347,U_13346] : hAPP(c_Relation_ODomain(U_13346,U_13347),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13346,U_13347),tc_HOL_Obool),U_13348)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13346,U_13347),tc_HOL_Obool),tc_fun(U_13346,tc_HOL_Obool)),U_13348),c_Relation_ODomain(U_13346,U_13347)),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

cnf(f_3441_3,plain,
    hAPP(c_Relation_ODomain(U_13346,U_13347),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13346,U_13347),tc_HOL_Obool),U_13348)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13346,U_13347),tc_HOL_Obool),tc_fun(U_13346,tc_HOL_Obool)),U_13348),c_Relation_ODomain(U_13346,U_13347)),
    inference(clausify,[status(thm)],[f_3441_2]) ).

fof(f_3442_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_3442_2,plain,
    ! [U_13350,U_13349] : c_HOL_OThe(U_13349,hAPP(c_fequal,U_13350)) = U_13350,
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

cnf(f_3442_3,plain,
    c_HOL_OThe(U_13349,hAPP(c_fequal,U_13350)) = U_13350,
    inference(clausify,[status(thm)],[f_3442_2]) ).

fof(f_3443_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_3443_2,plain,
    ! [U_13354,U_13353,U_13352,U_13351] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13351,U_13352,hAPP(hAPP(c_COMBC(U_13351,tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_fun(U_13352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13352,tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_fun(U_13352,tc_HOL_Obool)),U_13351),c_COMBC(U_13352,tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13352,tc_prod(U_13351,U_13352)),tc_fun(U_13352,tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),U_13351),hAPP(c_COMBB(tc_prod(U_13351,U_13352),tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool),U_13352),c_member(tc_prod(U_13351,U_13352)))),c_Product__Type_OPair(U_13351,U_13352)))),U_13353)),U_13354))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13351),U_13354),hAPP(c_Relation_ODomain(U_13351,U_13352),U_13353))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13351),U_13354),hAPP(c_Relation_ODomain(U_13351,U_13352),U_13353)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13351,U_13352,hAPP(hAPP(c_COMBC(U_13351,tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_fun(U_13352,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13352,tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_fun(U_13352,tc_HOL_Obool)),U_13351),c_COMBC(U_13352,tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13352,tc_prod(U_13351,U_13352)),tc_fun(U_13352,tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool)),U_13351),hAPP(c_COMBB(tc_prod(U_13351,U_13352),tc_fun(tc_fun(tc_prod(U_13351,U_13352),tc_HOL_Obool),tc_HOL_Obool),U_13352),c_member(tc_prod(U_13351,U_13352)))),c_Product__Type_OPair(U_13351,U_13352)))),U_13353)),U_13354)) ) ),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

fof(f_3443_3,plain,
    ( ! [U_13362,U_13360,U_13358,U_13356] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_13356,U_13358,hAPP(hAPP(c_COMBC(U_13356,tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_fun(U_13358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13358,tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_fun(U_13358,tc_HOL_Obool)),U_13356),c_COMBC(U_13358,tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13358,tc_prod(U_13356,U_13358)),tc_fun(U_13358,tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),U_13356),hAPP(c_COMBB(tc_prod(U_13356,U_13358),tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool),U_13358),c_member(tc_prod(U_13356,U_13358)))),c_Product__Type_OPair(U_13356,U_13358)))),U_13360)),U_13362))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13356),U_13362),hAPP(c_Relation_ODomain(U_13356,U_13358),U_13360))) )
    & ! [U_13361,U_13359,U_13357,U_13355] :
        ( hBOOL(hAPP(hAPP(c_member(U_13355),U_13361),hAPP(c_Relation_ODomain(U_13355,U_13357),U_13359)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13355,U_13357,hAPP(hAPP(c_COMBC(U_13355,tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13357,tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),U_13355),c_COMBC(U_13357,tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13357,tc_prod(U_13355,U_13357)),tc_fun(U_13357,tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),U_13355),hAPP(c_COMBB(tc_prod(U_13355,U_13357),tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool),U_13357),c_member(tc_prod(U_13355,U_13357)))),c_Product__Type_OPair(U_13355,U_13357)))),U_13359)),U_13361)) ) ),
    inference(miniscope,[status(thm)],[f_3443_2]) ).

cnf(f_3443_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13355),U_13361),hAPP(c_Relation_ODomain(U_13355,U_13357),U_13359)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13355,U_13357,hAPP(hAPP(c_COMBC(U_13355,tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13357,tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_fun(U_13357,tc_HOL_Obool)),U_13355),c_COMBC(U_13357,tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13357,tc_prod(U_13355,U_13357)),tc_fun(U_13357,tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool)),U_13355),hAPP(c_COMBB(tc_prod(U_13355,U_13357),tc_fun(tc_fun(tc_prod(U_13355,U_13357),tc_HOL_Obool),tc_HOL_Obool),U_13357),c_member(tc_prod(U_13355,U_13357)))),c_Product__Type_OPair(U_13355,U_13357)))),U_13359)),U_13361)) ),
    inference(clausify,[status(thm)],[f_3443_3]) ).

cnf(f_3443_5,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13356,U_13358,hAPP(hAPP(c_COMBC(U_13356,tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_fun(U_13358,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13358,tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_fun(U_13358,tc_HOL_Obool)),U_13356),c_COMBC(U_13358,tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13358,tc_prod(U_13356,U_13358)),tc_fun(U_13358,tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool)),U_13356),hAPP(c_COMBB(tc_prod(U_13356,U_13358),tc_fun(tc_fun(tc_prod(U_13356,U_13358),tc_HOL_Obool),tc_HOL_Obool),U_13358),c_member(tc_prod(U_13356,U_13358)))),c_Product__Type_OPair(U_13356,U_13358)))),U_13360)),U_13362))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13356),U_13362),hAPP(c_Relation_ODomain(U_13356,U_13358),U_13360))) ),
    inference(clausify,[status(thm)],[f_3443_3]) ).

fof(f_3444_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_3444_2,plain,
    ! [U_13364,U_13363] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13363),c_List_Olenlex(U_13363,U_13364))
      | ~ c_Wellfounded_Owf(U_13363,U_13364) ),
    inference(variable_rename,[status(thm)],[f_3444_1]) ).

cnf(f_3444_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13363),c_List_Olenlex(U_13363,U_13364))
    | ~ c_Wellfounded_Owf(U_13363,U_13364) ),
    inference(clausify,[status(thm)],[f_3444_2]) ).

fof(f_3445_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_3445_2,plain,
    ! [U_13369,U_13368,U_13367,U_13366] :
      ( ? [U_13365] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13366,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13366,U_13368),U_13367),U_13365)),U_13369))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13366),U_13367),hAPP(c_Relation_ODomain(U_13366,U_13368),U_13369))) ),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

fof(f_3445_3,plain,
    ! [U_13369,U_13368,U_13367,U_13366] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13366,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13366,U_13368),U_13367),sK316(U_13369,U_13368,U_13367,U_13366))),U_13369))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13366),U_13367),hAPP(c_Relation_ODomain(U_13366,U_13368),U_13369))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_13365,sK316(U_13369,U_13368,U_13367,U_13366))],[f_3445_2]) ).

cnf(f_3445_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13366,U_13368)),hAPP(hAPP(c_Product__Type_OPair(U_13366,U_13368),U_13367),sK316(U_13369,U_13368,U_13367,U_13366))),U_13369))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13366),U_13367),hAPP(c_Relation_ODomain(U_13366,U_13368),U_13369))) ),
    inference(clausify,[status(thm)],[f_3445_3]) ).

fof(f_3446_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_3446_2,plain,
    ! [U_13374,U_13373,U_13372,U_13371,U_13370] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_13373,U_13374,U_13370),U_13371))
      | ~ hBOOL(hAPP(hAPP(U_13370,U_13371),U_13372)) ),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

cnf(f_3446_3,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13373,U_13374,U_13370),U_13371))
    | ~ hBOOL(hAPP(hAPP(U_13370,U_13371),U_13372)) ),
    inference(clausify,[status(thm)],[f_3446_2]) ).

fof(f_3447_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_3447_2,plain,
    ! [U_13380,U_13379,U_13378,U_13377] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13377,U_13378,U_13379),U_13380))
        | ! [U_13376] : ~ hBOOL(hAPP(hAPP(U_13379,U_13380),U_13376)) )
      & ( ? [U_13375] : hBOOL(hAPP(hAPP(U_13379,U_13380),U_13375))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13377,U_13378,U_13379),U_13380)) ) ),
    inference(variable_rename,[status(thm)],[f_3447_1]) ).

fof(f_3447_3,plain,
    ( ! [U_13388,U_13386] :
        ( ! [U_13384,U_13382] : hBOOL(hAPP(c_Predicate_ODomainP(U_13382,U_13384,U_13386),U_13388))
        | ! [U_13376] : ~ hBOOL(hAPP(hAPP(U_13386,U_13388),U_13376)) )
    & ! [U_13387,U_13385] :
        ( ! [U_13383,U_13381] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13381,U_13383,U_13385),U_13387))
        | ? [U_13375] : hBOOL(hAPP(hAPP(U_13385,U_13387),U_13375)) ) ),
    inference(miniscope,[status(thm)],[f_3447_2]) ).

fof(f_3447_4,plain,
    ( ! [U_13388,U_13386] :
        ( ! [U_13384,U_13382] : hBOOL(hAPP(c_Predicate_ODomainP(U_13382,U_13384,U_13386),U_13388))
        | ! [U_13376] : ~ hBOOL(hAPP(hAPP(U_13386,U_13388),U_13376)) )
    & ! [U_13387,U_13385] :
        ( ! [U_13383,U_13381] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13381,U_13383,U_13385),U_13387))
        | hBOOL(hAPP(hAPP(U_13385,U_13387),sK317(U_13387,U_13385))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_13375,sK317(U_13387,U_13385))],[f_3447_3]) ).

cnf(f_3447_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13381,U_13383,U_13385),U_13387))
    | hBOOL(hAPP(hAPP(U_13385,U_13387),sK317(U_13387,U_13385))) ),
    inference(clausify,[status(thm)],[f_3447_4]) ).

cnf(f_3447_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13382,U_13384,U_13386),U_13388))
    | ~ hBOOL(hAPP(hAPP(U_13386,U_13388),U_13376)) ),
    inference(clausify,[status(thm)],[f_3447_4]) ).

fof(f_3448_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_3448_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_3448_1]) ).

fof(f_3449_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_3449_2,plain,
    ! [U_13390,U_13389] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13389),c_List_Olex(U_13389,U_13390))
      | ~ c_Wellfounded_Owf(U_13389,U_13390) ),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

cnf(f_3449_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13389),c_List_Olex(U_13389,U_13390))
    | ~ c_Wellfounded_Owf(U_13389,U_13390) ),
    inference(clausify,[status(thm)],[f_3449_2]) ).

fof(f_3450_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_3450_2,plain,
    ! [U_13393,U_13392,U_13391] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13391),hAPP(c_List_Olexn(U_13391,U_13392),U_13393))
      | ~ c_Wellfounded_Owf(U_13391,U_13392) ),
    inference(variable_rename,[status(thm)],[f_3450_1]) ).

cnf(f_3450_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13391),hAPP(c_List_Olexn(U_13391,U_13392),U_13393))
    | ~ c_Wellfounded_Owf(U_13391,U_13392) ),
    inference(clausify,[status(thm)],[f_3450_2]) ).

fof(f_3451_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_3451_2,plain,
    ! [U_13395,U_13394] : c_List_Olex(U_13394,U_13395) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13394),tc_List_Olist(U_13394)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13394,U_13395)),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

cnf(f_3451_3,plain,
    c_List_Olex(U_13394,U_13395) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13394),tc_List_Olist(U_13394)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13394,U_13395)),
    inference(clausify,[status(thm)],[f_3451_2]) ).

fof(f_3452_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_3452_2,plain,
    ! [U_13397,U_13396] : hAPP(c_List_Olexn(U_13396,U_13397),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13396),tc_List_Olist(U_13396)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

cnf(f_3452_3,plain,
    hAPP(c_List_Olexn(U_13396,U_13397),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13396),tc_List_Olist(U_13396)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3452_2]) ).

fof(f_3453_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

cnf(f_3453_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3453_1]) ).

fof(f_3454_1,plain,
    ! [T_b,V_R_2,T_c,V_Pa_2] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))
      | ? [B_x] :
          ( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
          & hBOOL(hAPP(V_Pa_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).

fof(f_3454_2,plain,
    ! [U_13402,U_13401,U_13400,U_13399] :
      ( c_Wellfounded_Owf(tc_prod(U_13402,U_13400),c_Recdef_Osame__fst(U_13402,U_13400,U_13399,U_13401))
      | ? [U_13398] :
          ( ~ c_Wellfounded_Owf(U_13400,hAPP(U_13401,U_13398))
          & hBOOL(hAPP(U_13399,U_13398)) ) ),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

fof(f_3454_3,plain,
    ! [U_13402,U_13401,U_13400,U_13399] :
      ( c_Wellfounded_Owf(tc_prod(U_13402,U_13400),c_Recdef_Osame__fst(U_13402,U_13400,U_13399,U_13401))
      | ( ~ c_Wellfounded_Owf(U_13400,hAPP(U_13401,sK318(U_13402,U_13401,U_13400,U_13399)))
        & hBOOL(hAPP(U_13399,sK318(U_13402,U_13401,U_13400,U_13399))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_13398,sK318(U_13402,U_13401,U_13400,U_13399))],[f_3454_2]) ).

cnf(f_3454_4,plain,
    ( hBOOL(hAPP(U_13399,sK318(U_13402,U_13401,U_13400,U_13399)))
    | c_Wellfounded_Owf(tc_prod(U_13402,U_13400),c_Recdef_Osame__fst(U_13402,U_13400,U_13399,U_13401)) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

cnf(f_3454_5,plain,
    ( ~ c_Wellfounded_Owf(U_13400,hAPP(U_13401,sK318(U_13402,U_13401,U_13400,U_13399)))
    | c_Wellfounded_Owf(tc_prod(U_13402,U_13400),c_Recdef_Osame__fst(U_13402,U_13400,U_13399,U_13401)) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

fof(f_3455_1,plain,
    ! [T_b,V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).

fof(f_3455_2,plain,
    ! [U_13407,U_13406,U_13405,U_13404] :
      ( c_Wellfounded_Owf(U_13407,hAPP(c_Set_OCollect(tc_prod(U_13407,U_13407)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13407,U_13407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(U_13407,tc_HOL_Obool),U_13407),hAPP(c_COMBS(U_13407,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13407),c_fconj),U_13404))),hAPP(hAPP(c_COMBC(U_13407,tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),U_13407),c_COMBB(U_13407,tc_HOL_Obool,U_13407)),c_fequal)),U_13406)))))
      | ? [U_13403] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13405,hAPP(U_13406,U_13403))),hAPP(U_13405,U_13403)))
          & hBOOL(hAPP(U_13404,U_13403)) ) ),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

fof(f_3455_3,plain,
    ! [U_13407,U_13406,U_13405,U_13404] :
      ( c_Wellfounded_Owf(U_13407,hAPP(c_Set_OCollect(tc_prod(U_13407,U_13407)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13407,U_13407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(U_13407,tc_HOL_Obool),U_13407),hAPP(c_COMBS(U_13407,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13407),c_fconj),U_13404))),hAPP(hAPP(c_COMBC(U_13407,tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),U_13407),c_COMBB(U_13407,tc_HOL_Obool,U_13407)),c_fequal)),U_13406)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13405,hAPP(U_13406,sK319(U_13407,U_13406,U_13405,U_13404)))),hAPP(U_13405,sK319(U_13407,U_13406,U_13405,U_13404))))
        & hBOOL(hAPP(U_13404,sK319(U_13407,U_13406,U_13405,U_13404))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13403,sK319(U_13407,U_13406,U_13405,U_13404))],[f_3455_2]) ).

cnf(f_3455_4,plain,
    ( hBOOL(hAPP(U_13404,sK319(U_13407,U_13406,U_13405,U_13404)))
    | c_Wellfounded_Owf(U_13407,hAPP(c_Set_OCollect(tc_prod(U_13407,U_13407)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13407,U_13407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(U_13407,tc_HOL_Obool),U_13407),hAPP(c_COMBS(U_13407,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13407),c_fconj),U_13404))),hAPP(hAPP(c_COMBC(U_13407,tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),U_13407),c_COMBB(U_13407,tc_HOL_Obool,U_13407)),c_fequal)),U_13406))))) ),
    inference(clausify,[status(thm)],[f_3455_3]) ).

cnf(f_3455_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13405,hAPP(U_13406,sK319(U_13407,U_13406,U_13405,U_13404)))),hAPP(U_13405,sK319(U_13407,U_13406,U_13405,U_13404))))
    | c_Wellfounded_Owf(U_13407,hAPP(c_Set_OCollect(tc_prod(U_13407,U_13407)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13407,U_13407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(U_13407,tc_HOL_Obool),U_13407),hAPP(c_COMBS(U_13407,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13407),c_fconj),U_13404))),hAPP(hAPP(c_COMBC(U_13407,tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13407,tc_HOL_Obool),tc_fun(tc_fun(U_13407,U_13407),tc_fun(U_13407,tc_HOL_Obool)),U_13407),c_COMBB(U_13407,tc_HOL_Obool,U_13407)),c_fequal)),U_13406))))) ),
    inference(clausify,[status(thm)],[f_3455_3]) ).

fof(f_3456_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_3456_2,plain,
    ! [U_13409,U_13408] :
      ( ( c_Wellfounded_OwfP(U_13408,U_13409)
        | ~ c_Wellfounded_Owf(U_13408,hAPP(c_Set_OCollect(tc_prod(U_13408,U_13408)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13408,U_13408,tc_HOL_Obool),U_13409))) )
      & ( c_Wellfounded_Owf(U_13408,hAPP(c_Set_OCollect(tc_prod(U_13408,U_13408)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13408,U_13408,tc_HOL_Obool),U_13409)))
        | ~ c_Wellfounded_OwfP(U_13408,U_13409) ) ),
    inference(variable_rename,[status(thm)],[f_3456_1]) ).

fof(f_3456_3,plain,
    ( ! [U_13413,U_13411] :
        ( c_Wellfounded_OwfP(U_13411,U_13413)
        | ~ c_Wellfounded_Owf(U_13411,hAPP(c_Set_OCollect(tc_prod(U_13411,U_13411)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13411,U_13411,tc_HOL_Obool),U_13413))) )
    & ! [U_13412,U_13410] :
        ( c_Wellfounded_Owf(U_13410,hAPP(c_Set_OCollect(tc_prod(U_13410,U_13410)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13410,U_13410,tc_HOL_Obool),U_13412)))
        | ~ c_Wellfounded_OwfP(U_13410,U_13412) ) ),
    inference(miniscope,[status(thm)],[f_3456_2]) ).

cnf(f_3456_4,plain,
    ( c_Wellfounded_Owf(U_13410,hAPP(c_Set_OCollect(tc_prod(U_13410,U_13410)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13410,U_13410,tc_HOL_Obool),U_13412)))
    | ~ c_Wellfounded_OwfP(U_13410,U_13412) ),
    inference(clausify,[status(thm)],[f_3456_3]) ).

cnf(f_3456_5,plain,
    ( c_Wellfounded_OwfP(U_13411,U_13413)
    | ~ c_Wellfounded_Owf(U_13411,hAPP(c_Set_OCollect(tc_prod(U_13411,U_13411)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13411,U_13411,tc_HOL_Obool),U_13413))) ),
    inference(clausify,[status(thm)],[f_3456_3]) ).

fof(f_3457_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_3457_2,plain,
    ! [U_13414] : c_Wellfounded_OwfP(U_13414,hAPP(c_COMBK(tc_fun(U_13414,tc_HOL_Obool),U_13414),hAPP(c_COMBK(tc_HOL_Obool,U_13414),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

cnf(f_3457_3,plain,
    c_Wellfounded_OwfP(U_13414,hAPP(c_COMBK(tc_fun(U_13414,tc_HOL_Obool),U_13414),hAPP(c_COMBK(tc_HOL_Obool,U_13414),c_fFalse))),
    inference(clausify,[status(thm)],[f_3457_2]) ).

fof(f_3458_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_3458_2,plain,
    ! [U_13417,U_13416,U_13415] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13415,U_13416),U_13417))
      | ~ c_Wellfounded_OwfP(U_13415,U_13416) ),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

cnf(f_3458_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13415,U_13416),U_13417))
    | ~ c_Wellfounded_OwfP(U_13415,U_13416) ),
    inference(clausify,[status(thm)],[f_3458_2]) ).

fof(f_3459_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_3459_2,plain,
    ! [U_13421,U_13420] :
      ( ( c_Wellfounded_OwfP(U_13420,U_13421)
        | ? [U_13419] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13420,U_13421),U_13419)) )
      & ( ! [U_13418] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13420,U_13421),U_13418))
        | ~ c_Wellfounded_OwfP(U_13420,U_13421) ) ),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

fof(f_3459_3,plain,
    ( ! [U_13425,U_13423] :
        ( c_Wellfounded_OwfP(U_13423,U_13425)
        | ? [U_13419] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13423,U_13425),U_13419)) )
    & ! [U_13424,U_13422] :
        ( ! [U_13418] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13422,U_13424),U_13418))
        | ~ c_Wellfounded_OwfP(U_13422,U_13424) ) ),
    inference(miniscope,[status(thm)],[f_3459_2]) ).

fof(f_3459_4,plain,
    ( ! [U_13425,U_13423] :
        ( c_Wellfounded_OwfP(U_13423,U_13425)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13423,U_13425),sK320(U_13425,U_13423))) )
    & ! [U_13424,U_13422] :
        ( ! [U_13418] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13422,U_13424),U_13418))
        | ~ c_Wellfounded_OwfP(U_13422,U_13424) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13419,sK320(U_13425,U_13423))],[f_3459_3]) ).

cnf(f_3459_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13422,U_13424),U_13418))
    | ~ c_Wellfounded_OwfP(U_13422,U_13424) ),
    inference(clausify,[status(thm)],[f_3459_4]) ).

cnf(f_3459_6,plain,
    ( c_Wellfounded_OwfP(U_13423,U_13425)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13423,U_13425),sK320(U_13425,U_13423))) ),
    inference(clausify,[status(thm)],[f_3459_4]) ).

fof(f_3460_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_3460_2,plain,
    ! [U_13428,U_13427,U_13426] :
      ( c_Wellfounded_OwfP(U_13426,U_13428)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13426,tc_fun(U_13426,tc_HOL_Obool))),U_13428),U_13427))
      | ~ c_Wellfounded_OwfP(U_13426,U_13427) ),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

cnf(f_3460_3,plain,
    ( c_Wellfounded_OwfP(U_13426,U_13428)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13426,tc_fun(U_13426,tc_HOL_Obool))),U_13428),U_13427))
    | ~ c_Wellfounded_OwfP(U_13426,U_13427) ),
    inference(clausify,[status(thm)],[f_3460_2]) ).

fof(f_3461_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_3461_2,plain,
    ! [U_13430,U_13429] :
      ( c_Wellfounded_OwfP(U_13429,c_FunDef_Oin__rel(U_13429,U_13429,U_13430))
      | ~ c_Wellfounded_Owf(U_13429,U_13430) ),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

cnf(f_3461_3,plain,
    ( c_Wellfounded_OwfP(U_13429,c_FunDef_Oin__rel(U_13429,U_13429,U_13430))
    | ~ c_Wellfounded_Owf(U_13429,U_13430) ),
    inference(clausify,[status(thm)],[f_3461_2]) ).

fof(f_3462_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_3462_2,plain,
    ! [U_13432,U_13431] :
      ( ( c_Wellfounded_OwfP(U_13431,hAPP(hAPP(c_COMBC(U_13431,tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_fun(U_13431,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13431,tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_fun(U_13431,tc_HOL_Obool)),U_13431),c_COMBC(U_13431,tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13431,tc_prod(U_13431,U_13431)),tc_fun(U_13431,tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),U_13431),hAPP(c_COMBB(tc_prod(U_13431,U_13431),tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool),U_13431),c_member(tc_prod(U_13431,U_13431)))),c_Product__Type_OPair(U_13431,U_13431)))),U_13432))
        | ~ c_Wellfounded_Owf(U_13431,U_13432) )
      & ( c_Wellfounded_Owf(U_13431,U_13432)
        | ~ c_Wellfounded_OwfP(U_13431,hAPP(hAPP(c_COMBC(U_13431,tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_fun(U_13431,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13431,tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_fun(U_13431,tc_HOL_Obool)),U_13431),c_COMBC(U_13431,tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13431,tc_prod(U_13431,U_13431)),tc_fun(U_13431,tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool)),U_13431),hAPP(c_COMBB(tc_prod(U_13431,U_13431),tc_fun(tc_fun(tc_prod(U_13431,U_13431),tc_HOL_Obool),tc_HOL_Obool),U_13431),c_member(tc_prod(U_13431,U_13431)))),c_Product__Type_OPair(U_13431,U_13431)))),U_13432)) ) ),
    inference(variable_rename,[status(thm)],[f_3462_1]) ).

fof(f_3462_3,plain,
    ( ! [U_13436,U_13434] :
        ( c_Wellfounded_OwfP(U_13434,hAPP(hAPP(c_COMBC(U_13434,tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_fun(U_13434,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13434,tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_fun(U_13434,tc_HOL_Obool)),U_13434),c_COMBC(U_13434,tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13434,tc_prod(U_13434,U_13434)),tc_fun(U_13434,tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),U_13434),hAPP(c_COMBB(tc_prod(U_13434,U_13434),tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool),U_13434),c_member(tc_prod(U_13434,U_13434)))),c_Product__Type_OPair(U_13434,U_13434)))),U_13436))
        | ~ c_Wellfounded_Owf(U_13434,U_13436) )
    & ! [U_13435,U_13433] :
        ( c_Wellfounded_Owf(U_13433,U_13435)
        | ~ c_Wellfounded_OwfP(U_13433,hAPP(hAPP(c_COMBC(U_13433,tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13433,tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_fun(U_13433,tc_HOL_Obool)),U_13433),c_COMBC(U_13433,tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13433,tc_prod(U_13433,U_13433)),tc_fun(U_13433,tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),U_13433),hAPP(c_COMBB(tc_prod(U_13433,U_13433),tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool),U_13433),c_member(tc_prod(U_13433,U_13433)))),c_Product__Type_OPair(U_13433,U_13433)))),U_13435)) ) ),
    inference(miniscope,[status(thm)],[f_3462_2]) ).

cnf(f_3462_4,plain,
    ( c_Wellfounded_Owf(U_13433,U_13435)
    | ~ c_Wellfounded_OwfP(U_13433,hAPP(hAPP(c_COMBC(U_13433,tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13433,tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_fun(U_13433,tc_HOL_Obool)),U_13433),c_COMBC(U_13433,tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13433,tc_prod(U_13433,U_13433)),tc_fun(U_13433,tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool)),U_13433),hAPP(c_COMBB(tc_prod(U_13433,U_13433),tc_fun(tc_fun(tc_prod(U_13433,U_13433),tc_HOL_Obool),tc_HOL_Obool),U_13433),c_member(tc_prod(U_13433,U_13433)))),c_Product__Type_OPair(U_13433,U_13433)))),U_13435)) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

cnf(f_3462_5,plain,
    ( c_Wellfounded_OwfP(U_13434,hAPP(hAPP(c_COMBC(U_13434,tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_fun(U_13434,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13434,tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_fun(U_13434,tc_HOL_Obool)),U_13434),c_COMBC(U_13434,tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13434,tc_prod(U_13434,U_13434)),tc_fun(U_13434,tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool)),U_13434),hAPP(c_COMBB(tc_prod(U_13434,U_13434),tc_fun(tc_fun(tc_prod(U_13434,U_13434),tc_HOL_Obool),tc_HOL_Obool),U_13434),c_member(tc_prod(U_13434,U_13434)))),c_Product__Type_OPair(U_13434,U_13434)))),U_13436))
    | ~ c_Wellfounded_Owf(U_13434,U_13436) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

fof(f_3463_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_3463_2,plain,
    ! [U_13438,U_13437] :
      ( c_Wellfounded_Oacyclic(U_13437,hAPP(c_Set_OCollect(tc_prod(U_13437,U_13437)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13437,U_13437,tc_HOL_Obool),U_13438)))
      | ~ c_Wellfounded_OwfP(U_13437,U_13438) ),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

cnf(f_3463_3,plain,
    ( c_Wellfounded_Oacyclic(U_13437,hAPP(c_Set_OCollect(tc_prod(U_13437,U_13437)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13437,U_13437,tc_HOL_Obool),U_13438)))
    | ~ c_Wellfounded_OwfP(U_13437,U_13438) ),
    inference(clausify,[status(thm)],[f_3463_2]) ).

fof(f_3464_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_3464_2,plain,
    ! [U_13443,U_13442,U_13441,U_13440] :
      ( ? [U_13439] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),hAPP(c_Set_OCollect(U_13440),hAPP(hAPP(c_COMBS(U_13440,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13440),c_fconj),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13440)),U_13441))),hAPP(hAPP(c_COMBC(U_13440,U_13442,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13442,tc_fun(U_13442,tc_HOL_Obool),U_13440),c_fequal),U_13443)),hAPP(U_13443,U_13439))))))
          & hBOOL(hAPP(hAPP(c_member(U_13440),U_13439),U_13441)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13442),hAPP(c_Set_Oimage(U_13440,U_13442,U_13443),U_13441)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),U_13441)) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

fof(f_3464_3,plain,
    ! [U_13443,U_13442,U_13441,U_13440] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),hAPP(c_Set_OCollect(U_13440),hAPP(hAPP(c_COMBS(U_13440,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13440),c_fconj),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13440)),U_13441))),hAPP(hAPP(c_COMBC(U_13440,U_13442,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13442,tc_fun(U_13442,tc_HOL_Obool),U_13440),c_fequal),U_13443)),hAPP(U_13443,sK321(U_13443,U_13442,U_13441,U_13440)))))))
        & hBOOL(hAPP(hAPP(c_member(U_13440),sK321(U_13443,U_13442,U_13441,U_13440)),U_13441)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13442),hAPP(c_Set_Oimage(U_13440,U_13442,U_13443),U_13441)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),U_13441)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_13439,sK321(U_13443,U_13442,U_13441,U_13440))],[f_3464_2]) ).

cnf(f_3464_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13440),sK321(U_13443,U_13442,U_13441,U_13440)),U_13441))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13442),hAPP(c_Set_Oimage(U_13440,U_13442,U_13443),U_13441)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),U_13441)) ),
    inference(clausify,[status(thm)],[f_3464_3]) ).

cnf(f_3464_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),hAPP(c_Set_OCollect(U_13440),hAPP(hAPP(c_COMBS(U_13440,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13440),c_fconj),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13440,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13440)),U_13441))),hAPP(hAPP(c_COMBC(U_13440,U_13442,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13442,tc_fun(U_13442,tc_HOL_Obool),U_13440),c_fequal),U_13443)),hAPP(U_13443,sK321(U_13443,U_13442,U_13441,U_13440)))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13442),hAPP(c_Set_Oimage(U_13440,U_13442,U_13443),U_13441)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13440),U_13441)) ),
    inference(clausify,[status(thm)],[f_3464_3]) ).

fof(f_3465_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_3465_2,plain,
    ! [U_13450,U_13449,U_13448] :
      ( ( c_Relation_Orefl__on(U_13448,U_13449,U_13450)
        | ? [U_13447] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13448,U_13448)),hAPP(hAPP(c_Product__Type_OPair(U_13448,U_13448),U_13447),U_13447)),U_13450))
            & hBOOL(hAPP(hAPP(c_member(U_13448),U_13447),U_13449)) )
        | ? [U_13446] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13448,U_13448,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_fun(U_13448,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13448,tc_HOL_Obool),tc_fun(U_13448,tc_HOL_Obool)),U_13448),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13448)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13448),c_fconj),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13448)),U_13449)))),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13448)),U_13449))),U_13446))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13448,U_13448)),U_13446),U_13450)) ) )
      & ( ( ! [U_13445] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13448,U_13448)),hAPP(hAPP(c_Product__Type_OPair(U_13448,U_13448),U_13445),U_13445)),U_13450))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13448),U_13445),U_13449)) )
          & ! [U_13444] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13448,U_13448,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_fun(U_13448,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13448,tc_HOL_Obool),tc_fun(U_13448,tc_HOL_Obool)),U_13448),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13448)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13448),c_fconj),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13448)),U_13449)))),hAPP(hAPP(c_COMBC(U_13448,tc_fun(U_13448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13448)),U_13449))),U_13444))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13448,U_13448)),U_13444),U_13450)) ) )
        | ~ c_Relation_Orefl__on(U_13448,U_13449,U_13450) ) ),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

fof(f_3465_3,plain,
    ( ! [U_13456,U_13454,U_13452] :
        ( c_Relation_Orefl__on(U_13452,U_13454,U_13456)
        | ? [U_13447] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),hAPP(hAPP(c_Product__Type_OPair(U_13452,U_13452),U_13447),U_13447)),U_13456))
            & hBOOL(hAPP(hAPP(c_member(U_13452),U_13447),U_13454)) )
        | ? [U_13446] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13452,U_13452,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),U_13452),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13452)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13452),c_fconj),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454)))),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454))),U_13446))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),U_13446),U_13456)) ) )
    & ! [U_13455,U_13453,U_13451] :
        ( ( ! [U_13445] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),hAPP(hAPP(c_Product__Type_OPair(U_13451,U_13451),U_13445),U_13445)),U_13455))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13451),U_13445),U_13453)) )
          & ! [U_13444] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13451,U_13451,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13451),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13451)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13451),c_fconj),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453)))),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453))),U_13444))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),U_13444),U_13455)) ) )
        | ~ c_Relation_Orefl__on(U_13451,U_13453,U_13455) ) ),
    inference(miniscope,[status(thm)],[f_3465_2]) ).

fof(f_3465_4,plain,
    ( ! [U_13456,U_13454,U_13452] :
        ( c_Relation_Orefl__on(U_13452,U_13454,U_13456)
        | ? [U_13447] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),hAPP(hAPP(c_Product__Type_OPair(U_13452,U_13452),U_13447),U_13447)),U_13456))
            & hBOOL(hAPP(hAPP(c_member(U_13452),U_13447),U_13454)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13452,U_13452,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),U_13452),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13452)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13452),c_fconj),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454)))),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454))),sK322(U_13456,U_13454,U_13452)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),sK322(U_13456,U_13454,U_13452)),U_13456)) ) )
    & ! [U_13455,U_13453,U_13451] :
        ( ( ! [U_13445] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),hAPP(hAPP(c_Product__Type_OPair(U_13451,U_13451),U_13445),U_13445)),U_13455))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13451),U_13445),U_13453)) )
          & ! [U_13444] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13451,U_13451,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13451),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13451)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13451),c_fconj),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453)))),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453))),U_13444))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),U_13444),U_13455)) ) )
        | ~ c_Relation_Orefl__on(U_13451,U_13453,U_13455) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_13446,sK322(U_13456,U_13454,U_13452))],[f_3465_3]) ).

fof(f_3465_5,plain,
    ( ! [U_13456,U_13454,U_13452] :
        ( c_Relation_Orefl__on(U_13452,U_13454,U_13456)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),hAPP(hAPP(c_Product__Type_OPair(U_13452,U_13452),sK323(U_13456,U_13454,U_13452)),sK323(U_13456,U_13454,U_13452))),U_13456))
          & hBOOL(hAPP(hAPP(c_member(U_13452),sK323(U_13456,U_13454,U_13452)),U_13454)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13452,U_13452,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),U_13452),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13452)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13452),c_fconj),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454)))),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454))),sK322(U_13456,U_13454,U_13452)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),sK322(U_13456,U_13454,U_13452)),U_13456)) ) )
    & ! [U_13455,U_13453,U_13451] :
        ( ( ! [U_13445] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),hAPP(hAPP(c_Product__Type_OPair(U_13451,U_13451),U_13445),U_13445)),U_13455))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13451),U_13445),U_13453)) )
          & ! [U_13444] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13451,U_13451,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13451),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13451)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13451),c_fconj),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453)))),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453))),U_13444))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),U_13444),U_13455)) ) )
        | ~ c_Relation_Orefl__on(U_13451,U_13453,U_13455) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_13447,sK323(U_13456,U_13454,U_13452))],[f_3465_4]) ).

cnf(f_3465_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13451,U_13451,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13451,tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13451),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13451)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13451),c_fconj),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453)))),hAPP(hAPP(c_COMBC(U_13451,tc_fun(U_13451,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13451)),U_13453))),U_13444))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),U_13444),U_13455))
    | ~ c_Relation_Orefl__on(U_13451,U_13453,U_13455) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

cnf(f_3465_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13451,U_13451)),hAPP(hAPP(c_Product__Type_OPair(U_13451,U_13451),U_13445),U_13445)),U_13455))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13451),U_13445),U_13453))
    | ~ c_Relation_Orefl__on(U_13451,U_13453,U_13455) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

cnf(f_3465_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13452),sK323(U_13456,U_13454,U_13452)),U_13454))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),sK322(U_13456,U_13454,U_13452)),U_13456))
    | c_Relation_Orefl__on(U_13452,U_13454,U_13456) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

cnf(f_3465_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),hAPP(hAPP(c_Product__Type_OPair(U_13452,U_13452),sK323(U_13456,U_13454,U_13452)),sK323(U_13456,U_13454,U_13452))),U_13456))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),sK322(U_13456,U_13454,U_13452)),U_13456))
    | c_Relation_Orefl__on(U_13452,U_13454,U_13456) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

cnf(f_3465_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13452),sK323(U_13456,U_13454,U_13452)),U_13454))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13452,U_13452,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),U_13452),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13452)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13452),c_fconj),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454)))),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454))),sK322(U_13456,U_13454,U_13452)))
    | c_Relation_Orefl__on(U_13452,U_13454,U_13456) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

cnf(f_3465_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13452,U_13452)),hAPP(hAPP(c_Product__Type_OPair(U_13452,U_13452),sK323(U_13456,U_13454,U_13452)),sK323(U_13456,U_13454,U_13452))),U_13456))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13452,U_13452,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13452,tc_HOL_Obool),tc_fun(U_13452,tc_HOL_Obool)),U_13452),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13452)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13452),c_fconj),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454)))),hAPP(hAPP(c_COMBC(U_13452,tc_fun(U_13452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13452)),U_13454))),sK322(U_13456,U_13454,U_13452)))
    | c_Relation_Orefl__on(U_13452,U_13454,U_13456) ),
    inference(clausify,[status(thm)],[f_3465_5]) ).

fof(f_3466_1,plain,
    ! [V_Pa_2,T_b,B_x] :
      ( hBOOL(hAPP(V_Pa_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_3466_2,plain,
    ! [U_13459,U_13458,U_13457] :
      ( hBOOL(hAPP(U_13459,U_13457))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13457),c_Orderings_Obot__class_Obot(tc_fun(U_13458,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

cnf(f_3466_3,plain,
    ( hBOOL(hAPP(U_13459,U_13457))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13457),c_Orderings_Obot__class_Obot(tc_fun(U_13458,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3466_2]) ).

fof(f_3467_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_3467_2,plain,
    ! [U_13461,U_13460] :
      ( c_Wellfounded_Oacyclic(U_13460,U_13461)
      | ~ c_Wellfounded_Owf(U_13460,U_13461) ),
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

cnf(f_3467_3,plain,
    ( c_Wellfounded_Oacyclic(U_13460,U_13461)
    | ~ c_Wellfounded_Owf(U_13460,U_13461) ),
    inference(clausify,[status(thm)],[f_3467_2]) ).

fof(f_3468_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_3468_2,plain,
    ! [U_13464,U_13463,U_13462] :
      ( c_Wellfounded_Oacyclic(U_13462,U_13464)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)),U_13464),U_13463))
      | ~ c_Wellfounded_Oacyclic(U_13462,U_13463) ),
    inference(variable_rename,[status(thm)],[f_3468_1]) ).

cnf(f_3468_3,plain,
    ( c_Wellfounded_Oacyclic(U_13462,U_13464)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)),U_13464),U_13463))
    | ~ c_Wellfounded_Oacyclic(U_13462,U_13463) ),
    inference(clausify,[status(thm)],[f_3468_2]) ).

fof(f_3469_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_3469_2,plain,
    ! [U_13469,U_13468,U_13467] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_13467,U_13468),U_13469))
        | ? [U_13466] :
            ( ~ hBOOL(hAPP(U_13468,U_13466))
            & hBOOL(hAPP(hAPP(c_member(U_13467),U_13466),U_13469)) ) )
      & ( ! [U_13465] :
            ( hBOOL(hAPP(U_13468,U_13465))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13467),U_13465),U_13469)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13467,U_13468),U_13469)) ) ),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

fof(f_3469_3,plain,
    ( ! [U_13475,U_13473,U_13471] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_13471,U_13473),U_13475))
        | ? [U_13466] :
            ( ~ hBOOL(hAPP(U_13473,U_13466))
            & hBOOL(hAPP(hAPP(c_member(U_13471),U_13466),U_13475)) ) )
    & ! [U_13474,U_13472,U_13470] :
        ( ! [U_13465] :
            ( hBOOL(hAPP(U_13472,U_13465))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13465),U_13474)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13470,U_13472),U_13474)) ) ),
    inference(miniscope,[status(thm)],[f_3469_2]) ).

fof(f_3469_4,plain,
    ( ! [U_13475,U_13473,U_13471] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_13471,U_13473),U_13475))
        | ( ~ hBOOL(hAPP(U_13473,sK324(U_13475,U_13473,U_13471)))
          & hBOOL(hAPP(hAPP(c_member(U_13471),sK324(U_13475,U_13473,U_13471)),U_13475)) ) )
    & ! [U_13474,U_13472,U_13470] :
        ( ! [U_13465] :
            ( hBOOL(hAPP(U_13472,U_13465))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13465),U_13474)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13470,U_13472),U_13474)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_13466,sK324(U_13475,U_13473,U_13471))],[f_3469_3]) ).

cnf(f_3469_5,plain,
    ( hBOOL(hAPP(U_13472,U_13465))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13470),U_13465),U_13474))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13470,U_13472),U_13474)) ),
    inference(clausify,[status(thm)],[f_3469_4]) ).

cnf(f_3469_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13471),sK324(U_13475,U_13473,U_13471)),U_13475))
    | hBOOL(hAPP(c_Predicate_OPowp(U_13471,U_13473),U_13475)) ),
    inference(clausify,[status(thm)],[f_3469_4]) ).

cnf(f_3469_7,plain,
    ( ~ hBOOL(hAPP(U_13473,sK324(U_13475,U_13473,U_13471)))
    | hBOOL(hAPP(c_Predicate_OPowp(U_13471,U_13473),U_13475)) ),
    inference(clausify,[status(thm)],[f_3469_4]) ).

fof(f_3470_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_3470_2,plain,
    ! [U_13476] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13476,tc_HOL_Obool) = c_Set_OBall(U_13476),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

cnf(f_3470_3,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13476,tc_HOL_Obool) = c_Set_OBall(U_13476),
    inference(clausify,[status(thm)],[f_3470_2]) ).

fof(f_3471_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).

fof(f_3471_2,plain,
    ! [U_13480,U_13479,U_13478,U_13477] : hAPP(c_Set_OCollect(U_13477),hAPP(hAPP(c_COMBB(tc_fun(U_13478,tc_HOL_Obool),tc_HOL_Obool,U_13477),c_HOL_OAll(U_13478)),hAPP(hAPP(c_COMBB(tc_fun(U_13478,tc_HOL_Obool),tc_fun(U_13478,tc_HOL_Obool),U_13477),hAPP(c_COMBS(U_13478,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13478),c_fimplies),hAPP(hAPP(c_COMBC(U_13478,tc_fun(U_13478,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13478)),U_13479)))),U_13480))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13478,tc_fun(U_13477,tc_HOL_Obool)),U_13479),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool),U_13478),c_Set_OCollect(U_13477)),hAPP(c_COMBC(U_13477,U_13478,tc_HOL_Obool),U_13480))),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

cnf(f_3471_3,plain,
    hAPP(c_Set_OCollect(U_13477),hAPP(hAPP(c_COMBB(tc_fun(U_13478,tc_HOL_Obool),tc_HOL_Obool,U_13477),c_HOL_OAll(U_13478)),hAPP(hAPP(c_COMBB(tc_fun(U_13478,tc_HOL_Obool),tc_fun(U_13478,tc_HOL_Obool),U_13477),hAPP(c_COMBS(U_13478,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13478),c_fimplies),hAPP(hAPP(c_COMBC(U_13478,tc_fun(U_13478,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13478)),U_13479)))),U_13480))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13478,tc_fun(U_13477,tc_HOL_Obool)),U_13479),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool),U_13478),c_Set_OCollect(U_13477)),hAPP(c_COMBC(U_13477,U_13478,tc_HOL_Obool),U_13480))),
    inference(clausify,[status(thm)],[f_3471_2]) ).

fof(f_3472_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_3472_2,plain,
    ! [U_13486,U_13485,U_13484,U_13483] :
      ( ( c_Equiv__Relations_Ocongruent(U_13483,U_13484,U_13485,U_13486)
        | ? [U_13482] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13483,U_13483,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13483,tc_fun(U_13483,U_13484),tc_fun(U_13483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13484,tc_HOL_Obool),tc_fun(tc_fun(U_13483,U_13484),tc_fun(U_13483,tc_HOL_Obool)),U_13483),c_COMBB(U_13484,tc_HOL_Obool,U_13483)),hAPP(hAPP(c_COMBB(U_13484,tc_fun(U_13484,tc_HOL_Obool),U_13483),c_fequal),U_13486))),U_13486)),U_13482))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13483,U_13483)),U_13482),U_13485)) ) )
      & ( ! [U_13481] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13483,U_13483,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13483,tc_fun(U_13483,U_13484),tc_fun(U_13483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13484,tc_HOL_Obool),tc_fun(tc_fun(U_13483,U_13484),tc_fun(U_13483,tc_HOL_Obool)),U_13483),c_COMBB(U_13484,tc_HOL_Obool,U_13483)),hAPP(hAPP(c_COMBB(U_13484,tc_fun(U_13484,tc_HOL_Obool),U_13483),c_fequal),U_13486))),U_13486)),U_13481))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13483,U_13483)),U_13481),U_13485)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13483,U_13484,U_13485,U_13486) ) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

fof(f_3472_3,plain,
    ( ! [U_13494,U_13492,U_13490,U_13488] :
        ( c_Equiv__Relations_Ocongruent(U_13488,U_13490,U_13492,U_13494)
        | ? [U_13482] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13488,U_13488,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13488,tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_HOL_Obool),tc_fun(tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),U_13488),c_COMBB(U_13490,tc_HOL_Obool,U_13488)),hAPP(hAPP(c_COMBB(U_13490,tc_fun(U_13490,tc_HOL_Obool),U_13488),c_fequal),U_13494))),U_13494)),U_13482))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13488,U_13488)),U_13482),U_13492)) ) )
    & ! [U_13493,U_13491,U_13489,U_13487] :
        ( ! [U_13481] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13487,U_13487,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13487,tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_HOL_Obool),tc_fun(tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),U_13487),c_COMBB(U_13489,tc_HOL_Obool,U_13487)),hAPP(hAPP(c_COMBB(U_13489,tc_fun(U_13489,tc_HOL_Obool),U_13487),c_fequal),U_13493))),U_13493)),U_13481))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13487,U_13487)),U_13481),U_13491)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13487,U_13489,U_13491,U_13493) ) ),
    inference(miniscope,[status(thm)],[f_3472_2]) ).

fof(f_3472_4,plain,
    ( ! [U_13494,U_13492,U_13490,U_13488] :
        ( c_Equiv__Relations_Ocongruent(U_13488,U_13490,U_13492,U_13494)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13488,U_13488,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13488,tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_HOL_Obool),tc_fun(tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),U_13488),c_COMBB(U_13490,tc_HOL_Obool,U_13488)),hAPP(hAPP(c_COMBB(U_13490,tc_fun(U_13490,tc_HOL_Obool),U_13488),c_fequal),U_13494))),U_13494)),sK325(U_13494,U_13492,U_13490,U_13488)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13488,U_13488)),sK325(U_13494,U_13492,U_13490,U_13488)),U_13492)) ) )
    & ! [U_13493,U_13491,U_13489,U_13487] :
        ( ! [U_13481] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13487,U_13487,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13487,tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_HOL_Obool),tc_fun(tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),U_13487),c_COMBB(U_13489,tc_HOL_Obool,U_13487)),hAPP(hAPP(c_COMBB(U_13489,tc_fun(U_13489,tc_HOL_Obool),U_13487),c_fequal),U_13493))),U_13493)),U_13481))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13487,U_13487)),U_13481),U_13491)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13487,U_13489,U_13491,U_13493) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_13482,sK325(U_13494,U_13492,U_13490,U_13488))],[f_3472_3]) ).

cnf(f_3472_5,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13487,U_13487,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13487,tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_HOL_Obool),tc_fun(tc_fun(U_13487,U_13489),tc_fun(U_13487,tc_HOL_Obool)),U_13487),c_COMBB(U_13489,tc_HOL_Obool,U_13487)),hAPP(hAPP(c_COMBB(U_13489,tc_fun(U_13489,tc_HOL_Obool),U_13487),c_fequal),U_13493))),U_13493)),U_13481))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13487,U_13487)),U_13481),U_13491))
    | ~ c_Equiv__Relations_Ocongruent(U_13487,U_13489,U_13491,U_13493) ),
    inference(clausify,[status(thm)],[f_3472_4]) ).

cnf(f_3472_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13488,U_13488)),sK325(U_13494,U_13492,U_13490,U_13488)),U_13492))
    | c_Equiv__Relations_Ocongruent(U_13488,U_13490,U_13492,U_13494) ),
    inference(clausify,[status(thm)],[f_3472_4]) ).

cnf(f_3472_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13488,U_13488,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13488,tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_HOL_Obool),tc_fun(tc_fun(U_13488,U_13490),tc_fun(U_13488,tc_HOL_Obool)),U_13488),c_COMBB(U_13490,tc_HOL_Obool,U_13488)),hAPP(hAPP(c_COMBB(U_13490,tc_fun(U_13490,tc_HOL_Obool),U_13488),c_fequal),U_13494))),U_13494)),sK325(U_13494,U_13492,U_13490,U_13488)))
    | c_Equiv__Relations_Ocongruent(U_13488,U_13490,U_13492,U_13494) ),
    inference(clausify,[status(thm)],[f_3472_4]) ).

fof(f_3473_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_3473_2,plain,
    ! [U_13498,U_13497,U_13496,U_13495] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13495,tc_fun(U_13496,tc_HOL_Obool)),U_13497),U_13498) = hAPP(c_Set_OCollect(U_13496),hAPP(hAPP(c_COMBB(tc_fun(U_13495,tc_HOL_Obool),tc_HOL_Obool,U_13496),c_HOL_OAll(U_13495)),hAPP(hAPP(c_COMBB(tc_fun(U_13495,tc_HOL_Obool),tc_fun(U_13495,tc_HOL_Obool),U_13496),hAPP(c_COMBS(U_13495,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13495),c_fimplies),hAPP(hAPP(c_COMBC(U_13495,tc_fun(U_13495,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13495)),U_13497)))),hAPP(hAPP(c_COMBC(U_13496,tc_fun(U_13495,tc_fun(U_13496,tc_HOL_Obool)),tc_fun(U_13495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13496,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13495,tc_fun(U_13496,tc_HOL_Obool)),tc_fun(U_13495,tc_HOL_Obool)),U_13496),c_COMBB(tc_fun(U_13496,tc_HOL_Obool),tc_HOL_Obool,U_13495)),c_member(U_13496))),U_13498)))),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

cnf(f_3473_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13495,tc_fun(U_13496,tc_HOL_Obool)),U_13497),U_13498) = hAPP(c_Set_OCollect(U_13496),hAPP(hAPP(c_COMBB(tc_fun(U_13495,tc_HOL_Obool),tc_HOL_Obool,U_13496),c_HOL_OAll(U_13495)),hAPP(hAPP(c_COMBB(tc_fun(U_13495,tc_HOL_Obool),tc_fun(U_13495,tc_HOL_Obool),U_13496),hAPP(c_COMBS(U_13495,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13495),c_fimplies),hAPP(hAPP(c_COMBC(U_13495,tc_fun(U_13495,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13495)),U_13497)))),hAPP(hAPP(c_COMBC(U_13496,tc_fun(U_13495,tc_fun(U_13496,tc_HOL_Obool)),tc_fun(U_13495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13496,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13495,tc_fun(U_13496,tc_HOL_Obool)),tc_fun(U_13495,tc_HOL_Obool)),U_13496),c_COMBB(tc_fun(U_13496,tc_HOL_Obool),tc_HOL_Obool,U_13495)),c_member(U_13496))),U_13498)))),
    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)
          | ~ 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_3474_2,plain,
    ! [U_13500,U_13499] :
      ( ( ( c_Wellfounded_Owf(U_13499,U_13500)
          | ~ c_Wellfounded_Oacyclic(U_13499,U_13500) )
        & ( c_Wellfounded_Oacyclic(U_13499,U_13500)
          | ~ c_Wellfounded_Owf(U_13499,U_13500) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13499,U_13499)),U_13500)) ),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

cnf(f_3474_3,plain,
    ( c_Wellfounded_Oacyclic(U_13499,U_13500)
    | ~ c_Wellfounded_Owf(U_13499,U_13500)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13499,U_13499)),U_13500)) ),
    inference(clausify,[status(thm)],[f_3474_2]) ).

cnf(f_3474_4,plain,
    ( c_Wellfounded_Owf(U_13499,U_13500)
    | ~ c_Wellfounded_Oacyclic(U_13499,U_13500)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13499,U_13499)),U_13500)) ),
    inference(clausify,[status(thm)],[f_3474_2]) ).

fof(f_3475_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_3475_2,plain,
    ! [U_13502,U_13501] :
      ( c_Wellfounded_Owf(U_13501,U_13502)
      | ~ c_Wellfounded_Oacyclic(U_13501,U_13502)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13501,U_13501)),U_13502)) ),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

cnf(f_3475_3,plain,
    ( c_Wellfounded_Owf(U_13501,U_13502)
    | ~ c_Wellfounded_Oacyclic(U_13501,U_13502)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13501,U_13501)),U_13502)) ),
    inference(clausify,[status(thm)],[f_3475_2]) ).

fof(f_3476_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_3476_2,plain,
    ! [U_13504,U_13503] :
      ( c_Complete__Lattice_OSup__class_OSup(U_13503,U_13504) = c_Complete__Lattice_OInf__class_OInf(U_13503,hAPP(c_Set_OCollect(U_13503),hAPP(hAPP(c_COMBB(tc_fun(U_13503,tc_HOL_Obool),tc_HOL_Obool,U_13503),c_HOL_OAll(U_13503)),hAPP(hAPP(c_COMBB(tc_fun(U_13503,tc_HOL_Obool),tc_fun(U_13503,tc_HOL_Obool),U_13503),hAPP(c_COMBS(U_13503,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13503),c_fimplies),hAPP(hAPP(c_COMBC(U_13503,tc_fun(U_13503,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13503)),U_13504)))),hAPP(c_COMBC(U_13503,U_13503,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13503))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13503) ),
    inference(variable_rename,[status(thm)],[f_3476_1]) ).

cnf(f_3476_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_13503,U_13504) = c_Complete__Lattice_OInf__class_OInf(U_13503,hAPP(c_Set_OCollect(U_13503),hAPP(hAPP(c_COMBB(tc_fun(U_13503,tc_HOL_Obool),tc_HOL_Obool,U_13503),c_HOL_OAll(U_13503)),hAPP(hAPP(c_COMBB(tc_fun(U_13503,tc_HOL_Obool),tc_fun(U_13503,tc_HOL_Obool),U_13503),hAPP(c_COMBS(U_13503,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13503),c_fimplies),hAPP(hAPP(c_COMBC(U_13503,tc_fun(U_13503,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13503)),U_13504)))),hAPP(c_COMBC(U_13503,U_13503,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13503))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13503) ),
    inference(clausify,[status(thm)],[f_3476_2]) ).

fof(f_3477_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_3477_2,plain,
    ! [U_13506,U_13505] :
      ( c_Complete__Lattice_OInf__class_OInf(U_13505,U_13506) = c_Complete__Lattice_OSup__class_OSup(U_13505,hAPP(c_Set_OCollect(U_13505),hAPP(hAPP(c_COMBB(tc_fun(U_13505,tc_HOL_Obool),tc_HOL_Obool,U_13505),c_HOL_OAll(U_13505)),hAPP(hAPP(c_COMBB(tc_fun(U_13505,tc_HOL_Obool),tc_fun(U_13505,tc_HOL_Obool),U_13505),hAPP(c_COMBS(U_13505,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13505),c_fimplies),hAPP(hAPP(c_COMBC(U_13505,tc_fun(U_13505,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13505)),U_13506)))),c_Orderings_Oord__class_Oless__eq(U_13505)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13505) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

cnf(f_3477_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_13505,U_13506) = c_Complete__Lattice_OSup__class_OSup(U_13505,hAPP(c_Set_OCollect(U_13505),hAPP(hAPP(c_COMBB(tc_fun(U_13505,tc_HOL_Obool),tc_HOL_Obool,U_13505),c_HOL_OAll(U_13505)),hAPP(hAPP(c_COMBB(tc_fun(U_13505,tc_HOL_Obool),tc_fun(U_13505,tc_HOL_Obool),U_13505),hAPP(c_COMBS(U_13505,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13505),c_fimplies),hAPP(hAPP(c_COMBC(U_13505,tc_fun(U_13505,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13505)),U_13506)))),c_Orderings_Oord__class_Oless__eq(U_13505)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13505) ),
    inference(clausify,[status(thm)],[f_3477_2]) ).

fof(f_3478_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_3478_2,plain,
    ! [U_13508,U_13507] :
      ( ( c_Nitpick_Owf_H(U_13507,U_13508)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13507,U_13507)),U_13508)) )
        | ~ c_Wellfounded_Oacyclic(U_13507,U_13508) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13507,U_13507)),U_13508)) )
          & c_Wellfounded_Oacyclic(U_13507,U_13508) )
        | ~ c_Nitpick_Owf_H(U_13507,U_13508) ) ),
    inference(variable_rename,[status(thm)],[f_3478_1]) ).

fof(f_3478_3,plain,
    ( ! [U_13512,U_13510] :
        ( c_Nitpick_Owf_H(U_13510,U_13512)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13510,U_13510)),U_13512)) )
        | ~ c_Wellfounded_Oacyclic(U_13510,U_13512) )
    & ! [U_13511,U_13509] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13509,U_13509)),U_13511)) )
          & c_Wellfounded_Oacyclic(U_13509,U_13511) )
        | ~ c_Nitpick_Owf_H(U_13509,U_13511) ) ),
    inference(miniscope,[status(thm)],[f_3478_2]) ).

cnf(f_3478_4,plain,
    ( c_Wellfounded_Oacyclic(U_13509,U_13511)
    | ~ c_Nitpick_Owf_H(U_13509,U_13511) ),
    inference(clausify,[status(thm)],[f_3478_3]) ).

cnf(f_3478_5,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13509,U_13509)),U_13511))
    | ~ c_Nitpick_Owf_H(U_13509,U_13511) ),
    inference(clausify,[status(thm)],[f_3478_3]) ).

cnf(f_3478_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13510,U_13510)),U_13512))
    | ~ c_Wellfounded_Oacyclic(U_13510,U_13512)
    | c_Nitpick_Owf_H(U_13510,U_13512) ),
    inference(clausify,[status(thm)],[f_3478_3]) ).

cnf(f_3478_7,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ c_Wellfounded_Oacyclic(U_13510,U_13512)
    | c_Nitpick_Owf_H(U_13510,U_13512) ),
    inference(clausify,[status(thm)],[f_3478_3]) ).

fof(f_3479_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_3479_2,plain,
    ! [U_13514] :
    ? [U_13513] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13513),c_Int_OInteg))
      & U_13514 = hAPP(c_Int_OAbs__Integ,U_13513) ),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

fof(f_3479_3,plain,
    ! [U_13514] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK326(U_13514)),c_Int_OInteg))
      & U_13514 = hAPP(c_Int_OAbs__Integ,sK326(U_13514)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_13513,sK326(U_13514))],[f_3479_2]) ).

cnf(f_3479_4,plain,
    U_13514 = hAPP(c_Int_OAbs__Integ,sK326(U_13514)),
    inference(clausify,[status(thm)],[f_3479_3]) ).

cnf(f_3479_5,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK326(U_13514)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3479_3]) ).

fof(f_3480_1,plain,
    ! [V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_Pa_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_3480_2,plain,
    ! [U_13517,U_13516] :
      ( hBOOL(hAPP(U_13516,U_13517))
      | ? [U_13515] :
          ( ~ hBOOL(hAPP(U_13516,hAPP(c_Int_OAbs__Integ,U_13515)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13515),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

fof(f_3480_3,plain,
    ! [U_13517,U_13516] :
      ( hBOOL(hAPP(U_13516,U_13517))
      | ( ~ hBOOL(hAPP(U_13516,hAPP(c_Int_OAbs__Integ,sK327(U_13517,U_13516))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK327(U_13517,U_13516)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_13515,sK327(U_13517,U_13516))],[f_3480_2]) ).

cnf(f_3480_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK327(U_13517,U_13516)),c_Int_OInteg))
    | hBOOL(hAPP(U_13516,U_13517)) ),
    inference(clausify,[status(thm)],[f_3480_3]) ).

cnf(f_3480_5,plain,
    ( ~ hBOOL(hAPP(U_13516,hAPP(c_Int_OAbs__Integ,sK327(U_13517,U_13516))))
    | hBOOL(hAPP(U_13516,U_13517)) ),
    inference(clausify,[status(thm)],[f_3480_3]) ).

fof(f_3481_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_3481_2,plain,
    ! [U_13519,U_13518] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13518,tc_HOL_Obool),U_13519) = hAPP(c_Set_OCollect(U_13518),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13518),c_HOL_OAll(tc_fun(U_13518,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),U_13518),hAPP(c_COMBS(tc_fun(U_13518,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_13518,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13518,tc_HOL_Obool),tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13518,tc_HOL_Obool))),U_13519)))),c_member(U_13518)))),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

cnf(f_3481_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13518,tc_HOL_Obool),U_13519) = hAPP(c_Set_OCollect(U_13518),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13518),c_HOL_OAll(tc_fun(U_13518,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),U_13518),hAPP(c_COMBS(tc_fun(U_13518,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_13518,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13518,tc_HOL_Obool),tc_fun(tc_fun(U_13518,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13518,tc_HOL_Obool))),U_13519)))),c_member(U_13518)))),
    inference(clausify,[status(thm)],[f_3481_2]) ).

fof(f_3482_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_3482_2,plain,
    ! [U_13524,U_13523,U_13522,U_13521] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13521,tc_fun(U_13523,tc_HOL_Obool)),U_13522),U_13524)))
      | ? [U_13520] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(U_13524,U_13520)))
          & hBOOL(hAPP(hAPP(c_member(U_13521),U_13520),U_13522)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),U_13522)) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

fof(f_3482_3,plain,
    ! [U_13524,U_13523,U_13522,U_13521] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13521,tc_fun(U_13523,tc_HOL_Obool)),U_13522),U_13524)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(U_13524,sK328(U_13524,U_13523,U_13522,U_13521))))
        & hBOOL(hAPP(hAPP(c_member(U_13521),sK328(U_13524,U_13523,U_13522,U_13521)),U_13522)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),U_13522)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_13520,sK328(U_13524,U_13523,U_13522,U_13521))],[f_3482_2]) ).

cnf(f_3482_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13521),sK328(U_13524,U_13523,U_13522,U_13521)),U_13522))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13521,tc_fun(U_13523,tc_HOL_Obool)),U_13522),U_13524)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),U_13522)) ),
    inference(clausify,[status(thm)],[f_3482_3]) ).

cnf(f_3482_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(U_13524,sK328(U_13524,U_13523,U_13522,U_13521))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13521,tc_fun(U_13523,tc_HOL_Obool)),U_13522),U_13524)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),U_13522)) ),
    inference(clausify,[status(thm)],[f_3482_3]) ).

fof(f_3483_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_3483_2,plain,
    ! [U_13527,U_13526] :
      ( 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_13527),U_13526)
      | ? [U_13525] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13527),U_13525))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13525),U_13526)) ) ),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

fof(f_3483_3,plain,
    ! [U_13527,U_13526] :
      ( 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_13527),U_13526)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13527),sK329(U_13527,U_13526)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK329(U_13527,U_13526)),U_13526)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_13525,sK329(U_13527,U_13526))],[f_3483_2]) ).

cnf(f_3483_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK329(U_13527,U_13526)),U_13526))
    | 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_13527),U_13526) ),
    inference(clausify,[status(thm)],[f_3483_3]) ).

cnf(f_3483_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13527),sK329(U_13527,U_13526)))
    | 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_13527),U_13526) ),
    inference(clausify,[status(thm)],[f_3483_3]) ).

fof(f_3484_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_3484_2,plain,
    ! [U_13533,U_13532,U_13531] :
      ( c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
      | ? [U_13530,U_13529] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13531,tc_HOL_Obool)),c_Predicate_ODomainP(U_13531,U_13531,hAPP(U_13532,U_13530))),c_Predicate_ORangeP(U_13531,U_13531,hAPP(U_13532,U_13529))) != c_Orderings_Obot__class_Obot(tc_fun(U_13531,tc_HOL_Obool))
          & hAPP(U_13532,U_13530) != hAPP(U_13532,U_13529) )
      | ? [U_13528] : ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,U_13528)) ),
    inference(variable_rename,[status(thm)],[f_3484_1]) ).

fof(f_3484_3,plain,
    ! [U_13533,U_13532,U_13531] :
      ( c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
      | ? [U_13530,U_13529] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13531,tc_HOL_Obool)),c_Predicate_ODomainP(U_13531,U_13531,hAPP(U_13532,U_13530))),c_Predicate_ORangeP(U_13531,U_13531,hAPP(U_13532,U_13529))) != c_Orderings_Obot__class_Obot(tc_fun(U_13531,tc_HOL_Obool))
          & hAPP(U_13532,U_13530) != hAPP(U_13532,U_13529) )
      | ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,sK330(U_13533,U_13532,U_13531))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_13528,sK330(U_13533,U_13532,U_13531))],[f_3484_2]) ).

fof(f_3484_4,plain,
    ! [U_13533,U_13532,U_13531] :
      ( c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
      | ? [U_13529] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13531,tc_HOL_Obool)),c_Predicate_ODomainP(U_13531,U_13531,hAPP(U_13532,sK331(U_13533,U_13532,U_13531)))),c_Predicate_ORangeP(U_13531,U_13531,hAPP(U_13532,U_13529))) != c_Orderings_Obot__class_Obot(tc_fun(U_13531,tc_HOL_Obool))
          & hAPP(U_13532,sK331(U_13533,U_13532,U_13531)) != hAPP(U_13532,U_13529) )
      | ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,sK330(U_13533,U_13532,U_13531))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_13530,sK331(U_13533,U_13532,U_13531))],[f_3484_3]) ).

fof(f_3484_5,plain,
    ! [U_13533,U_13532,U_13531] :
      ( c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13531,tc_HOL_Obool)),c_Predicate_ODomainP(U_13531,U_13531,hAPP(U_13532,sK331(U_13533,U_13532,U_13531)))),c_Predicate_ORangeP(U_13531,U_13531,hAPP(U_13532,sK332(U_13533,U_13532,U_13531)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13531,tc_HOL_Obool))
        & hAPP(U_13532,sK331(U_13533,U_13532,U_13531)) != hAPP(U_13532,sK332(U_13533,U_13532,U_13531)) )
      | ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,sK330(U_13533,U_13532,U_13531))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_13529,sK332(U_13533,U_13532,U_13531))],[f_3484_4]) ).

cnf(f_3484_6,plain,
    ( hAPP(U_13532,sK331(U_13533,U_13532,U_13531)) != hAPP(U_13532,sK332(U_13533,U_13532,U_13531))
    | c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
    | ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,sK330(U_13533,U_13532,U_13531))) ),
    inference(clausify,[status(thm)],[f_3484_5]) ).

cnf(f_3484_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13531,tc_HOL_Obool)),c_Predicate_ODomainP(U_13531,U_13531,hAPP(U_13532,sK331(U_13533,U_13532,U_13531)))),c_Predicate_ORangeP(U_13531,U_13531,hAPP(U_13532,sK332(U_13533,U_13532,U_13531)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13531,tc_HOL_Obool))
    | c_Wellfounded_OwfP(U_13531,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13533,tc_fun(U_13531,tc_fun(U_13531,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13533,tc_HOL_Obool))),U_13532))
    | ~ c_Wellfounded_OwfP(U_13531,hAPP(U_13532,sK330(U_13533,U_13532,U_13531))) ),
    inference(clausify,[status(thm)],[f_3484_5]) ).

fof(f_3485_1,plain,
    ! [V_ca_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_ca_2),V_p_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_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_3485_2,plain,
    ! [U_13541,U_13540,U_13539,U_13538,U_13537,U_13536] :
      ( hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13537,U_13538,tc_fun(U_13539,tc_HOL_Obool)),U_13541),U_13536)))
      | ? [U_13535,U_13534] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(U_13541,U_13535),U_13534)))
          & U_13536 = hAPP(hAPP(c_Product__Type_OPair(U_13537,U_13538),U_13535),U_13534) ) ),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

fof(f_3485_3,plain,
    ! [U_13541,U_13540,U_13539,U_13538,U_13537,U_13536] :
      ( hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13537,U_13538,tc_fun(U_13539,tc_HOL_Obool)),U_13541),U_13536)))
      | ? [U_13534] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(U_13541,sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),U_13534)))
          & U_13536 = hAPP(hAPP(c_Product__Type_OPair(U_13537,U_13538),sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),U_13534) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_13535,sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536))],[f_3485_2]) ).

fof(f_3485_4,plain,
    ! [U_13541,U_13540,U_13539,U_13538,U_13537,U_13536] :
      ( hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13537,U_13538,tc_fun(U_13539,tc_HOL_Obool)),U_13541),U_13536)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(U_13541,sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),sK334(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536))))
        & U_13536 = hAPP(hAPP(c_Product__Type_OPair(U_13537,U_13538),sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),sK334(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_13534,sK334(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536))],[f_3485_3]) ).

cnf(f_3485_5,plain,
    ( U_13536 = hAPP(hAPP(c_Product__Type_OPair(U_13537,U_13538),sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),sK334(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536))
    | hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13537,U_13538,tc_fun(U_13539,tc_HOL_Obool)),U_13541),U_13536))) ),
    inference(clausify,[status(thm)],[f_3485_4]) ).

cnf(f_3485_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(U_13541,sK333(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536)),sK334(U_13541,U_13540,U_13539,U_13538,U_13537,U_13536))))
    | hBOOL(hAPP(hAPP(c_member(U_13539),U_13540),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13537,U_13538,tc_fun(U_13539,tc_HOL_Obool)),U_13541),U_13536))) ),
    inference(clausify,[status(thm)],[f_3485_4]) ).

fof(f_3486_1,plain,
    ! [V_p_2,V_ca_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_ca_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_ca_2),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).

fof(f_3486_2,plain,
    ! [U_13549,U_13548,U_13547,U_13546,U_13545,U_13544] :
      ( ? [U_13543,U_13542] :
          ( hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(U_13548,U_13543),U_13542)))
          & U_13549 = hAPP(hAPP(c_Product__Type_OPair(U_13546,U_13547),U_13543),U_13542) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13546,U_13547,tc_fun(U_13544,tc_HOL_Obool)),U_13548),U_13549))) ),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

fof(f_3486_3,plain,
    ! [U_13549,U_13548,U_13547,U_13546,U_13545,U_13544] :
      ( ? [U_13542] :
          ( hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(U_13548,sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),U_13542)))
          & U_13549 = hAPP(hAPP(c_Product__Type_OPair(U_13546,U_13547),sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),U_13542) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13546,U_13547,tc_fun(U_13544,tc_HOL_Obool)),U_13548),U_13549))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_13543,sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544))],[f_3486_2]) ).

fof(f_3486_4,plain,
    ! [U_13549,U_13548,U_13547,U_13546,U_13545,U_13544] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(U_13548,sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),sK336(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544))))
        & U_13549 = hAPP(hAPP(c_Product__Type_OPair(U_13546,U_13547),sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),sK336(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13546,U_13547,tc_fun(U_13544,tc_HOL_Obool)),U_13548),U_13549))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_13542,sK336(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544))],[f_3486_3]) ).

cnf(f_3486_5,plain,
    ( U_13549 = hAPP(hAPP(c_Product__Type_OPair(U_13546,U_13547),sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),sK336(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13546,U_13547,tc_fun(U_13544,tc_HOL_Obool)),U_13548),U_13549))) ),
    inference(clausify,[status(thm)],[f_3486_4]) ).

cnf(f_3486_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(U_13548,sK335(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544)),sK336(U_13549,U_13548,U_13547,U_13546,U_13545,U_13544))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13544),U_13545),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13546,U_13547,tc_fun(U_13544,tc_HOL_Obool)),U_13548),U_13549))) ),
    inference(clausify,[status(thm)],[f_3486_4]) ).

fof(f_3487_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_3487_2,plain,
    ! [U_13555,U_13554,U_13553,U_13552,U_13551,U_13550] : hAPP(c_Set_Ovimage(U_13550,tc_prod(U_13551,U_13552),U_13553),hAPP(hAPP(c_Product__Type_OSigma(U_13551,U_13552),U_13554),hAPP(c_COMBK(tc_fun(U_13552,tc_HOL_Obool),U_13551),U_13555))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13550,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13550,U_13551,hAPP(c_Fun_Ocomp(tc_prod(U_13551,U_13552),U_13551,U_13550,c_Product__Type_Ofst(U_13551,U_13552)),U_13553)),U_13554)),hAPP(c_Set_Ovimage(U_13550,U_13552,hAPP(c_Fun_Ocomp(tc_prod(U_13551,U_13552),U_13552,U_13550,c_Product__Type_Osnd(U_13551,U_13552)),U_13553)),U_13555)),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

cnf(f_3487_3,plain,
    hAPP(c_Set_Ovimage(U_13550,tc_prod(U_13551,U_13552),U_13553),hAPP(hAPP(c_Product__Type_OSigma(U_13551,U_13552),U_13554),hAPP(c_COMBK(tc_fun(U_13552,tc_HOL_Obool),U_13551),U_13555))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13550,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13550,U_13551,hAPP(c_Fun_Ocomp(tc_prod(U_13551,U_13552),U_13551,U_13550,c_Product__Type_Ofst(U_13551,U_13552)),U_13553)),U_13554)),hAPP(c_Set_Ovimage(U_13550,U_13552,hAPP(c_Fun_Ocomp(tc_prod(U_13551,U_13552),U_13552,U_13550,c_Product__Type_Osnd(U_13551,U_13552)),U_13553)),U_13555)),
    inference(clausify,[status(thm)],[f_3487_2]) ).

fof(f_3488_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_3488_2,plain,
    ! [U_13558,U_13557,U_13556] : hAPP(c_Fun_Ocomp(U_13556,U_13556,U_13557,c_Fun_Oid(U_13556)),U_13558) = U_13558,
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

cnf(f_3488_3,plain,
    hAPP(c_Fun_Ocomp(U_13556,U_13556,U_13557,c_Fun_Oid(U_13556)),U_13558) = U_13558,
    inference(clausify,[status(thm)],[f_3488_2]) ).

fof(f_3489_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_3489_2,plain,
    ! [U_13561,U_13560,U_13559] : hAPP(c_Fun_Ocomp(U_13559,U_13560,U_13559,U_13561),c_Fun_Oid(U_13559)) = U_13561,
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

cnf(f_3489_3,plain,
    hAPP(c_Fun_Ocomp(U_13559,U_13560,U_13559,U_13561),c_Fun_Oid(U_13559)) = U_13561,
    inference(clausify,[status(thm)],[f_3489_2]) ).

fof(f_3490_1,plain,
    ! [V_v_2,V_ca_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_ca_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_ca_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).

fof(f_3490_2,plain,
    ! [U_13568,U_13567,U_13566,U_13565,U_13564,U_13563,U_13562] :
      ( hAPP(U_13565,hAPP(U_13566,U_13568)) = hAPP(U_13567,U_13568)
      | hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13564,U_13565),U_13566) != hAPP(c_Fun_Ocomp(U_13563,U_13563,U_13564,c_Fun_Oid(U_13563)),U_13567) ),
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

fof(f_3490_3,plain,
    ! [U_13568,U_13567,U_13566,U_13565] :
      ( ! [U_13564,U_13563,U_13562] : hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13564,U_13565),U_13566) != hAPP(c_Fun_Ocomp(U_13563,U_13563,U_13564,c_Fun_Oid(U_13563)),U_13567)
      | hAPP(U_13565,hAPP(U_13566,U_13568)) = hAPP(U_13567,U_13568) ),
    inference(miniscope,[status(thm)],[f_3490_2]) ).

cnf(f_3490_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13564,U_13565),U_13566) != hAPP(c_Fun_Ocomp(U_13563,U_13563,U_13564,c_Fun_Oid(U_13563)),U_13567)
    | hAPP(U_13565,hAPP(U_13566,U_13568)) = hAPP(U_13567,U_13568) ),
    inference(clausify,[status(thm)],[f_3490_3]) ).

fof(f_3491_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_3491_2,plain,
    ! [U_13579,U_13578,U_13577,U_13576,U_13575,U_13574,U_13573,U_13572,U_13571,U_13570,U_13569] : hAPP(c_Product__Type_Omap__pair(U_13569,U_13570,U_13571,U_13572,U_13573,U_13574),hAPP(c_Product__Type_Omap__pair(U_13575,U_13569,U_13576,U_13571,U_13577,U_13578),U_13579)) = hAPP(c_Product__Type_Omap__pair(U_13575,U_13570,U_13576,U_13572,hAPP(c_Fun_Ocomp(U_13569,U_13570,U_13575,U_13573),U_13577),hAPP(c_Fun_Ocomp(U_13571,U_13572,U_13576,U_13574),U_13578)),U_13579),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

cnf(f_3491_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_13569,U_13570,U_13571,U_13572,U_13573,U_13574),hAPP(c_Product__Type_Omap__pair(U_13575,U_13569,U_13576,U_13571,U_13577,U_13578),U_13579)) = hAPP(c_Product__Type_Omap__pair(U_13575,U_13570,U_13576,U_13572,hAPP(c_Fun_Ocomp(U_13569,U_13570,U_13575,U_13573),U_13577),hAPP(c_Fun_Ocomp(U_13571,U_13572,U_13576,U_13574),U_13578)),U_13579),
    inference(clausify,[status(thm)],[f_3491_2]) ).

fof(f_3492_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_3492_2,plain,
    ! [U_13589,U_13588,U_13587,U_13586,U_13585,U_13584,U_13583,U_13582,U_13581,U_13580] : c_Product__Type_Omap__pair(U_13580,U_13581,U_13582,U_13583,hAPP(c_Fun_Ocomp(U_13584,U_13581,U_13580,U_13585),U_13586),hAPP(c_Fun_Ocomp(U_13587,U_13583,U_13582,U_13588),U_13589)) = hAPP(c_Fun_Ocomp(tc_prod(U_13584,U_13587),tc_prod(U_13581,U_13583),tc_prod(U_13580,U_13582),c_Product__Type_Omap__pair(U_13584,U_13581,U_13587,U_13583,U_13585,U_13588)),c_Product__Type_Omap__pair(U_13580,U_13584,U_13582,U_13587,U_13586,U_13589)),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

cnf(f_3492_3,plain,
    c_Product__Type_Omap__pair(U_13580,U_13581,U_13582,U_13583,hAPP(c_Fun_Ocomp(U_13584,U_13581,U_13580,U_13585),U_13586),hAPP(c_Fun_Ocomp(U_13587,U_13583,U_13582,U_13588),U_13589)) = hAPP(c_Fun_Ocomp(tc_prod(U_13584,U_13587),tc_prod(U_13581,U_13583),tc_prod(U_13580,U_13582),c_Product__Type_Omap__pair(U_13584,U_13581,U_13587,U_13583,U_13585,U_13588)),c_Product__Type_Omap__pair(U_13580,U_13584,U_13582,U_13587,U_13586,U_13589)),
    inference(clausify,[status(thm)],[f_3492_2]) ).

fof(f_3493_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_3493_2,plain,
    ! [U_13599,U_13598,U_13597,U_13596,U_13595,U_13594,U_13593,U_13592,U_13591,U_13590] : hAPP(c_Fun_Ocomp(tc_prod(U_13590,U_13591),tc_prod(U_13592,U_13593),tc_prod(U_13594,U_13595),c_Product__Type_Omap__pair(U_13590,U_13592,U_13591,U_13593,U_13596,U_13597)),c_Product__Type_Omap__pair(U_13594,U_13590,U_13595,U_13591,U_13598,U_13599)) = c_Product__Type_Omap__pair(U_13594,U_13592,U_13595,U_13593,hAPP(c_Fun_Ocomp(U_13590,U_13592,U_13594,U_13596),U_13598),hAPP(c_Fun_Ocomp(U_13591,U_13593,U_13595,U_13597),U_13599)),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

cnf(f_3493_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_13590,U_13591),tc_prod(U_13592,U_13593),tc_prod(U_13594,U_13595),c_Product__Type_Omap__pair(U_13590,U_13592,U_13591,U_13593,U_13596,U_13597)),c_Product__Type_Omap__pair(U_13594,U_13590,U_13595,U_13591,U_13598,U_13599)) = c_Product__Type_Omap__pair(U_13594,U_13592,U_13595,U_13593,hAPP(c_Fun_Ocomp(U_13590,U_13592,U_13594,U_13596),U_13598),hAPP(c_Fun_Ocomp(U_13591,U_13593,U_13595,U_13597),U_13599)),
    inference(clausify,[status(thm)],[f_3493_2]) ).

fof(f_3494_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_3494_2,plain,
    ! [U_13605,U_13604,U_13603,U_13602,U_13601,U_13600] : hAPP(c_Set_Ovimage(U_13600,U_13601,hAPP(c_Fun_Ocomp(U_13602,U_13601,U_13600,U_13603),U_13604)),U_13605) = hAPP(c_Set_Ovimage(U_13600,U_13602,U_13604),hAPP(c_Set_Ovimage(U_13602,U_13601,U_13603),U_13605)),
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

cnf(f_3494_3,plain,
    hAPP(c_Set_Ovimage(U_13600,U_13601,hAPP(c_Fun_Ocomp(U_13602,U_13601,U_13600,U_13603),U_13604)),U_13605) = hAPP(c_Set_Ovimage(U_13600,U_13602,U_13604),hAPP(c_Set_Ovimage(U_13602,U_13601,U_13603),U_13605)),
    inference(clausify,[status(thm)],[f_3494_2]) ).

fof(f_3495_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_3495_2,plain,
    ! [U_13612,U_13611,U_13610,U_13609,U_13608,U_13607,U_13606] : hAPP(c_Fun_Ocomp(U_13606,U_13607,U_13608,U_13609),hAPP(c_Fun_Ocomp(U_13610,U_13606,U_13608,U_13611),U_13612)) = hAPP(c_Fun_Ocomp(U_13610,U_13607,U_13608,hAPP(c_Fun_Ocomp(U_13606,U_13607,U_13610,U_13609),U_13611)),U_13612),
    inference(variable_rename,[status(thm)],[f_3495_1]) ).

cnf(f_3495_3,plain,
    hAPP(c_Fun_Ocomp(U_13606,U_13607,U_13608,U_13609),hAPP(c_Fun_Ocomp(U_13610,U_13606,U_13608,U_13611),U_13612)) = hAPP(c_Fun_Ocomp(U_13610,U_13607,U_13608,hAPP(c_Fun_Ocomp(U_13606,U_13607,U_13610,U_13609),U_13611)),U_13612),
    inference(clausify,[status(thm)],[f_3495_2]) ).

fof(f_3496_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_3496_2,plain,
    ! [U_13618,U_13617,U_13616,U_13615,U_13614,U_13613] : hAPP(hAPP(c_Fun_Ocomp(U_13613,U_13614,U_13615,U_13616),U_13617),U_13618) = hAPP(U_13616,hAPP(U_13617,U_13618)),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

cnf(f_3496_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13613,U_13614,U_13615,U_13616),U_13617),U_13618) = hAPP(U_13616,hAPP(U_13617,U_13618)),
    inference(clausify,[status(thm)],[f_3496_2]) ).

fof(f_3497_1,plain,
    ! [V_v_2,V_d_2,V_ca_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_ca_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_ca_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).

fof(f_3497_2,plain,
    ! [U_13627,U_13626,U_13625,U_13624,U_13623,U_13622,U_13621,U_13620,U_13619] :
      ( hAPP(U_13622,hAPP(U_13623,U_13627)) = hAPP(U_13625,hAPP(U_13626,U_13627))
      | hAPP(c_Fun_Ocomp(U_13619,U_13620,U_13621,U_13622),U_13623) != hAPP(c_Fun_Ocomp(U_13624,U_13620,U_13621,U_13625),U_13626) ),
    inference(variable_rename,[status(thm)],[f_3497_1]) ).

fof(f_3497_3,plain,
    ! [U_13627,U_13626,U_13625,U_13624,U_13623,U_13622] :
      ( ! [U_13621,U_13620,U_13619] : hAPP(c_Fun_Ocomp(U_13619,U_13620,U_13621,U_13622),U_13623) != hAPP(c_Fun_Ocomp(U_13624,U_13620,U_13621,U_13625),U_13626)
      | hAPP(U_13622,hAPP(U_13623,U_13627)) = hAPP(U_13625,hAPP(U_13626,U_13627)) ),
    inference(miniscope,[status(thm)],[f_3497_2]) ).

cnf(f_3497_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13619,U_13620,U_13621,U_13622),U_13623) != hAPP(c_Fun_Ocomp(U_13624,U_13620,U_13621,U_13625),U_13626)
    | hAPP(U_13622,hAPP(U_13623,U_13627)) = hAPP(U_13625,hAPP(U_13626,U_13627)) ),
    inference(clausify,[status(thm)],[f_3497_3]) ).

fof(f_3498_1,plain,
    ! [V_d_2,V_ca_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_ca_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_ca_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).

fof(f_3498_2,plain,
    ! [U_13636,U_13635,U_13634,U_13633,U_13632,U_13631,U_13630,U_13629] :
      ( ! [U_13628] : hAPP(U_13632,hAPP(U_13633,U_13628)) = hAPP(U_13635,hAPP(U_13636,U_13628))
      | hAPP(c_Fun_Ocomp(U_13629,U_13630,U_13631,U_13632),U_13633) != hAPP(c_Fun_Ocomp(U_13634,U_13630,U_13631,U_13635),U_13636) ),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

fof(f_3498_3,plain,
    ! [U_13636,U_13635,U_13634,U_13633,U_13632] :
      ( ! [U_13631,U_13630,U_13629] : hAPP(c_Fun_Ocomp(U_13629,U_13630,U_13631,U_13632),U_13633) != hAPP(c_Fun_Ocomp(U_13634,U_13630,U_13631,U_13635),U_13636)
      | ! [U_13628] : hAPP(U_13632,hAPP(U_13633,U_13628)) = hAPP(U_13635,hAPP(U_13636,U_13628)) ),
    inference(miniscope,[status(thm)],[f_3498_2]) ).

cnf(f_3498_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13629,U_13630,U_13631,U_13632),U_13633) != hAPP(c_Fun_Ocomp(U_13634,U_13630,U_13631,U_13635),U_13636)
    | hAPP(U_13632,hAPP(U_13633,U_13628)) = hAPP(U_13635,hAPP(U_13636,U_13628)) ),
    inference(clausify,[status(thm)],[f_3498_3]) ).

fof(f_3499_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_3499_2,plain,
    ! [U_13642,U_13641,U_13640,U_13639,U_13638,U_13637] : hAPP(hAPP(c_Fun_Ocomp(U_13637,U_13638,U_13639,U_13640),U_13641),U_13642) = hAPP(U_13640,hAPP(U_13641,U_13642)),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

cnf(f_3499_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13637,U_13638,U_13639,U_13640),U_13641),U_13642) = hAPP(U_13640,hAPP(U_13641,U_13642)),
    inference(clausify,[status(thm)],[f_3499_2]) ).

fof(f_3500_1,plain,
    ! [V_x_2,V_f_2,V_ca_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_ca_2)),V_f_2),V_x_2) = V_ca_2,
    inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).

fof(f_3500_2,plain,
    ! [U_13648,U_13647,U_13646,U_13645,U_13644,U_13643] : hAPP(hAPP(c_Fun_Ocomp(U_13643,U_13644,U_13645,hAPP(c_COMBK(U_13644,U_13643),U_13646)),U_13647),U_13648) = U_13646,
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

cnf(f_3500_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13643,U_13644,U_13645,hAPP(c_COMBK(U_13644,U_13643),U_13646)),U_13647),U_13648) = U_13646,
    inference(clausify,[status(thm)],[f_3500_2]) ).

fof(f_3501_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_3501_2,plain,
    ! [U_13653,U_13652,U_13651,U_13650,U_13649] :
      ( hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13652)),hAPP(U_13651,U_13653)) = hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13653)),hAPP(U_13651,U_13652))
      | ~ c_Finite__Set_Ofun__left__comm(U_13649,U_13650,U_13651) ),
    inference(variable_rename,[status(thm)],[f_3501_1]) ).

fof(f_3501_3,plain,
    ! [U_13653,U_13652,U_13651,U_13650] :
      ( ! [U_13649] : ~ c_Finite__Set_Ofun__left__comm(U_13649,U_13650,U_13651)
      | hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13652)),hAPP(U_13651,U_13653)) = hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13653)),hAPP(U_13651,U_13652)) ),
    inference(miniscope,[status(thm)],[f_3501_2]) ).

cnf(f_3501_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_13649,U_13650,U_13651)
    | hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13652)),hAPP(U_13651,U_13653)) = hAPP(c_Fun_Ocomp(U_13650,U_13650,U_13650,hAPP(U_13651,U_13653)),hAPP(U_13651,U_13652)) ),
    inference(clausify,[status(thm)],[f_3501_3]) ).

fof(f_3502_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_3502_2,plain,
    ! [U_13664,U_13663,U_13662,U_13661,U_13660,U_13659,U_13658,U_13657,U_13656,U_13655,U_13654] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_13660,U_13661,U_13662,U_13654),U_13655),U_13656) = hAPP(hAPP(c_Fun_Ocomp(U_13663,U_13661,U_13664,U_13657),U_13658),U_13659)
      | hAPP(U_13654,hAPP(U_13655,U_13656)) != hAPP(U_13657,hAPP(U_13658,U_13659)) ),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

cnf(f_3502_3,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_13660,U_13661,U_13662,U_13654),U_13655),U_13656) = hAPP(hAPP(c_Fun_Ocomp(U_13663,U_13661,U_13664,U_13657),U_13658),U_13659)
    | hAPP(U_13654,hAPP(U_13655,U_13656)) != hAPP(U_13657,hAPP(U_13658,U_13659)) ),
    inference(clausify,[status(thm)],[f_3502_2]) ).

fof(f_3503_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_3503_2,plain,
    ! [U_13668,U_13667,U_13666,U_13665] :
      ( hAPP(c_Fun_Ocomp(U_13666,U_13666,U_13666,hAPP(U_13667,U_13668)),hAPP(U_13667,U_13668)) = hAPP(U_13667,U_13668)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_13665,U_13666,U_13667) ),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

fof(f_3503_3,plain,
    ! [U_13668,U_13667,U_13666] :
      ( ! [U_13665] : ~ c_Finite__Set_Ofun__left__comm__idem(U_13665,U_13666,U_13667)
      | hAPP(c_Fun_Ocomp(U_13666,U_13666,U_13666,hAPP(U_13667,U_13668)),hAPP(U_13667,U_13668)) = hAPP(U_13667,U_13668) ),
    inference(miniscope,[status(thm)],[f_3503_2]) ).

cnf(f_3503_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_13665,U_13666,U_13667)
    | hAPP(c_Fun_Ocomp(U_13666,U_13666,U_13666,hAPP(U_13667,U_13668)),hAPP(U_13667,U_13668)) = hAPP(U_13667,U_13668) ),
    inference(clausify,[status(thm)],[f_3503_3]) ).

fof(f_3504_1,plain,
    ! [V_v_2,V_ca_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_ca_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != V_ca_2 ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).

fof(f_3504_2,plain,
    ! [U_13675,U_13674,U_13673,U_13672,U_13671,U_13670,U_13669] :
      ( hAPP(U_13672,hAPP(U_13673,U_13675)) = hAPP(U_13674,U_13675)
      | hAPP(c_Fun_Ocomp(U_13669,U_13670,U_13671,U_13672),U_13673) != U_13674 ),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

fof(f_3504_3,plain,
    ! [U_13675,U_13674,U_13673,U_13672] :
      ( ! [U_13671,U_13670,U_13669] : hAPP(c_Fun_Ocomp(U_13669,U_13670,U_13671,U_13672),U_13673) != U_13674
      | hAPP(U_13672,hAPP(U_13673,U_13675)) = hAPP(U_13674,U_13675) ),
    inference(miniscope,[status(thm)],[f_3504_2]) ).

cnf(f_3504_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13669,U_13670,U_13671,U_13672),U_13673) != U_13674
    | hAPP(U_13672,hAPP(U_13673,U_13675)) = hAPP(U_13674,U_13675) ),
    inference(clausify,[status(thm)],[f_3504_3]) ).

fof(f_3505_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_3505_2,plain,
    ! [U_13682,U_13681,U_13680,U_13679,U_13678,U_13677,U_13676] : hAPP(c_Product__Type_Oapsnd(U_13676,U_13677,U_13678,U_13679),hAPP(c_Product__Type_Oapsnd(U_13680,U_13676,U_13678,U_13681),U_13682)) = hAPP(c_Product__Type_Oapsnd(U_13680,U_13677,U_13678,hAPP(c_Fun_Ocomp(U_13676,U_13677,U_13680,U_13679),U_13681)),U_13682),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

cnf(f_3505_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_13676,U_13677,U_13678,U_13679),hAPP(c_Product__Type_Oapsnd(U_13680,U_13676,U_13678,U_13681),U_13682)) = hAPP(c_Product__Type_Oapsnd(U_13680,U_13677,U_13678,hAPP(c_Fun_Ocomp(U_13676,U_13677,U_13680,U_13679),U_13681)),U_13682),
    inference(clausify,[status(thm)],[f_3505_2]) ).

fof(f_3506_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_3506_2,plain,
    ! [U_13689,U_13688,U_13687,U_13686,U_13685,U_13684,U_13683] : hAPP(c_Product__Type_Oapfst(U_13683,U_13684,U_13685,U_13686),hAPP(c_Product__Type_Oapfst(U_13687,U_13683,U_13685,U_13688),U_13689)) = hAPP(c_Product__Type_Oapfst(U_13687,U_13684,U_13685,hAPP(c_Fun_Ocomp(U_13683,U_13684,U_13687,U_13686),U_13688)),U_13689),
    inference(variable_rename,[status(thm)],[f_3506_1]) ).

cnf(f_3506_3,plain,
    hAPP(c_Product__Type_Oapfst(U_13683,U_13684,U_13685,U_13686),hAPP(c_Product__Type_Oapfst(U_13687,U_13683,U_13685,U_13688),U_13689)) = hAPP(c_Product__Type_Oapfst(U_13687,U_13684,U_13685,hAPP(c_Fun_Ocomp(U_13683,U_13684,U_13687,U_13686),U_13688)),U_13689),
    inference(clausify,[status(thm)],[f_3506_2]) ).

fof(f_3507_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_3507_2,plain,
    ! [U_13696,U_13695,U_13694,U_13693,U_13692,U_13691,U_13690] : hAPP(c_Fun_Ocomp(U_13690,U_13691,U_13692,U_13693),c_Fun_Ofun__upd(U_13692,U_13690,U_13694,U_13695,U_13696)) = c_Fun_Ofun__upd(U_13692,U_13691,hAPP(c_Fun_Ocomp(U_13690,U_13691,U_13692,U_13693),U_13694),U_13695,hAPP(U_13693,U_13696)),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

cnf(f_3507_3,plain,
    hAPP(c_Fun_Ocomp(U_13690,U_13691,U_13692,U_13693),c_Fun_Ofun__upd(U_13692,U_13690,U_13694,U_13695,U_13696)) = c_Fun_Ofun__upd(U_13692,U_13691,hAPP(c_Fun_Ocomp(U_13690,U_13691,U_13692,U_13693),U_13694),U_13695,hAPP(U_13693,U_13696)),
    inference(clausify,[status(thm)],[f_3507_2]) ).

fof(f_3508_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_3508_2,plain,
    ! [U_13701,U_13700,U_13699,U_13698,U_13697] :
      ( hAPP(c_Set_Oimage(U_13697,U_13700,hAPP(c_Fun_Ocomp(U_13698,U_13700,U_13697,U_13701),U_13699)),c_Orderings_Otop__class_Otop(tc_fun(U_13697,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13700,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13698,U_13700,U_13701),c_Orderings_Otop__class_Otop(tc_fun(U_13698,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13700,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13697,U_13698,U_13699),c_Orderings_Otop__class_Otop(tc_fun(U_13697,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13698,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

cnf(f_3508_3,plain,
    ( hAPP(c_Set_Oimage(U_13697,U_13700,hAPP(c_Fun_Ocomp(U_13698,U_13700,U_13697,U_13701),U_13699)),c_Orderings_Otop__class_Otop(tc_fun(U_13697,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13700,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13698,U_13700,U_13701),c_Orderings_Otop__class_Otop(tc_fun(U_13698,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13700,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13697,U_13698,U_13699),c_Orderings_Otop__class_Otop(tc_fun(U_13697,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13698,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3508_2]) ).

fof(f_3509_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_3509_2,plain,
    ! [U_13707,U_13706,U_13705,U_13704,U_13703,U_13702] : hAPP(c_Set_Oimage(U_13702,U_13703,hAPP(c_Fun_Ocomp(U_13704,U_13703,U_13702,U_13705),U_13706)),U_13707) = hAPP(c_Set_Oimage(U_13704,U_13703,U_13705),hAPP(c_Set_Oimage(U_13702,U_13704,U_13706),U_13707)),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

cnf(f_3509_3,plain,
    hAPP(c_Set_Oimage(U_13702,U_13703,hAPP(c_Fun_Ocomp(U_13704,U_13703,U_13702,U_13705),U_13706)),U_13707) = hAPP(c_Set_Oimage(U_13704,U_13703,U_13705),hAPP(c_Set_Oimage(U_13702,U_13704,U_13706),U_13707)),
    inference(clausify,[status(thm)],[f_3509_2]) ).

fof(f_3510_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_3510_2,plain,
    ! [U_13712,U_13711,U_13710,U_13709,U_13708] :
      ( c_Fun_Oinj__on(U_13711,U_13709,hAPP(c_Fun_Ocomp(U_13708,U_13709,U_13711,U_13710),U_13712),c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13711,U_13708,U_13712,c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13708,U_13709,U_13710,c_Orderings_Otop__class_Otop(tc_fun(U_13708,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

cnf(f_3510_3,plain,
    ( c_Fun_Oinj__on(U_13711,U_13709,hAPP(c_Fun_Ocomp(U_13708,U_13709,U_13711,U_13710),U_13712),c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_13711,U_13708,U_13712,c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_13708,U_13709,U_13710,c_Orderings_Otop__class_Otop(tc_fun(U_13708,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3510_2]) ).

fof(f_3511_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_3511_2,plain,
    ! [U_13718,U_13717,U_13716,U_13715,U_13714,U_13713] :
      ( c_Fun_Oinj__on(U_13713,U_13715,U_13717,U_13718)
      | ~ c_Fun_Oinj__on(U_13713,U_13714,hAPP(c_Fun_Ocomp(U_13715,U_13714,U_13713,U_13716),U_13717),U_13718) ),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

cnf(f_3511_3,plain,
    ( c_Fun_Oinj__on(U_13713,U_13715,U_13717,U_13718)
    | ~ c_Fun_Oinj__on(U_13713,U_13714,hAPP(c_Fun_Ocomp(U_13715,U_13714,U_13713,U_13716),U_13717),U_13718) ),
    inference(clausify,[status(thm)],[f_3511_2]) ).

fof(f_3512_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_3512_2,plain,
    ! [U_13724,U_13723,U_13722,U_13721,U_13720,U_13719] :
      ( c_Fun_Oinj__on(U_13721,U_13720,U_13722,hAPP(c_Set_Oimage(U_13719,U_13721,U_13723),U_13724))
      | ~ c_Fun_Oinj__on(U_13719,U_13720,hAPP(c_Fun_Ocomp(U_13721,U_13720,U_13719,U_13722),U_13723),U_13724) ),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

cnf(f_3512_3,plain,
    ( c_Fun_Oinj__on(U_13721,U_13720,U_13722,hAPP(c_Set_Oimage(U_13719,U_13721,U_13723),U_13724))
    | ~ c_Fun_Oinj__on(U_13719,U_13720,hAPP(c_Fun_Ocomp(U_13721,U_13720,U_13719,U_13722),U_13723),U_13724) ),
    inference(clausify,[status(thm)],[f_3512_2]) ).

fof(f_3513_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_3513_2,plain,
    ! [U_13730,U_13729,U_13728,U_13727,U_13726,U_13725] :
      ( c_Fun_Oinj__on(U_13725,U_13729,hAPP(c_Fun_Ocomp(U_13726,U_13729,U_13725,U_13730),U_13727),U_13728)
      | ~ c_Fun_Oinj__on(U_13726,U_13729,U_13730,hAPP(c_Set_Oimage(U_13725,U_13726,U_13727),U_13728))
      | ~ c_Fun_Oinj__on(U_13725,U_13726,U_13727,U_13728) ),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

cnf(f_3513_3,plain,
    ( c_Fun_Oinj__on(U_13725,U_13729,hAPP(c_Fun_Ocomp(U_13726,U_13729,U_13725,U_13730),U_13727),U_13728)
    | ~ c_Fun_Oinj__on(U_13726,U_13729,U_13730,hAPP(c_Set_Oimage(U_13725,U_13726,U_13727),U_13728))
    | ~ c_Fun_Oinj__on(U_13725,U_13726,U_13727,U_13728) ),
    inference(clausify,[status(thm)],[f_3513_2]) ).

fof(f_3514_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_3514_2,plain,
    ! [U_13736,U_13735,U_13734,U_13733,U_13732,U_13731] :
      ( ( ( c_Fun_Oinj__on(U_13732,U_13735,U_13736,hAPP(c_Set_Oimage(U_13731,U_13732,U_13733),U_13734))
          | ~ c_Fun_Oinj__on(U_13731,U_13735,hAPP(c_Fun_Ocomp(U_13732,U_13735,U_13731,U_13736),U_13733),U_13734) )
        & ( c_Fun_Oinj__on(U_13731,U_13735,hAPP(c_Fun_Ocomp(U_13732,U_13735,U_13731,U_13736),U_13733),U_13734)
          | ~ c_Fun_Oinj__on(U_13732,U_13735,U_13736,hAPP(c_Set_Oimage(U_13731,U_13732,U_13733),U_13734)) ) )
      | ~ c_Fun_Oinj__on(U_13731,U_13732,U_13733,U_13734) ),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

cnf(f_3514_3,plain,
    ( c_Fun_Oinj__on(U_13731,U_13735,hAPP(c_Fun_Ocomp(U_13732,U_13735,U_13731,U_13736),U_13733),U_13734)
    | ~ c_Fun_Oinj__on(U_13732,U_13735,U_13736,hAPP(c_Set_Oimage(U_13731,U_13732,U_13733),U_13734))
    | ~ c_Fun_Oinj__on(U_13731,U_13732,U_13733,U_13734) ),
    inference(clausify,[status(thm)],[f_3514_2]) ).

cnf(f_3514_4,plain,
    ( c_Fun_Oinj__on(U_13732,U_13735,U_13736,hAPP(c_Set_Oimage(U_13731,U_13732,U_13733),U_13734))
    | ~ c_Fun_Oinj__on(U_13731,U_13735,hAPP(c_Fun_Ocomp(U_13732,U_13735,U_13731,U_13736),U_13733),U_13734)
    | ~ c_Fun_Oinj__on(U_13731,U_13732,U_13733,U_13734) ),
    inference(clausify,[status(thm)],[f_3514_2]) ).

fof(f_3515_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_3515_2,plain,
    ! [U_13742,U_13741,U_13740,U_13739,U_13738,U_13737] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13739,U_13737),U_13742),hAPP(c_Set_Oimage(U_13738,U_13739,U_13740),U_13741)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13738,U_13737),hAPP(c_Fun_Ocomp(U_13739,U_13737,U_13738,U_13742),U_13740)),U_13741)
      | ~ c_Fun_Oinj__on(U_13738,U_13739,U_13740,U_13741)
      | ~ class_Groups_Ocomm__monoid__add(U_13737) ),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

cnf(f_3515_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13739,U_13737),U_13742),hAPP(c_Set_Oimage(U_13738,U_13739,U_13740),U_13741)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13738,U_13737),hAPP(c_Fun_Ocomp(U_13739,U_13737,U_13738,U_13742),U_13740)),U_13741)
    | ~ c_Fun_Oinj__on(U_13738,U_13739,U_13740,U_13741)
    | ~ class_Groups_Ocomm__monoid__add(U_13737) ),
    inference(clausify,[status(thm)],[f_3515_2]) ).

fof(f_3516_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_3516_2,plain,
    ! [U_13748,U_13747,U_13746,U_13745,U_13744,U_13743] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13745,U_13743),U_13748),hAPP(c_Set_Oimage(U_13744,U_13745,U_13746),U_13747)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13744,U_13743),hAPP(c_Fun_Ocomp(U_13745,U_13743,U_13744,U_13748),U_13746)),U_13747)
      | ~ c_Fun_Oinj__on(U_13744,U_13745,U_13746,U_13747)
      | ~ class_Groups_Ocomm__monoid__mult(U_13743) ),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

cnf(f_3516_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13745,U_13743),U_13748),hAPP(c_Set_Oimage(U_13744,U_13745,U_13746),U_13747)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13744,U_13743),hAPP(c_Fun_Ocomp(U_13745,U_13743,U_13744,U_13748),U_13746)),U_13747)
    | ~ c_Fun_Oinj__on(U_13744,U_13745,U_13746,U_13747)
    | ~ class_Groups_Ocomm__monoid__mult(U_13743) ),
    inference(clausify,[status(thm)],[f_3516_2]) ).

fof(f_3517_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_3517_2,plain,
    ! [U_13756,U_13755,U_13754,U_13753,U_13752,U_13751,U_13750,U_13749] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13751,U_13749),U_13756),U_13754) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13750,U_13749),U_13755),U_13753)
      | U_13755 != hAPP(c_Fun_Ocomp(U_13751,U_13749,U_13750,U_13756),U_13752)
      | U_13754 != hAPP(c_Set_Oimage(U_13750,U_13751,U_13752),U_13753)
      | ~ c_Fun_Oinj__on(U_13750,U_13751,U_13752,U_13753)
      | ~ class_Groups_Ocomm__monoid__mult(U_13749) ),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

cnf(f_3517_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13751,U_13749),U_13756),U_13754) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13750,U_13749),U_13755),U_13753)
    | U_13755 != hAPP(c_Fun_Ocomp(U_13751,U_13749,U_13750,U_13756),U_13752)
    | U_13754 != hAPP(c_Set_Oimage(U_13750,U_13751,U_13752),U_13753)
    | ~ c_Fun_Oinj__on(U_13750,U_13751,U_13752,U_13753)
    | ~ class_Groups_Ocomm__monoid__mult(U_13749) ),
    inference(clausify,[status(thm)],[f_3517_2]) ).

fof(f_3518_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_3518_2,plain,
    ! [U_13761,U_13760,U_13759,U_13758,U_13757] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13758,U_13757),U_13761),hAPP(c_Set_Oimage(U_13758,U_13758,U_13760),U_13759)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13758,U_13757),hAPP(c_Fun_Ocomp(U_13758,U_13757,U_13758,U_13761),U_13760)),U_13759)
      | ~ c_Fun_Oinj__on(U_13758,U_13758,U_13760,U_13759)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13758),U_13759))
      | ~ class_Groups_Ocomm__monoid__add(U_13757) ),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

cnf(f_3518_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13758,U_13757),U_13761),hAPP(c_Set_Oimage(U_13758,U_13758,U_13760),U_13759)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13758,U_13757),hAPP(c_Fun_Ocomp(U_13758,U_13757,U_13758,U_13761),U_13760)),U_13759)
    | ~ c_Fun_Oinj__on(U_13758,U_13758,U_13760,U_13759)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13758),U_13759))
    | ~ class_Groups_Ocomm__monoid__add(U_13757) ),
    inference(clausify,[status(thm)],[f_3518_2]) ).

fof(f_3519_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_3519_2,plain,
    ! [U_13766,U_13765,U_13764,U_13763,U_13762] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13763,U_13762),U_13766),hAPP(c_Set_Oimage(U_13763,U_13763,U_13765),U_13764)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13763,U_13762),hAPP(c_Fun_Ocomp(U_13763,U_13762,U_13763,U_13766),U_13765)),U_13764)
      | ~ c_Fun_Oinj__on(U_13763,U_13763,U_13765,U_13764)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13763),U_13764))
      | ~ class_Groups_Ocomm__monoid__mult(U_13762) ),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

cnf(f_3519_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13763,U_13762),U_13766),hAPP(c_Set_Oimage(U_13763,U_13763,U_13765),U_13764)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13763,U_13762),hAPP(c_Fun_Ocomp(U_13763,U_13762,U_13763,U_13766),U_13765)),U_13764)
    | ~ c_Fun_Oinj__on(U_13763,U_13763,U_13765,U_13764)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13763),U_13764))
    | ~ class_Groups_Ocomm__monoid__mult(U_13762) ),
    inference(clausify,[status(thm)],[f_3519_2]) ).

fof(f_3520_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_3520_2,plain,
    ! [U_13773,U_13772,U_13771,U_13770,U_13769,U_13768,U_13767] :
      ( hAPP(c_Fun_Othe__inv__into(U_13770,U_13768,U_13772,hAPP(c_Fun_Ocomp(U_13767,U_13768,U_13770,U_13769),U_13771)),U_13773) = hAPP(hAPP(c_Fun_Ocomp(U_13767,U_13770,U_13768,c_Fun_Othe__inv__into(U_13770,U_13767,U_13772,U_13771)),c_Fun_Othe__inv__into(U_13767,U_13768,hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772),U_13769)),U_13773)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13768),U_13773),hAPP(c_Set_Oimage(U_13767,U_13768,U_13769),hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772))))
      | ~ c_Fun_Oinj__on(U_13770,U_13767,U_13771,U_13772)
      | ~ c_Fun_Oinj__on(U_13767,U_13768,U_13769,hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772)) ),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

cnf(f_3520_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_13770,U_13768,U_13772,hAPP(c_Fun_Ocomp(U_13767,U_13768,U_13770,U_13769),U_13771)),U_13773) = hAPP(hAPP(c_Fun_Ocomp(U_13767,U_13770,U_13768,c_Fun_Othe__inv__into(U_13770,U_13767,U_13772,U_13771)),c_Fun_Othe__inv__into(U_13767,U_13768,hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772),U_13769)),U_13773)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13768),U_13773),hAPP(c_Set_Oimage(U_13767,U_13768,U_13769),hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772))))
    | ~ c_Fun_Oinj__on(U_13770,U_13767,U_13771,U_13772)
    | ~ c_Fun_Oinj__on(U_13767,U_13768,U_13769,hAPP(c_Set_Oimage(U_13770,U_13767,U_13771),U_13772)) ),
    inference(clausify,[status(thm)],[f_3520_2]) ).

fof(f_3521_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_3521_2,plain,
    ! [U_13780,U_13779,U_13778,U_13777,U_13776,U_13775,U_13774] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13774,U_13777,c_Groups_Otimes__class_Otimes(U_13774)),U_13779),U_13780),hAPP(c_Set_Oimage(U_13775,U_13777,U_13778),U_13776)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13774,U_13775,c_Groups_Otimes__class_Otimes(U_13774)),hAPP(c_Fun_Ocomp(U_13777,U_13774,U_13775,U_13779),U_13778)),U_13780),U_13776)
      | ~ c_Fun_Oinj__on(U_13775,U_13777,U_13778,U_13776)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13775),U_13776))
      | ~ class_Groups_Oab__semigroup__mult(U_13774) ),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

cnf(f_3521_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13774,U_13777,c_Groups_Otimes__class_Otimes(U_13774)),U_13779),U_13780),hAPP(c_Set_Oimage(U_13775,U_13777,U_13778),U_13776)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13774,U_13775,c_Groups_Otimes__class_Otimes(U_13774)),hAPP(c_Fun_Ocomp(U_13777,U_13774,U_13775,U_13779),U_13778)),U_13780),U_13776)
    | ~ c_Fun_Oinj__on(U_13775,U_13777,U_13778,U_13776)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13775),U_13776))
    | ~ class_Groups_Oab__semigroup__mult(U_13774) ),
    inference(clausify,[status(thm)],[f_3521_2]) ).

fof(f_3522_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_3522_2,plain,
    ! [U_13786,U_13785,U_13784,U_13783,U_13782,U_13781] :
      ( hAPP(U_13784,U_13785) = hAPP(c_Fun_Ocomp(U_13782,U_13782,U_13782,hAPP(U_13784,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13781,tc_HOL_Obool)),U_13785),hAPP(hAPP(c_Set_Oinsert(U_13781),U_13786),c_Orderings_Obot__class_Obot(tc_fun(U_13781,tc_HOL_Obool)))))),hAPP(U_13783,U_13786))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13781),U_13786),U_13785))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13781),U_13785))
      | ~ c_Finite__Set_Ofolding(U_13781,U_13782,U_13783,U_13784) ),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

cnf(f_3522_3,plain,
    ( hAPP(U_13784,U_13785) = hAPP(c_Fun_Ocomp(U_13782,U_13782,U_13782,hAPP(U_13784,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13781,tc_HOL_Obool)),U_13785),hAPP(hAPP(c_Set_Oinsert(U_13781),U_13786),c_Orderings_Obot__class_Obot(tc_fun(U_13781,tc_HOL_Obool)))))),hAPP(U_13783,U_13786))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13781),U_13786),U_13785))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13781),U_13785))
    | ~ c_Finite__Set_Ofolding(U_13781,U_13782,U_13783,U_13784) ),
    inference(clausify,[status(thm)],[f_3522_2]) ).

fof(f_3523_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_3523_2,plain,
    ! [U_13794,U_13793,U_13792,U_13791,U_13790,U_13789,U_13788,U_13787] :
      ( hAPP(hAPP(U_13791,U_13794),hAPP(c_Set_Oimage(U_13788,U_13788,U_13793),U_13792)) = hAPP(hAPP(U_13791,hAPP(c_Fun_Ocomp(U_13788,U_13787,U_13788,U_13794),U_13793)),U_13792)
      | ~ c_Fun_Oinj__on(U_13788,U_13788,U_13793,U_13792)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13788),U_13792))
      | ~ c_Finite__Set_Ofolding__image(U_13787,U_13788,U_13789,U_13790,U_13791) ),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

cnf(f_3523_3,plain,
    ( hAPP(hAPP(U_13791,U_13794),hAPP(c_Set_Oimage(U_13788,U_13788,U_13793),U_13792)) = hAPP(hAPP(U_13791,hAPP(c_Fun_Ocomp(U_13788,U_13787,U_13788,U_13794),U_13793)),U_13792)
    | ~ c_Fun_Oinj__on(U_13788,U_13788,U_13793,U_13792)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13788),U_13792))
    | ~ c_Finite__Set_Ofolding__image(U_13787,U_13788,U_13789,U_13790,U_13791) ),
    inference(clausify,[status(thm)],[f_3523_2]) ).

fof(f_3524_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_3524_2,plain,
    ! [U_13800,U_13799,U_13798,U_13797,U_13796,U_13795] :
      ( hAPP(U_13798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13795,tc_HOL_Obool)),U_13799),U_13800)) = hAPP(c_Fun_Ocomp(U_13796,U_13796,U_13796,hAPP(U_13798,U_13799)),hAPP(U_13798,U_13800))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13795,tc_HOL_Obool)),U_13799),U_13800) != c_Orderings_Obot__class_Obot(tc_fun(U_13795,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13795),U_13800))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13795),U_13799))
      | ~ c_Finite__Set_Ofolding(U_13795,U_13796,U_13797,U_13798) ),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

cnf(f_3524_3,plain,
    ( hAPP(U_13798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13795,tc_HOL_Obool)),U_13799),U_13800)) = hAPP(c_Fun_Ocomp(U_13796,U_13796,U_13796,hAPP(U_13798,U_13799)),hAPP(U_13798,U_13800))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13795,tc_HOL_Obool)),U_13799),U_13800) != c_Orderings_Obot__class_Obot(tc_fun(U_13795,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13795),U_13800))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13795),U_13799))
    | ~ c_Finite__Set_Ofolding(U_13795,U_13796,U_13797,U_13798) ),
    inference(clausify,[status(thm)],[f_3524_2]) ).

fof(f_3525_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_3525_2,plain,
    ! [U_13811,U_13810,U_13809,U_13808,U_13807,U_13806,U_13805,U_13804,U_13803,U_13802,U_13801] :
      ( hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13807,U_13808),hAPP(c_Fun_Ocomp(U_13809,U_13805,U_13807,U_13810),U_13811)) = hAPP(c_Fun_Ocomp(U_13809,U_13806,U_13807,hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13809,U_13808),U_13810)),U_13811)
      | ~ c_Finite__Set_Ofolding(U_13801,U_13802,U_13803,U_13804) ),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

fof(f_3525_3,plain,
    ( ! [U_13811,U_13810,U_13809,U_13808,U_13807,U_13806,U_13805] : hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13807,U_13808),hAPP(c_Fun_Ocomp(U_13809,U_13805,U_13807,U_13810),U_13811)) = hAPP(c_Fun_Ocomp(U_13809,U_13806,U_13807,hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13809,U_13808),U_13810)),U_13811)
    | ! [U_13804,U_13803,U_13802,U_13801] : ~ c_Finite__Set_Ofolding(U_13801,U_13802,U_13803,U_13804) ),
    inference(miniscope,[status(thm)],[f_3525_2]) ).

cnf(f_3525_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13807,U_13808),hAPP(c_Fun_Ocomp(U_13809,U_13805,U_13807,U_13810),U_13811)) = hAPP(c_Fun_Ocomp(U_13809,U_13806,U_13807,hAPP(c_Fun_Ocomp(U_13805,U_13806,U_13809,U_13808),U_13810)),U_13811)
    | ~ c_Finite__Set_Ofolding(U_13801,U_13802,U_13803,U_13804) ),
    inference(clausify,[status(thm)],[f_3525_3]) ).

fof(f_3526_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_3526_2,plain,
    ! [U_13817,U_13816,U_13815,U_13814,U_13813,U_13812] :
      ( hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13816)),hAPP(U_13814,U_13817)) = hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13817)),hAPP(U_13814,U_13816))
      | ~ c_Finite__Set_Ofolding(U_13812,U_13813,U_13814,U_13815) ),
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

fof(f_3526_3,plain,
    ! [U_13817,U_13816,U_13815,U_13814,U_13813] :
      ( ! [U_13812] : ~ c_Finite__Set_Ofolding(U_13812,U_13813,U_13814,U_13815)
      | hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13816)),hAPP(U_13814,U_13817)) = hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13817)),hAPP(U_13814,U_13816)) ),
    inference(miniscope,[status(thm)],[f_3526_2]) ).

cnf(f_3526_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_13812,U_13813,U_13814,U_13815)
    | hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13816)),hAPP(U_13814,U_13817)) = hAPP(c_Fun_Ocomp(U_13813,U_13813,U_13813,hAPP(U_13814,U_13817)),hAPP(U_13814,U_13816)) ),
    inference(clausify,[status(thm)],[f_3526_3]) ).

fof(f_3527_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_3527_2,plain,
    ! [U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818] :
      ( hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),U_13825)) = hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),U_13825))
      | ~ c_Finite__Set_Ofolding(U_13818,U_13819,U_13820,U_13821) ),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

fof(f_3527_3,plain,
    ! [U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819] :
      ( ! [U_13818] : ~ c_Finite__Set_Ofolding(U_13818,U_13819,U_13820,U_13821)
      | hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),U_13825)) = hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),U_13825)) ),
    inference(miniscope,[status(thm)],[f_3527_2]) ).

cnf(f_3527_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_13818,U_13819,U_13820,U_13821)
    | hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),U_13825)) = hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13824)),hAPP(c_Fun_Ocomp(U_13819,U_13819,U_13822,hAPP(U_13820,U_13823)),U_13825)) ),
    inference(clausify,[status(thm)],[f_3527_3]) ).

fof(f_3528_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_3528_2,plain,
    ! [U_13831,U_13830,U_13829,U_13828,U_13827,U_13826] : hAPP(c_Fun_Ocomp(tc_prod(U_13826,U_13827),U_13826,tc_prod(U_13828,U_13829),c_Product__Type_Ofst(U_13826,U_13827)),c_Product__Type_Omap__pair(U_13828,U_13826,U_13829,U_13827,U_13830,U_13831)) = hAPP(c_Fun_Ocomp(U_13828,U_13826,tc_prod(U_13828,U_13829),U_13830),c_Product__Type_Ofst(U_13828,U_13829)),
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

cnf(f_3528_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_13826,U_13827),U_13826,tc_prod(U_13828,U_13829),c_Product__Type_Ofst(U_13826,U_13827)),c_Product__Type_Omap__pair(U_13828,U_13826,U_13829,U_13827,U_13830,U_13831)) = hAPP(c_Fun_Ocomp(U_13828,U_13826,tc_prod(U_13828,U_13829),U_13830),c_Product__Type_Ofst(U_13828,U_13829)),
    inference(clausify,[status(thm)],[f_3528_2]) ).

fof(f_3529_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_3529_2,plain,
    ! [U_13837,U_13836,U_13835,U_13834,U_13833,U_13832] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13832,tc_fun(U_13833,tc_HOL_Obool)),U_13834),hAPP(c_Fun_Ocomp(U_13835,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13836),U_13837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13835,tc_fun(U_13833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13832,U_13835,U_13837),U_13834)),U_13836),
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

cnf(f_3529_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13832,tc_fun(U_13833,tc_HOL_Obool)),U_13834),hAPP(c_Fun_Ocomp(U_13835,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13836),U_13837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13835,tc_fun(U_13833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13832,U_13835,U_13837),U_13834)),U_13836),
    inference(clausify,[status(thm)],[f_3529_2]) ).

fof(f_3530_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_3530_2,plain,
    ! [U_13843,U_13842,U_13841,U_13840,U_13839,U_13838] : hAPP(c_Fun_Ocomp(tc_prod(U_13838,U_13839),U_13839,tc_prod(U_13840,U_13841),c_Product__Type_Osnd(U_13838,U_13839)),c_Product__Type_Omap__pair(U_13840,U_13838,U_13841,U_13839,U_13842,U_13843)) = hAPP(c_Fun_Ocomp(U_13841,U_13839,tc_prod(U_13840,U_13841),U_13843),c_Product__Type_Osnd(U_13840,U_13841)),
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

cnf(f_3530_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_13838,U_13839),U_13839,tc_prod(U_13840,U_13841),c_Product__Type_Osnd(U_13838,U_13839)),c_Product__Type_Omap__pair(U_13840,U_13838,U_13841,U_13839,U_13842,U_13843)) = hAPP(c_Fun_Ocomp(U_13841,U_13839,tc_prod(U_13840,U_13841),U_13843),c_Product__Type_Osnd(U_13840,U_13841)),
    inference(clausify,[status(thm)],[f_3530_2]) ).

fof(f_3531_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_3531_2,plain,
    ! [U_13851,U_13850,U_13849,U_13848,U_13847,U_13846,U_13845,U_13844] :
      ( hAPP(hAPP(U_13848,hAPP(hAPP(c_COMBS(U_13845,U_13844,U_13844),hAPP(hAPP(c_COMBB(U_13844,tc_fun(U_13844,U_13844),U_13845),U_13846),U_13850)),U_13851)),U_13849) = hAPP(hAPP(U_13846,hAPP(hAPP(U_13848,U_13850),U_13849)),hAPP(hAPP(U_13848,U_13851),U_13849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13845),U_13849))
      | ~ c_Finite__Set_Ofolding__image(U_13844,U_13845,U_13846,U_13847,U_13848) ),
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

cnf(f_3531_3,plain,
    ( hAPP(hAPP(U_13848,hAPP(hAPP(c_COMBS(U_13845,U_13844,U_13844),hAPP(hAPP(c_COMBB(U_13844,tc_fun(U_13844,U_13844),U_13845),U_13846),U_13850)),U_13851)),U_13849) = hAPP(hAPP(U_13846,hAPP(hAPP(U_13848,U_13850),U_13849)),hAPP(hAPP(U_13848,U_13851),U_13849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13845),U_13849))
    | ~ c_Finite__Set_Ofolding__image(U_13844,U_13845,U_13846,U_13847,U_13848) ),
    inference(clausify,[status(thm)],[f_3531_2]) ).

fof(f_3532_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_3532_2,plain,
    ! [U_13858,U_13857,U_13856,U_13855,U_13854,U_13853,U_13852] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13852,U_13853,U_13854),hAPP(c_Fun_Ocomp(U_13855,tc_fun(U_13853,U_13854),U_13852,U_13856),U_13857)),U_13858) = hAPP(hAPP(U_13856,hAPP(U_13857,hAPP(c_Product__Type_Ofst(U_13852,U_13853),U_13858))),hAPP(c_Product__Type_Osnd(U_13852,U_13853),U_13858)),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

cnf(f_3532_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13852,U_13853,U_13854),hAPP(c_Fun_Ocomp(U_13855,tc_fun(U_13853,U_13854),U_13852,U_13856),U_13857)),U_13858) = hAPP(hAPP(U_13856,hAPP(U_13857,hAPP(c_Product__Type_Ofst(U_13852,U_13853),U_13858))),hAPP(c_Product__Type_Osnd(U_13852,U_13853),U_13858)),
    inference(clausify,[status(thm)],[f_3532_2]) ).

fof(f_3533_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_3533_2,plain,
    ! [U_13864,U_13863,U_13862,U_13861,U_13860,U_13859] :
      ( hAPP(c_Fun_Ocomp(U_13860,U_13860,U_13860,hAPP(U_13861,U_13864)),hAPP(U_13862,U_13863)) = hAPP(c_Fun_Ocomp(U_13860,U_13860,U_13860,hAPP(U_13862,U_13863)),hAPP(U_13861,U_13864))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13859),U_13863))
      | ~ c_Finite__Set_Ofolding(U_13859,U_13860,U_13861,U_13862) ),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

cnf(f_3533_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13860,U_13860,U_13860,hAPP(U_13861,U_13864)),hAPP(U_13862,U_13863)) = hAPP(c_Fun_Ocomp(U_13860,U_13860,U_13860,hAPP(U_13862,U_13863)),hAPP(U_13861,U_13864))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13859),U_13863))
    | ~ c_Finite__Set_Ofolding(U_13859,U_13860,U_13861,U_13862) ),
    inference(clausify,[status(thm)],[f_3533_2]) ).

fof(f_3534_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_3534_2,plain,
    ! [U_13872,U_13871,U_13870,U_13869,U_13868,U_13867,U_13866,U_13865] :
      ( hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13867,U_13871)),hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13868,U_13869)),U_13872)) = hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13868,U_13869)),hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13867,U_13871)),U_13872))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13865),U_13869))
      | ~ c_Finite__Set_Ofolding(U_13865,U_13866,U_13867,U_13868) ),
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

cnf(f_3534_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13867,U_13871)),hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13868,U_13869)),U_13872)) = hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13868,U_13869)),hAPP(c_Fun_Ocomp(U_13866,U_13866,U_13870,hAPP(U_13867,U_13871)),U_13872))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13865),U_13869))
    | ~ c_Finite__Set_Ofolding(U_13865,U_13866,U_13867,U_13868) ),
    inference(clausify,[status(thm)],[f_3534_2]) ).

fof(f_3535_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_3535_2,plain,
    ! [U_13878,U_13877,U_13876,U_13875,U_13874,U_13873] :
      ( hAPP(c_Fun_Ocomp(U_13874,U_13874,U_13874,hAPP(U_13876,U_13878)),hAPP(U_13876,U_13877)) = hAPP(c_Fun_Ocomp(U_13874,U_13874,U_13874,hAPP(U_13876,U_13877)),hAPP(U_13876,U_13878))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13873),U_13878))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13873),U_13877))
      | ~ c_Finite__Set_Ofolding(U_13873,U_13874,U_13875,U_13876) ),
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

cnf(f_3535_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13874,U_13874,U_13874,hAPP(U_13876,U_13878)),hAPP(U_13876,U_13877)) = hAPP(c_Fun_Ocomp(U_13874,U_13874,U_13874,hAPP(U_13876,U_13877)),hAPP(U_13876,U_13878))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13873),U_13878))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13873),U_13877))
    | ~ c_Finite__Set_Ofolding(U_13873,U_13874,U_13875,U_13876) ),
    inference(clausify,[status(thm)],[f_3535_2]) ).

fof(f_3536_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_3536_2,plain,
    ! [U_13886,U_13885,U_13884,U_13883,U_13882,U_13881,U_13880,U_13879] :
      ( hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13884)),hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13883)),U_13886)) = hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13883)),hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13884)),U_13886))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13879),U_13884))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13879),U_13883))
      | ~ c_Finite__Set_Ofolding(U_13879,U_13880,U_13881,U_13882) ),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

cnf(f_3536_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13884)),hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13883)),U_13886)) = hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13883)),hAPP(c_Fun_Ocomp(U_13880,U_13880,U_13885,hAPP(U_13882,U_13884)),U_13886))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13879),U_13884))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13879),U_13883))
    | ~ c_Finite__Set_Ofolding(U_13879,U_13880,U_13881,U_13882) ),
    inference(clausify,[status(thm)],[f_3536_2]) ).

fof(f_3537_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_3537_2,plain,
    ! [U_13890,U_13889,U_13888,U_13887] :
      ( hAPP(U_13890,c_Orderings_Obot__class_Obot(tc_fun(U_13887,tc_HOL_Obool))) = c_Fun_Oid(U_13888)
      | ~ c_Finite__Set_Ofolding(U_13887,U_13888,U_13889,U_13890) ),
    inference(variable_rename,[status(thm)],[f_3537_1]) ).

cnf(f_3537_3,plain,
    ( hAPP(U_13890,c_Orderings_Obot__class_Obot(tc_fun(U_13887,tc_HOL_Obool))) = c_Fun_Oid(U_13888)
    | ~ c_Finite__Set_Ofolding(U_13887,U_13888,U_13889,U_13890) ),
    inference(clausify,[status(thm)],[f_3537_2]) ).

fof(f_3538_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_3538_2,plain,
    ! [U_13896,U_13895,U_13894,U_13893,U_13892,U_13891] :
      ( hAPP(hAPP(U_13894,U_13895),U_13896) = hAPP(hAPP(c_Finite__Set_Ofold(U_13891,U_13892,U_13893),U_13896),U_13895)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13891),U_13895))
      | ~ c_Finite__Set_Ofolding(U_13891,U_13892,U_13893,U_13894) ),
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

cnf(f_3538_3,plain,
    ( hAPP(hAPP(U_13894,U_13895),U_13896) = hAPP(hAPP(c_Finite__Set_Ofold(U_13891,U_13892,U_13893),U_13896),U_13895)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13891),U_13895))
    | ~ c_Finite__Set_Ofolding(U_13891,U_13892,U_13893,U_13894) ),
    inference(clausify,[status(thm)],[f_3538_2]) ).

fof(f_3539_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_3539_2,plain,
    ! [U_13903,U_13902,U_13901,U_13900,U_13899,U_13898,U_13897] :
      ( hAPP(hAPP(U_13901,U_13903),U_13902) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13897,U_13898,U_13899),U_13903),U_13900),U_13902)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13898),U_13902))
      | ~ c_Finite__Set_Ofolding__image(U_13897,U_13898,U_13899,U_13900,U_13901) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

cnf(f_3539_3,plain,
    ( hAPP(hAPP(U_13901,U_13903),U_13902) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13897,U_13898,U_13899),U_13903),U_13900),U_13902)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13898),U_13902))
    | ~ c_Finite__Set_Ofolding__image(U_13897,U_13898,U_13899,U_13900,U_13901) ),
    inference(clausify,[status(thm)],[f_3539_2]) ).

fof(f_3540_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_3540_2,plain,
    ! [U_13909,U_13908,U_13907,U_13906,U_13905,U_13904] :
      ( hAPP(U_13907,hAPP(hAPP(c_Set_Oinsert(U_13904),U_13909),U_13908)) = hAPP(c_Fun_Ocomp(U_13905,U_13905,U_13905,hAPP(U_13907,U_13908)),hAPP(U_13906,U_13909))
      | hBOOL(hAPP(hAPP(c_member(U_13904),U_13909),U_13908))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13904),U_13908))
      | ~ c_Finite__Set_Ofolding(U_13904,U_13905,U_13906,U_13907) ),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

cnf(f_3540_3,plain,
    ( hAPP(U_13907,hAPP(hAPP(c_Set_Oinsert(U_13904),U_13909),U_13908)) = hAPP(c_Fun_Ocomp(U_13905,U_13905,U_13905,hAPP(U_13907,U_13908)),hAPP(U_13906,U_13909))
    | hBOOL(hAPP(hAPP(c_member(U_13904),U_13909),U_13908))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13904),U_13908))
    | ~ c_Finite__Set_Ofolding(U_13904,U_13905,U_13906,U_13907) ),
    inference(clausify,[status(thm)],[f_3540_2]) ).

fof(f_3541_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_3541_2,plain,
    ! [U_13915,U_13914,U_13913,U_13912,U_13911,U_13910] :
      ( hAPP(c_Fun_Ocomp(U_13911,U_13911,U_13911,hAPP(U_13913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13910,tc_HOL_Obool)),U_13914),U_13915))),hAPP(U_13913,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13910,tc_HOL_Obool)),U_13914),U_13915))) = hAPP(c_Fun_Ocomp(U_13911,U_13911,U_13911,hAPP(U_13913,U_13914)),hAPP(U_13913,U_13915))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13910),U_13915))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13910),U_13914))
      | ~ c_Finite__Set_Ofolding(U_13910,U_13911,U_13912,U_13913) ),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

cnf(f_3541_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13911,U_13911,U_13911,hAPP(U_13913,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13910,tc_HOL_Obool)),U_13914),U_13915))),hAPP(U_13913,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13910,tc_HOL_Obool)),U_13914),U_13915))) = hAPP(c_Fun_Ocomp(U_13911,U_13911,U_13911,hAPP(U_13913,U_13914)),hAPP(U_13913,U_13915))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13910),U_13915))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13910),U_13914))
    | ~ c_Finite__Set_Ofolding(U_13910,U_13911,U_13912,U_13913) ),
    inference(clausify,[status(thm)],[f_3541_2]) ).

fof(f_3542_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_3542_2,plain,
    ! [U_13921,U_13920,U_13919,U_13918,U_13917,U_13916] :
      ( hAPP(U_13919,hAPP(hAPP(c_Set_Oinsert(U_13916),U_13921),U_13920)) = hAPP(c_Fun_Ocomp(U_13917,U_13917,U_13917,hAPP(U_13919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),U_13920),hAPP(hAPP(c_Set_Oinsert(U_13916),U_13921),c_Orderings_Obot__class_Obot(tc_fun(U_13916,tc_HOL_Obool)))))),hAPP(U_13918,U_13921))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13916),U_13920))
      | ~ c_Finite__Set_Ofolding(U_13916,U_13917,U_13918,U_13919) ),
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

cnf(f_3542_3,plain,
    ( hAPP(U_13919,hAPP(hAPP(c_Set_Oinsert(U_13916),U_13921),U_13920)) = hAPP(c_Fun_Ocomp(U_13917,U_13917,U_13917,hAPP(U_13919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13916,tc_HOL_Obool)),U_13920),hAPP(hAPP(c_Set_Oinsert(U_13916),U_13921),c_Orderings_Obot__class_Obot(tc_fun(U_13916,tc_HOL_Obool)))))),hAPP(U_13918,U_13921))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13916),U_13920))
    | ~ c_Finite__Set_Ofolding(U_13916,U_13917,U_13918,U_13919) ),
    inference(clausify,[status(thm)],[f_3542_2]) ).

fof(f_3543_1,plain,
    ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2),V_Qa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)),V_d_2,V_Qa_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Qa_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_OIf]) ).

fof(f_3543_2,plain,
    ! [U_13928,U_13927,U_13926,U_13925,U_13924,U_13923,U_13922] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,U_13924,c_Com_Ocom_OCond(U_13925,U_13926,U_13928),U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,c_Hoare__Mirabelle_Opeek__and(U_13922,U_13924,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13925)),U_13928,U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,c_Hoare__Mirabelle_Opeek__and(U_13922,U_13924,U_13925),U_13926,U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

cnf(f_3543_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,U_13924,c_Com_Ocom_OCond(U_13925,U_13926,U_13928),U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,c_Hoare__Mirabelle_Opeek__and(U_13922,U_13924,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13925)),U_13928,U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13922,U_13923,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13922)),c_Hoare__Mirabelle_Otriple_Otriple(U_13922,c_Hoare__Mirabelle_Opeek__and(U_13922,U_13924,U_13925),U_13926,U_13927)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13922),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3543_2]) ).

fof(f_3544_1,plain,
    ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OWhile(V_b_2,V_ca_2),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_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_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2),V_ca_2,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_Loop]) ).

fof(f_3544_2,plain,
    ! [U_13933,U_13932,U_13931,U_13930,U_13929] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13929,U_13930,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13929)),c_Hoare__Mirabelle_Otriple_Otriple(U_13929,U_13931,c_Com_Ocom_OWhile(U_13932,U_13933),c_Hoare__Mirabelle_Opeek__and(U_13929,U_13931,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13932)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13929),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13929,U_13930,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13929)),c_Hoare__Mirabelle_Otriple_Otriple(U_13929,c_Hoare__Mirabelle_Opeek__and(U_13929,U_13931,U_13932),U_13933,U_13931)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13929),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

cnf(f_3544_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_13929,U_13930,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13929)),c_Hoare__Mirabelle_Otriple_Otriple(U_13929,U_13931,c_Com_Ocom_OWhile(U_13932,U_13933),c_Hoare__Mirabelle_Opeek__and(U_13929,U_13931,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13932)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13929),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13929,U_13930,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13929)),c_Hoare__Mirabelle_Otriple_Otriple(U_13929,c_Hoare__Mirabelle_Opeek__and(U_13929,U_13931,U_13932),U_13933,U_13931)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13929),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3544_2]) ).

fof(f_3545_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_3545_2,plain,
    ! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
      | ? [U_13935] :
          ( ? [U_13934] :
              ( hAPP(U_13940,hAPP(U_13939,U_13935)) != c_Groups_Ozero__class_Ozero(U_13936)
              & hAPP(U_13939,U_13935) = hAPP(U_13939,U_13934)
              & U_13935 != U_13934
              & hBOOL(hAPP(hAPP(c_member(U_13937),U_13934),U_13938)) )
          & hBOOL(hAPP(hAPP(c_member(U_13937),U_13935),U_13938)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
      | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(variable_rename,[status(thm)],[f_3545_1]) ).

fof(f_3545_3,plain,
    ! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
      | ( ? [U_13934] :
            ( hAPP(U_13940,hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))) != c_Groups_Ozero__class_Ozero(U_13936)
            & hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)) = hAPP(U_13939,U_13934)
            & sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936) != U_13934
            & hBOOL(hAPP(hAPP(c_member(U_13937),U_13934),U_13938)) )
        & hBOOL(hAPP(hAPP(c_member(U_13937),sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13938)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
      | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_13935,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))],[f_3545_2]) ).

fof(f_3545_4,plain,
    ! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
      | ( hAPP(U_13940,hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))) != c_Groups_Ozero__class_Ozero(U_13936)
        & hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)) = hAPP(U_13939,sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))
        & sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936) != sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)
        & hBOOL(hAPP(hAPP(c_member(U_13937),sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13938))
        & hBOOL(hAPP(hAPP(c_member(U_13937),sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13938)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
      | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_13934,sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))],[f_3545_3]) ).

cnf(f_3545_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13937),sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13938))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
    | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(clausify,[status(thm)],[f_3545_4]) ).

cnf(f_3545_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13937),sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13938))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
    | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(clausify,[status(thm)],[f_3545_4]) ).

cnf(f_3545_7,plain,
    ( sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936) != sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
    | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(clausify,[status(thm)],[f_3545_4]) ).

cnf(f_3545_8,plain,
    ( hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)) = hAPP(U_13939,sK338(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
    | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(clausify,[status(thm)],[f_3545_4]) ).

cnf(f_3545_9,plain,
    ( hAPP(U_13940,hAPP(U_13939,sK337(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))) != c_Groups_Ozero__class_Ozero(U_13936)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13941,U_13936),U_13940),hAPP(c_Set_Oimage(U_13937,U_13941,U_13939),U_13938)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13937,U_13936),hAPP(c_Fun_Ocomp(U_13941,U_13936,U_13937,U_13940),U_13939)),U_13938)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13937),U_13938))
    | ~ class_Groups_Ocomm__monoid__add(U_13936) ),
    inference(clausify,[status(thm)],[f_3545_4]) ).

fof(f_3546_1,plain,
    ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
        | ~ hBOOL(hAPP(V_p_2,V_s_2))
        | ~ hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) )
      & ( ( hBOOL(hAPP(V_p_2,V_s_2))
          & hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_peek__and__def]) ).

fof(f_3546_2,plain,
    ! [U_13946,U_13945,U_13944,U_13943,U_13942] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13942,U_13943,U_13944),U_13945),U_13946))
        | ~ hBOOL(hAPP(U_13944,U_13946))
        | ~ hBOOL(hAPP(hAPP(U_13943,U_13945),U_13946)) )
      & ( ( hBOOL(hAPP(U_13944,U_13946))
          & hBOOL(hAPP(hAPP(U_13943,U_13945),U_13946)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13942,U_13943,U_13944),U_13945),U_13946)) ) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

fof(f_3546_3,plain,
    ( ! [U_13956,U_13954,U_13952,U_13950] :
        ( ! [U_13948] : hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13948,U_13950,U_13952),U_13954),U_13956))
        | ~ hBOOL(hAPP(U_13952,U_13956))
        | ~ hBOOL(hAPP(hAPP(U_13950,U_13954),U_13956)) )
    & ! [U_13955,U_13953,U_13951,U_13949] :
        ( ! [U_13947] : ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13947,U_13949,U_13951),U_13953),U_13955))
        | ( hBOOL(hAPP(U_13951,U_13955))
          & hBOOL(hAPP(hAPP(U_13949,U_13953),U_13955)) ) ) ),
    inference(miniscope,[status(thm)],[f_3546_2]) ).

cnf(f_3546_4,plain,
    ( hBOOL(hAPP(hAPP(U_13949,U_13953),U_13955))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13947,U_13949,U_13951),U_13953),U_13955)) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

cnf(f_3546_5,plain,
    ( hBOOL(hAPP(U_13951,U_13955))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13947,U_13949,U_13951),U_13953),U_13955)) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

cnf(f_3546_6,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13948,U_13950,U_13952),U_13954),U_13956))
    | ~ hBOOL(hAPP(U_13952,U_13956))
    | ~ hBOOL(hAPP(hAPP(U_13950,U_13954),U_13956)) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

fof(f_3547_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_3547_2,plain,
    ! [U_13962,U_13961,U_13960,U_13959,U_13958,U_13957] :
      ( hAPP(U_13960,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13957,tc_HOL_Obool)),U_13961),U_13962)) = hAPP(c_Fun_Ocomp(U_13958,U_13958,U_13958,hAPP(U_13960,U_13961)),hAPP(U_13960,U_13962))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13957),U_13962))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13957),U_13961))
      | ~ c_Finite__Set_Ofolding__idem(U_13957,U_13958,U_13959,U_13960) ),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

cnf(f_3547_3,plain,
    ( hAPP(U_13960,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13957,tc_HOL_Obool)),U_13961),U_13962)) = hAPP(c_Fun_Ocomp(U_13958,U_13958,U_13958,hAPP(U_13960,U_13961)),hAPP(U_13960,U_13962))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13957),U_13962))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13957),U_13961))
    | ~ c_Finite__Set_Ofolding__idem(U_13957,U_13958,U_13959,U_13960) ),
    inference(clausify,[status(thm)],[f_3547_2]) ).

fof(f_3548_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_3548_2,plain,
    ! [U_13968,U_13967,U_13966,U_13965,U_13964,U_13963] :
      ( hAPP(c_Fun_Ocomp(U_13964,U_13964,U_13964,hAPP(U_13966,U_13967)),hAPP(U_13966,U_13968)) = hAPP(U_13966,U_13967)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13963,tc_HOL_Obool)),U_13968),U_13967))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13963),U_13967))
      | ~ c_Finite__Set_Ofolding__idem(U_13963,U_13964,U_13965,U_13966) ),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

cnf(f_3548_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13964,U_13964,U_13964,hAPP(U_13966,U_13967)),hAPP(U_13966,U_13968)) = hAPP(U_13966,U_13967)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13963,tc_HOL_Obool)),U_13968),U_13967))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13963),U_13967))
    | ~ c_Finite__Set_Ofolding__idem(U_13963,U_13964,U_13965,U_13966) ),
    inference(clausify,[status(thm)],[f_3548_2]) ).

fof(f_3549_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_3549_2,plain,
    ! [U_13974,U_13973,U_13972,U_13971,U_13970,U_13969] :
      ( hAPP(U_13972,hAPP(hAPP(c_Set_Oinsert(U_13969),U_13974),U_13973)) = hAPP(c_Fun_Ocomp(U_13970,U_13970,U_13970,hAPP(U_13972,U_13973)),hAPP(U_13971,U_13974))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13969),U_13973))
      | ~ c_Finite__Set_Ofolding__idem(U_13969,U_13970,U_13971,U_13972) ),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

cnf(f_3549_3,plain,
    ( hAPP(U_13972,hAPP(hAPP(c_Set_Oinsert(U_13969),U_13974),U_13973)) = hAPP(c_Fun_Ocomp(U_13970,U_13970,U_13970,hAPP(U_13972,U_13973)),hAPP(U_13971,U_13974))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13969),U_13973))
    | ~ c_Finite__Set_Ofolding__idem(U_13969,U_13970,U_13971,U_13972) ),
    inference(clausify,[status(thm)],[f_3549_2]) ).

fof(f_3550_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_3550_2,plain,
    ! [U_13981,U_13980,U_13979,U_13978,U_13977,U_13976,U_13975] :
      ( hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981)) = hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981)
      | ~ c_Finite__Set_Ofolding__idem(U_13975,U_13976,U_13977,U_13978) ),
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

fof(f_3550_3,plain,
    ! [U_13981,U_13980,U_13979,U_13978,U_13977,U_13976] :
      ( ! [U_13975] : ~ c_Finite__Set_Ofolding__idem(U_13975,U_13976,U_13977,U_13978)
      | hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981)) = hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981) ),
    inference(miniscope,[status(thm)],[f_3550_2]) ).

cnf(f_3550_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_13975,U_13976,U_13977,U_13978)
    | hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981)) = hAPP(c_Fun_Ocomp(U_13976,U_13976,U_13979,hAPP(U_13977,U_13980)),U_13981) ),
    inference(clausify,[status(thm)],[f_3550_3]) ).

fof(f_3551_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_3551_2,plain,
    ! [U_13986,U_13985,U_13984,U_13983,U_13982] :
      ( hAPP(c_Fun_Ocomp(U_13983,U_13983,U_13983,hAPP(U_13984,U_13986)),hAPP(U_13984,U_13986)) = hAPP(U_13984,U_13986)
      | ~ c_Finite__Set_Ofolding__idem(U_13982,U_13983,U_13984,U_13985) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

fof(f_3551_3,plain,
    ! [U_13986,U_13985,U_13984,U_13983] :
      ( ! [U_13982] : ~ c_Finite__Set_Ofolding__idem(U_13982,U_13983,U_13984,U_13985)
      | hAPP(c_Fun_Ocomp(U_13983,U_13983,U_13983,hAPP(U_13984,U_13986)),hAPP(U_13984,U_13986)) = hAPP(U_13984,U_13986) ),
    inference(miniscope,[status(thm)],[f_3551_2]) ).

cnf(f_3551_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_13982,U_13983,U_13984,U_13985)
    | hAPP(c_Fun_Ocomp(U_13983,U_13983,U_13983,hAPP(U_13984,U_13986)),hAPP(U_13984,U_13986)) = hAPP(U_13984,U_13986) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

fof(f_3552_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_3552_2,plain,
    ! [U_13992,U_13991,U_13990,U_13989,U_13988,U_13987] :
      ( hAPP(c_Fun_Ocomp(U_13988,U_13988,U_13988,hAPP(U_13990,U_13991)),hAPP(U_13989,U_13992)) = hAPP(U_13990,U_13991)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13992),U_13991))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
      | ~ c_Finite__Set_Ofolding__idem(U_13987,U_13988,U_13989,U_13990) ),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

cnf(f_3552_3,plain,
    ( hAPP(c_Fun_Ocomp(U_13988,U_13988,U_13988,hAPP(U_13990,U_13991)),hAPP(U_13989,U_13992)) = hAPP(U_13990,U_13991)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13992),U_13991))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
    | ~ c_Finite__Set_Ofolding__idem(U_13987,U_13988,U_13989,U_13990) ),
    inference(clausify,[status(thm)],[f_3552_2]) ).

fof(f_3553_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_3553_2,plain,
    ! [U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13996,U_13994),U_14001),U_13999) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13995,U_13994),U_14000),U_13998)
      | ? [U_13993] :
          ( hAPP(U_14000,U_13993) != hAPP(hAPP(c_Fun_Ocomp(U_13996,U_13994,U_13995,U_14001),U_13997),U_13993)
          & hBOOL(hAPP(hAPP(c_member(U_13995),U_13993),U_13998)) )
      | U_13999 != hAPP(c_Set_Oimage(U_13995,U_13996,U_13997),U_13998)
      | ~ c_Fun_Oinj__on(U_13995,U_13996,U_13997,U_13998)
      | ~ class_Groups_Ocomm__monoid__mult(U_13994) ),
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

fof(f_3553_3,plain,
    ! [U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13996,U_13994),U_14001),U_13999) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13995,U_13994),U_14000),U_13998)
      | ( hAPP(U_14000,sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994)) != hAPP(hAPP(c_Fun_Ocomp(U_13996,U_13994,U_13995,U_14001),U_13997),sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994))
        & hBOOL(hAPP(hAPP(c_member(U_13995),sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994)),U_13998)) )
      | U_13999 != hAPP(c_Set_Oimage(U_13995,U_13996,U_13997),U_13998)
      | ~ c_Fun_Oinj__on(U_13995,U_13996,U_13997,U_13998)
      | ~ class_Groups_Ocomm__monoid__mult(U_13994) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_13993,sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994))],[f_3553_2]) ).

cnf(f_3553_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13995),sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994)),U_13998))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13996,U_13994),U_14001),U_13999) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13995,U_13994),U_14000),U_13998)
    | U_13999 != hAPP(c_Set_Oimage(U_13995,U_13996,U_13997),U_13998)
    | ~ c_Fun_Oinj__on(U_13995,U_13996,U_13997,U_13998)
    | ~ class_Groups_Ocomm__monoid__mult(U_13994) ),
    inference(clausify,[status(thm)],[f_3553_3]) ).

cnf(f_3553_5,plain,
    ( hAPP(U_14000,sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994)) != hAPP(hAPP(c_Fun_Ocomp(U_13996,U_13994,U_13995,U_14001),U_13997),sK339(U_14001,U_14000,U_13999,U_13998,U_13997,U_13996,U_13995,U_13994))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13996,U_13994),U_14001),U_13999) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13995,U_13994),U_14000),U_13998)
    | U_13999 != hAPP(c_Set_Oimage(U_13995,U_13996,U_13997),U_13998)
    | ~ c_Fun_Oinj__on(U_13995,U_13996,U_13997,U_13998)
    | ~ class_Groups_Ocomm__monoid__mult(U_13994) ),
    inference(clausify,[status(thm)],[f_3553_3]) ).

fof(f_3554_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_3554_2,plain,
    ! [U_14004,U_14003,U_14002] : c_Hilbert__Choice_OEps(tc_prod(U_14002,U_14003),hAPP(c_Product__Type_Oprod_Oprod__case(U_14002,U_14003,tc_HOL_Obool),U_14004)) = c_Hilbert__Choice_OEps(tc_prod(U_14002,U_14003),hAPP(hAPP(c_COMBS(tc_prod(U_14002,U_14003),U_14003,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14002,tc_fun(U_14003,tc_HOL_Obool),tc_prod(U_14002,U_14003)),U_14004),c_Product__Type_Ofst(U_14002,U_14003))),c_Product__Type_Osnd(U_14002,U_14003))),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

cnf(f_3554_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14002,U_14003),hAPP(c_Product__Type_Oprod_Oprod__case(U_14002,U_14003,tc_HOL_Obool),U_14004)) = c_Hilbert__Choice_OEps(tc_prod(U_14002,U_14003),hAPP(hAPP(c_COMBS(tc_prod(U_14002,U_14003),U_14003,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14002,tc_fun(U_14003,tc_HOL_Obool),tc_prod(U_14002,U_14003)),U_14004),c_Product__Type_Ofst(U_14002,U_14003))),c_Product__Type_Osnd(U_14002,U_14003))),
    inference(clausify,[status(thm)],[f_3554_2]) ).

fof(f_3555_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_3555_2,plain,
    ! [U_14007,U_14006] :
      ( c_Wellfounded_Owf(U_14006,U_14007)
      | ? [U_14005] :
          ( U_14005 != c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14006,tc_HOL_Obool)),U_14005),hAPP(c_Relation_OImage(U_14006,U_14006,U_14007),U_14005))) ) ),
    inference(variable_rename,[status(thm)],[f_3555_1]) ).

fof(f_3555_3,plain,
    ! [U_14007,U_14006] :
      ( c_Wellfounded_Owf(U_14006,U_14007)
      | ( sK340(U_14007,U_14006) != c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14006,tc_HOL_Obool)),sK340(U_14007,U_14006)),hAPP(c_Relation_OImage(U_14006,U_14006,U_14007),sK340(U_14007,U_14006)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_14005,sK340(U_14007,U_14006))],[f_3555_2]) ).

cnf(f_3555_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14006,tc_HOL_Obool)),sK340(U_14007,U_14006)),hAPP(c_Relation_OImage(U_14006,U_14006,U_14007),sK340(U_14007,U_14006))))
    | c_Wellfounded_Owf(U_14006,U_14007) ),
    inference(clausify,[status(thm)],[f_3555_3]) ).

cnf(f_3555_5,plain,
    ( sK340(U_14007,U_14006) != c_Orderings_Obot__class_Obot(tc_fun(U_14006,tc_HOL_Obool))
    | c_Wellfounded_Owf(U_14006,U_14007) ),
    inference(clausify,[status(thm)],[f_3555_3]) ).

fof(f_3556_1,plain,
    ! [T_b,V_ca_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_ca_2))
      | V_ca_2 != c_Hilbert__Choice_OEps(T_b,V_Pa_2)
      | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_exE__some]) ).

fof(f_3556_2,plain,
    ! [U_14011,U_14010,U_14009] :
      ( hBOOL(hAPP(U_14009,U_14010))
      | U_14010 != c_Hilbert__Choice_OEps(U_14011,U_14009)
      | ! [U_14008] : ~ hBOOL(hAPP(U_14009,U_14008)) ),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

cnf(f_3556_3,plain,
    ( hBOOL(hAPP(U_14009,U_14010))
    | U_14010 != c_Hilbert__Choice_OEps(U_14011,U_14009)
    | ~ hBOOL(hAPP(U_14009,U_14008)) ),
    inference(clausify,[status(thm)],[f_3556_2]) ).

fof(f_3557_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_3557_2,plain,
    ! [U_14013,U_14012] : c_Hilbert__Choice_OEps(U_14012,hAPP(c_fequal,U_14013)) = U_14013,
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

cnf(f_3557_3,plain,
    c_Hilbert__Choice_OEps(U_14012,hAPP(c_fequal,U_14013)) = U_14013,
    inference(clausify,[status(thm)],[f_3557_2]) ).

fof(f_3558_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_3558_2,plain,
    ! [U_14015,U_14014] : c_Hilbert__Choice_OEps(U_14014,hAPP(hAPP(c_COMBC(U_14014,U_14014,tc_HOL_Obool),c_fequal),U_14015)) = U_14015,
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

cnf(f_3558_3,plain,
    c_Hilbert__Choice_OEps(U_14014,hAPP(hAPP(c_COMBC(U_14014,U_14014,tc_HOL_Obool),c_fequal),U_14015)) = U_14015,
    inference(clausify,[status(thm)],[f_3558_2]) ).

fof(f_3559_1,plain,
    ! [T_b,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
        | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ~ hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).

fof(f_3559_2,plain,
    ! [U_14019,U_14018] :
      ( ( hBOOL(hAPP(U_14018,c_Hilbert__Choice_OEps(U_14019,U_14018)))
        | ! [U_14017] : ~ hBOOL(hAPP(U_14018,U_14017)) )
      & ( ? [U_14016] : hBOOL(hAPP(U_14018,U_14016))
        | ~ hBOOL(hAPP(U_14018,c_Hilbert__Choice_OEps(U_14019,U_14018))) ) ),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

fof(f_3559_3,plain,
    ( ! [U_14023,U_14021] :
        ( hBOOL(hAPP(U_14021,c_Hilbert__Choice_OEps(U_14023,U_14021)))
        | ! [U_14017] : ~ hBOOL(hAPP(U_14021,U_14017)) )
    & ! [U_14022,U_14020] :
        ( ? [U_14016] : hBOOL(hAPP(U_14020,U_14016))
        | ~ hBOOL(hAPP(U_14020,c_Hilbert__Choice_OEps(U_14022,U_14020))) ) ),
    inference(miniscope,[status(thm)],[f_3559_2]) ).

fof(f_3559_4,plain,
    ( ! [U_14023,U_14021] :
        ( hBOOL(hAPP(U_14021,c_Hilbert__Choice_OEps(U_14023,U_14021)))
        | ! [U_14017] : ~ hBOOL(hAPP(U_14021,U_14017)) )
    & ! [U_14022,U_14020] :
        ( hBOOL(hAPP(U_14020,sK341(U_14022,U_14020)))
        | ~ hBOOL(hAPP(U_14020,c_Hilbert__Choice_OEps(U_14022,U_14020))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_14016,sK341(U_14022,U_14020))],[f_3559_3]) ).

cnf(f_3559_5,plain,
    ( hBOOL(hAPP(U_14020,sK341(U_14022,U_14020)))
    | ~ hBOOL(hAPP(U_14020,c_Hilbert__Choice_OEps(U_14022,U_14020))) ),
    inference(clausify,[status(thm)],[f_3559_4]) ).

cnf(f_3559_6,plain,
    ( hBOOL(hAPP(U_14021,c_Hilbert__Choice_OEps(U_14023,U_14021)))
    | ~ hBOOL(hAPP(U_14021,U_14017)) ),
    inference(clausify,[status(thm)],[f_3559_4]) ).

fof(f_3560_1,plain,
    ! [T_b,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).

fof(f_3560_2,plain,
    ! [U_14026,U_14025] :
      ( hBOOL(hAPP(U_14025,c_Hilbert__Choice_OEps(U_14026,U_14025)))
      | ! [U_14024] : ~ hBOOL(hAPP(U_14025,U_14024)) ),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

cnf(f_3560_3,plain,
    ( hBOOL(hAPP(U_14025,c_Hilbert__Choice_OEps(U_14026,U_14025)))
    | ~ hBOOL(hAPP(U_14025,U_14024)) ),
    inference(clausify,[status(thm)],[f_3560_2]) ).

fof(f_3561_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_3561_2,plain,
    ! [U_14029,U_14028] :
      ( hBOOL(hAPP(U_14028,c_Hilbert__Choice_OEps(U_14029,U_14028)))
      | ! [U_14027] : ~ hBOOL(hAPP(U_14028,U_14027)) ),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

cnf(f_3561_3,plain,
    ( hBOOL(hAPP(U_14028,c_Hilbert__Choice_OEps(U_14029,U_14028)))
    | ~ hBOOL(hAPP(U_14028,U_14027)) ),
    inference(clausify,[status(thm)],[f_3561_2]) ).

fof(f_3562_1,plain,
    ! [T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_someI]) ).

fof(f_3562_2,plain,
    ! [U_14032,U_14031,U_14030] :
      ( hBOOL(hAPP(U_14030,c_Hilbert__Choice_OEps(U_14032,U_14030)))
      | ~ hBOOL(hAPP(U_14030,U_14031)) ),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

cnf(f_3562_3,plain,
    ( hBOOL(hAPP(U_14030,c_Hilbert__Choice_OEps(U_14032,U_14030)))
    | ~ hBOOL(hAPP(U_14030,U_14031)) ),
    inference(clausify,[status(thm)],[f_3562_2]) ).

fof(f_3563_1,plain,
    ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).

fof(f_3563_2,plain,
    ! [U_14035,U_14034,U_14033] : c_Hilbert__Choice_OEps(tc_prod(U_14033,U_14034),U_14035) = c_Hilbert__Choice_OEps(tc_prod(U_14033,U_14034),hAPP(c_Product__Type_Oprod_Oprod__case(U_14033,U_14034,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_prod(U_14033,U_14034)),tc_fun(U_14034,tc_HOL_Obool),U_14033),hAPP(c_COMBB(tc_prod(U_14033,U_14034),tc_HOL_Obool,U_14034),U_14035)),c_Product__Type_OPair(U_14033,U_14034)))),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

cnf(f_3563_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14033,U_14034),U_14035) = c_Hilbert__Choice_OEps(tc_prod(U_14033,U_14034),hAPP(c_Product__Type_Oprod_Oprod__case(U_14033,U_14034,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_prod(U_14033,U_14034)),tc_fun(U_14034,tc_HOL_Obool),U_14033),hAPP(c_COMBB(tc_prod(U_14033,U_14034),tc_HOL_Obool,U_14034),U_14035)),c_Product__Type_OPair(U_14033,U_14034)))),
    inference(clausify,[status(thm)],[f_3563_2]) ).

fof(f_3564_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_3564_2,plain,
    ! [U_14039,U_14038,U_14037,U_14036] : c_Hilbert__Choice_OEps(tc_prod(U_14036,U_14037),hAPP(c_Product__Type_Oprod_Oprod__case(U_14036,U_14037,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_HOL_Obool),tc_fun(U_14037,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14037,tc_HOL_Obool),tc_fun(U_14037,tc_HOL_Obool)),U_14036),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14037)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14036),c_fconj),hAPP(c_fequal,U_14038)))),hAPP(c_fequal,U_14039)))) = hAPP(hAPP(c_Product__Type_OPair(U_14036,U_14037),U_14038),U_14039),
    inference(variable_rename,[status(thm)],[f_3564_1]) ).

cnf(f_3564_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_14036,U_14037),hAPP(c_Product__Type_Oprod_Oprod__case(U_14036,U_14037,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14036,tc_fun(U_14037,tc_HOL_Obool),tc_fun(U_14037,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14037,tc_HOL_Obool),tc_fun(U_14037,tc_HOL_Obool)),U_14036),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14037)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14036),c_fconj),hAPP(c_fequal,U_14038)))),hAPP(c_fequal,U_14039)))) = hAPP(hAPP(c_Product__Type_OPair(U_14036,U_14037),U_14038),U_14039),
    inference(clausify,[status(thm)],[f_3564_2]) ).

fof(f_3565_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_3565_2,plain,
    ! [U_14046,U_14045,U_14044,U_14043,U_14042,U_14041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14041,U_14044),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14042),U_14045)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14043),U_14046)))
      | ? [U_14040] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14044,tc_HOL_Obool)),hAPP(U_14045,U_14040)),hAPP(U_14046,U_14040)))
          & hBOOL(hAPP(hAPP(c_member(U_14041),U_14040),U_14042)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14042),U_14043)) ),
    inference(variable_rename,[status(thm)],[f_3565_1]) ).

fof(f_3565_3,plain,
    ! [U_14046,U_14045,U_14044,U_14043,U_14042,U_14041] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14041,U_14044),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14042),U_14045)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14043),U_14046)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14044,tc_HOL_Obool)),hAPP(U_14045,sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041))),hAPP(U_14046,sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041))))
        & hBOOL(hAPP(hAPP(c_member(U_14041),sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041)),U_14042)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14042),U_14043)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_14040,sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041))],[f_3565_2]) ).

cnf(f_3565_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14041),sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041)),U_14042))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14041,U_14044),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14042),U_14045)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14043),U_14046)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14042),U_14043)) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

cnf(f_3565_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14044,tc_HOL_Obool)),hAPP(U_14045,sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041))),hAPP(U_14046,sK342(U_14046,U_14045,U_14044,U_14043,U_14042,U_14041))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14041,U_14044),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14042),U_14045)),hAPP(hAPP(c_Product__Type_OSigma(U_14041,U_14044),U_14043),U_14046)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14042),U_14043)) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

fof(f_3566_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_3566_2,plain,
    ! [U_14050,U_14049,U_14048] :
      ( ? [U_14047] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14048),U_14047),c_Wellfounded_Oacc(U_14048,U_14050)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14048,U_14048)),hAPP(hAPP(c_Product__Type_OPair(U_14048,U_14048),U_14047),U_14049)),U_14050)) )
      | hBOOL(hAPP(hAPP(c_member(U_14048),U_14049),c_Wellfounded_Oacc(U_14048,U_14050))) ),
    inference(variable_rename,[status(thm)],[f_3566_1]) ).

fof(f_3566_3,plain,
    ! [U_14050,U_14049,U_14048] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14048),sK343(U_14050,U_14049,U_14048)),c_Wellfounded_Oacc(U_14048,U_14050)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14048,U_14048)),hAPP(hAPP(c_Product__Type_OPair(U_14048,U_14048),sK343(U_14050,U_14049,U_14048)),U_14049)),U_14050)) )
      | hBOOL(hAPP(hAPP(c_member(U_14048),U_14049),c_Wellfounded_Oacc(U_14048,U_14050))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_14047,sK343(U_14050,U_14049,U_14048))],[f_3566_2]) ).

cnf(f_3566_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14048,U_14048)),hAPP(hAPP(c_Product__Type_OPair(U_14048,U_14048),sK343(U_14050,U_14049,U_14048)),U_14049)),U_14050))
    | hBOOL(hAPP(hAPP(c_member(U_14048),U_14049),c_Wellfounded_Oacc(U_14048,U_14050))) ),
    inference(clausify,[status(thm)],[f_3566_3]) ).

cnf(f_3566_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14048),sK343(U_14050,U_14049,U_14048)),c_Wellfounded_Oacc(U_14048,U_14050)))
    | hBOOL(hAPP(hAPP(c_member(U_14048),U_14049),c_Wellfounded_Oacc(U_14048,U_14050))) ),
    inference(clausify,[status(thm)],[f_3566_3]) ).

fof(f_3567_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_3567_2,plain,
    ! [U_14054,U_14053,U_14052] :
      ( hBOOL(hAPP(hAPP(c_member(U_14052),U_14053),c_Wellfounded_Oacc(U_14052,U_14054)))
      | ? [U_14051] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14052),U_14051),c_Wellfounded_Oacc(U_14052,U_14054)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14052,U_14052)),hAPP(hAPP(c_Product__Type_OPair(U_14052,U_14052),U_14051),U_14053)),U_14054)) ) ),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

fof(f_3567_3,plain,
    ! [U_14054,U_14053,U_14052] :
      ( hBOOL(hAPP(hAPP(c_member(U_14052),U_14053),c_Wellfounded_Oacc(U_14052,U_14054)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_14052),sK344(U_14054,U_14053,U_14052)),c_Wellfounded_Oacc(U_14052,U_14054)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14052,U_14052)),hAPP(hAPP(c_Product__Type_OPair(U_14052,U_14052),sK344(U_14054,U_14053,U_14052)),U_14053)),U_14054)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_14051,sK344(U_14054,U_14053,U_14052))],[f_3567_2]) ).

cnf(f_3567_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14052,U_14052)),hAPP(hAPP(c_Product__Type_OPair(U_14052,U_14052),sK344(U_14054,U_14053,U_14052)),U_14053)),U_14054))
    | hBOOL(hAPP(hAPP(c_member(U_14052),U_14053),c_Wellfounded_Oacc(U_14052,U_14054))) ),
    inference(clausify,[status(thm)],[f_3567_3]) ).

cnf(f_3567_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14052),sK344(U_14054,U_14053,U_14052)),c_Wellfounded_Oacc(U_14052,U_14054)))
    | hBOOL(hAPP(hAPP(c_member(U_14052),U_14053),c_Wellfounded_Oacc(U_14052,U_14054))) ),
    inference(clausify,[status(thm)],[f_3567_3]) ).

fof(f_3568_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_3568_2,plain,
    ! [U_14062,U_14061,U_14060,U_14059] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14059,tc_HOL_Obool),tc_fun(U_14059,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14059,tc_HOL_Obool),tc_fun(U_14059,tc_HOL_Obool)),U_14060),U_14061)),c_Wellfounded_Omax__ext(U_14059,U_14062)))
        | ? [U_14058] :
            ( ! [U_14057] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14059,U_14059)),hAPP(hAPP(c_Product__Type_OPair(U_14059,U_14059),U_14058),U_14057)),U_14062))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14059),U_14057),U_14061)) )
            & hBOOL(hAPP(hAPP(c_member(U_14059),U_14058),U_14060)) )
        | U_14061 = c_Orderings_Obot__class_Obot(tc_fun(U_14059,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14059),U_14061))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14059),U_14060)) )
      & ( ( ! [U_14056] :
              ( ? [U_14055] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14059,U_14059)),hAPP(hAPP(c_Product__Type_OPair(U_14059,U_14059),U_14056),U_14055)),U_14062))
                  & hBOOL(hAPP(hAPP(c_member(U_14059),U_14055),U_14061)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14059),U_14056),U_14060)) )
          & U_14061 != c_Orderings_Obot__class_Obot(tc_fun(U_14059,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14059),U_14061))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14059),U_14060)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14059,tc_HOL_Obool),tc_fun(U_14059,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14059,tc_HOL_Obool),tc_fun(U_14059,tc_HOL_Obool)),U_14060),U_14061)),c_Wellfounded_Omax__ext(U_14059,U_14062))) ) ),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

fof(f_3568_3,plain,
    ( ! [U_14070,U_14068,U_14066,U_14064] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool)),U_14066),U_14068)),c_Wellfounded_Omax__ext(U_14064,U_14070)))
        | ? [U_14058] :
            ( ! [U_14057] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14064)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14064),U_14058),U_14057)),U_14070))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14057),U_14068)) )
            & hBOOL(hAPP(hAPP(c_member(U_14064),U_14058),U_14066)) )
        | U_14068 = c_Orderings_Obot__class_Obot(tc_fun(U_14064,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14068))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14066)) )
    & ! [U_14069,U_14067,U_14065,U_14063] :
        ( ( ! [U_14056] :
              ( ? [U_14055] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14063,U_14063)),hAPP(hAPP(c_Product__Type_OPair(U_14063,U_14063),U_14056),U_14055)),U_14069))
                  & hBOOL(hAPP(hAPP(c_member(U_14063),U_14055),U_14067)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14063),U_14056),U_14065)) )
          & U_14067 != c_Orderings_Obot__class_Obot(tc_fun(U_14063,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14067))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14065)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ) ),
    inference(miniscope,[status(thm)],[f_3568_2]) ).

fof(f_3568_4,plain,
    ( ! [U_14070,U_14068,U_14066,U_14064] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool)),U_14066),U_14068)),c_Wellfounded_Omax__ext(U_14064,U_14070)))
        | ? [U_14058] :
            ( ! [U_14057] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14064)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14064),U_14058),U_14057)),U_14070))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14057),U_14068)) )
            & hBOOL(hAPP(hAPP(c_member(U_14064),U_14058),U_14066)) )
        | U_14068 = c_Orderings_Obot__class_Obot(tc_fun(U_14064,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14068))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14066)) )
    & ! [U_14069,U_14067,U_14065,U_14063] :
        ( ( ! [U_14056] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14063,U_14063)),hAPP(hAPP(c_Product__Type_OPair(U_14063,U_14063),U_14056),sK345(U_14069,U_14067,U_14065,U_14063,U_14056))),U_14069))
                & hBOOL(hAPP(hAPP(c_member(U_14063),sK345(U_14069,U_14067,U_14065,U_14063,U_14056)),U_14067)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14063),U_14056),U_14065)) )
          & U_14067 != c_Orderings_Obot__class_Obot(tc_fun(U_14063,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14067))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14065)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_14055,sK345(U_14069,U_14067,U_14065,U_14063,U_14056))],[f_3568_3]) ).

fof(f_3568_5,plain,
    ( ! [U_14070,U_14068,U_14066,U_14064] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool)),U_14066),U_14068)),c_Wellfounded_Omax__ext(U_14064,U_14070)))
        | ( ! [U_14057] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14064)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14064),sK346(U_14070,U_14068,U_14066,U_14064)),U_14057)),U_14070))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14057),U_14068)) )
          & hBOOL(hAPP(hAPP(c_member(U_14064),sK346(U_14070,U_14068,U_14066,U_14064)),U_14066)) )
        | U_14068 = c_Orderings_Obot__class_Obot(tc_fun(U_14064,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14068))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14066)) )
    & ! [U_14069,U_14067,U_14065,U_14063] :
        ( ( ! [U_14056] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14063,U_14063)),hAPP(hAPP(c_Product__Type_OPair(U_14063,U_14063),U_14056),sK345(U_14069,U_14067,U_14065,U_14063,U_14056))),U_14069))
                & hBOOL(hAPP(hAPP(c_member(U_14063),sK345(U_14069,U_14067,U_14065,U_14063,U_14056)),U_14067)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14063),U_14056),U_14065)) )
          & U_14067 != c_Orderings_Obot__class_Obot(tc_fun(U_14063,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14067))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14065)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_14058,sK346(U_14070,U_14068,U_14066,U_14064))],[f_3568_4]) ).

cnf(f_3568_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14065))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14063),U_14067))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_8,plain,
    ( U_14067 != c_Orderings_Obot__class_Obot(tc_fun(U_14063,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14063),sK345(U_14069,U_14067,U_14065,U_14063,U_14056)),U_14067))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14063),U_14056),U_14065))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14063,U_14063)),hAPP(hAPP(c_Product__Type_OPair(U_14063,U_14063),U_14056),sK345(U_14069,U_14067,U_14065,U_14063,U_14056))),U_14069))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14063),U_14056),U_14065))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14063,tc_HOL_Obool),tc_fun(U_14063,tc_HOL_Obool)),U_14065),U_14067)),c_Wellfounded_Omax__ext(U_14063,U_14069))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14064),sK346(U_14070,U_14068,U_14066,U_14064)),U_14066))
    | U_14068 = c_Orderings_Obot__class_Obot(tc_fun(U_14064,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14068))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14066))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool)),U_14066),U_14068)),c_Wellfounded_Omax__ext(U_14064,U_14070))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

cnf(f_3568_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14064,U_14064)),hAPP(hAPP(c_Product__Type_OPair(U_14064,U_14064),sK346(U_14070,U_14068,U_14066,U_14064)),U_14057)),U_14070))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14064),U_14057),U_14068))
    | U_14068 = c_Orderings_Obot__class_Obot(tc_fun(U_14064,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14068))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14064),U_14066))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14064,tc_HOL_Obool),tc_fun(U_14064,tc_HOL_Obool)),U_14066),U_14068)),c_Wellfounded_Omax__ext(U_14064,U_14070))) ),
    inference(clausify,[status(thm)],[f_3568_5]) ).

fof(f_3569_1,plain,
    ! [V_ca_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_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_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_3569_2,plain,
    ! [U_14075,U_14074,U_14073,U_14072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),hAPP(hAPP(c_Finite__Set_Ofold(U_14072,U_14072,c_Orderings_Oord__class_Omax(U_14072)),U_14075),U_14073)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14072),U_14074),U_14075)))
      | ? [U_14071] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),U_14071),U_14074))
          & hBOOL(hAPP(hAPP(c_member(U_14072),U_14071),U_14073)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14072),U_14073))
      | ~ class_Orderings_Olinorder(U_14072) ),
    inference(variable_rename,[status(thm)],[f_3569_1]) ).

fof(f_3569_3,plain,
    ! [U_14075,U_14074,U_14073,U_14072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),hAPP(hAPP(c_Finite__Set_Ofold(U_14072,U_14072,c_Orderings_Oord__class_Omax(U_14072)),U_14075),U_14073)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14072),U_14074),U_14075)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),sK347(U_14075,U_14074,U_14073,U_14072)),U_14074))
        & hBOOL(hAPP(hAPP(c_member(U_14072),sK347(U_14075,U_14074,U_14073,U_14072)),U_14073)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14072),U_14073))
      | ~ class_Orderings_Olinorder(U_14072) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_14071,sK347(U_14075,U_14074,U_14073,U_14072))],[f_3569_2]) ).

cnf(f_3569_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14072),sK347(U_14075,U_14074,U_14073,U_14072)),U_14073))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),hAPP(hAPP(c_Finite__Set_Ofold(U_14072,U_14072,c_Orderings_Oord__class_Omax(U_14072)),U_14075),U_14073)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14072),U_14074),U_14075)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14072),U_14073))
    | ~ class_Orderings_Olinorder(U_14072) ),
    inference(clausify,[status(thm)],[f_3569_3]) ).

cnf(f_3569_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),sK347(U_14075,U_14074,U_14073,U_14072)),U_14074))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14072),hAPP(hAPP(c_Finite__Set_Ofold(U_14072,U_14072,c_Orderings_Oord__class_Omax(U_14072)),U_14075),U_14073)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14072),U_14074),U_14075)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14072),U_14073))
    | ~ class_Orderings_Olinorder(U_14072) ),
    inference(clausify,[status(thm)],[f_3569_3]) ).

fof(f_3570_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_3570_2,plain,
    ! [U_14079,U_14078,U_14077] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14077,U_14078) = U_14079
      | ~ hBOOL(hAPP(hAPP(c_member(U_14077),U_14079),U_14078))
      | ? [U_14076] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14077),U_14076),U_14079))
          & hBOOL(hAPP(hAPP(c_member(U_14077),U_14076),U_14078)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14077),U_14078))
      | ~ class_Orderings_Olinorder(U_14077) ),
    inference(variable_rename,[status(thm)],[f_3570_1]) ).

fof(f_3570_3,plain,
    ! [U_14079,U_14078,U_14077] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14077,U_14078) = U_14079
      | ~ hBOOL(hAPP(hAPP(c_member(U_14077),U_14079),U_14078))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14077),sK348(U_14079,U_14078,U_14077)),U_14079))
        & hBOOL(hAPP(hAPP(c_member(U_14077),sK348(U_14079,U_14078,U_14077)),U_14078)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14077),U_14078))
      | ~ class_Orderings_Olinorder(U_14077) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_14076,sK348(U_14079,U_14078,U_14077))],[f_3570_2]) ).

cnf(f_3570_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14077),sK348(U_14079,U_14078,U_14077)),U_14078))
    | c_Big__Operators_Olinorder__class_OMax(U_14077,U_14078) = U_14079
    | ~ hBOOL(hAPP(hAPP(c_member(U_14077),U_14079),U_14078))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14077),U_14078))
    | ~ class_Orderings_Olinorder(U_14077) ),
    inference(clausify,[status(thm)],[f_3570_3]) ).

cnf(f_3570_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14077),sK348(U_14079,U_14078,U_14077)),U_14079))
    | c_Big__Operators_Olinorder__class_OMax(U_14077,U_14078) = U_14079
    | ~ hBOOL(hAPP(hAPP(c_member(U_14077),U_14079),U_14078))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14077),U_14078))
    | ~ class_Orderings_Olinorder(U_14077) ),
    inference(clausify,[status(thm)],[f_3570_3]) ).

fof(f_3571_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_3571_2,plain,
    ! [U_14083,U_14082,U_14081] :
      ( ? [U_14080] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14081)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14081),hAPP(U_14083,hAPP(c_Nat_OSuc,U_14080))),hAPP(U_14083,U_14080))),U_14082))
      | ~ c_Wellfounded_Owf(U_14081,U_14082) ),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

fof(f_3571_3,plain,
    ! [U_14083,U_14082,U_14081] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14081)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14081),hAPP(U_14083,hAPP(c_Nat_OSuc,sK349(U_14083,U_14082,U_14081)))),hAPP(U_14083,sK349(U_14083,U_14082,U_14081)))),U_14082))
      | ~ c_Wellfounded_Owf(U_14081,U_14082) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_14080,sK349(U_14083,U_14082,U_14081))],[f_3571_2]) ).

cnf(f_3571_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14081)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14081),hAPP(U_14083,hAPP(c_Nat_OSuc,sK349(U_14083,U_14082,U_14081)))),hAPP(U_14083,sK349(U_14083,U_14082,U_14081)))),U_14082))
    | ~ c_Wellfounded_Owf(U_14081,U_14082) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

fof(f_3572_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_3572_2,plain,
    ! [U_14088,U_14087,U_14086,U_14085,U_14084] :
      ( ( hAPP(c_Random_Oiterate(U_14085,U_14086,U_14084,U_14087),U_14088) = hAPP(hAPP(c_Product__Type_Oscomp(U_14086,U_14085,U_14086,tc_prod(U_14085,U_14086)),hAPP(U_14087,U_14088)),c_Random_Oiterate(U_14085,U_14086,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14084),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14087))
        | U_14084 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_14085,U_14086,U_14084,U_14087),U_14088) = hAPP(c_Product__Type_OPair(U_14085,U_14086),U_14088)
        | U_14084 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3572_1]) ).

fof(f_3572_3,plain,
    ( ! [U_14098,U_14096,U_14094,U_14092,U_14090] :
        ( hAPP(c_Random_Oiterate(U_14092,U_14094,U_14090,U_14096),U_14098) = hAPP(hAPP(c_Product__Type_Oscomp(U_14094,U_14092,U_14094,tc_prod(U_14092,U_14094)),hAPP(U_14096,U_14098)),c_Random_Oiterate(U_14092,U_14094,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14090),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14096))
        | U_14090 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_14097,U_14095,U_14093,U_14091,U_14089] :
        ( hAPP(c_Random_Oiterate(U_14091,U_14093,U_14089,U_14095),U_14097) = hAPP(c_Product__Type_OPair(U_14091,U_14093),U_14097)
        | U_14089 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3572_2]) ).

cnf(f_3572_4,plain,
    ( hAPP(c_Random_Oiterate(U_14091,U_14093,U_14089,U_14095),U_14097) = hAPP(c_Product__Type_OPair(U_14091,U_14093),U_14097)
    | U_14089 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

cnf(f_3572_5,plain,
    ( hAPP(c_Random_Oiterate(U_14092,U_14094,U_14090,U_14096),U_14098) = hAPP(hAPP(c_Product__Type_Oscomp(U_14094,U_14092,U_14094,tc_prod(U_14092,U_14094)),hAPP(U_14096,U_14098)),c_Random_Oiterate(U_14092,U_14094,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14090),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14096))
    | U_14090 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

fof(f_3573_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_3573_2,plain,
    ! [U_14105,U_14104,U_14103,U_14102,U_14101,U_14100,U_14099] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14099,U_14100,U_14101,U_14102),U_14103),U_14104),U_14105) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14100,U_14101,U_14102),U_14104),hAPP(U_14103,U_14105)),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

cnf(f_3573_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14099,U_14100,U_14101,U_14102),U_14103),U_14104),U_14105) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14100,U_14101,U_14102),U_14104),hAPP(U_14103,U_14105)),
    inference(clausify,[status(thm)],[f_3573_2]) ).

fof(f_3574_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_3574_2,plain,
    ! [U_14110,U_14109,U_14108,U_14107,U_14106] : hAPP(hAPP(c_Product__Type_Oscomp(U_14106,U_14107,U_14106,U_14108),hAPP(c_Product__Type_OPair(U_14107,U_14106),U_14109)),U_14110) = hAPP(U_14110,U_14109),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

cnf(f_3574_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14106,U_14107,U_14106,U_14108),hAPP(c_Product__Type_OPair(U_14107,U_14106),U_14109)),U_14110) = hAPP(U_14110,U_14109),
    inference(clausify,[status(thm)],[f_3574_2]) ).

fof(f_3575_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_3575_2,plain,
    ! [U_14119,U_14118,U_14117,U_14116,U_14115,U_14114,U_14113,U_14112,U_14111] : hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14112,U_14113,U_14114),hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14115,U_14116,tc_prod(U_14112,U_14113)),U_14117),U_14118)),U_14119) = hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14115,U_14116,U_14114),U_14117),hAPP(hAPP(c_COMBC(U_14115,tc_fun(U_14112,tc_fun(U_14113,U_14114)),tc_fun(U_14116,U_14114)),hAPP(hAPP(c_COMBB(tc_fun(U_14116,tc_prod(U_14112,U_14113)),tc_fun(tc_fun(U_14112,tc_fun(U_14113,U_14114)),tc_fun(U_14116,U_14114)),U_14115),c_Product__Type_Oscomp(U_14116,U_14112,U_14113,U_14114)),U_14118)),U_14119)),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

cnf(f_3575_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14112,U_14113,U_14114),hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14115,U_14116,tc_prod(U_14112,U_14113)),U_14117),U_14118)),U_14119) = hAPP(hAPP(c_Product__Type_Oscomp(U_14111,U_14115,U_14116,U_14114),U_14117),hAPP(hAPP(c_COMBC(U_14115,tc_fun(U_14112,tc_fun(U_14113,U_14114)),tc_fun(U_14116,U_14114)),hAPP(hAPP(c_COMBB(tc_fun(U_14116,tc_prod(U_14112,U_14113)),tc_fun(tc_fun(U_14112,tc_fun(U_14113,U_14114)),tc_fun(U_14116,U_14114)),U_14115),c_Product__Type_Oscomp(U_14116,U_14112,U_14113,U_14114)),U_14118)),U_14119)),
    inference(clausify,[status(thm)],[f_3575_2]) ).

fof(f_3576_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_3576_2,plain,
    ! [U_14123,U_14122,U_14121,U_14120] : hAPP(hAPP(c_Product__Type_Oscomp(U_14120,U_14121,U_14122,tc_prod(U_14121,U_14122)),U_14123),c_Product__Type_OPair(U_14121,U_14122)) = U_14123,
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

cnf(f_3576_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14120,U_14121,U_14122,tc_prod(U_14121,U_14122)),U_14123),c_Product__Type_OPair(U_14121,U_14122)) = U_14123,
    inference(clausify,[status(thm)],[f_3576_2]) ).

fof(f_3577_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_3577_2,plain,
    ! [U_14130,U_14129,U_14128,U_14127,U_14126,U_14125,U_14124] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14124,U_14125,U_14126,U_14127),U_14128),U_14129),U_14130) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14125,U_14126,U_14127),U_14129),hAPP(U_14128,U_14130)),
    inference(variable_rename,[status(thm)],[f_3577_1]) ).

cnf(f_3577_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14124,U_14125,U_14126,U_14127),U_14128),U_14129),U_14130) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14125,U_14126,U_14127),U_14129),hAPP(U_14128,U_14130)),
    inference(clausify,[status(thm)],[f_3577_2]) ).

fof(f_3578_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_3578_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(U_14136,hAPP(c_Product__Type_Ofst(U_14132,U_14133),hAPP(U_14135,U_14137))),hAPP(c_Product__Type_Osnd(U_14132,U_14133),hAPP(U_14135,U_14137))),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

cnf(f_3578_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(U_14136,hAPP(c_Product__Type_Ofst(U_14132,U_14133),hAPP(U_14135,U_14137))),hAPP(c_Product__Type_Osnd(U_14132,U_14133),hAPP(U_14135,U_14137))),
    inference(clausify,[status(thm)],[f_3578_2]) ).

fof(f_3579_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_3579_2,plain,
    ! [U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14141,U_14139),U_14146),U_14144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14140,U_14139),U_14145),U_14143)
      | ? [U_14138] :
          ( hAPP(U_14145,U_14138) != hAPP(U_14146,hAPP(U_14142,U_14138))
          & hBOOL(hAPP(hAPP(c_member(U_14140),U_14138),U_14143)) )
      | U_14144 != hAPP(c_Set_Oimage(U_14140,U_14141,U_14142),U_14143)
      | ~ c_Fun_Oinj__on(U_14140,U_14141,U_14142,U_14143)
      | ~ class_Groups_Ocomm__monoid__add(U_14139) ),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

fof(f_3579_3,plain,
    ! [U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14141,U_14139),U_14146),U_14144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14140,U_14139),U_14145),U_14143)
      | ( hAPP(U_14145,sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)) != hAPP(U_14146,hAPP(U_14142,sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)))
        & hBOOL(hAPP(hAPP(c_member(U_14140),sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)),U_14143)) )
      | U_14144 != hAPP(c_Set_Oimage(U_14140,U_14141,U_14142),U_14143)
      | ~ c_Fun_Oinj__on(U_14140,U_14141,U_14142,U_14143)
      | ~ class_Groups_Ocomm__monoid__add(U_14139) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_14138,sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139))],[f_3579_2]) ).

cnf(f_3579_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14140),sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)),U_14143))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14141,U_14139),U_14146),U_14144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14140,U_14139),U_14145),U_14143)
    | U_14144 != hAPP(c_Set_Oimage(U_14140,U_14141,U_14142),U_14143)
    | ~ c_Fun_Oinj__on(U_14140,U_14141,U_14142,U_14143)
    | ~ class_Groups_Ocomm__monoid__add(U_14139) ),
    inference(clausify,[status(thm)],[f_3579_3]) ).

cnf(f_3579_5,plain,
    ( hAPP(U_14145,sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)) != hAPP(U_14146,hAPP(U_14142,sK350(U_14146,U_14145,U_14144,U_14143,U_14142,U_14141,U_14140,U_14139)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14141,U_14139),U_14146),U_14144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14140,U_14139),U_14145),U_14143)
    | U_14144 != hAPP(c_Set_Oimage(U_14140,U_14141,U_14142),U_14143)
    | ~ c_Fun_Oinj__on(U_14140,U_14141,U_14142,U_14143)
    | ~ class_Groups_Ocomm__monoid__add(U_14139) ),
    inference(clausify,[status(thm)],[f_3579_3]) ).

fof(f_3580_1,plain,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_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_ca_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_ca_2),B_x)) )
      | V_b_2 != V_d_2
      | V_a_2 != V_ca_2
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).

fof(f_3580_2,plain,
    ! [U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14150),U_14152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14155),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14151),U_14153))
      | ? [U_14147] :
          ( hAPP(U_14154,U_14147) != hAPP(U_14155,U_14147)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14149),U_14147),U_14153))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14149),U_14151),U_14147)) )
      | U_14152 != U_14153
      | U_14150 != U_14151
      | ~ class_Orderings_Oord(U_14149)
      | ~ class_Groups_Ocomm__monoid__add(U_14148) ),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

fof(f_3580_3,plain,
    ! [U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14150),U_14152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14155),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14151),U_14153))
      | ( hAPP(U_14154,sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148)) != hAPP(U_14155,sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14149),sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148)),U_14153))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14149),U_14151),sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148))) )
      | U_14152 != U_14153
      | U_14150 != U_14151
      | ~ class_Orderings_Oord(U_14149)
      | ~ class_Groups_Ocomm__monoid__add(U_14148) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_14147,sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148))],[f_3580_2]) ).

cnf(f_3580_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14149),U_14151),sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14150),U_14152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14155),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14151),U_14153))
    | U_14152 != U_14153
    | U_14150 != U_14151
    | ~ class_Orderings_Oord(U_14149)
    | ~ class_Groups_Ocomm__monoid__add(U_14148) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

cnf(f_3580_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14149),sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148)),U_14153))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14150),U_14152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14155),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14151),U_14153))
    | U_14152 != U_14153
    | U_14150 != U_14151
    | ~ class_Orderings_Oord(U_14149)
    | ~ class_Groups_Ocomm__monoid__add(U_14148) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

cnf(f_3580_6,plain,
    ( hAPP(U_14154,sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148)) != hAPP(U_14155,sK351(U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149,U_14148))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14150),U_14152)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14149,U_14148),U_14155),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_14149,U_14151),U_14153))
    | U_14152 != U_14153
    | U_14150 != U_14151
    | ~ class_Orderings_Oord(U_14149)
    | ~ class_Groups_Ocomm__monoid__add(U_14148) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

fof(f_3581_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_3581_2,plain,
    ! [U_14157,U_14156] :
      ( ( 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_14156),U_14157)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14156),U_14157)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14156),U_14157))
        | ~ 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_14156),U_14157)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

fof(f_3581_3,plain,
    ( ! [U_14161,U_14159] :
        ( 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_14159),U_14161)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14159),U_14161)) )
    & ! [U_14160,U_14158] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14158),U_14160))
        | ~ 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_14158),U_14160)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3581_2]) ).

cnf(f_3581_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14158),U_14160))
    | ~ 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_14158),U_14160)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

cnf(f_3581_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_14159),U_14161)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14159),U_14161)) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

fof(f_3582_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_3582_2,plain,
    ! [U_14171,U_14170] :
      ( ( c_Wellfounded_Owf(U_14170,U_14171)
        | ? [U_14169] :
            ( ! [U_14168] :
                ( ? [U_14167] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14170),U_14167),U_14169))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14170,U_14170)),hAPP(hAPP(c_Product__Type_OPair(U_14170,U_14170),U_14167),U_14168)),U_14171)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14170),U_14168),U_14169)) )
            & ? [U_14166] : hBOOL(hAPP(hAPP(c_member(U_14170),U_14166),U_14169)) ) )
      & ( ! [U_14165] :
            ( ? [U_14164] :
                ( ! [U_14163] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_14170),U_14163),U_14165))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14170,U_14170)),hAPP(hAPP(c_Product__Type_OPair(U_14170,U_14170),U_14163),U_14164)),U_14171)) )
                & hBOOL(hAPP(hAPP(c_member(U_14170),U_14164),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14170),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14170,U_14171) ) ),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

fof(f_3582_3,plain,
    ( ! [U_14175,U_14173] :
        ( c_Wellfounded_Owf(U_14173,U_14175)
        | ? [U_14169] :
            ( ! [U_14168] :
                ( ? [U_14167] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14173),U_14167),U_14169))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),U_14167),U_14168)),U_14175)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),U_14169)) )
            & ? [U_14166] : hBOOL(hAPP(hAPP(c_member(U_14173),U_14166),U_14169)) ) )
    & ! [U_14174,U_14172] :
        ( ! [U_14165] :
            ( ? [U_14164] :
                ( ! [U_14163] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),U_14164)),U_14174)) )
                & hBOOL(hAPP(hAPP(c_member(U_14172),U_14164),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14172,U_14174) ) ),
    inference(miniscope,[status(thm)],[f_3582_2]) ).

fof(f_3582_4,plain,
    ( ! [U_14175,U_14173] :
        ( c_Wellfounded_Owf(U_14173,U_14175)
        | ? [U_14169] :
            ( ! [U_14168] :
                ( ? [U_14167] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14173),U_14167),U_14169))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),U_14167),U_14168)),U_14175)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),U_14169)) )
            & ? [U_14166] : hBOOL(hAPP(hAPP(c_member(U_14173),U_14166),U_14169)) ) )
    & ! [U_14174,U_14172] :
        ( ! [U_14165] :
            ( ( ! [U_14163] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),sK352(U_14174,U_14172,U_14165))),U_14174)) )
              & hBOOL(hAPP(hAPP(c_member(U_14172),sK352(U_14174,U_14172,U_14165)),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14172,U_14174) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_14164,sK352(U_14174,U_14172,U_14165))],[f_3582_3]) ).

fof(f_3582_5,plain,
    ( ! [U_14175,U_14173] :
        ( c_Wellfounded_Owf(U_14173,U_14175)
        | ( ! [U_14168] :
              ( ? [U_14167] :
                  ( hBOOL(hAPP(hAPP(c_member(U_14173),U_14167),sK353(U_14175,U_14173)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),U_14167),U_14168)),U_14175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK353(U_14175,U_14173))) )
          & ? [U_14166] : hBOOL(hAPP(hAPP(c_member(U_14173),U_14166),sK353(U_14175,U_14173))) ) )
    & ! [U_14174,U_14172] :
        ( ! [U_14165] :
            ( ( ! [U_14163] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),sK352(U_14174,U_14172,U_14165))),U_14174)) )
              & hBOOL(hAPP(hAPP(c_member(U_14172),sK352(U_14174,U_14172,U_14165)),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14172,U_14174) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_14169,sK353(U_14175,U_14173))],[f_3582_4]) ).

fof(f_3582_6,plain,
    ( ! [U_14175,U_14173] :
        ( c_Wellfounded_Owf(U_14173,U_14175)
        | ( ! [U_14168] :
              ( ? [U_14167] :
                  ( hBOOL(hAPP(hAPP(c_member(U_14173),U_14167),sK353(U_14175,U_14173)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),U_14167),U_14168)),U_14175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK353(U_14175,U_14173))) )
          & hBOOL(hAPP(hAPP(c_member(U_14173),sK354(U_14175,U_14173)),sK353(U_14175,U_14173))) ) )
    & ! [U_14174,U_14172] :
        ( ! [U_14165] :
            ( ( ! [U_14163] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),sK352(U_14174,U_14172,U_14165))),U_14174)) )
              & hBOOL(hAPP(hAPP(c_member(U_14172),sK352(U_14174,U_14172,U_14165)),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14172,U_14174) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_14166,sK354(U_14175,U_14173))],[f_3582_5]) ).

fof(f_3582_7,plain,
    ( ! [U_14175,U_14173] :
        ( c_Wellfounded_Owf(U_14173,U_14175)
        | ( ! [U_14168] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_14173),sK355(U_14175,U_14173,U_14168)),sK353(U_14175,U_14173)))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),sK355(U_14175,U_14173,U_14168)),U_14168)),U_14175)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK353(U_14175,U_14173))) )
          & hBOOL(hAPP(hAPP(c_member(U_14173),sK354(U_14175,U_14173)),sK353(U_14175,U_14173))) ) )
    & ! [U_14174,U_14172] :
        ( ! [U_14165] :
            ( ( ! [U_14163] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),sK352(U_14174,U_14172,U_14165))),U_14174)) )
              & hBOOL(hAPP(hAPP(c_member(U_14172),sK352(U_14174,U_14172,U_14165)),U_14165)) )
            | ! [U_14162] : ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165)) )
        | ~ c_Wellfounded_Owf(U_14172,U_14174) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_14167,sK355(U_14175,U_14173,U_14168))],[f_3582_6]) ).

cnf(f_3582_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14172),sK352(U_14174,U_14172,U_14165)),U_14165))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165))
    | ~ c_Wellfounded_Owf(U_14172,U_14174) ),
    inference(clausify,[status(thm)],[f_3582_7]) ).

cnf(f_3582_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14163),U_14165))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14163),sK352(U_14174,U_14172,U_14165))),U_14174))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14172),U_14162),U_14165))
    | ~ c_Wellfounded_Owf(U_14172,U_14174) ),
    inference(clausify,[status(thm)],[f_3582_7]) ).

cnf(f_3582_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14173),sK354(U_14175,U_14173)),sK353(U_14175,U_14173)))
    | c_Wellfounded_Owf(U_14173,U_14175) ),
    inference(clausify,[status(thm)],[f_3582_7]) ).

cnf(f_3582_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),sK355(U_14175,U_14173,U_14168)),U_14168)),U_14175))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK353(U_14175,U_14173)))
    | c_Wellfounded_Owf(U_14173,U_14175) ),
    inference(clausify,[status(thm)],[f_3582_7]) ).

cnf(f_3582_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14173),sK355(U_14175,U_14173,U_14168)),sK353(U_14175,U_14173)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK353(U_14175,U_14173)))
    | c_Wellfounded_Owf(U_14173,U_14175) ),
    inference(clausify,[status(thm)],[f_3582_7]) ).

fof(f_3583_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_3583_2,plain,
    ! [U_14177,U_14176] :
      ( c_Wellfounded_Owf(U_14176,c_Transitive__Closure_Otrancl(U_14176,U_14177))
      | ~ c_Wellfounded_Owf(U_14176,U_14177) ),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

cnf(f_3583_3,plain,
    ( c_Wellfounded_Owf(U_14176,c_Transitive__Closure_Otrancl(U_14176,U_14177))
    | ~ c_Wellfounded_Owf(U_14176,U_14177) ),
    inference(clausify,[status(thm)],[f_3583_2]) ).

fof(f_3584_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_3584_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3584_1]) ).

fof(f_3585_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_3585_2,plain,
    ! [U_14181,U_14180] :
      ( ( c_Wellfounded_Oacyclic(U_14180,U_14181)
        | ? [U_14179] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14180,U_14180)),hAPP(hAPP(c_Product__Type_OPair(U_14180,U_14180),U_14179),U_14179)),c_Transitive__Closure_Otrancl(U_14180,U_14181))) )
      & ( ! [U_14178] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14180,U_14180)),hAPP(hAPP(c_Product__Type_OPair(U_14180,U_14180),U_14178),U_14178)),c_Transitive__Closure_Otrancl(U_14180,U_14181)))
        | ~ c_Wellfounded_Oacyclic(U_14180,U_14181) ) ),
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

fof(f_3585_3,plain,
    ( ! [U_14185,U_14183] :
        ( c_Wellfounded_Oacyclic(U_14183,U_14185)
        | ? [U_14179] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14183,U_14183)),hAPP(hAPP(c_Product__Type_OPair(U_14183,U_14183),U_14179),U_14179)),c_Transitive__Closure_Otrancl(U_14183,U_14185))) )
    & ! [U_14184,U_14182] :
        ( ! [U_14178] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14182,U_14182)),hAPP(hAPP(c_Product__Type_OPair(U_14182,U_14182),U_14178),U_14178)),c_Transitive__Closure_Otrancl(U_14182,U_14184)))
        | ~ c_Wellfounded_Oacyclic(U_14182,U_14184) ) ),
    inference(miniscope,[status(thm)],[f_3585_2]) ).

fof(f_3585_4,plain,
    ( ! [U_14185,U_14183] :
        ( c_Wellfounded_Oacyclic(U_14183,U_14185)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14183,U_14183)),hAPP(hAPP(c_Product__Type_OPair(U_14183,U_14183),sK356(U_14185,U_14183)),sK356(U_14185,U_14183))),c_Transitive__Closure_Otrancl(U_14183,U_14185))) )
    & ! [U_14184,U_14182] :
        ( ! [U_14178] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14182,U_14182)),hAPP(hAPP(c_Product__Type_OPair(U_14182,U_14182),U_14178),U_14178)),c_Transitive__Closure_Otrancl(U_14182,U_14184)))
        | ~ c_Wellfounded_Oacyclic(U_14182,U_14184) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_14179,sK356(U_14185,U_14183))],[f_3585_3]) ).

cnf(f_3585_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14182,U_14182)),hAPP(hAPP(c_Product__Type_OPair(U_14182,U_14182),U_14178),U_14178)),c_Transitive__Closure_Otrancl(U_14182,U_14184)))
    | ~ c_Wellfounded_Oacyclic(U_14182,U_14184) ),
    inference(clausify,[status(thm)],[f_3585_4]) ).

cnf(f_3585_6,plain,
    ( c_Wellfounded_Oacyclic(U_14183,U_14185)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14183,U_14183)),hAPP(hAPP(c_Product__Type_OPair(U_14183,U_14183),sK356(U_14185,U_14183)),sK356(U_14185,U_14183))),c_Transitive__Closure_Otrancl(U_14183,U_14185))) ),
    inference(clausify,[status(thm)],[f_3585_4]) ).

fof(f_3586_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_3586_2,plain,
    ! [U_14189,U_14188,U_14187,U_14186] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14186,U_14186)),hAPP(hAPP(c_Product__Type_OPair(U_14186,U_14186),U_14187),U_14188)),c_Transitive__Closure_Otrancl(U_14186,U_14189)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14186,U_14186)),hAPP(hAPP(c_Product__Type_OPair(U_14186,U_14186),U_14187),U_14188)),U_14189)) ),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

cnf(f_3586_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14186,U_14186)),hAPP(hAPP(c_Product__Type_OPair(U_14186,U_14186),U_14187),U_14188)),c_Transitive__Closure_Otrancl(U_14186,U_14189)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14186,U_14186)),hAPP(hAPP(c_Product__Type_OPair(U_14186,U_14186),U_14187),U_14188)),U_14189)) ),
    inference(clausify,[status(thm)],[f_3586_2]) ).

fof(f_3587_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_3587_2,plain,
    ! [U_14191,U_14190] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14190,U_14190),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14190,U_14191)),hAPP(hAPP(c_Product__Type_OSigma(U_14190,U_14190),hAPP(c_Relation_OField(U_14190),U_14191)),hAPP(c_COMBK(tc_fun(U_14190,tc_HOL_Obool),U_14190),hAPP(c_Relation_OField(U_14190),U_14191))))),
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

cnf(f_3587_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14190,U_14190),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14190,U_14191)),hAPP(hAPP(c_Product__Type_OSigma(U_14190,U_14190),hAPP(c_Relation_OField(U_14190),U_14191)),hAPP(c_COMBK(tc_fun(U_14190,tc_HOL_Obool),U_14190),hAPP(c_Relation_OField(U_14190),U_14191))))),
    inference(clausify,[status(thm)],[f_3587_2]) ).

fof(f_3588_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_3588_2,plain,
    ! [U_14194,U_14193,U_14192] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14192,U_14192)),U_14193),c_Transitive__Closure_Otrancl(U_14192,U_14194)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14192,U_14192)),U_14193),U_14194)) ),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

cnf(f_3588_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14192,U_14192)),U_14193),c_Transitive__Closure_Otrancl(U_14192,U_14194)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14192,U_14192)),U_14193),U_14194)) ),
    inference(clausify,[status(thm)],[f_3588_2]) ).

fof(f_3589_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_3589_2,plain,
    ! [U_14195] : c_Transitive__Closure_Otrancl(U_14195,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14195,U_14195),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14195,U_14195),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

cnf(f_3589_3,plain,
    c_Transitive__Closure_Otrancl(U_14195,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14195,U_14195),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14195,U_14195),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3589_2]) ).

fof(f_3590_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_3590_2,plain,
    ! [U_14197,U_14196] : hAPP(c_Relation_ODomain(U_14196,U_14196),c_Transitive__Closure_Otrancl(U_14196,U_14197)) = hAPP(c_Relation_ODomain(U_14196,U_14196),U_14197),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

cnf(f_3590_3,plain,
    hAPP(c_Relation_ODomain(U_14196,U_14196),c_Transitive__Closure_Otrancl(U_14196,U_14197)) = hAPP(c_Relation_ODomain(U_14196,U_14196),U_14197),
    inference(clausify,[status(thm)],[f_3590_2]) ).

fof(f_3591_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_3591_2,plain,
    ! [U_14199,U_14198] : hAPP(c_Relation_ORange(U_14198,U_14198),c_Transitive__Closure_Otrancl(U_14198,U_14199)) = hAPP(c_Relation_ORange(U_14198,U_14198),U_14199),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

cnf(f_3591_3,plain,
    hAPP(c_Relation_ORange(U_14198,U_14198),c_Transitive__Closure_Otrancl(U_14198,U_14199)) = hAPP(c_Relation_ORange(U_14198,U_14198),U_14199),
    inference(clausify,[status(thm)],[f_3591_2]) ).

fof(f_3592_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_3592_2,plain,
    ! [U_14201,U_14200] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14200,U_14200)),c_Transitive__Closure_Otrancl(U_14200,U_14201)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14200,U_14200)),U_14201)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14200,U_14200)),U_14201))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14200,U_14200)),c_Transitive__Closure_Otrancl(U_14200,U_14201))) ) ),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

fof(f_3592_3,plain,
    ( ! [U_14205,U_14203] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14203,U_14203)),c_Transitive__Closure_Otrancl(U_14203,U_14205)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14203,U_14203)),U_14205)) )
    & ! [U_14204,U_14202] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14202,U_14202)),U_14204))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14202,U_14202)),c_Transitive__Closure_Otrancl(U_14202,U_14204))) ) ),
    inference(miniscope,[status(thm)],[f_3592_2]) ).

cnf(f_3592_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14202,U_14202)),U_14204))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14202,U_14202)),c_Transitive__Closure_Otrancl(U_14202,U_14204))) ),
    inference(clausify,[status(thm)],[f_3592_3]) ).

cnf(f_3592_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14203,U_14203)),c_Transitive__Closure_Otrancl(U_14203,U_14205)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14203,U_14203)),U_14205)) ),
    inference(clausify,[status(thm)],[f_3592_3]) ).

fof(f_3593_1,plain,
    ! [V_ca_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_ca_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_ca_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_3593_2,plain,
    ! [U_14210,U_14209,U_14208,U_14207,U_14206] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14207),U_14210)),c_Transitive__Closure_Otrancl(U_14206,U_14209)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14208),U_14210)),c_Transitive__Closure_Otrancl(U_14206,U_14209)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14207),U_14208)),c_Transitive__Closure_Otrancl(U_14206,U_14209))) ),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

cnf(f_3593_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14207),U_14210)),c_Transitive__Closure_Otrancl(U_14206,U_14209)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14208),U_14210)),c_Transitive__Closure_Otrancl(U_14206,U_14209)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),hAPP(hAPP(c_Product__Type_OPair(U_14206,U_14206),U_14207),U_14208)),c_Transitive__Closure_Otrancl(U_14206,U_14209))) ),
    inference(clausify,[status(thm)],[f_3593_2]) ).

fof(f_3594_1,plain,
    ! [V_ca_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_ca_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_ca_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_3594_2,plain,
    ! [U_14215,U_14214,U_14213,U_14212,U_14211] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14212),U_14215)),c_Transitive__Closure_Otrancl(U_14211,U_14214)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14213),U_14215)),U_14214))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14212),U_14213)),c_Transitive__Closure_Otrancl(U_14211,U_14214))) ),
    inference(variable_rename,[status(thm)],[f_3594_1]) ).

cnf(f_3594_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14212),U_14215)),c_Transitive__Closure_Otrancl(U_14211,U_14214)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14213),U_14215)),U_14214))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14211,U_14211)),hAPP(hAPP(c_Product__Type_OPair(U_14211,U_14211),U_14212),U_14213)),c_Transitive__Closure_Otrancl(U_14211,U_14214))) ),
    inference(clausify,[status(thm)],[f_3594_2]) ).

fof(f_3595_1,plain,
    ! [V_ca_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_ca_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_ca_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_3595_2,plain,
    ! [U_14220,U_14219,U_14218,U_14217,U_14216] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14217),U_14220)),c_Transitive__Closure_Otrancl(U_14216,U_14219)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14218),U_14220)),c_Transitive__Closure_Otrancl(U_14216,U_14219)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14217),U_14218)),U_14219)) ),
    inference(variable_rename,[status(thm)],[f_3595_1]) ).

cnf(f_3595_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14217),U_14220)),c_Transitive__Closure_Otrancl(U_14216,U_14219)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14218),U_14220)),c_Transitive__Closure_Otrancl(U_14216,U_14219)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14216,U_14216)),hAPP(hAPP(c_Product__Type_OPair(U_14216,U_14216),U_14217),U_14218)),U_14219)) ),
    inference(clausify,[status(thm)],[f_3595_2]) ).

fof(f_3596_1,plain,
    ! [V_ca_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_ca_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_ca_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_3596_2,plain,
    ! [U_14225,U_14224,U_14223,U_14222,U_14221] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14222),U_14225)),c_Transitive__Closure_Otrancl(U_14221,U_14224)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14223),U_14225)),U_14224))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14222),U_14223)),U_14224)) ),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

cnf(f_3596_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14222),U_14225)),c_Transitive__Closure_Otrancl(U_14221,U_14224)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14223),U_14225)),U_14224))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14221,U_14221)),hAPP(hAPP(c_Product__Type_OPair(U_14221,U_14221),U_14222),U_14223)),U_14224)) ),
    inference(clausify,[status(thm)],[f_3596_2]) ).

fof(f_3597_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_3597_2,plain,
    ! [U_14229,U_14228,U_14227,U_14226] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14226,U_14226)),U_14227),c_Transitive__Closure_Otrancl(U_14226,U_14229)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14226,U_14226),tc_HOL_Obool)),U_14228),U_14229))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14226,U_14226)),U_14227),c_Transitive__Closure_Otrancl(U_14226,U_14228))) ),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

cnf(f_3597_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14226,U_14226)),U_14227),c_Transitive__Closure_Otrancl(U_14226,U_14229)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14226,U_14226),tc_HOL_Obool)),U_14228),U_14229))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14226,U_14226)),U_14227),c_Transitive__Closure_Otrancl(U_14226,U_14228))) ),
    inference(clausify,[status(thm)],[f_3597_2]) ).

fof(f_3598_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_3598_2,plain,
    ! [U_14231,U_14230] : c_Transitive__Closure_Otrancl(U_14230,U_14231) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14230,U_14230),tc_HOL_Obool)),U_14231),hAPP(hAPP(c_Relation_Orel__comp(U_14230,U_14230,U_14230),c_Transitive__Closure_Otrancl(U_14230,U_14231)),U_14231)),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

cnf(f_3598_3,plain,
    c_Transitive__Closure_Otrancl(U_14230,U_14231) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14230,U_14230),tc_HOL_Obool)),U_14231),hAPP(hAPP(c_Relation_Orel__comp(U_14230,U_14230,U_14230),c_Transitive__Closure_Otrancl(U_14230,U_14231)),U_14231)),
    inference(clausify,[status(thm)],[f_3598_2]) ).

fof(f_3599_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_3599_2,plain,
    ! [U_14234,U_14233,U_14232] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14232,U_14232),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14232,U_14233)),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14232),U_14234),hAPP(c_COMBK(tc_fun(U_14232,tc_HOL_Obool),U_14232),U_14234))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14232,U_14232),tc_HOL_Obool)),U_14233),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14232),U_14234),hAPP(c_COMBK(tc_fun(U_14232,tc_HOL_Obool),U_14232),U_14234)))) ),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

cnf(f_3599_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14232,U_14232),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14232,U_14233)),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14232),U_14234),hAPP(c_COMBK(tc_fun(U_14232,tc_HOL_Obool),U_14232),U_14234))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14232,U_14232),tc_HOL_Obool)),U_14233),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14232),U_14234),hAPP(c_COMBK(tc_fun(U_14232,tc_HOL_Obool),U_14232),U_14234)))) ),
    inference(clausify,[status(thm)],[f_3599_2]) ).

fof(f_3600_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_3600_2,plain,
    ! [U_14237,U_14236,U_14235] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14235,U_14236)),U_14237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14235,U_14235,U_14235),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14235,U_14236)),U_14237)),U_14236)),U_14237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),U_14236),U_14237)) ),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

cnf(f_3600_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14235,U_14236)),U_14237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14235,U_14235,U_14235),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14235,U_14236)),U_14237)),U_14236)),U_14237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),U_14236),U_14237)) ),
    inference(clausify,[status(thm)],[f_3600_2]) ).

fof(f_3601_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_3601_2,plain,
    ! [U_14241,U_14240,U_14239,U_14238] : c_Transitive__Closure_Otrancl(U_14238,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14238,U_14238)),hAPP(hAPP(c_Product__Type_OPair(U_14238,U_14238),U_14239),U_14240)),U_14241)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14238,U_14241)),hAPP(c_Set_OCollect(tc_prod(U_14238,U_14238)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14238,U_14238,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14238,tc_fun(U_14238,tc_HOL_Obool),tc_fun(U_14238,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14238,tc_HOL_Obool),tc_fun(U_14238,tc_HOL_Obool)),U_14238),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14238),c_fconj),hAPP(hAPP(c_COMBC(U_14238,tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14238,U_14238),tc_fun(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),U_14238),c_member(tc_prod(U_14238,U_14238))),hAPP(hAPP(c_COMBC(U_14238,U_14238,tc_prod(U_14238,U_14238)),c_Product__Type_OPair(U_14238,U_14238)),U_14239))),c_Transitive__Closure_Ortrancl(U_14238,U_14241))))),hAPP(hAPP(c_COMBC(U_14238,tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14238,U_14238),tc_fun(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),U_14238),c_member(tc_prod(U_14238,U_14238))),hAPP(c_Product__Type_OPair(U_14238,U_14238),U_14240))),c_Transitive__Closure_Ortrancl(U_14238,U_14241)))))),
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

cnf(f_3601_3,plain,
    c_Transitive__Closure_Otrancl(U_14238,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14238,U_14238)),hAPP(hAPP(c_Product__Type_OPair(U_14238,U_14238),U_14239),U_14240)),U_14241)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14238,U_14241)),hAPP(c_Set_OCollect(tc_prod(U_14238,U_14238)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14238,U_14238,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14238,tc_fun(U_14238,tc_HOL_Obool),tc_fun(U_14238,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14238,tc_HOL_Obool),tc_fun(U_14238,tc_HOL_Obool)),U_14238),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14238)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14238),c_fconj),hAPP(hAPP(c_COMBC(U_14238,tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14238,U_14238),tc_fun(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),U_14238),c_member(tc_prod(U_14238,U_14238))),hAPP(hAPP(c_COMBC(U_14238,U_14238,tc_prod(U_14238,U_14238)),c_Product__Type_OPair(U_14238,U_14238)),U_14239))),c_Transitive__Closure_Ortrancl(U_14238,U_14241))))),hAPP(hAPP(c_COMBC(U_14238,tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14238,U_14238),tc_fun(tc_fun(tc_prod(U_14238,U_14238),tc_HOL_Obool),tc_HOL_Obool),U_14238),c_member(tc_prod(U_14238,U_14238))),hAPP(c_Product__Type_OPair(U_14238,U_14238),U_14240))),c_Transitive__Closure_Ortrancl(U_14238,U_14241)))))),
    inference(clausify,[status(thm)],[f_3601_2]) ).

fof(f_3602_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_3602_2,plain,
    ! [U_14245,U_14244,U_14243,U_14242] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14242,tc_fun(U_14242,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14242,tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_fun(U_14242,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14242,tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_fun(U_14242,tc_HOL_Obool)),U_14242),c_COMBC(U_14242,tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14242,tc_prod(U_14242,U_14242)),tc_fun(U_14242,tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),U_14242),hAPP(c_COMBB(tc_prod(U_14242,U_14242),tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool),U_14242),c_member(tc_prod(U_14242,U_14242)))),c_Product__Type_OPair(U_14242,U_14242)))),U_14243)),c_fequal),U_14244),U_14245))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14242,U_14242)),hAPP(hAPP(c_Product__Type_OPair(U_14242,U_14242),U_14244),U_14245)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool)),U_14243),c_Relation_OId(U_14242)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14242,U_14242)),hAPP(hAPP(c_Product__Type_OPair(U_14242,U_14242),U_14244),U_14245)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool)),U_14243),c_Relation_OId(U_14242))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14242,tc_fun(U_14242,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14242,tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_fun(U_14242,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14242,tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_fun(U_14242,tc_HOL_Obool)),U_14242),c_COMBC(U_14242,tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14242,tc_prod(U_14242,U_14242)),tc_fun(U_14242,tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool)),U_14242),hAPP(c_COMBB(tc_prod(U_14242,U_14242),tc_fun(tc_fun(tc_prod(U_14242,U_14242),tc_HOL_Obool),tc_HOL_Obool),U_14242),c_member(tc_prod(U_14242,U_14242)))),c_Product__Type_OPair(U_14242,U_14242)))),U_14243)),c_fequal),U_14244),U_14245)) ) ),
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

fof(f_3602_3,plain,
    ( ! [U_14253,U_14251,U_14249,U_14247] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14247,tc_fun(U_14247,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14247,tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_fun(U_14247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14247,tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_fun(U_14247,tc_HOL_Obool)),U_14247),c_COMBC(U_14247,tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14247,tc_prod(U_14247,U_14247)),tc_fun(U_14247,tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),U_14247),hAPP(c_COMBB(tc_prod(U_14247,U_14247),tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool),U_14247),c_member(tc_prod(U_14247,U_14247)))),c_Product__Type_OPair(U_14247,U_14247)))),U_14249)),c_fequal),U_14251),U_14253))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14247,U_14247)),hAPP(hAPP(c_Product__Type_OPair(U_14247,U_14247),U_14251),U_14253)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool)),U_14249),c_Relation_OId(U_14247)))) )
    & ! [U_14252,U_14250,U_14248,U_14246] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14246,U_14246)),hAPP(hAPP(c_Product__Type_OPair(U_14246,U_14246),U_14250),U_14252)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool)),U_14248),c_Relation_OId(U_14246))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14246,tc_fun(U_14246,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14246,tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_fun(U_14246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14246,tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_fun(U_14246,tc_HOL_Obool)),U_14246),c_COMBC(U_14246,tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14246,tc_prod(U_14246,U_14246)),tc_fun(U_14246,tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),U_14246),hAPP(c_COMBB(tc_prod(U_14246,U_14246),tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool),U_14246),c_member(tc_prod(U_14246,U_14246)))),c_Product__Type_OPair(U_14246,U_14246)))),U_14248)),c_fequal),U_14250),U_14252)) ) ),
    inference(miniscope,[status(thm)],[f_3602_2]) ).

cnf(f_3602_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14246,U_14246)),hAPP(hAPP(c_Product__Type_OPair(U_14246,U_14246),U_14250),U_14252)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool)),U_14248),c_Relation_OId(U_14246))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14246,tc_fun(U_14246,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14246,tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_fun(U_14246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14246,tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_fun(U_14246,tc_HOL_Obool)),U_14246),c_COMBC(U_14246,tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14246,tc_prod(U_14246,U_14246)),tc_fun(U_14246,tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool)),U_14246),hAPP(c_COMBB(tc_prod(U_14246,U_14246),tc_fun(tc_fun(tc_prod(U_14246,U_14246),tc_HOL_Obool),tc_HOL_Obool),U_14246),c_member(tc_prod(U_14246,U_14246)))),c_Product__Type_OPair(U_14246,U_14246)))),U_14248)),c_fequal),U_14250),U_14252)) ),
    inference(clausify,[status(thm)],[f_3602_3]) ).

cnf(f_3602_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14247,tc_fun(U_14247,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14247,tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_fun(U_14247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14247,tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_fun(U_14247,tc_HOL_Obool)),U_14247),c_COMBC(U_14247,tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14247,tc_prod(U_14247,U_14247)),tc_fun(U_14247,tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool)),U_14247),hAPP(c_COMBB(tc_prod(U_14247,U_14247),tc_fun(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool),tc_HOL_Obool),U_14247),c_member(tc_prod(U_14247,U_14247)))),c_Product__Type_OPair(U_14247,U_14247)))),U_14249)),c_fequal),U_14251),U_14253))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14247,U_14247)),hAPP(hAPP(c_Product__Type_OPair(U_14247,U_14247),U_14251),U_14253)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14247,U_14247),tc_HOL_Obool)),U_14249),c_Relation_OId(U_14247)))) ),
    inference(clausify,[status(thm)],[f_3602_3]) ).

fof(f_3603_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_3603_2,plain,
    ! [U_14256,U_14255,U_14254] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14254,U_14254)),U_14255),c_Transitive__Closure_Ortrancl(U_14254,U_14256)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14254,U_14254)),U_14255),U_14256)) ),
    inference(variable_rename,[status(thm)],[f_3603_1]) ).

cnf(f_3603_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14254,U_14254)),U_14255),c_Transitive__Closure_Ortrancl(U_14254,U_14256)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14254,U_14254)),U_14255),U_14256)) ),
    inference(clausify,[status(thm)],[f_3603_2]) ).

fof(f_3604_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_3604_2,plain,
    ! [U_14259,U_14258,U_14257] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14257,U_14257)),hAPP(hAPP(c_Product__Type_OPair(U_14257,U_14257),U_14258),U_14258)),c_Transitive__Closure_Ortrancl(U_14257,U_14259))),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

cnf(f_3604_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14257,U_14257)),hAPP(hAPP(c_Product__Type_OPair(U_14257,U_14257),U_14258),U_14258)),c_Transitive__Closure_Ortrancl(U_14257,U_14259))),
    inference(clausify,[status(thm)],[f_3604_2]) ).

fof(f_3605_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_3605_2,plain,
    ! [U_14261,U_14260] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14260,U_14260)),hAPP(hAPP(c_Product__Type_OPair(U_14260,U_14260),U_14261),U_14261)),c_Relation_OId(U_14260))),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

cnf(f_3605_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14260,U_14260)),hAPP(hAPP(c_Product__Type_OPair(U_14260,U_14260),U_14261),U_14261)),c_Relation_OId(U_14260))),
    inference(clausify,[status(thm)],[f_3605_2]) ).

fof(f_3606_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_3606_2,plain,
    ! [U_14265,U_14264,U_14263,U_14262] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14262,U_14262)),hAPP(hAPP(c_Product__Type_OPair(U_14262,U_14262),U_14263),U_14264)),c_Transitive__Closure_Ortrancl(U_14262,U_14265)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14262,U_14262)),hAPP(hAPP(c_Product__Type_OPair(U_14262,U_14262),U_14263),U_14264)),c_Transitive__Closure_Otrancl(U_14262,U_14265))) ),
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

cnf(f_3606_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14262,U_14262)),hAPP(hAPP(c_Product__Type_OPair(U_14262,U_14262),U_14263),U_14264)),c_Transitive__Closure_Ortrancl(U_14262,U_14265)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14262,U_14262)),hAPP(hAPP(c_Product__Type_OPair(U_14262,U_14262),U_14263),U_14264)),c_Transitive__Closure_Otrancl(U_14262,U_14265))) ),
    inference(clausify,[status(thm)],[f_3606_2]) ).

fof(f_3607_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_3607_2,plain,
    ! [U_14267,U_14266] : c_Transitive__Closure_Otrancl(U_14266,U_14267) = hAPP(hAPP(c_Relation_Orel__comp(U_14266,U_14266,U_14266),U_14267),c_Transitive__Closure_Ortrancl(U_14266,U_14267)),
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

cnf(f_3607_3,plain,
    c_Transitive__Closure_Otrancl(U_14266,U_14267) = hAPP(hAPP(c_Relation_Orel__comp(U_14266,U_14266,U_14266),U_14267),c_Transitive__Closure_Ortrancl(U_14266,U_14267)),
    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_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_3608_2,plain,
    ! [U_14269,U_14268] : c_Transitive__Closure_Otrancl(U_14268,U_14269) = hAPP(hAPP(c_Relation_Orel__comp(U_14268,U_14268,U_14268),c_Transitive__Closure_Ortrancl(U_14268,U_14269)),U_14269),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

cnf(f_3608_3,plain,
    c_Transitive__Closure_Otrancl(U_14268,U_14269) = hAPP(hAPP(c_Relation_Orel__comp(U_14268,U_14268,U_14268),c_Transitive__Closure_Ortrancl(U_14268,U_14269)),U_14269),
    inference(clausify,[status(thm)],[f_3608_2]) ).

fof(f_3609_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_3609_2,plain,
    ! [U_14271,U_14270] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14270,U_14270),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14270,U_14271)),c_Relation_OId(U_14270)) = c_Transitive__Closure_Ortrancl(U_14270,U_14271),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

cnf(f_3609_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14270,U_14270),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14270,U_14271)),c_Relation_OId(U_14270)) = c_Transitive__Closure_Ortrancl(U_14270,U_14271),
    inference(clausify,[status(thm)],[f_3609_2]) ).

fof(f_3610_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_3610_2,plain,
    ! [U_14273,U_14272] : c_Transitive__Closure_Otrancl(U_14272,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14272,U_14272),tc_HOL_Obool)),U_14273),c_Relation_OId(U_14272))) = c_Transitive__Closure_Ortrancl(U_14272,U_14273),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

cnf(f_3610_3,plain,
    c_Transitive__Closure_Otrancl(U_14272,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14272,U_14272),tc_HOL_Obool)),U_14273),c_Relation_OId(U_14272))) = c_Transitive__Closure_Ortrancl(U_14272,U_14273),
    inference(clausify,[status(thm)],[f_3610_2]) ).

fof(f_3611_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_3611_2,plain,
    ! [U_14275,U_14274] : c_Transitive__Closure_Otrancl(U_14274,c_Transitive__Closure_Ortrancl(U_14274,U_14275)) = c_Transitive__Closure_Ortrancl(U_14274,U_14275),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

cnf(f_3611_3,plain,
    c_Transitive__Closure_Otrancl(U_14274,c_Transitive__Closure_Ortrancl(U_14274,U_14275)) = c_Transitive__Closure_Ortrancl(U_14274,U_14275),
    inference(clausify,[status(thm)],[f_3611_2]) ).

fof(f_3612_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_3612_2,plain,
    ! [U_14277,U_14276] : c_Transitive__Closure_Ortrancl(U_14276,c_Transitive__Closure_Otrancl(U_14276,U_14277)) = c_Transitive__Closure_Ortrancl(U_14276,U_14277),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

cnf(f_3612_3,plain,
    c_Transitive__Closure_Ortrancl(U_14276,c_Transitive__Closure_Otrancl(U_14276,U_14277)) = c_Transitive__Closure_Ortrancl(U_14276,U_14277),
    inference(clausify,[status(thm)],[f_3612_2]) ).

fof(f_3613_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_3613_2,plain,
    ! [U_14279,U_14278] : hAPP(c_Relation_ODomain(U_14278,U_14278),c_Transitive__Closure_Ortrancl(U_14278,U_14279)) = c_Orderings_Otop__class_Otop(tc_fun(U_14278,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

cnf(f_3613_3,plain,
    hAPP(c_Relation_ODomain(U_14278,U_14278),c_Transitive__Closure_Ortrancl(U_14278,U_14279)) = c_Orderings_Otop__class_Otop(tc_fun(U_14278,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3613_2]) ).

fof(f_3614_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_3614_2,plain,
    ! [U_14281,U_14280] : hAPP(c_Relation_ORange(U_14280,U_14280),c_Transitive__Closure_Ortrancl(U_14280,U_14281)) = c_Orderings_Otop__class_Otop(tc_fun(U_14280,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

cnf(f_3614_3,plain,
    hAPP(c_Relation_ORange(U_14280,U_14280),c_Transitive__Closure_Ortrancl(U_14280,U_14281)) = c_Orderings_Otop__class_Otop(tc_fun(U_14280,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3614_2]) ).

fof(f_3615_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_3615_2,plain,
    ! [U_14283,U_14282] : c_Transitive__Closure_Ortrancl(U_14282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14282,U_14282),tc_HOL_Obool)),U_14283),c_Relation_OId(U_14282))) = c_Transitive__Closure_Ortrancl(U_14282,U_14283),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

cnf(f_3615_3,plain,
    c_Transitive__Closure_Ortrancl(U_14282,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14282,U_14282),tc_HOL_Obool)),U_14283),c_Relation_OId(U_14282))) = c_Transitive__Closure_Ortrancl(U_14282,U_14283),
    inference(clausify,[status(thm)],[f_3615_2]) ).

fof(f_3616_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_3616_2,plain,
    ! [U_14285,U_14284] : c_Transitive__Closure_Ortrancl(U_14284,c_Transitive__Closure_Ortrancl(U_14284,U_14285)) = c_Transitive__Closure_Ortrancl(U_14284,U_14285),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

cnf(f_3616_3,plain,
    c_Transitive__Closure_Ortrancl(U_14284,c_Transitive__Closure_Ortrancl(U_14284,U_14285)) = c_Transitive__Closure_Ortrancl(U_14284,U_14285),
    inference(clausify,[status(thm)],[f_3616_2]) ).

fof(f_3617_1,plain,
    ! [V_ca_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_ca_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_ca_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_3617_2,plain,
    ! [U_14290,U_14289,U_14288,U_14287,U_14286] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14287),U_14290)),c_Transitive__Closure_Ortrancl(U_14286,U_14289)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14288),U_14290)),c_Transitive__Closure_Ortrancl(U_14286,U_14289)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14287),U_14288)),c_Transitive__Closure_Ortrancl(U_14286,U_14289))) ),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

cnf(f_3617_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14287),U_14290)),c_Transitive__Closure_Ortrancl(U_14286,U_14289)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14288),U_14290)),c_Transitive__Closure_Ortrancl(U_14286,U_14289)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14286,U_14286)),hAPP(hAPP(c_Product__Type_OPair(U_14286,U_14286),U_14287),U_14288)),c_Transitive__Closure_Ortrancl(U_14286,U_14289))) ),
    inference(clausify,[status(thm)],[f_3617_2]) ).

fof(f_3618_1,plain,
    ! [V_ca_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_ca_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_ca_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_3618_2,plain,
    ! [U_14295,U_14294,U_14293,U_14292,U_14291] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14292),U_14295)),c_Transitive__Closure_Ortrancl(U_14291,U_14294)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14293),U_14295)),U_14294))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14292),U_14293)),c_Transitive__Closure_Ortrancl(U_14291,U_14294))) ),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

cnf(f_3618_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14292),U_14295)),c_Transitive__Closure_Ortrancl(U_14291,U_14294)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14293),U_14295)),U_14294))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14291,U_14291)),hAPP(hAPP(c_Product__Type_OPair(U_14291,U_14291),U_14292),U_14293)),c_Transitive__Closure_Ortrancl(U_14291,U_14294))) ),
    inference(clausify,[status(thm)],[f_3618_2]) ).

fof(f_3619_1,plain,
    ! [V_ca_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_ca_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_ca_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_3619_2,plain,
    ! [U_14300,U_14299,U_14298,U_14297,U_14296] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14297),U_14300)),c_Transitive__Closure_Ortrancl(U_14296,U_14299)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14298),U_14300)),c_Transitive__Closure_Ortrancl(U_14296,U_14299)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14297),U_14298)),U_14299)) ),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

cnf(f_3619_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14297),U_14300)),c_Transitive__Closure_Ortrancl(U_14296,U_14299)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14298),U_14300)),c_Transitive__Closure_Ortrancl(U_14296,U_14299)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14296,U_14296)),hAPP(hAPP(c_Product__Type_OPair(U_14296,U_14296),U_14297),U_14298)),U_14299)) ),
    inference(clausify,[status(thm)],[f_3619_2]) ).

fof(f_3620_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_3620_2,plain,
    ! [U_14302,U_14301] : c_Relation_Orefl__on(U_14301,c_Orderings_Otop__class_Otop(tc_fun(U_14301,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14301,U_14302)),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

cnf(f_3620_3,plain,
    c_Relation_Orefl__on(U_14301,c_Orderings_Otop__class_Otop(tc_fun(U_14301,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14301,U_14302)),
    inference(clausify,[status(thm)],[f_3620_2]) ).

fof(f_3621_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_3621_2,plain,
    ! [U_14306,U_14305,U_14304,U_14303] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14303,U_14303),tc_HOL_Obool)),U_14305),U_14306))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,U_14306)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,U_14305))) ) ),
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

cnf(f_3621_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,U_14305)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14303,U_14303),tc_HOL_Obool)),U_14305),U_14306)))) ),
    inference(clausify,[status(thm)],[f_3621_2]) ).

cnf(f_3621_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,U_14306)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14303,U_14303)),U_14304),c_Transitive__Closure_Ortrancl(U_14303,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14303,U_14303),tc_HOL_Obool)),U_14305),U_14306)))) ),
    inference(clausify,[status(thm)],[f_3621_2]) ).

fof(f_3622_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_3622_2,plain,
    ! [U_14309,U_14308,U_14307] :
      ( hAPP(c_Relation_OImage(U_14307,U_14307,c_Transitive__Closure_Ortrancl(U_14307,U_14308)),U_14309) = U_14309
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14307,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14307,U_14307,U_14308),U_14309)),U_14309)) ),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

cnf(f_3622_3,plain,
    ( hAPP(c_Relation_OImage(U_14307,U_14307,c_Transitive__Closure_Ortrancl(U_14307,U_14308)),U_14309) = U_14309
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14307,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14307,U_14307,U_14308),U_14309)),U_14309)) ),
    inference(clausify,[status(thm)],[f_3622_2]) ).

fof(f_3623_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_3623_2,plain,
    ! [U_14312,U_14311,U_14310] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14310,U_14311)),c_Transitive__Closure_Ortrancl(U_14310,U_14312))),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),U_14312)))),
    inference(variable_rename,[status(thm)],[f_3623_1]) ).

cnf(f_3623_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14310,U_14311)),c_Transitive__Closure_Ortrancl(U_14310,U_14312))),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),U_14312)))),
    inference(clausify,[status(thm)],[f_3623_2]) ).

fof(f_3624_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_3624_2,plain,
    ! [U_14314,U_14313] : c_Transitive__Closure_Ortrancl(U_14313,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),U_14314),c_Relation_OId(U_14313))) = c_Transitive__Closure_Ortrancl(U_14313,U_14314),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

cnf(f_3624_3,plain,
    c_Transitive__Closure_Ortrancl(U_14313,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),U_14314),c_Relation_OId(U_14313))) = c_Transitive__Closure_Ortrancl(U_14313,U_14314),
    inference(clausify,[status(thm)],[f_3624_2]) ).

fof(f_3625_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_3625_2,plain,
    ! [U_14317,U_14316,U_14315] : c_Transitive__Closure_Ortrancl(U_14315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14315,U_14315),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14315,U_14316)),c_Transitive__Closure_Ortrancl(U_14315,U_14317))) = c_Transitive__Closure_Ortrancl(U_14315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14315,U_14315),tc_HOL_Obool)),U_14316),U_14317)),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

cnf(f_3625_3,plain,
    c_Transitive__Closure_Ortrancl(U_14315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14315,U_14315),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14315,U_14316)),c_Transitive__Closure_Ortrancl(U_14315,U_14317))) = c_Transitive__Closure_Ortrancl(U_14315,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14315,U_14315),tc_HOL_Obool)),U_14316),U_14317)),
    inference(clausify,[status(thm)],[f_3625_2]) ).

fof(f_3626_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_3626_2,plain,
    ! [U_14319,U_14318] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14318,U_14318),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14318,U_14319)),c_Relation_OId(U_14318)) = c_Transitive__Closure_Ortrancl(U_14318,U_14319),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

cnf(f_3626_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14318,U_14318),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14318,U_14319)),c_Relation_OId(U_14318)) = c_Transitive__Closure_Ortrancl(U_14318,U_14319),
    inference(clausify,[status(thm)],[f_3626_2]) ).

fof(f_3627_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_3627_2,plain,
    ! [U_14322,U_14321,U_14320] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14320,U_14321)),c_Transitive__Closure_Ortrancl(U_14320,U_14322)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),U_14321),c_Transitive__Closure_Ortrancl(U_14320,U_14322))) ),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

cnf(f_3627_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14320,U_14321)),c_Transitive__Closure_Ortrancl(U_14320,U_14322)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14320,U_14320),tc_HOL_Obool)),U_14321),c_Transitive__Closure_Ortrancl(U_14320,U_14322))) ),
    inference(clausify,[status(thm)],[f_3627_2]) ).

fof(f_3628_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_3628_2,plain,
    ! [U_14325,U_14324,U_14323] :
      ( c_Transitive__Closure_Ortrancl(U_14323,U_14325) = c_Transitive__Closure_Ortrancl(U_14323,U_14324)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14323,U_14323),tc_HOL_Obool)),U_14325),c_Transitive__Closure_Ortrancl(U_14323,U_14324)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14323,U_14323),tc_HOL_Obool)),U_14324),U_14325)) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

cnf(f_3628_3,plain,
    ( c_Transitive__Closure_Ortrancl(U_14323,U_14325) = c_Transitive__Closure_Ortrancl(U_14323,U_14324)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14323,U_14323),tc_HOL_Obool)),U_14325),c_Transitive__Closure_Ortrancl(U_14323,U_14324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14323,U_14323),tc_HOL_Obool)),U_14324),U_14325)) ),
    inference(clausify,[status(thm)],[f_3628_2]) ).

fof(f_3629_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_3629_2,plain,
    ! [U_14328,U_14327,U_14326] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14326,U_14327)),c_Transitive__Closure_Ortrancl(U_14326,U_14328)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14327),U_14328)) ),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

cnf(f_3629_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14326,U_14327)),c_Transitive__Closure_Ortrancl(U_14326,U_14328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14326,U_14326),tc_HOL_Obool)),U_14327),U_14328)) ),
    inference(clausify,[status(thm)],[f_3629_2]) ).

fof(f_3630_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_3630_2,plain,
    ! [U_14330,U_14329] : hAPP(hAPP(c_Relation_Orel__comp(U_14329,U_14329,U_14329),c_Transitive__Closure_Ortrancl(U_14329,U_14330)),c_Transitive__Closure_Ortrancl(U_14329,U_14330)) = c_Transitive__Closure_Ortrancl(U_14329,U_14330),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

cnf(f_3630_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14329,U_14329,U_14329),c_Transitive__Closure_Ortrancl(U_14329,U_14330)),c_Transitive__Closure_Ortrancl(U_14329,U_14330)) = c_Transitive__Closure_Ortrancl(U_14329,U_14330),
    inference(clausify,[status(thm)],[f_3630_2]) ).

fof(f_3631_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_3631_2,plain,
    ! [U_14332,U_14331] : hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14331),U_14332),c_Transitive__Closure_Ortrancl(U_14331,U_14332)) = hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14331),c_Transitive__Closure_Ortrancl(U_14331,U_14332)),U_14332),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

cnf(f_3631_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14331),U_14332),c_Transitive__Closure_Ortrancl(U_14331,U_14332)) = hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14331),c_Transitive__Closure_Ortrancl(U_14331,U_14332)),U_14332),
    inference(clausify,[status(thm)],[f_3631_2]) ).

fof(f_3632_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_3632_2,plain,
    ! [U_14334,U_14333] : c_Transitive__Closure_Ortrancl(U_14333,U_14334) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14333,U_14333),tc_HOL_Obool)),c_Relation_OId(U_14333)),hAPP(hAPP(c_Relation_Orel__comp(U_14333,U_14333,U_14333),c_Transitive__Closure_Ortrancl(U_14333,U_14334)),U_14334)),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

cnf(f_3632_3,plain,
    c_Transitive__Closure_Ortrancl(U_14333,U_14334) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14333,U_14333),tc_HOL_Obool)),c_Relation_OId(U_14333)),hAPP(hAPP(c_Relation_Orel__comp(U_14333,U_14333,U_14333),c_Transitive__Closure_Ortrancl(U_14333,U_14334)),U_14334)),
    inference(clausify,[status(thm)],[f_3632_2]) ).

fof(f_3633_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_3633_2,plain,
    ! [U_14337,U_14336,U_14335] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14335,U_14337)),U_14336))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14335,U_14335,U_14335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14335,U_14337)),U_14336)),U_14337)),U_14336))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Relation_OId(U_14335)),U_14336)) ),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

cnf(f_3633_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14335,U_14337)),U_14336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14335,U_14335,U_14335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14335,U_14337)),U_14336)),U_14337)),U_14336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14335,U_14335),tc_HOL_Obool)),c_Relation_OId(U_14335)),U_14336)) ),
    inference(clausify,[status(thm)],[f_3633_2]) ).

fof(f_3634_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_3634_2,plain,
    ! [U_14338] : c_Transitive__Closure_Ortrancl(U_14338,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14338,U_14338),tc_HOL_Obool))) = c_Relation_OId(U_14338),
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

cnf(f_3634_3,plain,
    c_Transitive__Closure_Ortrancl(U_14338,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14338,U_14338),tc_HOL_Obool))) = c_Relation_OId(U_14338),
    inference(clausify,[status(thm)],[f_3634_2]) ).

fof(f_3635_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_3635_2,plain,
    ! [U_14341,U_14340,U_14339] : hAPP(hAPP(c_Relation_Orel__comp(U_14339,U_14340,U_14340),U_14341),c_Relation_OId(U_14340)) = U_14341,
    inference(variable_rename,[status(thm)],[f_3635_1]) ).

cnf(f_3635_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14339,U_14340,U_14340),U_14341),c_Relation_OId(U_14340)) = U_14341,
    inference(clausify,[status(thm)],[f_3635_2]) ).

fof(f_3636_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_3636_2,plain,
    ! [U_14344,U_14343,U_14342] : hAPP(hAPP(c_Relation_Orel__comp(U_14342,U_14342,U_14343),c_Relation_OId(U_14342)),U_14344) = U_14344,
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

cnf(f_3636_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14342,U_14342,U_14343),c_Relation_OId(U_14342)),U_14344) = U_14344,
    inference(clausify,[status(thm)],[f_3636_2]) ).

fof(f_3637_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_3637_2,plain,
    ! [U_14346,U_14345] : hAPP(c_Relation_OImage(U_14345,U_14345,c_Relation_OId(U_14345)),U_14346) = U_14346,
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

cnf(f_3637_3,plain,
    hAPP(c_Relation_OImage(U_14345,U_14345,c_Relation_OId(U_14345)),U_14346) = U_14346,
    inference(clausify,[status(thm)],[f_3637_2]) ).

fof(f_3638_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_3638_2,plain,
    ! [U_14349,U_14348,U_14347] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14347,U_14347)),hAPP(hAPP(c_Product__Type_OPair(U_14347,U_14347),U_14348),U_14349)),c_Relation_OId(U_14347)))
        | U_14348 != U_14349 )
      & ( U_14348 = U_14349
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14347,U_14347)),hAPP(hAPP(c_Product__Type_OPair(U_14347,U_14347),U_14348),U_14349)),c_Relation_OId(U_14347))) ) ),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

fof(f_3638_3,plain,
    ( ! [U_14355,U_14353] :
        ( ! [U_14351] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14351,U_14351)),hAPP(hAPP(c_Product__Type_OPair(U_14351,U_14351),U_14353),U_14355)),c_Relation_OId(U_14351)))
        | U_14353 != U_14355 )
    & ! [U_14354,U_14352] :
        ( ! [U_14350] : ~ 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_Relation_OId(U_14350)))
        | U_14352 = U_14354 ) ),
    inference(miniscope,[status(thm)],[f_3638_2]) ).

cnf(f_3638_4,plain,
    ( ~ 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_Relation_OId(U_14350)))
    | U_14352 = U_14354 ),
    inference(clausify,[status(thm)],[f_3638_3]) ).

cnf(f_3638_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14351,U_14351)),hAPP(hAPP(c_Product__Type_OPair(U_14351,U_14351),U_14353),U_14355)),c_Relation_OId(U_14351)))
    | U_14353 != U_14355 ),
    inference(clausify,[status(thm)],[f_3638_3]) ).

fof(f_3639_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_3639_2,plain,
    ! [U_14360,U_14359,U_14358,U_14357,U_14356] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14357),U_14360)),c_Transitive__Closure_Otrancl(U_14356,U_14359)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14358),U_14360)),c_Transitive__Closure_Otrancl(U_14356,U_14359)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14357),U_14358)),c_Transitive__Closure_Ortrancl(U_14356,U_14359))) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

cnf(f_3639_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14357),U_14360)),c_Transitive__Closure_Otrancl(U_14356,U_14359)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14358),U_14360)),c_Transitive__Closure_Otrancl(U_14356,U_14359)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14356,U_14356)),hAPP(hAPP(c_Product__Type_OPair(U_14356,U_14356),U_14357),U_14358)),c_Transitive__Closure_Ortrancl(U_14356,U_14359))) ),
    inference(clausify,[status(thm)],[f_3639_2]) ).

fof(f_3640_1,plain,
    ! [V_ca_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_ca_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_ca_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_3640_2,plain,
    ! [U_14365,U_14364,U_14363,U_14362,U_14361] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14362),U_14365)),c_Transitive__Closure_Otrancl(U_14361,U_14364)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14363),U_14365)),c_Transitive__Closure_Ortrancl(U_14361,U_14364)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14362),U_14363)),c_Transitive__Closure_Otrancl(U_14361,U_14364))) ),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

cnf(f_3640_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14362),U_14365)),c_Transitive__Closure_Otrancl(U_14361,U_14364)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14363),U_14365)),c_Transitive__Closure_Ortrancl(U_14361,U_14364)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14361,U_14361)),hAPP(hAPP(c_Product__Type_OPair(U_14361,U_14361),U_14362),U_14363)),c_Transitive__Closure_Otrancl(U_14361,U_14364))) ),
    inference(clausify,[status(thm)],[f_3640_2]) ).

fof(f_3641_1,plain,
    ! [V_ca_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_ca_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_ca_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_3641_2,plain,
    ! [U_14370,U_14369,U_14368,U_14367,U_14366] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14367),U_14370)),c_Transitive__Closure_Otrancl(U_14366,U_14369)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14368),U_14370)),U_14369))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14367),U_14368)),c_Transitive__Closure_Ortrancl(U_14366,U_14369))) ),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

cnf(f_3641_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14367),U_14370)),c_Transitive__Closure_Otrancl(U_14366,U_14369)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14368),U_14370)),U_14369))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14366,U_14366)),hAPP(hAPP(c_Product__Type_OPair(U_14366,U_14366),U_14367),U_14368)),c_Transitive__Closure_Ortrancl(U_14366,U_14369))) ),
    inference(clausify,[status(thm)],[f_3641_2]) ).

fof(f_3642_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_3642_2,plain,
    ! [U_14374,U_14373,U_14372,U_14371] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14371,U_14371)),hAPP(hAPP(c_Product__Type_OPair(U_14371,U_14371),U_14372),U_14373)),c_Transitive__Closure_Otrancl(U_14371,U_14374)))
        & U_14372 != U_14373 )
      | U_14372 = U_14373
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14371,U_14371)),hAPP(hAPP(c_Product__Type_OPair(U_14371,U_14371),U_14372),U_14373)),c_Transitive__Closure_Ortrancl(U_14371,U_14374))) ),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

cnf(f_3642_3,plain,
    ( U_14372 != U_14373
    | U_14372 = U_14373
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14371,U_14371)),hAPP(hAPP(c_Product__Type_OPair(U_14371,U_14371),U_14372),U_14373)),c_Transitive__Closure_Ortrancl(U_14371,U_14374))) ),
    inference(clausify,[status(thm)],[f_3642_2]) ).

cnf(f_3642_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14371,U_14371)),hAPP(hAPP(c_Product__Type_OPair(U_14371,U_14371),U_14372),U_14373)),c_Transitive__Closure_Otrancl(U_14371,U_14374)))
    | U_14372 = U_14373
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14371,U_14371)),hAPP(hAPP(c_Product__Type_OPair(U_14371,U_14371),U_14372),U_14373)),c_Transitive__Closure_Ortrancl(U_14371,U_14374))) ),
    inference(clausify,[status(thm)],[f_3642_2]) ).

fof(f_3643_1,plain,
    ! [V_ca_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_ca_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_ca_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_3643_2,plain,
    ! [U_14379,U_14378,U_14377,U_14376,U_14375] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14376),U_14379)),c_Transitive__Closure_Otrancl(U_14375,U_14378)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14377),U_14379)),c_Transitive__Closure_Ortrancl(U_14375,U_14378)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14376),U_14377)),U_14378)) ),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

cnf(f_3643_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14376),U_14379)),c_Transitive__Closure_Otrancl(U_14375,U_14378)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14377),U_14379)),c_Transitive__Closure_Ortrancl(U_14375,U_14378)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14375,U_14375)),hAPP(hAPP(c_Product__Type_OPair(U_14375,U_14375),U_14376),U_14377)),U_14378)) ),
    inference(clausify,[status(thm)],[f_3643_2]) ).

fof(f_3644_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_3644_2,plain,
    ! [U_14383,U_14382,U_14381,U_14380] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),hAPP(hAPP(c_Product__Type_OPair(U_14380,U_14380),U_14381),U_14382)),c_Transitive__Closure_Ortrancl(U_14380,U_14383)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),hAPP(hAPP(c_Product__Type_OPair(U_14380,U_14380),U_14381),U_14382)),c_Transitive__Closure_Otrancl(U_14380,U_14383)))
            | U_14381 = U_14382 )
          & U_14381 != U_14382 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),hAPP(hAPP(c_Product__Type_OPair(U_14380,U_14380),U_14381),U_14382)),c_Transitive__Closure_Otrancl(U_14380,U_14383)))
          & U_14381 != U_14382 )
        | U_14381 = U_14382
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14380,U_14380)),hAPP(hAPP(c_Product__Type_OPair(U_14380,U_14380),U_14381),U_14382)),c_Transitive__Closure_Ortrancl(U_14380,U_14383))) ) ),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

fof(f_3644_3,plain,
    ( ! [U_14391,U_14389,U_14387,U_14385] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14385,U_14385)),hAPP(hAPP(c_Product__Type_OPair(U_14385,U_14385),U_14387),U_14389)),c_Transitive__Closure_Ortrancl(U_14385,U_14391)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14385,U_14385)),hAPP(hAPP(c_Product__Type_OPair(U_14385,U_14385),U_14387),U_14389)),c_Transitive__Closure_Otrancl(U_14385,U_14391)))
            | U_14387 = U_14389 )
          & U_14387 != U_14389 ) )
    & ! [U_14390,U_14388,U_14386,U_14384] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14386),U_14388)),c_Transitive__Closure_Otrancl(U_14384,U_14390)))
          & U_14386 != U_14388 )
        | U_14386 = U_14388
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14386),U_14388)),c_Transitive__Closure_Ortrancl(U_14384,U_14390))) ) ),
    inference(miniscope,[status(thm)],[f_3644_2]) ).

cnf(f_3644_4,plain,
    ( U_14386 != U_14388
    | U_14386 = U_14388
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14386),U_14388)),c_Transitive__Closure_Ortrancl(U_14384,U_14390))) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

cnf(f_3644_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14386),U_14388)),c_Transitive__Closure_Otrancl(U_14384,U_14390)))
    | U_14386 = U_14388
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14386),U_14388)),c_Transitive__Closure_Ortrancl(U_14384,U_14390))) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

cnf(f_3644_6,plain,
    ( U_14387 != U_14389
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14385,U_14385)),hAPP(hAPP(c_Product__Type_OPair(U_14385,U_14385),U_14387),U_14389)),c_Transitive__Closure_Ortrancl(U_14385,U_14391))) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

cnf(f_3644_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14385,U_14385)),hAPP(hAPP(c_Product__Type_OPair(U_14385,U_14385),U_14387),U_14389)),c_Transitive__Closure_Otrancl(U_14385,U_14391)))
    | U_14387 = U_14389
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14385,U_14385)),hAPP(hAPP(c_Product__Type_OPair(U_14385,U_14385),U_14387),U_14389)),c_Transitive__Closure_Ortrancl(U_14385,U_14391))) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

fof(f_3645_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_3645_2,plain,
    ! [U_14392] : hAPP(c_Relation_ODomain(U_14392,U_14392),c_Relation_OId(U_14392)) = c_Orderings_Otop__class_Otop(tc_fun(U_14392,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3645_1]) ).

cnf(f_3645_3,plain,
    hAPP(c_Relation_ODomain(U_14392,U_14392),c_Relation_OId(U_14392)) = c_Orderings_Otop__class_Otop(tc_fun(U_14392,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3645_2]) ).

fof(f_3646_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_3646_2,plain,
    ! [U_14393] : hAPP(c_Relation_ORange(U_14393,U_14393),c_Relation_OId(U_14393)) = c_Orderings_Otop__class_Otop(tc_fun(U_14393,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

cnf(f_3646_3,plain,
    hAPP(c_Relation_ORange(U_14393,U_14393),c_Relation_OId(U_14393)) = c_Orderings_Otop__class_Otop(tc_fun(U_14393,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3646_2]) ).

fof(f_3647_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_3647_2,plain,
    ! [U_14394] : c_Relation_Orefl__on(U_14394,c_Orderings_Otop__class_Otop(tc_fun(U_14394,tc_HOL_Obool)),c_Relation_OId(U_14394)),
    inference(variable_rename,[status(thm)],[f_3647_1]) ).

cnf(f_3647_3,plain,
    c_Relation_Orefl__on(U_14394,c_Orderings_Otop__class_Otop(tc_fun(U_14394,tc_HOL_Obool)),c_Relation_OId(U_14394)),
    inference(clausify,[status(thm)],[f_3647_2]) ).

fof(f_3648_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_3648_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_3648_1]) ).

fof(f_3649_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_3649_2,plain,
    ! [U_14398,U_14397,U_14396,U_14395] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14395,U_14395)),hAPP(hAPP(c_Product__Type_OPair(U_14395,U_14395),U_14396),U_14398)),c_Transitive__Closure_Ortrancl(U_14395,U_14397)))
          | U_14396 != U_14398 )
        & ( U_14396 = U_14398
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14395,U_14395)),hAPP(hAPP(c_Product__Type_OPair(U_14395,U_14395),U_14396),U_14398)),c_Transitive__Closure_Ortrancl(U_14395,U_14397))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_14395),U_14396),hAPP(c_Relation_ODomain(U_14395,U_14395),U_14397))) ),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

cnf(f_3649_3,plain,
    ( U_14396 = U_14398
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14395,U_14395)),hAPP(hAPP(c_Product__Type_OPair(U_14395,U_14395),U_14396),U_14398)),c_Transitive__Closure_Ortrancl(U_14395,U_14397)))
    | hBOOL(hAPP(hAPP(c_member(U_14395),U_14396),hAPP(c_Relation_ODomain(U_14395,U_14395),U_14397))) ),
    inference(clausify,[status(thm)],[f_3649_2]) ).

cnf(f_3649_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14395,U_14395)),hAPP(hAPP(c_Product__Type_OPair(U_14395,U_14395),U_14396),U_14398)),c_Transitive__Closure_Ortrancl(U_14395,U_14397)))
    | U_14396 != U_14398
    | hBOOL(hAPP(hAPP(c_member(U_14395),U_14396),hAPP(c_Relation_ODomain(U_14395,U_14395),U_14397))) ),
    inference(clausify,[status(thm)],[f_3649_2]) ).

fof(f_3650_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_3650_2,plain,
    ! [U_14402,U_14401,U_14400,U_14399] :
      ( hBOOL(hAPP(hAPP(c_member(U_14399),U_14400),c_Wellfounded_Oacc(U_14399,U_14402)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14399),U_14401),c_Wellfounded_Oacc(U_14399,U_14402)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14399,U_14399)),hAPP(hAPP(c_Product__Type_OPair(U_14399,U_14399),U_14400),U_14401)),c_Transitive__Closure_Ortrancl(U_14399,U_14402))) ),
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

cnf(f_3650_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14399),U_14400),c_Wellfounded_Oacc(U_14399,U_14402)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14399),U_14401),c_Wellfounded_Oacc(U_14399,U_14402)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14399,U_14399)),hAPP(hAPP(c_Product__Type_OPair(U_14399,U_14399),U_14400),U_14401)),c_Transitive__Closure_Ortrancl(U_14399,U_14402))) ),
    inference(clausify,[status(thm)],[f_3650_2]) ).

fof(f_3651_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_3651_2,plain,
    ! [U_14406,U_14405,U_14404,U_14403] :
      ( hBOOL(hAPP(hAPP(c_member(U_14403),U_14406),c_Wellfounded_Oacc(U_14403,U_14405)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14403,U_14403)),hAPP(hAPP(c_Product__Type_OPair(U_14403,U_14403),U_14406),U_14404)),c_Transitive__Closure_Ortrancl(U_14403,U_14405)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14403),U_14404),c_Wellfounded_Oacc(U_14403,U_14405))) ),
    inference(variable_rename,[status(thm)],[f_3651_1]) ).

cnf(f_3651_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14403),U_14406),c_Wellfounded_Oacc(U_14403,U_14405)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14403,U_14403)),hAPP(hAPP(c_Product__Type_OPair(U_14403,U_14403),U_14406),U_14404)),c_Transitive__Closure_Ortrancl(U_14403,U_14405)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14403),U_14404),c_Wellfounded_Oacc(U_14403,U_14405))) ),
    inference(clausify,[status(thm)],[f_3651_2]) ).

fof(f_3652_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_3652_2,plain,
    ! [U_14410,U_14409,U_14408,U_14407] :
      ( ( c_Wellfounded_Owf(U_14407,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14407,U_14407)),hAPP(hAPP(c_Product__Type_OPair(U_14407,U_14407),U_14408),U_14409)),U_14410))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14407,U_14407)),hAPP(hAPP(c_Product__Type_OPair(U_14407,U_14407),U_14409),U_14408)),c_Transitive__Closure_Ortrancl(U_14407,U_14410)))
        | ~ c_Wellfounded_Owf(U_14407,U_14410) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14407,U_14407)),hAPP(hAPP(c_Product__Type_OPair(U_14407,U_14407),U_14409),U_14408)),c_Transitive__Closure_Ortrancl(U_14407,U_14410)))
          & c_Wellfounded_Owf(U_14407,U_14410) )
        | ~ c_Wellfounded_Owf(U_14407,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14407,U_14407)),hAPP(hAPP(c_Product__Type_OPair(U_14407,U_14407),U_14408),U_14409)),U_14410)) ) ),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

fof(f_3652_3,plain,
    ( ! [U_14418,U_14416,U_14414,U_14412] :
        ( c_Wellfounded_Owf(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))
        | 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_Owf(U_14412,U_14418) )
    & ! [U_14417,U_14415,U_14413,U_14411] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14411,U_14411)),hAPP(hAPP(c_Product__Type_OPair(U_14411,U_14411),U_14415),U_14413)),c_Transitive__Closure_Ortrancl(U_14411,U_14417)))
          & c_Wellfounded_Owf(U_14411,U_14417) )
        | ~ c_Wellfounded_Owf(U_14411,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14411,U_14411)),hAPP(hAPP(c_Product__Type_OPair(U_14411,U_14411),U_14413),U_14415)),U_14417)) ) ),
    inference(miniscope,[status(thm)],[f_3652_2]) ).

cnf(f_3652_4,plain,
    ( c_Wellfounded_Owf(U_14411,U_14417)
    | ~ c_Wellfounded_Owf(U_14411,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14411,U_14411)),hAPP(hAPP(c_Product__Type_OPair(U_14411,U_14411),U_14413),U_14415)),U_14417)) ),
    inference(clausify,[status(thm)],[f_3652_3]) ).

cnf(f_3652_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14411,U_14411)),hAPP(hAPP(c_Product__Type_OPair(U_14411,U_14411),U_14415),U_14413)),c_Transitive__Closure_Ortrancl(U_14411,U_14417)))
    | ~ c_Wellfounded_Owf(U_14411,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14411,U_14411)),hAPP(hAPP(c_Product__Type_OPair(U_14411,U_14411),U_14413),U_14415)),U_14417)) ),
    inference(clausify,[status(thm)],[f_3652_3]) ).

cnf(f_3652_6,plain,
    ( c_Wellfounded_Owf(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))
    | 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_Owf(U_14412,U_14418) ),
    inference(clausify,[status(thm)],[f_3652_3]) ).

fof(f_3653_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_3653_2,plain,
    ! [U_14422,U_14421,U_14420,U_14419] :
      ( ( c_Wellfounded_Oacyclic(U_14419,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14419,U_14419)),hAPP(hAPP(c_Product__Type_OPair(U_14419,U_14419),U_14420),U_14421)),U_14422))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14419,U_14419)),hAPP(hAPP(c_Product__Type_OPair(U_14419,U_14419),U_14421),U_14420)),c_Transitive__Closure_Ortrancl(U_14419,U_14422)))
        | ~ c_Wellfounded_Oacyclic(U_14419,U_14422) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14419,U_14419)),hAPP(hAPP(c_Product__Type_OPair(U_14419,U_14419),U_14421),U_14420)),c_Transitive__Closure_Ortrancl(U_14419,U_14422)))
          & c_Wellfounded_Oacyclic(U_14419,U_14422) )
        | ~ c_Wellfounded_Oacyclic(U_14419,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14419,U_14419)),hAPP(hAPP(c_Product__Type_OPair(U_14419,U_14419),U_14420),U_14421)),U_14422)) ) ),
    inference(variable_rename,[status(thm)],[f_3653_1]) ).

fof(f_3653_3,plain,
    ( ! [U_14430,U_14428,U_14426,U_14424] :
        ( c_Wellfounded_Oacyclic(U_14424,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14424,U_14424)),hAPP(hAPP(c_Product__Type_OPair(U_14424,U_14424),U_14426),U_14428)),U_14430))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14424,U_14424)),hAPP(hAPP(c_Product__Type_OPair(U_14424,U_14424),U_14428),U_14426)),c_Transitive__Closure_Ortrancl(U_14424,U_14430)))
        | ~ c_Wellfounded_Oacyclic(U_14424,U_14430) )
    & ! [U_14429,U_14427,U_14425,U_14423] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14423,U_14423)),hAPP(hAPP(c_Product__Type_OPair(U_14423,U_14423),U_14427),U_14425)),c_Transitive__Closure_Ortrancl(U_14423,U_14429)))
          & c_Wellfounded_Oacyclic(U_14423,U_14429) )
        | ~ c_Wellfounded_Oacyclic(U_14423,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14423,U_14423)),hAPP(hAPP(c_Product__Type_OPair(U_14423,U_14423),U_14425),U_14427)),U_14429)) ) ),
    inference(miniscope,[status(thm)],[f_3653_2]) ).

cnf(f_3653_4,plain,
    ( c_Wellfounded_Oacyclic(U_14423,U_14429)
    | ~ c_Wellfounded_Oacyclic(U_14423,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14423,U_14423)),hAPP(hAPP(c_Product__Type_OPair(U_14423,U_14423),U_14425),U_14427)),U_14429)) ),
    inference(clausify,[status(thm)],[f_3653_3]) ).

cnf(f_3653_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14423,U_14423)),hAPP(hAPP(c_Product__Type_OPair(U_14423,U_14423),U_14427),U_14425)),c_Transitive__Closure_Ortrancl(U_14423,U_14429)))
    | ~ c_Wellfounded_Oacyclic(U_14423,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14423,U_14423)),hAPP(hAPP(c_Product__Type_OPair(U_14423,U_14423),U_14425),U_14427)),U_14429)) ),
    inference(clausify,[status(thm)],[f_3653_3]) ).

cnf(f_3653_6,plain,
    ( c_Wellfounded_Oacyclic(U_14424,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14424,U_14424)),hAPP(hAPP(c_Product__Type_OPair(U_14424,U_14424),U_14426),U_14428)),U_14430))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14424,U_14424)),hAPP(hAPP(c_Product__Type_OPair(U_14424,U_14424),U_14428),U_14426)),c_Transitive__Closure_Ortrancl(U_14424,U_14430)))
    | ~ c_Wellfounded_Oacyclic(U_14424,U_14430) ),
    inference(clausify,[status(thm)],[f_3653_3]) ).

fof(f_3654_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_3654_2,plain,
    ! [U_14432,U_14431] : c_Relation_Orefl__on(U_14431,c_Orderings_Otop__class_Otop(tc_fun(U_14431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14431,U_14431),tc_HOL_Obool)),U_14432),c_Relation_OId(U_14431))),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

cnf(f_3654_3,plain,
    c_Relation_Orefl__on(U_14431,c_Orderings_Otop__class_Otop(tc_fun(U_14431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14431,U_14431),tc_HOL_Obool)),U_14432),c_Relation_OId(U_14431))),
    inference(clausify,[status(thm)],[f_3654_2]) ).

fof(f_3655_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_3655_2,plain,
    ! [U_14433] : c_Relation_OId(U_14433) = hAPP(c_Set_OCollect(tc_prod(U_14433,U_14433)),hAPP(hAPP(c_COMBB(tc_fun(U_14433,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14433,U_14433)),c_HOL_OEx(U_14433)),hAPP(hAPP(c_COMBC(tc_prod(U_14433,U_14433),tc_fun(U_14433,tc_prod(U_14433,U_14433)),tc_fun(U_14433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14433,U_14433),tc_HOL_Obool),tc_fun(tc_fun(U_14433,tc_prod(U_14433,U_14433)),tc_fun(U_14433,tc_HOL_Obool)),tc_prod(U_14433,U_14433)),c_COMBB(tc_prod(U_14433,U_14433),tc_HOL_Obool,U_14433)),c_fequal)),hAPP(hAPP(c_COMBS(U_14433,U_14433,tc_prod(U_14433,U_14433)),c_Product__Type_OPair(U_14433,U_14433)),c_COMBI(U_14433))))),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

cnf(f_3655_3,plain,
    c_Relation_OId(U_14433) = hAPP(c_Set_OCollect(tc_prod(U_14433,U_14433)),hAPP(hAPP(c_COMBB(tc_fun(U_14433,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14433,U_14433)),c_HOL_OEx(U_14433)),hAPP(hAPP(c_COMBC(tc_prod(U_14433,U_14433),tc_fun(U_14433,tc_prod(U_14433,U_14433)),tc_fun(U_14433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14433,U_14433),tc_HOL_Obool),tc_fun(tc_fun(U_14433,tc_prod(U_14433,U_14433)),tc_fun(U_14433,tc_HOL_Obool)),tc_prod(U_14433,U_14433)),c_COMBB(tc_prod(U_14433,U_14433),tc_HOL_Obool,U_14433)),c_fequal)),hAPP(hAPP(c_COMBS(U_14433,U_14433,tc_prod(U_14433,U_14433)),c_Product__Type_OPair(U_14433,U_14433)),c_COMBI(U_14433))))),
    inference(clausify,[status(thm)],[f_3655_2]) ).

fof(f_3656_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_3656_2,plain,
    ! [U_14435,U_14434] : c_Relation_Oirrefl(U_14434,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14434,U_14434),tc_HOL_Obool)),U_14435),c_Relation_OId(U_14434))),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

cnf(f_3656_3,plain,
    c_Relation_Oirrefl(U_14434,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14434,U_14434),tc_HOL_Obool)),U_14435),c_Relation_OId(U_14434))),
    inference(clausify,[status(thm)],[f_3656_2]) ).

fof(f_3657_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_3657_2,plain,
    ! [U_14437,U_14436] :
      ( ( 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_14436),U_14437)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14436),U_14437)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14436),U_14437))
        | ~ 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_14436),U_14437)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3657_1]) ).

fof(f_3657_3,plain,
    ( ! [U_14441,U_14439] :
        ( 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_14439),U_14441)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14439),U_14441)) )
    & ! [U_14440,U_14438] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14438),U_14440))
        | ~ 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_14438),U_14440)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3657_2]) ).

cnf(f_3657_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14438),U_14440))
    | ~ 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_14438),U_14440)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3657_3]) ).

cnf(f_3657_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_14439),U_14441)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14439),U_14441)) ),
    inference(clausify,[status(thm)],[f_3657_3]) ).

fof(f_3658_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_3658_2,plain,
    ! [U_14446,U_14445,U_14444,U_14443,U_14442] :
      ( hBOOL(hAPP(hAPP(c_member(U_14442),U_14443),U_14446))
      | U_14443 = U_14444
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14442,U_14442),tc_HOL_Obool)),U_14445),hAPP(hAPP(c_Product__Type_OSigma(U_14442,U_14442),U_14446),hAPP(c_COMBK(tc_fun(U_14442,tc_HOL_Obool),U_14442),U_14446))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14442,U_14442)),hAPP(hAPP(c_Product__Type_OPair(U_14442,U_14442),U_14443),U_14444)),c_Transitive__Closure_Ortrancl(U_14442,U_14445))) ),
    inference(variable_rename,[status(thm)],[f_3658_1]) ).

cnf(f_3658_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14442),U_14443),U_14446))
    | U_14443 = U_14444
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14442,U_14442),tc_HOL_Obool)),U_14445),hAPP(hAPP(c_Product__Type_OSigma(U_14442,U_14442),U_14446),hAPP(c_COMBK(tc_fun(U_14442,tc_HOL_Obool),U_14442),U_14446))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14442,U_14442)),hAPP(hAPP(c_Product__Type_OPair(U_14442,U_14442),U_14443),U_14444)),c_Transitive__Closure_Ortrancl(U_14442,U_14445))) ),
    inference(clausify,[status(thm)],[f_3658_2]) ).

fof(f_3659_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_3659_2,plain,
    ! [U_14449,U_14448,U_14447] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14447,U_14447)),hAPP(hAPP(c_Product__Type_OPair(U_14447,U_14447),U_14449),U_14449)),c_Transitive__Closure_Otrancl(U_14447,U_14448)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14447,U_14447),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14447,U_14447),U_14448)),c_Transitive__Closure_Ortrancl(U_14447,U_14448)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14447,U_14447),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3659_1]) ).

cnf(f_3659_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14447,U_14447)),hAPP(hAPP(c_Product__Type_OPair(U_14447,U_14447),U_14449),U_14449)),c_Transitive__Closure_Otrancl(U_14447,U_14448)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14447,U_14447),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14447,U_14447),U_14448)),c_Transitive__Closure_Ortrancl(U_14447,U_14448)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14447,U_14447),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3659_2]) ).

fof(f_3660_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_3660_2,plain,
    ! [U_14455,U_14454,U_14453,U_14452,U_14451] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14454),U_14455))),hAPP(U_14452,U_14454))),c_Transitive__Closure_Ortrancl(U_14451,U_14453)))
      | ? [U_14450] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(c_Nat_OSuc,U_14450))),hAPP(U_14452,U_14450))),c_Transitive__Closure_Ortrancl(U_14451,U_14453))) ),
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

fof(f_3660_3,plain,
    ! [U_14455,U_14454,U_14453,U_14452,U_14451] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14454),U_14455))),hAPP(U_14452,U_14454))),c_Transitive__Closure_Ortrancl(U_14451,U_14453)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(c_Nat_OSuc,sK357(U_14455,U_14454,U_14453,U_14452,U_14451)))),hAPP(U_14452,sK357(U_14455,U_14454,U_14453,U_14452,U_14451)))),c_Transitive__Closure_Ortrancl(U_14451,U_14453))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_14450,sK357(U_14455,U_14454,U_14453,U_14452,U_14451))],[f_3660_2]) ).

cnf(f_3660_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14454),U_14455))),hAPP(U_14452,U_14454))),c_Transitive__Closure_Ortrancl(U_14451,U_14453)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),hAPP(U_14452,hAPP(c_Nat_OSuc,sK357(U_14455,U_14454,U_14453,U_14452,U_14451)))),hAPP(U_14452,sK357(U_14455,U_14454,U_14453,U_14452,U_14451)))),c_Transitive__Closure_Ortrancl(U_14451,U_14453))) ),
    inference(clausify,[status(thm)],[f_3660_3]) ).

fof(f_3661_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_3661_2,plain,
    ! [U_14457,U_14456] : c_Transitive__Closure_Ortrancl(U_14456,hAPP(c_Relation_Oconverse(U_14456,U_14456),U_14457)) = hAPP(c_Relation_Oconverse(U_14456,U_14456),c_Transitive__Closure_Ortrancl(U_14456,U_14457)),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

cnf(f_3661_3,plain,
    c_Transitive__Closure_Ortrancl(U_14456,hAPP(c_Relation_Oconverse(U_14456,U_14456),U_14457)) = hAPP(c_Relation_Oconverse(U_14456,U_14456),c_Transitive__Closure_Ortrancl(U_14456,U_14457)),
    inference(clausify,[status(thm)],[f_3661_2]) ).

fof(f_3662_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_3662_2,plain,
    ! [U_14458] : hAPP(c_Relation_Oconverse(U_14458,U_14458),c_Relation_OId(U_14458)) = c_Relation_OId(U_14458),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

cnf(f_3662_3,plain,
    hAPP(c_Relation_Oconverse(U_14458,U_14458),c_Relation_OId(U_14458)) = c_Relation_OId(U_14458),
    inference(clausify,[status(thm)],[f_3662_2]) ).

fof(f_3663_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_3663_2,plain,
    ! [U_14460,U_14459] :
      ( ( c_Wellfounded_Oacyclic(U_14459,hAPP(c_Relation_Oconverse(U_14459,U_14459),U_14460))
        | ~ c_Wellfounded_Oacyclic(U_14459,U_14460) )
      & ( c_Wellfounded_Oacyclic(U_14459,U_14460)
        | ~ c_Wellfounded_Oacyclic(U_14459,hAPP(c_Relation_Oconverse(U_14459,U_14459),U_14460)) ) ),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

fof(f_3663_3,plain,
    ( ! [U_14464,U_14462] :
        ( c_Wellfounded_Oacyclic(U_14462,hAPP(c_Relation_Oconverse(U_14462,U_14462),U_14464))
        | ~ c_Wellfounded_Oacyclic(U_14462,U_14464) )
    & ! [U_14463,U_14461] :
        ( c_Wellfounded_Oacyclic(U_14461,U_14463)
        | ~ c_Wellfounded_Oacyclic(U_14461,hAPP(c_Relation_Oconverse(U_14461,U_14461),U_14463)) ) ),
    inference(miniscope,[status(thm)],[f_3663_2]) ).

cnf(f_3663_4,plain,
    ( c_Wellfounded_Oacyclic(U_14461,U_14463)
    | ~ c_Wellfounded_Oacyclic(U_14461,hAPP(c_Relation_Oconverse(U_14461,U_14461),U_14463)) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

cnf(f_3663_5,plain,
    ( c_Wellfounded_Oacyclic(U_14462,hAPP(c_Relation_Oconverse(U_14462,U_14462),U_14464))
    | ~ c_Wellfounded_Oacyclic(U_14462,U_14464) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

fof(f_3664_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_3664_2,plain,
    ! [U_14466,U_14465] : hAPP(c_Relation_Oconverse(U_14465,U_14465),c_Relation_OId__on(U_14465,U_14466)) = c_Relation_OId__on(U_14465,U_14466),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

cnf(f_3664_3,plain,
    hAPP(c_Relation_Oconverse(U_14465,U_14465),c_Relation_OId__on(U_14465,U_14466)) = c_Relation_OId__on(U_14465,U_14466),
    inference(clausify,[status(thm)],[f_3664_2]) ).

fof(f_3665_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_3665_2,plain,
    ! [U_14470,U_14469,U_14468,U_14467] : hAPP(c_Relation_Oconverse(U_14467,U_14467),hAPP(hAPP(c_Relation_Oinv__image(U_14468,U_14467),U_14469),U_14470)) = hAPP(hAPP(c_Relation_Oinv__image(U_14468,U_14467),hAPP(c_Relation_Oconverse(U_14468,U_14468),U_14469)),U_14470),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

cnf(f_3665_3,plain,
    hAPP(c_Relation_Oconverse(U_14467,U_14467),hAPP(hAPP(c_Relation_Oinv__image(U_14468,U_14467),U_14469),U_14470)) = hAPP(hAPP(c_Relation_Oinv__image(U_14468,U_14467),hAPP(c_Relation_Oconverse(U_14468,U_14468),U_14469)),U_14470),
    inference(clausify,[status(thm)],[f_3665_2]) ).

fof(f_3666_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_3666_2,plain,
    ! [U_14473,U_14472,U_14471] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14471,U_14472)),hAPP(c_Relation_Oconverse(U_14472,U_14471),U_14473)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14472,U_14471)),U_14473)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14472,U_14471)),U_14473))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14471,U_14472)),hAPP(c_Relation_Oconverse(U_14472,U_14471),U_14473))) ) ),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

fof(f_3666_3,plain,
    ( ! [U_14479,U_14477,U_14475] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14477)),hAPP(c_Relation_Oconverse(U_14477,U_14475),U_14479)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14477,U_14475)),U_14479)) )
    & ! [U_14478,U_14476,U_14474] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14476,U_14474)),U_14478))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14476)),hAPP(c_Relation_Oconverse(U_14476,U_14474),U_14478))) ) ),
    inference(miniscope,[status(thm)],[f_3666_2]) ).

cnf(f_3666_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14476,U_14474)),U_14478))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14476)),hAPP(c_Relation_Oconverse(U_14476,U_14474),U_14478))) ),
    inference(clausify,[status(thm)],[f_3666_3]) ).

cnf(f_3666_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14477)),hAPP(c_Relation_Oconverse(U_14477,U_14475),U_14479)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14477,U_14475)),U_14479)) ),
    inference(clausify,[status(thm)],[f_3666_3]) ).

fof(f_3667_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_3667_2,plain,
    ! [U_14482,U_14481,U_14480] : hAPP(c_Relation_Oconverse(U_14480,U_14481),hAPP(c_Relation_Oconverse(U_14481,U_14480),U_14482)) = U_14482,
    inference(variable_rename,[status(thm)],[f_3667_1]) ).

cnf(f_3667_3,plain,
    hAPP(c_Relation_Oconverse(U_14480,U_14481),hAPP(c_Relation_Oconverse(U_14481,U_14480),U_14482)) = U_14482,
    inference(clausify,[status(thm)],[f_3667_2]) ).

fof(f_3668_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_3668_2,plain,
    ! [U_14484,U_14483] : hAPP(c_Relation_OField(U_14483),hAPP(c_Relation_Oconverse(U_14483,U_14483),U_14484)) = hAPP(c_Relation_OField(U_14483),U_14484),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

cnf(f_3668_3,plain,
    hAPP(c_Relation_OField(U_14483),hAPP(c_Relation_Oconverse(U_14483,U_14483),U_14484)) = hAPP(c_Relation_OField(U_14483),U_14484),
    inference(clausify,[status(thm)],[f_3668_2]) ).

fof(f_3669_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_3669_2,plain,
    ! [U_14488,U_14487,U_14486,U_14485] : hAPP(c_Relation_Oconverse(U_14485,U_14486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14485,U_14486),tc_HOL_Obool)),U_14487),U_14488)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14486,U_14485),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14485,U_14486),U_14487)),hAPP(c_Relation_Oconverse(U_14485,U_14486),U_14488)),
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

cnf(f_3669_3,plain,
    hAPP(c_Relation_Oconverse(U_14485,U_14486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14485,U_14486),tc_HOL_Obool)),U_14487),U_14488)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14486,U_14485),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14485,U_14486),U_14487)),hAPP(c_Relation_Oconverse(U_14485,U_14486),U_14488)),
    inference(clausify,[status(thm)],[f_3669_2]) ).

fof(f_3670_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_3670_2,plain,
    ! [U_14491,U_14490,U_14489] :
      ( ( c_Relation_Orefl__on(U_14489,U_14490,hAPP(c_Relation_Oconverse(U_14489,U_14489),U_14491))
        | ~ c_Relation_Orefl__on(U_14489,U_14490,U_14491) )
      & ( c_Relation_Orefl__on(U_14489,U_14490,U_14491)
        | ~ c_Relation_Orefl__on(U_14489,U_14490,hAPP(c_Relation_Oconverse(U_14489,U_14489),U_14491)) ) ),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

fof(f_3670_3,plain,
    ( ! [U_14497,U_14495,U_14493] :
        ( c_Relation_Orefl__on(U_14493,U_14495,hAPP(c_Relation_Oconverse(U_14493,U_14493),U_14497))
        | ~ c_Relation_Orefl__on(U_14493,U_14495,U_14497) )
    & ! [U_14496,U_14494,U_14492] :
        ( c_Relation_Orefl__on(U_14492,U_14494,U_14496)
        | ~ c_Relation_Orefl__on(U_14492,U_14494,hAPP(c_Relation_Oconverse(U_14492,U_14492),U_14496)) ) ),
    inference(miniscope,[status(thm)],[f_3670_2]) ).

cnf(f_3670_4,plain,
    ( c_Relation_Orefl__on(U_14492,U_14494,U_14496)
    | ~ c_Relation_Orefl__on(U_14492,U_14494,hAPP(c_Relation_Oconverse(U_14492,U_14492),U_14496)) ),
    inference(clausify,[status(thm)],[f_3670_3]) ).

cnf(f_3670_5,plain,
    ( c_Relation_Orefl__on(U_14493,U_14495,hAPP(c_Relation_Oconverse(U_14493,U_14493),U_14497))
    | ~ c_Relation_Orefl__on(U_14493,U_14495,U_14497) ),
    inference(clausify,[status(thm)],[f_3670_3]) ).

fof(f_3671_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_3671_2,plain,
    ! [U_14501,U_14500,U_14499,U_14498] : hAPP(c_Relation_Oconverse(U_14498,U_14499),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool)),U_14500),U_14501)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14498,U_14499),U_14500)),hAPP(c_Relation_Oconverse(U_14498,U_14499),U_14501)),
    inference(variable_rename,[status(thm)],[f_3671_1]) ).

cnf(f_3671_3,plain,
    hAPP(c_Relation_Oconverse(U_14498,U_14499),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool)),U_14500),U_14501)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14498,U_14499),U_14500)),hAPP(c_Relation_Oconverse(U_14498,U_14499),U_14501)),
    inference(clausify,[status(thm)],[f_3671_2]) ).

fof(f_3672_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_3672_2,plain,
    ! [U_14506,U_14505,U_14504,U_14503,U_14502] : hAPP(c_Relation_Oconverse(U_14502,U_14503),hAPP(hAPP(c_Relation_Orel__comp(U_14502,U_14504,U_14503),U_14505),U_14506)) = hAPP(hAPP(c_Relation_Orel__comp(U_14503,U_14504,U_14502),hAPP(c_Relation_Oconverse(U_14504,U_14503),U_14506)),hAPP(c_Relation_Oconverse(U_14502,U_14504),U_14505)),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

cnf(f_3672_3,plain,
    hAPP(c_Relation_Oconverse(U_14502,U_14503),hAPP(hAPP(c_Relation_Orel__comp(U_14502,U_14504,U_14503),U_14505),U_14506)) = hAPP(hAPP(c_Relation_Orel__comp(U_14503,U_14504,U_14502),hAPP(c_Relation_Oconverse(U_14504,U_14503),U_14506)),hAPP(c_Relation_Oconverse(U_14502,U_14504),U_14505)),
    inference(clausify,[status(thm)],[f_3672_2]) ).

fof(f_3673_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_3673_2,plain,
    ! [U_14511,U_14510,U_14509,U_14508,U_14507] :
      ( ( 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)))
        | ~ 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_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_3673_1]) ).

fof(f_3673_3,plain,
    ( ! [U_14521,U_14519,U_14517,U_14515,U_14513] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14513,U_14515)),hAPP(hAPP(c_Product__Type_OPair(U_14513,U_14515),U_14517),U_14519)),hAPP(c_Relation_Oconverse(U_14515,U_14513),U_14521)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14513),U_14519),U_14517)),U_14521)) )
    & ! [U_14520,U_14518,U_14516,U_14514,U_14512] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14512)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14512),U_14518),U_14516)),U_14520))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14512,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14512,U_14514),U_14516),U_14518)),hAPP(c_Relation_Oconverse(U_14514,U_14512),U_14520))) ) ),
    inference(miniscope,[status(thm)],[f_3673_2]) ).

cnf(f_3673_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14512)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14512),U_14518),U_14516)),U_14520))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14512,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14512,U_14514),U_14516),U_14518)),hAPP(c_Relation_Oconverse(U_14514,U_14512),U_14520))) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

cnf(f_3673_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14513,U_14515)),hAPP(hAPP(c_Product__Type_OPair(U_14513,U_14515),U_14517),U_14519)),hAPP(c_Relation_Oconverse(U_14515,U_14513),U_14521)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14515,U_14513)),hAPP(hAPP(c_Product__Type_OPair(U_14515,U_14513),U_14519),U_14517)),U_14521)) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

fof(f_3674_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_3674_2,plain,
    ! [U_14526,U_14525,U_14524,U_14523,U_14522] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14522)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14522),U_14525),U_14524)),hAPP(c_Relation_Oconverse(U_14522,U_14523),U_14526)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14522,U_14523)),hAPP(hAPP(c_Product__Type_OPair(U_14522,U_14523),U_14524),U_14525)),U_14526)) ),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

cnf(f_3674_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14522)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14522),U_14525),U_14524)),hAPP(c_Relation_Oconverse(U_14522,U_14523),U_14526)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14522,U_14523)),hAPP(hAPP(c_Product__Type_OPair(U_14522,U_14523),U_14524),U_14525)),U_14526)) ),
    inference(clausify,[status(thm)],[f_3674_2]) ).

fof(f_3675_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_3675_2,plain,
    ! [U_14531,U_14530,U_14529,U_14528,U_14527] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14528,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14528,U_14527),U_14530),U_14529)),U_14531))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14527,U_14528)),hAPP(hAPP(c_Product__Type_OPair(U_14527,U_14528),U_14529),U_14530)),hAPP(c_Relation_Oconverse(U_14528,U_14527),U_14531))) ),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

cnf(f_3675_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14528,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14528,U_14527),U_14530),U_14529)),U_14531))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14527,U_14528)),hAPP(hAPP(c_Product__Type_OPair(U_14527,U_14528),U_14529),U_14530)),hAPP(c_Relation_Oconverse(U_14528,U_14527),U_14531))) ),
    inference(clausify,[status(thm)],[f_3675_2]) ).

fof(f_3676_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_3676_2,plain,
    ! [U_14536,U_14535,U_14534,U_14533,U_14532] : hAPP(c_Relation_Oconverse(U_14532,U_14533),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14534,tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool)),U_14535),U_14536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14534,tc_fun(tc_prod(U_14533,U_14532),tc_HOL_Obool)),U_14535),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool),tc_fun(tc_prod(U_14533,U_14532),tc_HOL_Obool),U_14534),c_Relation_Oconverse(U_14532,U_14533)),U_14536)),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

cnf(f_3676_3,plain,
    hAPP(c_Relation_Oconverse(U_14532,U_14533),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14534,tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool)),U_14535),U_14536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14534,tc_fun(tc_prod(U_14533,U_14532),tc_HOL_Obool)),U_14535),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14532,U_14533),tc_HOL_Obool),tc_fun(tc_prod(U_14533,U_14532),tc_HOL_Obool),U_14534),c_Relation_Oconverse(U_14532,U_14533)),U_14536)),
    inference(clausify,[status(thm)],[f_3676_2]) ).

fof(f_3677_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_3677_2,plain,
    ! [U_14541,U_14540,U_14539,U_14538,U_14537] : hAPP(c_Relation_Oconverse(U_14537,U_14538),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14539,tc_fun(tc_prod(U_14537,U_14538),tc_HOL_Obool)),U_14540),U_14541)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14539,tc_fun(tc_prod(U_14538,U_14537),tc_HOL_Obool)),U_14540),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14537,U_14538),tc_HOL_Obool),tc_fun(tc_prod(U_14538,U_14537),tc_HOL_Obool),U_14539),c_Relation_Oconverse(U_14537,U_14538)),U_14541)),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

cnf(f_3677_3,plain,
    hAPP(c_Relation_Oconverse(U_14537,U_14538),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14539,tc_fun(tc_prod(U_14537,U_14538),tc_HOL_Obool)),U_14540),U_14541)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14539,tc_fun(tc_prod(U_14538,U_14537),tc_HOL_Obool)),U_14540),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14537,U_14538),tc_HOL_Obool),tc_fun(tc_prod(U_14538,U_14537),tc_HOL_Obool),U_14539),c_Relation_Oconverse(U_14537,U_14538)),U_14541)),
    inference(clausify,[status(thm)],[f_3677_2]) ).

fof(f_3678_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_3678_2,plain,
    ! [U_14543,U_14542] : c_Transitive__Closure_Otrancl(U_14542,hAPP(c_Relation_Oconverse(U_14542,U_14542),U_14543)) = hAPP(c_Relation_Oconverse(U_14542,U_14542),c_Transitive__Closure_Otrancl(U_14542,U_14543)),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

cnf(f_3678_3,plain,
    c_Transitive__Closure_Otrancl(U_14542,hAPP(c_Relation_Oconverse(U_14542,U_14542),U_14543)) = hAPP(c_Relation_Oconverse(U_14542,U_14542),c_Transitive__Closure_Otrancl(U_14542,U_14543)),
    inference(clausify,[status(thm)],[f_3678_2]) ).

fof(f_3679_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_3679_2,plain,
    ! [U_14545,U_14544] :
      ( c_Wellfounded_Owf(U_14544,hAPP(c_Relation_Oconverse(U_14544,U_14544),c_Transitive__Closure_Otrancl(U_14544,U_14545)))
      | ~ c_Wellfounded_Owf(U_14544,hAPP(c_Relation_Oconverse(U_14544,U_14544),U_14545)) ),
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

cnf(f_3679_3,plain,
    ( c_Wellfounded_Owf(U_14544,hAPP(c_Relation_Oconverse(U_14544,U_14544),c_Transitive__Closure_Otrancl(U_14544,U_14545)))
    | ~ c_Wellfounded_Owf(U_14544,hAPP(c_Relation_Oconverse(U_14544,U_14544),U_14545)) ),
    inference(clausify,[status(thm)],[f_3679_2]) ).

fof(f_3680_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_3680_2,plain,
    ! [U_14548,U_14547,U_14546] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14546,U_14546,U_14546),hAPP(c_Relation_Oconverse(U_14546,U_14546),U_14548)),U_14548) = U_14548
      | ~ c_Equiv__Relations_Oequiv(U_14546,U_14547,U_14548) ),
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

cnf(f_3680_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_14546,U_14546,U_14546),hAPP(c_Relation_Oconverse(U_14546,U_14546),U_14548)),U_14548) = U_14548
    | ~ c_Equiv__Relations_Oequiv(U_14546,U_14547,U_14548) ),
    inference(clausify,[status(thm)],[f_3680_2]) ).

fof(f_3681_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_3681_2,plain,
    ! [U_14551,U_14550,U_14549] : hAPP(c_Relation_ORange(U_14549,U_14550),U_14551) = hAPP(c_Relation_ODomain(U_14550,U_14549),hAPP(c_Relation_Oconverse(U_14549,U_14550),U_14551)),
    inference(variable_rename,[status(thm)],[f_3681_1]) ).

cnf(f_3681_3,plain,
    hAPP(c_Relation_ORange(U_14549,U_14550),U_14551) = hAPP(c_Relation_ODomain(U_14550,U_14549),hAPP(c_Relation_Oconverse(U_14549,U_14550),U_14551)),
    inference(clausify,[status(thm)],[f_3681_2]) ).

fof(f_3682_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_3682_2,plain,
    ! [U_14554,U_14553,U_14552] : hAPP(c_Relation_ODomain(U_14552,U_14553),hAPP(c_Relation_Oconverse(U_14553,U_14552),U_14554)) = hAPP(c_Relation_ORange(U_14553,U_14552),U_14554),
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

cnf(f_3682_3,plain,
    hAPP(c_Relation_ODomain(U_14552,U_14553),hAPP(c_Relation_Oconverse(U_14553,U_14552),U_14554)) = hAPP(c_Relation_ORange(U_14553,U_14552),U_14554),
    inference(clausify,[status(thm)],[f_3682_2]) ).

fof(f_3683_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_3683_2,plain,
    ! [U_14557,U_14556,U_14555] : hAPP(c_Relation_ORange(U_14555,U_14556),hAPP(c_Relation_Oconverse(U_14556,U_14555),U_14557)) = hAPP(c_Relation_ODomain(U_14556,U_14555),U_14557),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

cnf(f_3683_3,plain,
    hAPP(c_Relation_ORange(U_14555,U_14556),hAPP(c_Relation_Oconverse(U_14556,U_14555),U_14557)) = hAPP(c_Relation_ODomain(U_14556,U_14555),U_14557),
    inference(clausify,[status(thm)],[f_3683_2]) ).

fof(f_3684_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_3684_2,plain,
    ! [U_14561,U_14560,U_14559,U_14558] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14558,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14558,U_14558),U_14560),U_14559)),c_Transitive__Closure_Ortrancl(U_14558,hAPP(c_Relation_Oconverse(U_14558,U_14558),U_14561))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14558,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14558,U_14558),U_14559),U_14560)),c_Transitive__Closure_Ortrancl(U_14558,U_14561))) ),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

cnf(f_3684_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14558,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14558,U_14558),U_14560),U_14559)),c_Transitive__Closure_Ortrancl(U_14558,hAPP(c_Relation_Oconverse(U_14558,U_14558),U_14561))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14558,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14558,U_14558),U_14559),U_14560)),c_Transitive__Closure_Ortrancl(U_14558,U_14561))) ),
    inference(clausify,[status(thm)],[f_3684_2]) ).

fof(f_3685_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_3685_2,plain,
    ! [U_14565,U_14564,U_14563,U_14562] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14562)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14562),U_14564),U_14563)),c_Transitive__Closure_Ortrancl(U_14562,U_14565)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14562)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14562),U_14563),U_14564)),c_Transitive__Closure_Ortrancl(U_14562,hAPP(c_Relation_Oconverse(U_14562,U_14562),U_14565)))) ),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

cnf(f_3685_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14562)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14562),U_14564),U_14563)),c_Transitive__Closure_Ortrancl(U_14562,U_14565)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14562,U_14562)),hAPP(hAPP(c_Product__Type_OPair(U_14562,U_14562),U_14563),U_14564)),c_Transitive__Closure_Ortrancl(U_14562,hAPP(c_Relation_Oconverse(U_14562,U_14562),U_14565)))) ),
    inference(clausify,[status(thm)],[f_3685_2]) ).

fof(f_3686_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_3686_2,plain,
    ! [U_14569,U_14568,U_14567,U_14566] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),c_Transitive__Closure_Otrancl(U_14566,hAPP(c_Relation_Oconverse(U_14566,U_14566),U_14569))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),hAPP(c_Relation_Oconverse(U_14566,U_14566),c_Transitive__Closure_Otrancl(U_14566,U_14569)))) ),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

cnf(f_3686_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),c_Transitive__Closure_Otrancl(U_14566,hAPP(c_Relation_Oconverse(U_14566,U_14566),U_14569))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),hAPP(c_Relation_Oconverse(U_14566,U_14566),c_Transitive__Closure_Otrancl(U_14566,U_14569)))) ),
    inference(clausify,[status(thm)],[f_3686_2]) ).

fof(f_3687_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_3687_2,plain,
    ! [U_14573,U_14572,U_14571,U_14570] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14571),U_14572)),hAPP(c_Relation_Oconverse(U_14570,U_14570),c_Transitive__Closure_Otrancl(U_14570,U_14573))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14571),U_14572)),c_Transitive__Closure_Otrancl(U_14570,hAPP(c_Relation_Oconverse(U_14570,U_14570),U_14573)))) ),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

cnf(f_3687_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14571),U_14572)),hAPP(c_Relation_Oconverse(U_14570,U_14570),c_Transitive__Closure_Otrancl(U_14570,U_14573))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14571),U_14572)),c_Transitive__Closure_Otrancl(U_14570,hAPP(c_Relation_Oconverse(U_14570,U_14570),U_14573)))) ),
    inference(clausify,[status(thm)],[f_3687_2]) ).

fof(f_3688_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_3688_2,plain,
    ! [U_14578,U_14577,U_14576,U_14575,U_14574] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14574,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14575,U_14574,U_14576),U_14577)),U_14578))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14575,tc_HOL_Obool)),U_14577),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14575,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14574,U_14575,hAPP(c_Relation_Oconverse(U_14575,U_14574),U_14576)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14574,tc_HOL_Obool)),U_14578))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14575,tc_HOL_Obool)),U_14577),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14575,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14574,U_14575,hAPP(c_Relation_Oconverse(U_14575,U_14574),U_14576)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14574,tc_HOL_Obool)),U_14578)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14574,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14575,U_14574,U_14576),U_14577)),U_14578)) ) ),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

fof(f_3688_3,plain,
    ( ! [U_14588,U_14586,U_14584,U_14582,U_14580] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14580,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14582,U_14580,U_14584),U_14586)),U_14588))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14582,tc_HOL_Obool)),U_14586),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14582,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14580,U_14582,hAPP(c_Relation_Oconverse(U_14582,U_14580),U_14584)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14580,tc_HOL_Obool)),U_14588))))) )
    & ! [U_14587,U_14585,U_14583,U_14581,U_14579] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14581,tc_HOL_Obool)),U_14585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14581,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14579,U_14581,hAPP(c_Relation_Oconverse(U_14581,U_14579),U_14583)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14579,tc_HOL_Obool)),U_14587)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14579,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14581,U_14579,U_14583),U_14585)),U_14587)) ) ),
    inference(miniscope,[status(thm)],[f_3688_2]) ).

cnf(f_3688_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14581,tc_HOL_Obool)),U_14585),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14581,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14579,U_14581,hAPP(c_Relation_Oconverse(U_14581,U_14579),U_14583)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14579,tc_HOL_Obool)),U_14587)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14579,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14581,U_14579,U_14583),U_14585)),U_14587)) ),
    inference(clausify,[status(thm)],[f_3688_3]) ).

cnf(f_3688_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14580,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14582,U_14580,U_14584),U_14586)),U_14588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14582,tc_HOL_Obool)),U_14586),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14582,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14580,U_14582,hAPP(c_Relation_Oconverse(U_14582,U_14580),U_14584)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14580,tc_HOL_Obool)),U_14588))))) ),
    inference(clausify,[status(thm)],[f_3688_3]) ).

fof(f_3689_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_3689_2,plain,
    ! [U_14591,U_14590,U_14589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14589,U_14589),tc_HOL_Obool)),U_14591),hAPP(hAPP(c_Relation_Orel__comp(U_14589,U_14589,U_14589),hAPP(c_Relation_Oconverse(U_14589,U_14589),U_14591)),U_14591)))
      | ~ c_Relation_Orefl__on(U_14589,U_14590,U_14591) ),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

cnf(f_3689_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14589,U_14589),tc_HOL_Obool)),U_14591),hAPP(hAPP(c_Relation_Orel__comp(U_14589,U_14589,U_14589),hAPP(c_Relation_Oconverse(U_14589,U_14589),U_14591)),U_14591)))
    | ~ c_Relation_Orefl__on(U_14589,U_14590,U_14591) ),
    inference(clausify,[status(thm)],[f_3689_2]) ).

fof(f_3690_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_3690_2,plain,
    ! [U_14594,U_14593,U_14592] :
      ( c_Equiv__Relations_Oequiv(U_14592,U_14594,U_14593)
      | hAPP(c_Relation_ODomain(U_14592,U_14592),U_14593) != U_14594
      | hAPP(hAPP(c_Relation_Orel__comp(U_14592,U_14592,U_14592),hAPP(c_Relation_Oconverse(U_14592,U_14592),U_14593)),U_14593) != U_14593 ),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

cnf(f_3690_3,plain,
    ( c_Equiv__Relations_Oequiv(U_14592,U_14594,U_14593)
    | hAPP(c_Relation_ODomain(U_14592,U_14592),U_14593) != U_14594
    | hAPP(hAPP(c_Relation_Orel__comp(U_14592,U_14592,U_14592),hAPP(c_Relation_Oconverse(U_14592,U_14592),U_14593)),U_14593) != U_14593 ),
    inference(clausify,[status(thm)],[f_3690_2]) ).

fof(f_3691_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_3691_2,plain,
    ! [U_14596,U_14595] :
      ( c_Wellfounded_Owf(U_14595,hAPP(c_Relation_Oconverse(U_14595,U_14595),U_14596))
      | ~ c_Wellfounded_Oacyclic(U_14595,U_14596)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14595,U_14595)),U_14596)) ),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

cnf(f_3691_3,plain,
    ( c_Wellfounded_Owf(U_14595,hAPP(c_Relation_Oconverse(U_14595,U_14595),U_14596))
    | ~ c_Wellfounded_Oacyclic(U_14595,U_14596)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14595,U_14595)),U_14596)) ),
    inference(clausify,[status(thm)],[f_3691_2]) ).

fof(f_3692_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_3692_2,plain,
    ! [U_14599,U_14598,U_14597] : hAPP(c_Relation_Oconverse(U_14597,U_14598),U_14599) = hAPP(c_Set_OCollect(tc_prod(U_14598,U_14597)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14598,U_14597,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14598,tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_fun(U_14597,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14597,tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_fun(U_14597,tc_HOL_Obool)),U_14598),c_COMBC(U_14597,tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14597,tc_prod(U_14597,U_14598)),tc_fun(U_14597,tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),U_14598),hAPP(c_COMBB(tc_prod(U_14597,U_14598),tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool),U_14597),c_member(tc_prod(U_14597,U_14598)))),hAPP(c_COMBC(U_14597,U_14598,tc_prod(U_14597,U_14598)),c_Product__Type_OPair(U_14597,U_14598))))),U_14599))),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

cnf(f_3692_3,plain,
    hAPP(c_Relation_Oconverse(U_14597,U_14598),U_14599) = hAPP(c_Set_OCollect(tc_prod(U_14598,U_14597)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14598,U_14597,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14598,tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_fun(U_14597,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14597,tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_fun(U_14597,tc_HOL_Obool)),U_14598),c_COMBC(U_14597,tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14597,tc_prod(U_14597,U_14598)),tc_fun(U_14597,tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool)),U_14598),hAPP(c_COMBB(tc_prod(U_14597,U_14598),tc_fun(tc_fun(tc_prod(U_14597,U_14598),tc_HOL_Obool),tc_HOL_Obool),U_14597),c_member(tc_prod(U_14597,U_14598)))),hAPP(c_COMBC(U_14597,U_14598,tc_prod(U_14597,U_14598)),c_Product__Type_OPair(U_14597,U_14598))))),U_14599))),
    inference(clausify,[status(thm)],[f_3692_2]) ).

fof(f_3693_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_3693_2,plain,
    ! [U_14605,U_14604,U_14603,U_14602,U_14601,U_14600] :
      ( hAPP(c_Relation_OImage(U_14601,U_14600,U_14602),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14604,tc_fun(U_14601,tc_HOL_Obool)),U_14603),U_14605)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14604,tc_fun(U_14600,tc_HOL_Obool)),U_14603),hAPP(hAPP(c_COMBB(tc_fun(U_14601,tc_HOL_Obool),tc_fun(U_14600,tc_HOL_Obool),U_14604),c_Relation_OImage(U_14601,U_14600,U_14602)),U_14605))
      | U_14603 = c_Orderings_Obot__class_Obot(tc_fun(U_14604,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_14600,U_14601,hAPP(c_Relation_Oconverse(U_14601,U_14600),U_14602)) ),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

cnf(f_3693_3,plain,
    ( hAPP(c_Relation_OImage(U_14601,U_14600,U_14602),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14604,tc_fun(U_14601,tc_HOL_Obool)),U_14603),U_14605)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14604,tc_fun(U_14600,tc_HOL_Obool)),U_14603),hAPP(hAPP(c_COMBB(tc_fun(U_14601,tc_HOL_Obool),tc_fun(U_14600,tc_HOL_Obool),U_14604),c_Relation_OImage(U_14601,U_14600,U_14602)),U_14605))
    | U_14603 = c_Orderings_Obot__class_Obot(tc_fun(U_14604,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_14600,U_14601,hAPP(c_Relation_Oconverse(U_14601,U_14600),U_14602)) ),
    inference(clausify,[status(thm)],[f_3693_2]) ).

fof(f_3694_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_3694_2,plain,
    ! [U_14608,U_14607,U_14606] :
      ( ( c_Relation_Ototal__on(U_14606,U_14607,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),U_14608),c_Relation_OId(U_14606)))
        | ~ c_Relation_Ototal__on(U_14606,U_14607,U_14608) )
      & ( c_Relation_Ototal__on(U_14606,U_14607,U_14608)
        | ~ c_Relation_Ototal__on(U_14606,U_14607,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),U_14608),c_Relation_OId(U_14606))) ) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

fof(f_3694_3,plain,
    ( ! [U_14614,U_14612,U_14610] :
        ( c_Relation_Ototal__on(U_14610,U_14612,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14610,U_14610),tc_HOL_Obool)),U_14614),c_Relation_OId(U_14610)))
        | ~ c_Relation_Ototal__on(U_14610,U_14612,U_14614) )
    & ! [U_14613,U_14611,U_14609] :
        ( c_Relation_Ototal__on(U_14609,U_14611,U_14613)
        | ~ c_Relation_Ototal__on(U_14609,U_14611,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14609,U_14609),tc_HOL_Obool)),U_14613),c_Relation_OId(U_14609))) ) ),
    inference(miniscope,[status(thm)],[f_3694_2]) ).

cnf(f_3694_4,plain,
    ( c_Relation_Ototal__on(U_14609,U_14611,U_14613)
    | ~ c_Relation_Ototal__on(U_14609,U_14611,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14609,U_14609),tc_HOL_Obool)),U_14613),c_Relation_OId(U_14609))) ),
    inference(clausify,[status(thm)],[f_3694_3]) ).

cnf(f_3694_5,plain,
    ( c_Relation_Ototal__on(U_14610,U_14612,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14610,U_14610),tc_HOL_Obool)),U_14614),c_Relation_OId(U_14610)))
    | ~ c_Relation_Ototal__on(U_14610,U_14612,U_14614) ),
    inference(clausify,[status(thm)],[f_3694_3]) ).

fof(f_3695_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_3695_2,plain,
    ! [U_14615] : c_Relation_Osingle__valued(U_14615,U_14615,c_Relation_OId(U_14615)),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

cnf(f_3695_3,plain,
    c_Relation_Osingle__valued(U_14615,U_14615,c_Relation_OId(U_14615)),
    inference(clausify,[status(thm)],[f_3695_2]) ).

fof(f_3696_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_3696_2,plain,
    ! [U_14620,U_14619,U_14618,U_14617,U_14616] :
      ( c_Relation_Osingle__valued(U_14616,U_14619,hAPP(hAPP(c_Relation_Orel__comp(U_14616,U_14617,U_14619),U_14618),U_14620))
      | ~ c_Relation_Osingle__valued(U_14617,U_14619,U_14620)
      | ~ c_Relation_Osingle__valued(U_14616,U_14617,U_14618) ),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

cnf(f_3696_3,plain,
    ( c_Relation_Osingle__valued(U_14616,U_14619,hAPP(hAPP(c_Relation_Orel__comp(U_14616,U_14617,U_14619),U_14618),U_14620))
    | ~ c_Relation_Osingle__valued(U_14617,U_14619,U_14620)
    | ~ c_Relation_Osingle__valued(U_14616,U_14617,U_14618) ),
    inference(clausify,[status(thm)],[f_3696_2]) ).

fof(f_3697_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_3697_2,plain,
    ! [U_14624,U_14623,U_14622,U_14621] :
      ( c_Relation_Osingle__valued(U_14621,U_14622,U_14623)
      | ~ c_Relation_Osingle__valued(U_14621,U_14622,U_14624)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14622),tc_HOL_Obool)),U_14623),U_14624)) ),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

cnf(f_3697_3,plain,
    ( c_Relation_Osingle__valued(U_14621,U_14622,U_14623)
    | ~ c_Relation_Osingle__valued(U_14621,U_14622,U_14624)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14622),tc_HOL_Obool)),U_14623),U_14624)) ),
    inference(clausify,[status(thm)],[f_3697_2]) ).

fof(f_3698_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_3698_2,plain,
    ! [U_14626,U_14625] : c_Relation_Osingle__valued(U_14625,U_14625,c_Relation_OId__on(U_14625,U_14626)),
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

cnf(f_3698_3,plain,
    c_Relation_Osingle__valued(U_14625,U_14625,c_Relation_OId__on(U_14625,U_14626)),
    inference(clausify,[status(thm)],[f_3698_2]) ).

fof(f_3699_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_3699_2,plain,
    ! [U_14628,U_14627] : c_Relation_Ototal__on(U_14627,c_Orderings_Obot__class_Obot(tc_fun(U_14627,tc_HOL_Obool)),U_14628),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

cnf(f_3699_3,plain,
    c_Relation_Ototal__on(U_14627,c_Orderings_Obot__class_Obot(tc_fun(U_14627,tc_HOL_Obool)),U_14628),
    inference(clausify,[status(thm)],[f_3699_2]) ).

fof(f_3700_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_3700_2,plain,
    ! [U_14631,U_14630,U_14629] :
      ( ( c_Relation_Ototal__on(U_14629,U_14630,hAPP(c_Relation_Oconverse(U_14629,U_14629),U_14631))
        | ~ c_Relation_Ototal__on(U_14629,U_14630,U_14631) )
      & ( c_Relation_Ototal__on(U_14629,U_14630,U_14631)
        | ~ c_Relation_Ototal__on(U_14629,U_14630,hAPP(c_Relation_Oconverse(U_14629,U_14629),U_14631)) ) ),
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

fof(f_3700_3,plain,
    ( ! [U_14637,U_14635,U_14633] :
        ( c_Relation_Ototal__on(U_14633,U_14635,hAPP(c_Relation_Oconverse(U_14633,U_14633),U_14637))
        | ~ c_Relation_Ototal__on(U_14633,U_14635,U_14637) )
    & ! [U_14636,U_14634,U_14632] :
        ( c_Relation_Ototal__on(U_14632,U_14634,U_14636)
        | ~ c_Relation_Ototal__on(U_14632,U_14634,hAPP(c_Relation_Oconverse(U_14632,U_14632),U_14636)) ) ),
    inference(miniscope,[status(thm)],[f_3700_2]) ).

cnf(f_3700_4,plain,
    ( c_Relation_Ototal__on(U_14632,U_14634,U_14636)
    | ~ c_Relation_Ototal__on(U_14632,U_14634,hAPP(c_Relation_Oconverse(U_14632,U_14632),U_14636)) ),
    inference(clausify,[status(thm)],[f_3700_3]) ).

cnf(f_3700_5,plain,
    ( c_Relation_Ototal__on(U_14633,U_14635,hAPP(c_Relation_Oconverse(U_14633,U_14633),U_14637))
    | ~ c_Relation_Ototal__on(U_14633,U_14635,U_14637) ),
    inference(clausify,[status(thm)],[f_3700_3]) ).

fof(f_3701_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_3701_2,plain,
    ! [U_14643,U_14642,U_14641,U_14640,U_14639,U_14638] :
      ( U_14642 = U_14643
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14638,U_14639)),hAPP(hAPP(c_Product__Type_OPair(U_14638,U_14639),U_14641),U_14643)),U_14640))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14638,U_14639)),hAPP(hAPP(c_Product__Type_OPair(U_14638,U_14639),U_14641),U_14642)),U_14640))
      | ~ c_Relation_Osingle__valued(U_14638,U_14639,U_14640) ),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

cnf(f_3701_3,plain,
    ( U_14642 = U_14643
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14638,U_14639)),hAPP(hAPP(c_Product__Type_OPair(U_14638,U_14639),U_14641),U_14643)),U_14640))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14638,U_14639)),hAPP(hAPP(c_Product__Type_OPair(U_14638,U_14639),U_14641),U_14642)),U_14640))
    | ~ c_Relation_Osingle__valued(U_14638,U_14639,U_14640) ),
    inference(clausify,[status(thm)],[f_3701_2]) ).

fof(f_3702_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_3702_2,plain,
    ! [U_14652,U_14651,U_14650] :
      ( ( c_Relation_Osingle__valued(U_14650,U_14651,U_14652)
        | ? [U_14649,U_14648] :
            ( ? [U_14647] :
                ( U_14648 != U_14647
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14651)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14651),U_14649),U_14647)),U_14652)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14651)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14651),U_14649),U_14648)),U_14652)) ) )
      & ( ! [U_14646,U_14645] :
            ( ! [U_14644] :
                ( U_14645 = U_14644
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14651)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14651),U_14646),U_14644)),U_14652)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14651)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14651),U_14646),U_14645)),U_14652)) )
        | ~ c_Relation_Osingle__valued(U_14650,U_14651,U_14652) ) ),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

fof(f_3702_3,plain,
    ( ! [U_14658,U_14656,U_14654] :
        ( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
        | ? [U_14649,U_14648] :
            ( ? [U_14647] :
                ( U_14648 != U_14647
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),U_14649),U_14647)),U_14658)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),U_14649),U_14648)),U_14658)) ) )
    & ! [U_14657,U_14655,U_14653] :
        ( ! [U_14646,U_14645] :
            ( ! [U_14644] :
                ( U_14645 = U_14644
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14644)),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14645)),U_14657)) )
        | ~ c_Relation_Osingle__valued(U_14653,U_14655,U_14657) ) ),
    inference(miniscope,[status(thm)],[f_3702_2]) ).

fof(f_3702_4,plain,
    ( ! [U_14658,U_14656,U_14654] :
        ( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
        | ? [U_14648] :
            ( ? [U_14647] :
                ( U_14648 != U_14647
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),U_14647)),U_14658)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),U_14648)),U_14658)) ) )
    & ! [U_14657,U_14655,U_14653] :
        ( ! [U_14646,U_14645] :
            ( ! [U_14644] :
                ( U_14645 = U_14644
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14644)),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14645)),U_14657)) )
        | ~ c_Relation_Osingle__valued(U_14653,U_14655,U_14657) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_14649,sK358(U_14658,U_14656,U_14654))],[f_3702_3]) ).

fof(f_3702_5,plain,
    ( ! [U_14658,U_14656,U_14654] :
        ( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
        | ( ? [U_14647] :
              ( sK359(U_14658,U_14656,U_14654) != U_14647
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),U_14647)),U_14658)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),sK359(U_14658,U_14656,U_14654))),U_14658)) ) )
    & ! [U_14657,U_14655,U_14653] :
        ( ! [U_14646,U_14645] :
            ( ! [U_14644] :
                ( U_14645 = U_14644
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14644)),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14645)),U_14657)) )
        | ~ c_Relation_Osingle__valued(U_14653,U_14655,U_14657) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_14648,sK359(U_14658,U_14656,U_14654))],[f_3702_4]) ).

fof(f_3702_6,plain,
    ( ! [U_14658,U_14656,U_14654] :
        ( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
        | ( sK359(U_14658,U_14656,U_14654) != sK360(U_14658,U_14656,U_14654)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),sK360(U_14658,U_14656,U_14654))),U_14658))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),sK359(U_14658,U_14656,U_14654))),U_14658)) ) )
    & ! [U_14657,U_14655,U_14653] :
        ( ! [U_14646,U_14645] :
            ( ! [U_14644] :
                ( U_14645 = U_14644
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14644)),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14645)),U_14657)) )
        | ~ c_Relation_Osingle__valued(U_14653,U_14655,U_14657) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_14647,sK360(U_14658,U_14656,U_14654))],[f_3702_5]) ).

cnf(f_3702_7,plain,
    ( U_14645 = U_14644
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14644)),U_14657))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14653,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14653,U_14655),U_14646),U_14645)),U_14657))
    | ~ c_Relation_Osingle__valued(U_14653,U_14655,U_14657) ),
    inference(clausify,[status(thm)],[f_3702_6]) ).

cnf(f_3702_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),sK359(U_14658,U_14656,U_14654))),U_14658))
    | c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
    inference(clausify,[status(thm)],[f_3702_6]) ).

cnf(f_3702_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK358(U_14658,U_14656,U_14654)),sK360(U_14658,U_14656,U_14654))),U_14658))
    | c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
    inference(clausify,[status(thm)],[f_3702_6]) ).

cnf(f_3702_10,plain,
    ( sK359(U_14658,U_14656,U_14654) != sK360(U_14658,U_14656,U_14654)
    | c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
    inference(clausify,[status(thm)],[f_3702_6]) ).

fof(f_3703_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_3703_2,plain,
    ! [U_14665,U_14664,U_14663] :
      ( ( c_Relation_Ototal__on(U_14663,U_14664,U_14665)
        | ? [U_14662] :
            ( ? [U_14661] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14663,U_14663)),hAPP(hAPP(c_Product__Type_OPair(U_14663,U_14663),U_14661),U_14662)),U_14665))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14663,U_14663)),hAPP(hAPP(c_Product__Type_OPair(U_14663,U_14663),U_14662),U_14661)),U_14665))
                & U_14662 != U_14661
                & hBOOL(hAPP(hAPP(c_member(U_14663),U_14661),U_14664)) )
            & hBOOL(hAPP(hAPP(c_member(U_14663),U_14662),U_14664)) ) )
      & ( ! [U_14660] :
            ( ! [U_14659] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14663,U_14663)),hAPP(hAPP(c_Product__Type_OPair(U_14663,U_14663),U_14659),U_14660)),U_14665))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14663,U_14663)),hAPP(hAPP(c_Product__Type_OPair(U_14663,U_14663),U_14660),U_14659)),U_14665))
                | U_14660 = U_14659
                | ~ hBOOL(hAPP(hAPP(c_member(U_14663),U_14659),U_14664)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14663),U_14660),U_14664)) )
        | ~ c_Relation_Ototal__on(U_14663,U_14664,U_14665) ) ),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

fof(f_3703_3,plain,
    ( ! [U_14671,U_14669,U_14667] :
        ( c_Relation_Ototal__on(U_14667,U_14669,U_14671)
        | ? [U_14662] :
            ( ? [U_14661] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),U_14661),U_14662)),U_14671))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),U_14662),U_14661)),U_14671))
                & U_14662 != U_14661
                & hBOOL(hAPP(hAPP(c_member(U_14667),U_14661),U_14669)) )
            & hBOOL(hAPP(hAPP(c_member(U_14667),U_14662),U_14669)) ) )
    & ! [U_14670,U_14668,U_14666] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14659),U_14660)),U_14670))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14660),U_14659)),U_14670))
                | U_14660 = U_14659
                | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14659),U_14668)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14660),U_14668)) )
        | ~ c_Relation_Ototal__on(U_14666,U_14668,U_14670) ) ),
    inference(miniscope,[status(thm)],[f_3703_2]) ).

fof(f_3703_4,plain,
    ( ! [U_14671,U_14669,U_14667] :
        ( c_Relation_Ototal__on(U_14667,U_14669,U_14671)
        | ( ? [U_14661] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),U_14661),sK361(U_14671,U_14669,U_14667))),U_14671))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK361(U_14671,U_14669,U_14667)),U_14661)),U_14671))
              & sK361(U_14671,U_14669,U_14667) != U_14661
              & hBOOL(hAPP(hAPP(c_member(U_14667),U_14661),U_14669)) )
          & hBOOL(hAPP(hAPP(c_member(U_14667),sK361(U_14671,U_14669,U_14667)),U_14669)) ) )
    & ! [U_14670,U_14668,U_14666] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14659),U_14660)),U_14670))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14660),U_14659)),U_14670))
                | U_14660 = U_14659
                | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14659),U_14668)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14660),U_14668)) )
        | ~ c_Relation_Ototal__on(U_14666,U_14668,U_14670) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_14662,sK361(U_14671,U_14669,U_14667))],[f_3703_3]) ).

fof(f_3703_5,plain,
    ( ! [U_14671,U_14669,U_14667] :
        ( c_Relation_Ototal__on(U_14667,U_14669,U_14671)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK362(U_14671,U_14669,U_14667)),sK361(U_14671,U_14669,U_14667))),U_14671))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK361(U_14671,U_14669,U_14667)),sK362(U_14671,U_14669,U_14667))),U_14671))
          & sK361(U_14671,U_14669,U_14667) != sK362(U_14671,U_14669,U_14667)
          & hBOOL(hAPP(hAPP(c_member(U_14667),sK362(U_14671,U_14669,U_14667)),U_14669))
          & hBOOL(hAPP(hAPP(c_member(U_14667),sK361(U_14671,U_14669,U_14667)),U_14669)) ) )
    & ! [U_14670,U_14668,U_14666] :
        ( ! [U_14660] :
            ( ! [U_14659] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14659),U_14660)),U_14670))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14660),U_14659)),U_14670))
                | U_14660 = U_14659
                | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14659),U_14668)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14660),U_14668)) )
        | ~ c_Relation_Ototal__on(U_14666,U_14668,U_14670) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_14661,sK362(U_14671,U_14669,U_14667))],[f_3703_4]) ).

cnf(f_3703_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14659),U_14660)),U_14670))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14666,U_14666)),hAPP(hAPP(c_Product__Type_OPair(U_14666,U_14666),U_14660),U_14659)),U_14670))
    | U_14660 = U_14659
    | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14659),U_14668))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14666),U_14660),U_14668))
    | ~ c_Relation_Ototal__on(U_14666,U_14668,U_14670) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

cnf(f_3703_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14667),sK361(U_14671,U_14669,U_14667)),U_14669))
    | c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

cnf(f_3703_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14667),sK362(U_14671,U_14669,U_14667)),U_14669))
    | c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

cnf(f_3703_9,plain,
    ( sK361(U_14671,U_14669,U_14667) != sK362(U_14671,U_14669,U_14667)
    | c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

cnf(f_3703_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK361(U_14671,U_14669,U_14667)),sK362(U_14671,U_14669,U_14667))),U_14671))
    | c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

cnf(f_3703_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK362(U_14671,U_14669,U_14667)),sK361(U_14671,U_14669,U_14667))),U_14671))
    | c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
    inference(clausify,[status(thm)],[f_3703_5]) ).

fof(f_3704_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_3704_2,plain,
    ! [U_14676,U_14675,U_14674,U_14673,U_14672] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14676),U_14675)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14675),U_14676)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14674),U_14676)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14674),U_14675)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
      | ~ c_Relation_Osingle__valued(U_14672,U_14672,U_14673) ),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

cnf(f_3704_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14676),U_14675)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14675),U_14676)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14674),U_14676)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14672,U_14672)),hAPP(hAPP(c_Product__Type_OPair(U_14672,U_14672),U_14674),U_14675)),c_Transitive__Closure_Ortrancl(U_14672,U_14673)))
    | ~ c_Relation_Osingle__valued(U_14672,U_14672,U_14673) ),
    inference(clausify,[status(thm)],[f_3704_2]) ).

fof(f_3705_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_3705_2,plain,
    ! [U_14681,U_14680,U_14679,U_14678,U_14677] :
      ( hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14678,tc_HOL_Obool)),U_14680),U_14681)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14677,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),U_14680)),hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),U_14681))
      | ~ c_Relation_Osingle__valued(U_14677,U_14678,hAPP(c_Relation_Oconverse(U_14678,U_14677),U_14679)) ),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

cnf(f_3705_3,plain,
    ( hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14678,tc_HOL_Obool)),U_14680),U_14681)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14677,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),U_14680)),hAPP(c_Relation_OImage(U_14678,U_14677,U_14679),U_14681))
    | ~ c_Relation_Osingle__valued(U_14677,U_14678,hAPP(c_Relation_Oconverse(U_14678,U_14677),U_14679)) ),
    inference(clausify,[status(thm)],[f_3705_2]) ).

fof(f_3706_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_3706_2,plain,
    ! [U_14684,U_14683,U_14682] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14682,U_14682)),U_14683),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14682,U_14682),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_14682,U_14682),tc_HOL_Obool),tc_fun(tc_prod(U_14682,U_14682),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14682,U_14682),tc_HOL_Obool)),U_14684))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14682,U_14682)),U_14683),c_Transitive__Closure_Ortrancl(U_14682,U_14684))) ),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

cnf(f_3706_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14682,U_14682)),U_14683),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14682,U_14682),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_14682,U_14682),tc_HOL_Obool),tc_fun(tc_prod(U_14682,U_14682),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14682,U_14682),tc_HOL_Obool)),U_14684))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14682,U_14682)),U_14683),c_Transitive__Closure_Ortrancl(U_14682,U_14684))) ),
    inference(clausify,[status(thm)],[f_3706_2]) ).

fof(f_3707_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_3707_2,plain,
    ! [U_14687,U_14686] :
      ( c_Wellfounded_Oacyclic(U_14686,U_14687)
      | ? [U_14685] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14686,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14686,U_14686),U_14685),U_14685)),c_Transitive__Closure_Otrancl(U_14686,U_14687))) ),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

fof(f_3707_3,plain,
    ! [U_14687,U_14686] :
      ( c_Wellfounded_Oacyclic(U_14686,U_14687)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14686,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14686,U_14686),sK363(U_14687,U_14686)),sK363(U_14687,U_14686))),c_Transitive__Closure_Otrancl(U_14686,U_14687))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_14685,sK363(U_14687,U_14686))],[f_3707_2]) ).

cnf(f_3707_4,plain,
    ( c_Wellfounded_Oacyclic(U_14686,U_14687)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14686,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14686,U_14686),sK363(U_14687,U_14686)),sK363(U_14687,U_14686))),c_Transitive__Closure_Otrancl(U_14686,U_14687))) ),
    inference(clausify,[status(thm)],[f_3707_3]) ).

fof(f_3708_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_3708_2,plain,
    ! [U_14690,U_14689,U_14688] :
      ( c_Relation_Osingle__valued(U_14688,U_14688,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14688,U_14688),tc_HOL_Obool),U_14690),U_14689))
      | ~ c_Relation_Osingle__valued(U_14688,U_14688,U_14689) ),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

cnf(f_3708_3,plain,
    ( c_Relation_Osingle__valued(U_14688,U_14688,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14688,U_14688),tc_HOL_Obool),U_14690),U_14689))
    | ~ c_Relation_Osingle__valued(U_14688,U_14688,U_14689) ),
    inference(clausify,[status(thm)],[f_3708_2]) ).

fof(f_3709_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_3709_2,plain,
    ! [U_14694,U_14693,U_14692,U_14691] : hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),U_14692),hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),U_14693),U_14694)) = hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14693),U_14692)),U_14694),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

cnf(f_3709_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),U_14692),hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),U_14693),U_14694)) = hAPP(hAPP(c_Nat_Ocompow(U_14691,U_14691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14693),U_14692)),U_14694),
    inference(clausify,[status(thm)],[f_3709_2]) ).

fof(f_3710_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_3710_2,plain,
    ! [U_14698,U_14697,U_14696,U_14695] : hAPP(U_14695,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14696,U_14696),U_14697),U_14695),U_14698)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14696,U_14696),U_14697),U_14695),hAPP(U_14695,U_14698)),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

cnf(f_3710_3,plain,
    hAPP(U_14695,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14696,U_14696),U_14697),U_14695),U_14698)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14696,U_14696),U_14697),U_14695),hAPP(U_14695,U_14698)),
    inference(clausify,[status(thm)],[f_3710_2]) ).

fof(f_3711_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_3711_2,plain,
    ! [U_14701,U_14700,U_14699] :
      ( c_Wellfounded_Owf(U_14699,U_14701)
      | ~ c_Wellfounded_Owf(U_14699,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14699,U_14699),tc_HOL_Obool),U_14700),U_14701)) ),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

cnf(f_3711_3,plain,
    ( c_Wellfounded_Owf(U_14699,U_14701)
    | ~ c_Wellfounded_Owf(U_14699,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14699,U_14699),tc_HOL_Obool),U_14700),U_14701)) ),
    inference(clausify,[status(thm)],[f_3711_2]) ).

fof(f_3712_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_3712_2,plain,
    ! [U_14705,U_14704,U_14703,U_14702] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14702,U_14703),tc_fun(U_14702,U_14703)),U_14704),c_Fun_Ocomp(U_14703,U_14703,U_14702,U_14705)) = c_Fun_Ocomp(U_14703,U_14703,U_14702,hAPP(hAPP(c_Nat_Ocompow(U_14703,U_14703),U_14704),U_14705)),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

cnf(f_3712_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14702,U_14703),tc_fun(U_14702,U_14703)),U_14704),c_Fun_Ocomp(U_14703,U_14703,U_14702,U_14705)) = c_Fun_Ocomp(U_14703,U_14703,U_14702,hAPP(hAPP(c_Nat_Ocompow(U_14703,U_14703),U_14704),U_14705)),
    inference(clausify,[status(thm)],[f_3712_2]) ).

fof(f_3713_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_3713_2,plain,
    ! [U_14708,U_14707,U_14706] : hAPP(hAPP(c_Relation_Orel__comp(U_14706,U_14706,U_14706),U_14707),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14708),U_14707)) = hAPP(hAPP(c_Relation_Orel__comp(U_14706,U_14706,U_14706),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14708),U_14707)),U_14707),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

cnf(f_3713_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14706,U_14706,U_14706),U_14707),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14708),U_14707)) = hAPP(hAPP(c_Relation_Orel__comp(U_14706,U_14706,U_14706),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14708),U_14707)),U_14707),
    inference(clausify,[status(thm)],[f_3713_2]) ).

fof(f_3714_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_3714_2,plain,
    ! [U_14710,U_14709] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14709,U_14709),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14710) = U_14710,
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

cnf(f_3714_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14709,U_14709),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14710) = U_14710,
    inference(clausify,[status(thm)],[f_3714_2]) ).

fof(f_3715_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_3715_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_3715_1]) ).

cnf(f_3715_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_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),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_3716_2,plain,
    ! [U_14719,U_14718,U_14717] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14718),c_Transitive__Closure_Ortrancl(U_14717,U_14719)))
        | ! [U_14716] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14717,U_14717),tc_HOL_Obool),U_14716),U_14719))) )
      & ( ? [U_14715] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14717,U_14717),tc_HOL_Obool),U_14715),U_14719)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14718),c_Transitive__Closure_Ortrancl(U_14717,U_14719))) ) ),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

fof(f_3716_3,plain,
    ( ! [U_14725,U_14723,U_14721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),c_Transitive__Closure_Ortrancl(U_14721,U_14725)))
        | ! [U_14716] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14721,U_14721),tc_HOL_Obool),U_14716),U_14725))) )
    & ! [U_14724,U_14722,U_14720] :
        ( ? [U_14715] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14720,U_14720),tc_HOL_Obool),U_14715),U_14724)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),c_Transitive__Closure_Ortrancl(U_14720,U_14724))) ) ),
    inference(miniscope,[status(thm)],[f_3716_2]) ).

fof(f_3716_4,plain,
    ( ! [U_14725,U_14723,U_14721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),c_Transitive__Closure_Ortrancl(U_14721,U_14725)))
        | ! [U_14716] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14721,U_14721),tc_HOL_Obool),U_14716),U_14725))) )
    & ! [U_14724,U_14722,U_14720] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14720,U_14720),tc_HOL_Obool),sK364(U_14724,U_14722,U_14720)),U_14724)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),c_Transitive__Closure_Ortrancl(U_14720,U_14724))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_14715,sK364(U_14724,U_14722,U_14720))],[f_3716_3]) ).

cnf(f_3716_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14720,U_14720),tc_HOL_Obool),sK364(U_14724,U_14722,U_14720)),U_14724)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14720,U_14720)),U_14722),c_Transitive__Closure_Ortrancl(U_14720,U_14724))) ),
    inference(clausify,[status(thm)],[f_3716_4]) ).

cnf(f_3716_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),c_Transitive__Closure_Ortrancl(U_14721,U_14725)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14721,U_14721)),U_14723),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14721,U_14721),tc_HOL_Obool),U_14716),U_14725))) ),
    inference(clausify,[status(thm)],[f_3716_4]) ).

fof(f_3717_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_3717_2,plain,
    ! [U_14728,U_14727,U_14726] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14726,U_14726),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14727)),U_14728) = hAPP(hAPP(c_Relation_Orel__comp(U_14726,U_14726,U_14726),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14726,U_14726),tc_HOL_Obool),U_14727),U_14728)),U_14728),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

cnf(f_3717_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14726,U_14726),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14727)),U_14728) = hAPP(hAPP(c_Relation_Orel__comp(U_14726,U_14726,U_14726),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14726,U_14726),tc_HOL_Obool),U_14727),U_14728)),U_14728),
    inference(clausify,[status(thm)],[f_3717_2]) ).

fof(f_3718_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_3718_2,plain,
    ! [U_14732,U_14731,U_14730,U_14729] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14730),U_14731)),U_14732) = hAPP(hAPP(c_Relation_Orel__comp(U_14729,U_14729,U_14729),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),U_14730),U_14732)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),U_14731),U_14732)),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

cnf(f_3718_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14730),U_14731)),U_14732) = hAPP(hAPP(c_Relation_Orel__comp(U_14729,U_14729,U_14729),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),U_14730),U_14732)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14729,U_14729),tc_HOL_Obool),U_14731),U_14732)),
    inference(clausify,[status(thm)],[f_3718_2]) ).

fof(f_3719_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_3719_2,plain,
    ! [U_14734,U_14733] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14733,U_14733),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14734) = c_Relation_OId(U_14733),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

cnf(f_3719_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14733,U_14733),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14734) = c_Relation_OId(U_14733),
    inference(clausify,[status(thm)],[f_3719_2]) ).

fof(f_3720_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_3720_2,plain,
    ! [U_14737,U_14736,U_14735] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14736),U_14736)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14735,U_14735),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14737))),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

cnf(f_3720_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14736),U_14736)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14735,U_14735),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14737))),
    inference(clausify,[status(thm)],[f_3720_2]) ).

fof(f_3721_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_3721_2,plain,
    ! [U_14741,U_14740,U_14739,U_14738] :
      ( U_14739 = U_14740
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14738,U_14738),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14741))) ),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

fof(f_3721_3,plain,
    ! [U_14741,U_14740,U_14739] :
      ( ! [U_14738] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14738,U_14738),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14741)))
      | U_14739 = U_14740 ),
    inference(miniscope,[status(thm)],[f_3721_2]) ).

cnf(f_3721_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14738,U_14738)),hAPP(hAPP(c_Product__Type_OPair(U_14738,U_14738),U_14739),U_14740)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14738,U_14738),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14741)))
    | U_14739 = U_14740 ),
    inference(clausify,[status(thm)],[f_3721_3]) ).

fof(f_3722_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_3722_2,plain,
    ! [U_14747,U_14746,U_14745,U_14744,U_14743,U_14742] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14743),U_14747)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14745)),U_14746)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14744),U_14747)),U_14746))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14743),U_14744)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),U_14745),U_14746))) ),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

cnf(f_3722_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14743),U_14747)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14745)),U_14746)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14744),U_14747)),U_14746))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14743),U_14744)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),U_14745),U_14746))) ),
    inference(clausify,[status(thm)],[f_3722_2]) ).

fof(f_3723_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_3723_2,plain,
    ! [U_14753,U_14752,U_14751,U_14750,U_14749,U_14748] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14749),U_14752)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14753)),U_14751)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14750),U_14752)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),U_14753),U_14751)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14749),U_14750)),U_14751)) ),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

cnf(f_3723_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14749),U_14752)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14753)),U_14751)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14750),U_14752)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),U_14753),U_14751)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14749),U_14750)),U_14751)) ),
    inference(clausify,[status(thm)],[f_3723_2]) ).

fof(f_3724_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_3724_2,plain,
    ! [U_14756,U_14755,U_14754] : hAPP(hAPP(c_Nat_Ocompow(U_14754,U_14754),hAPP(c_Nat_OSuc,U_14755)),U_14756) = hAPP(c_Fun_Ocomp(U_14754,U_14754,U_14754,U_14756),hAPP(hAPP(c_Nat_Ocompow(U_14754,U_14754),U_14755),U_14756)),
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

cnf(f_3724_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14754,U_14754),hAPP(c_Nat_OSuc,U_14755)),U_14756) = hAPP(c_Fun_Ocomp(U_14754,U_14754,U_14754,U_14756),hAPP(hAPP(c_Nat_Ocompow(U_14754,U_14754),U_14755),U_14756)),
    inference(clausify,[status(thm)],[f_3724_2]) ).

fof(f_3725_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_3725_2,plain,
    ! [U_14760,U_14759,U_14758,U_14757] : hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14758),U_14759)),U_14760) = hAPP(c_Fun_Ocomp(U_14757,U_14757,U_14757,hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),U_14758),U_14760)),hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),U_14759),U_14760)),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

cnf(f_3725_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14758),U_14759)),U_14760) = hAPP(c_Fun_Ocomp(U_14757,U_14757,U_14757,hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),U_14758),U_14760)),hAPP(hAPP(c_Nat_Ocompow(U_14757,U_14757),U_14759),U_14760)),
    inference(clausify,[status(thm)],[f_3725_2]) ).

fof(f_3726_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_3726_2,plain,
    ! [U_14762,U_14761] : hAPP(hAPP(c_Nat_Ocompow(U_14761,U_14761),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14762) = c_Fun_Oid(U_14761),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

cnf(f_3726_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14761,U_14761),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14762) = c_Fun_Oid(U_14761),
    inference(clausify,[status(thm)],[f_3726_2]) ).

fof(f_3727_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_3727_2,plain,
    ! [U_14767,U_14766,U_14765] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14765,U_14765)),U_14766),c_Transitive__Closure_Otrancl(U_14765,U_14767)))
        | ! [U_14764] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14765,U_14765)),U_14766),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14765,U_14765),tc_HOL_Obool),U_14764),U_14767)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14764)) ) )
      & ( ? [U_14763] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14765,U_14765)),U_14766),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14765,U_14765),tc_HOL_Obool),U_14763),U_14767)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14763)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14765,U_14765)),U_14766),c_Transitive__Closure_Otrancl(U_14765,U_14767))) ) ),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

fof(f_3727_3,plain,
    ( ! [U_14773,U_14771,U_14769] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),c_Transitive__Closure_Otrancl(U_14769,U_14773)))
        | ! [U_14764] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14769,U_14769),tc_HOL_Obool),U_14764),U_14773)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14764)) ) )
    & ! [U_14772,U_14770,U_14768] :
        ( ? [U_14763] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14763),U_14772)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14763)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),c_Transitive__Closure_Otrancl(U_14768,U_14772))) ) ),
    inference(miniscope,[status(thm)],[f_3727_2]) ).

fof(f_3727_4,plain,
    ( ! [U_14773,U_14771,U_14769] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),c_Transitive__Closure_Otrancl(U_14769,U_14773)))
        | ! [U_14764] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14769,U_14769),tc_HOL_Obool),U_14764),U_14773)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14764)) ) )
    & ! [U_14772,U_14770,U_14768] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),sK365(U_14772,U_14770,U_14768)),U_14772)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK365(U_14772,U_14770,U_14768))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),c_Transitive__Closure_Otrancl(U_14768,U_14772))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_14763,sK365(U_14772,U_14770,U_14768))],[f_3727_3]) ).

cnf(f_3727_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK365(U_14772,U_14770,U_14768)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),c_Transitive__Closure_Otrancl(U_14768,U_14772))) ),
    inference(clausify,[status(thm)],[f_3727_4]) ).

cnf(f_3727_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),sK365(U_14772,U_14770,U_14768)),U_14772)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),U_14770),c_Transitive__Closure_Otrancl(U_14768,U_14772))) ),
    inference(clausify,[status(thm)],[f_3727_4]) ).

cnf(f_3727_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),c_Transitive__Closure_Otrancl(U_14769,U_14773)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14769,U_14769)),U_14771),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14769,U_14769),tc_HOL_Obool),U_14764),U_14773)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14764)) ),
    inference(clausify,[status(thm)],[f_3727_4]) ).

fof(f_3728_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_3728_2,plain,
    ! [U_14775,U_14774] : c_Transitive__Closure_Ortrancl(U_14774,U_14775) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14774,U_14774),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_14774,U_14774),tc_HOL_Obool),tc_fun(tc_prod(U_14774,U_14774),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14774,U_14774),tc_HOL_Obool)),U_14775)),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

cnf(f_3728_3,plain,
    c_Transitive__Closure_Ortrancl(U_14774,U_14775) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14774,U_14774),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_14774,U_14774),tc_HOL_Obool),tc_fun(tc_prod(U_14774,U_14774),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14774,U_14774),tc_HOL_Obool)),U_14775)),
    inference(clausify,[status(thm)],[f_3728_2]) ).

fof(f_3729_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_3729_2,plain,
    ! [U_14776] : c_Nat_Ofunpow(U_14776) = c_Nat_Ocompow(U_14776,U_14776),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

cnf(f_3729_3,plain,
    c_Nat_Ofunpow(U_14776) = c_Nat_Ocompow(U_14776,U_14776),
    inference(clausify,[status(thm)],[f_3729_2]) ).

fof(f_3730_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_3730_2,plain,
    ! [U_14783,U_14782,U_14781,U_14780,U_14779] :
      ( ? [U_14778,U_14777] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14778),U_14781)),U_14783))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14778)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14777),U_14783)))
          & U_14782 = hAPP(c_Nat_OSuc,U_14777) )
      | ( U_14780 = U_14781
        & U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

fof(f_3730_3,plain,
    ! [U_14783,U_14782,U_14781,U_14780,U_14779] :
      ( ? [U_14777] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK366(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14781)),U_14783))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),sK366(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14777),U_14783)))
          & U_14782 = hAPP(c_Nat_OSuc,U_14777) )
      | ( U_14780 = U_14781
        & U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_14778,sK366(U_14783,U_14782,U_14781,U_14780,U_14779))],[f_3730_2]) ).

fof(f_3730_4,plain,
    ! [U_14783,U_14782,U_14781,U_14780,U_14779] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK366(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14781)),U_14783))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),sK366(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK367(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14783)))
        & U_14782 = hAPP(c_Nat_OSuc,sK367(U_14783,U_14782,U_14781,U_14780,U_14779)) )
      | ( U_14780 = U_14781
        & U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_14777,sK367(U_14783,U_14782,U_14781,U_14780,U_14779))],[f_3730_3]) ).

cnf(f_3730_5,plain,
    ( U_14782 = hAPP(c_Nat_OSuc,sK367(U_14783,U_14782,U_14781,U_14780,U_14779))
    | U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

cnf(f_3730_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),sK366(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK367(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14783)))
    | U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

cnf(f_3730_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK366(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14781)),U_14783))
    | U_14782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

cnf(f_3730_8,plain,
    ( U_14782 = hAPP(c_Nat_OSuc,sK367(U_14783,U_14782,U_14781,U_14780,U_14779))
    | U_14780 = U_14781
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

cnf(f_3730_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),sK366(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK367(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14783)))
    | U_14780 = U_14781
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

cnf(f_3730_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK366(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14781)),U_14783))
    | U_14780 = U_14781
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),U_14780),U_14781)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),U_14782),U_14783))) ),
    inference(clausify,[status(thm)],[f_3730_4]) ).

fof(f_3731_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_3731_2,plain,
    ! [U_14790,U_14789,U_14788,U_14787,U_14786] :
      ( ? [U_14785,U_14784] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14785),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14784),U_14790)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14785)),U_14790))
          & U_14789 = hAPP(c_Nat_OSuc,U_14784) )
      | ( U_14787 = U_14788
        & U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

fof(f_3731_3,plain,
    ! [U_14790,U_14789,U_14788,U_14787,U_14786] :
      ( ? [U_14784] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK368(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14784),U_14790)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),sK368(U_14790,U_14789,U_14788,U_14787,U_14786))),U_14790))
          & U_14789 = hAPP(c_Nat_OSuc,U_14784) )
      | ( U_14787 = U_14788
        & U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_14785,sK368(U_14790,U_14789,U_14788,U_14787,U_14786))],[f_3731_2]) ).

fof(f_3731_4,plain,
    ! [U_14790,U_14789,U_14788,U_14787,U_14786] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK368(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),sK369(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14790)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),sK368(U_14790,U_14789,U_14788,U_14787,U_14786))),U_14790))
        & U_14789 = hAPP(c_Nat_OSuc,sK369(U_14790,U_14789,U_14788,U_14787,U_14786)) )
      | ( U_14787 = U_14788
        & U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_14784,sK369(U_14790,U_14789,U_14788,U_14787,U_14786))],[f_3731_3]) ).

cnf(f_3731_5,plain,
    ( U_14789 = hAPP(c_Nat_OSuc,sK369(U_14790,U_14789,U_14788,U_14787,U_14786))
    | U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),sK368(U_14790,U_14789,U_14788,U_14787,U_14786))),U_14790))
    | U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK368(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),sK369(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14790)))
    | U_14789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_8,plain,
    ( U_14789 = hAPP(c_Nat_OSuc,sK369(U_14790,U_14789,U_14788,U_14787,U_14786))
    | U_14787 = U_14788
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),sK368(U_14790,U_14789,U_14788,U_14787,U_14786))),U_14790))
    | U_14787 = U_14788
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

cnf(f_3731_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK368(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),sK369(U_14790,U_14789,U_14788,U_14787,U_14786)),U_14790)))
    | U_14787 = U_14788
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),U_14787),U_14788)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14786,U_14786),tc_HOL_Obool),U_14789),U_14790))) ),
    inference(clausify,[status(thm)],[f_3731_4]) ).

fof(f_3732_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_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_Pa_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_Pa_2),V_Qa_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).

fof(f_3732_2,plain,
    ! [U_14797,U_14796,U_14795,U_14794,U_14793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
      | ? [U_14792] :
          ( ? [U_14791] :
              ( U_14791 != U_14792
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14791),U_14792)),U_14797)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14792),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

fof(f_3732_3,plain,
    ! [U_14797,U_14796,U_14795,U_14794,U_14793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
      | ( ? [U_14791] :
            ( U_14791 != sK370(U_14797,U_14796,U_14795,U_14794,U_14793)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14791),sK370(U_14797,U_14796,U_14795,U_14794,U_14793))),U_14797)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK370(U_14797,U_14796,U_14795,U_14794,U_14793)),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_14792,sK370(U_14797,U_14796,U_14795,U_14794,U_14793))],[f_3732_2]) ).

fof(f_3732_4,plain,
    ! [U_14797,U_14796,U_14795,U_14794,U_14793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
      | ( sK371(U_14797,U_14796,U_14795,U_14794,U_14793) != sK370(U_14797,U_14796,U_14795,U_14794,U_14793)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK371(U_14797,U_14796,U_14795,U_14794,U_14793)),sK370(U_14797,U_14796,U_14795,U_14794,U_14793))),U_14797))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK370(U_14797,U_14796,U_14795,U_14794,U_14793)),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_14791,sK371(U_14797,U_14796,U_14795,U_14794,U_14793))],[f_3732_3]) ).

cnf(f_3732_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK370(U_14797,U_14796,U_14795,U_14794,U_14793)),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

cnf(f_3732_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK371(U_14797,U_14796,U_14795,U_14794,U_14793)),sK370(U_14797,U_14796,U_14795,U_14794,U_14793))),U_14797))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

cnf(f_3732_7,plain,
    ( sK371(U_14797,U_14796,U_14795,U_14794,U_14793) != sK370(U_14797,U_14796,U_14795,U_14794,U_14793)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,U_14796)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),U_14794),U_14795)),c_Transitive__Closure_Ortrancl(U_14793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14793),tc_HOL_Obool)),U_14796),U_14797)))) ),
    inference(clausify,[status(thm)],[f_3732_4]) ).

fof(f_3733_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_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_Pa_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_Pa_2),V_Qa_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).

fof(f_3733_2,plain,
    ! [U_14804,U_14803,U_14802,U_14801,U_14800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
      | ? [U_14799] :
          ( ? [U_14798] :
              ( U_14799 != U_14798
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14799),U_14798)),U_14804)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14799)),c_Transitive__Closure_Ortrancl(U_14800,U_14803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

fof(f_3733_3,plain,
    ! [U_14804,U_14803,U_14802,U_14801,U_14800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
      | ( ? [U_14798] :
            ( sK372(U_14804,U_14803,U_14802,U_14801,U_14800) != U_14798
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),sK372(U_14804,U_14803,U_14802,U_14801,U_14800)),U_14798)),U_14804)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),sK372(U_14804,U_14803,U_14802,U_14801,U_14800))),c_Transitive__Closure_Ortrancl(U_14800,U_14803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_14799,sK372(U_14804,U_14803,U_14802,U_14801,U_14800))],[f_3733_2]) ).

fof(f_3733_4,plain,
    ! [U_14804,U_14803,U_14802,U_14801,U_14800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
      | ( sK372(U_14804,U_14803,U_14802,U_14801,U_14800) != sK373(U_14804,U_14803,U_14802,U_14801,U_14800)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),sK372(U_14804,U_14803,U_14802,U_14801,U_14800)),sK373(U_14804,U_14803,U_14802,U_14801,U_14800))),U_14804))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),sK372(U_14804,U_14803,U_14802,U_14801,U_14800))),c_Transitive__Closure_Ortrancl(U_14800,U_14803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_14798,sK373(U_14804,U_14803,U_14802,U_14801,U_14800))],[f_3733_3]) ).

cnf(f_3733_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),sK372(U_14804,U_14803,U_14802,U_14801,U_14800))),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

cnf(f_3733_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),sK372(U_14804,U_14803,U_14802,U_14801,U_14800)),sK373(U_14804,U_14803,U_14802,U_14801,U_14800))),U_14804))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

cnf(f_3733_7,plain,
    ( sK372(U_14804,U_14803,U_14802,U_14801,U_14800) != sK373(U_14804,U_14803,U_14802,U_14801,U_14800)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,U_14803)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),U_14801),U_14802)),c_Transitive__Closure_Ortrancl(U_14800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14800,U_14800),tc_HOL_Obool)),U_14803),U_14804)))) ),
    inference(clausify,[status(thm)],[f_3733_4]) ).

fof(f_3734_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_3734_2,plain,
    ! [U_14810,U_14809,U_14808,U_14807,U_14806] :
      ( ? [U_14805] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14805),U_14808)),U_14810))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),U_14805)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),U_14809),U_14810))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),U_14808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14809)),U_14810))) ),
    inference(variable_rename,[status(thm)],[f_3734_1]) ).

fof(f_3734_3,plain,
    ! [U_14810,U_14809,U_14808,U_14807,U_14806] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),sK374(U_14810,U_14809,U_14808,U_14807,U_14806)),U_14808)),U_14810))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),sK374(U_14810,U_14809,U_14808,U_14807,U_14806))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),U_14809),U_14810))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),U_14808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14809)),U_14810))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_14805,sK374(U_14810,U_14809,U_14808,U_14807,U_14806))],[f_3734_2]) ).

cnf(f_3734_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),sK374(U_14810,U_14809,U_14808,U_14807,U_14806))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),U_14809),U_14810)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),U_14808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14809)),U_14810))) ),
    inference(clausify,[status(thm)],[f_3734_3]) ).

cnf(f_3734_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),sK374(U_14810,U_14809,U_14808,U_14807,U_14806)),U_14808)),U_14810))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),U_14807),U_14808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14806,U_14806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14809)),U_14810))) ),
    inference(clausify,[status(thm)],[f_3734_3]) ).

fof(f_3735_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_3735_2,plain,
    ! [U_14816,U_14815,U_14814,U_14813,U_14812] :
      ( ? [U_14811] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14811),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),U_14815),U_14816)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14811)),U_14816)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14815)),U_14816))) ),
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

fof(f_3735_3,plain,
    ! [U_14816,U_14815,U_14814,U_14813,U_14812] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),sK375(U_14816,U_14815,U_14814,U_14813,U_14812)),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),U_14815),U_14816)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),sK375(U_14816,U_14815,U_14814,U_14813,U_14812))),U_14816)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14815)),U_14816))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_14811,sK375(U_14816,U_14815,U_14814,U_14813,U_14812))],[f_3735_2]) ).

cnf(f_3735_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),sK375(U_14816,U_14815,U_14814,U_14813,U_14812))),U_14816))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14815)),U_14816))) ),
    inference(clausify,[status(thm)],[f_3735_3]) ).

cnf(f_3735_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),sK375(U_14816,U_14815,U_14814,U_14813,U_14812)),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),U_14815),U_14816)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),U_14813),U_14814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14812,U_14812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14815)),U_14816))) ),
    inference(clausify,[status(thm)],[f_3735_3]) ).

fof(f_3736_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_3736_2,plain,
    ! [U_14822,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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),U_14821),U_14822)))
          & 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_14822)) )
      | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14821)),U_14822))) ),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

fof(f_3736_3,plain,
    ! [U_14822,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),sK376(U_14822,U_14821,U_14820,U_14819,U_14818)),U_14820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),U_14821),U_14822)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),sK376(U_14822,U_14821,U_14820,U_14819,U_14818))),U_14822)) )
      | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14821)),U_14822))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_14817,sK376(U_14822,U_14821,U_14820,U_14819,U_14818))],[f_3736_2]) ).

cnf(f_3736_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),sK376(U_14822,U_14821,U_14820,U_14819,U_14818))),U_14822))
    | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14821)),U_14822))) ),
    inference(clausify,[status(thm)],[f_3736_3]) ).

cnf(f_3736_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),sK376(U_14822,U_14821,U_14820,U_14819,U_14818)),U_14820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),U_14821),U_14822)))
    | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14818,U_14818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14821)),U_14822))) ),
    inference(clausify,[status(thm)],[f_3736_3]) ).

fof(f_3737_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_3737_2,plain,
    ! [U_14827,U_14826,U_14825,U_14824] :
      ( ? [U_14823] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14823),U_14826)),U_14827))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),U_14823)),c_Transitive__Closure_Ortrancl(U_14824,U_14827))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),U_14826)),c_Transitive__Closure_Otrancl(U_14824,U_14827))) ),
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

fof(f_3737_3,plain,
    ! [U_14827,U_14826,U_14825,U_14824] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),sK377(U_14827,U_14826,U_14825,U_14824)),U_14826)),U_14827))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),sK377(U_14827,U_14826,U_14825,U_14824))),c_Transitive__Closure_Ortrancl(U_14824,U_14827))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),U_14826)),c_Transitive__Closure_Otrancl(U_14824,U_14827))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_14823,sK377(U_14827,U_14826,U_14825,U_14824))],[f_3737_2]) ).

cnf(f_3737_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),sK377(U_14827,U_14826,U_14825,U_14824))),c_Transitive__Closure_Ortrancl(U_14824,U_14827)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),U_14826)),c_Transitive__Closure_Otrancl(U_14824,U_14827))) ),
    inference(clausify,[status(thm)],[f_3737_3]) ).

cnf(f_3737_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),sK377(U_14827,U_14826,U_14825,U_14824)),U_14826)),U_14827))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),U_14825),U_14826)),c_Transitive__Closure_Otrancl(U_14824,U_14827))) ),
    inference(clausify,[status(thm)],[f_3737_3]) ).

fof(f_3738_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_3738_2,plain,
    ! [U_14832,U_14831,U_14830,U_14829] :
      ( ? [U_14828] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14828),U_14831)),c_Transitive__Closure_Ortrancl(U_14829,U_14832)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),U_14828)),U_14832)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),U_14831)),c_Transitive__Closure_Otrancl(U_14829,U_14832))) ),
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

fof(f_3738_3,plain,
    ! [U_14832,U_14831,U_14830,U_14829] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),sK378(U_14832,U_14831,U_14830,U_14829)),U_14831)),c_Transitive__Closure_Ortrancl(U_14829,U_14832)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),sK378(U_14832,U_14831,U_14830,U_14829))),U_14832)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),U_14831)),c_Transitive__Closure_Otrancl(U_14829,U_14832))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_14828,sK378(U_14832,U_14831,U_14830,U_14829))],[f_3738_2]) ).

cnf(f_3738_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),sK378(U_14832,U_14831,U_14830,U_14829))),U_14832))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),U_14831)),c_Transitive__Closure_Otrancl(U_14829,U_14832))) ),
    inference(clausify,[status(thm)],[f_3738_3]) ).

cnf(f_3738_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),sK378(U_14832,U_14831,U_14830,U_14829)),U_14831)),c_Transitive__Closure_Ortrancl(U_14829,U_14832)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),U_14830),U_14831)),c_Transitive__Closure_Otrancl(U_14829,U_14832))) ),
    inference(clausify,[status(thm)],[f_3738_3]) ).

fof(f_3739_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_3739_2,plain,
    ! [U_14835,U_14834] :
      ( ? [U_14833] : U_14835 = hAPP(hAPP(c_Product__Type_OPair(U_14834,U_14834),U_14833),U_14833)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14834,U_14834)),U_14835),c_Relation_OId(U_14834))) ),
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

fof(f_3739_3,plain,
    ! [U_14835,U_14834] :
      ( U_14835 = hAPP(hAPP(c_Product__Type_OPair(U_14834,U_14834),sK379(U_14835,U_14834)),sK379(U_14835,U_14834))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14834,U_14834)),U_14835),c_Relation_OId(U_14834))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_14833,sK379(U_14835,U_14834))],[f_3739_2]) ).

cnf(f_3739_4,plain,
    ( U_14835 = hAPP(hAPP(c_Product__Type_OPair(U_14834,U_14834),sK379(U_14835,U_14834)),sK379(U_14835,U_14834))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14834,U_14834)),U_14835),c_Relation_OId(U_14834))) ),
    inference(clausify,[status(thm)],[f_3739_3]) ).

fof(f_3740_1,plain,
    ! [V_P_Ha_2,V_Pa_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_Pa_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_Ha_2))
      | ? [B_x] :
          ( ( ( ~ hBOOL(hAPP(V_Pa_2,B_x))
              & hBOOL(hAPP(V_P_Ha_2,B_x)) )
            | ( ~ hBOOL(hAPP(V_P_Ha_2,B_x))
              & hBOOL(hAPP(V_Pa_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_3740_2,plain,
    ! [U_14838,U_14837] :
      ( 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_14837)) = 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_14838))
      | ? [U_14836] :
          ( ( ( ~ hBOOL(hAPP(U_14837,U_14836))
              & hBOOL(hAPP(U_14838,U_14836)) )
            | ( ~ hBOOL(hAPP(U_14838,U_14836))
              & hBOOL(hAPP(U_14837,U_14836)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_14836)) ) ),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

fof(f_3740_3,plain,
    ! [U_14838,U_14837] :
      ( 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_14837)) = 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_14838))
      | ( ( ( ~ hBOOL(hAPP(U_14837,sK380(U_14838,U_14837)))
            & hBOOL(hAPP(U_14838,sK380(U_14838,U_14837))) )
          | ( ~ hBOOL(hAPP(U_14838,sK380(U_14838,U_14837)))
            & hBOOL(hAPP(U_14837,sK380(U_14838,U_14837))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK380(U_14838,U_14837))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_14836,sK380(U_14838,U_14837))],[f_3740_2]) ).

cnf(f_3740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK380(U_14838,U_14837)))
    | 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_14837)) = 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_14838)) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

cnf(f_3740_5,plain,
    ( hBOOL(hAPP(U_14838,sK380(U_14838,U_14837)))
    | hBOOL(hAPP(U_14837,sK380(U_14838,U_14837)))
    | 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_14837)) = 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_14838)) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

cnf(f_3740_6,plain,
    ( ~ hBOOL(hAPP(U_14837,sK380(U_14838,U_14837)))
    | hBOOL(hAPP(U_14837,sK380(U_14838,U_14837)))
    | 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_14837)) = 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_14838)) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

cnf(f_3740_7,plain,
    ( hBOOL(hAPP(U_14838,sK380(U_14838,U_14837)))
    | ~ hBOOL(hAPP(U_14838,sK380(U_14838,U_14837)))
    | 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_14837)) = 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_14838)) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

cnf(f_3740_8,plain,
    ( ~ hBOOL(hAPP(U_14837,sK380(U_14838,U_14837)))
    | ~ hBOOL(hAPP(U_14838,sK380(U_14838,U_14837)))
    | 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_14837)) = 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_14838)) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

fof(f_3741_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Qa_2,B_x))
          & hBOOL(hAPP(V_Pa_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_3741_2,plain,
    ! [U_14844,U_14843,U_14842,U_14841,U_14840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14841),hAPP(c_Set_OCollect(U_14840),U_14843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14842),hAPP(c_Set_OCollect(U_14840),U_14844))))
      | ? [U_14839] :
          ( ~ hBOOL(hAPP(U_14844,U_14839))
          & hBOOL(hAPP(U_14843,U_14839))
          & hBOOL(hAPP(hAPP(c_member(U_14840),U_14839),U_14841)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),U_14841),U_14842)) ),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ! [U_14844,U_14843,U_14842,U_14841,U_14840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14841),hAPP(c_Set_OCollect(U_14840),U_14843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14842),hAPP(c_Set_OCollect(U_14840),U_14844))))
      | ( ~ hBOOL(hAPP(U_14844,sK381(U_14844,U_14843,U_14842,U_14841,U_14840)))
        & hBOOL(hAPP(U_14843,sK381(U_14844,U_14843,U_14842,U_14841,U_14840)))
        & hBOOL(hAPP(hAPP(c_member(U_14840),sK381(U_14844,U_14843,U_14842,U_14841,U_14840)),U_14841)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),U_14841),U_14842)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_14839,sK381(U_14844,U_14843,U_14842,U_14841,U_14840))],[f_3741_2]) ).

cnf(f_3741_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14840),sK381(U_14844,U_14843,U_14842,U_14841,U_14840)),U_14841))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14841),hAPP(c_Set_OCollect(U_14840),U_14843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14842),hAPP(c_Set_OCollect(U_14840),U_14844))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),U_14841),U_14842)) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

cnf(f_3741_5,plain,
    ( hBOOL(hAPP(U_14843,sK381(U_14844,U_14843,U_14842,U_14841,U_14840)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14841),hAPP(c_Set_OCollect(U_14840),U_14843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14842),hAPP(c_Set_OCollect(U_14840),U_14844))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),U_14841),U_14842)) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

cnf(f_3741_6,plain,
    ( ~ hBOOL(hAPP(U_14844,sK381(U_14844,U_14843,U_14842,U_14841,U_14840)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14841),hAPP(c_Set_OCollect(U_14840),U_14843))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14840,tc_HOL_Obool)),U_14842),hAPP(c_Set_OCollect(U_14840),U_14844))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14840,tc_HOL_Obool)),U_14841),U_14842)) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

fof(f_3742_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_3742_2,plain,
    ! [U_14850,U_14849,U_14848,U_14847] :
      ( ? [U_14846,U_14845] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14848,U_14847)),hAPP(hAPP(c_Product__Type_OPair(U_14848,U_14847),U_14846),U_14845)),U_14850))
          & U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),U_14845),U_14846) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14847,U_14848)),U_14849),hAPP(c_Relation_Oconverse(U_14848,U_14847),U_14850))) ),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

fof(f_3742_3,plain,
    ! [U_14850,U_14849,U_14848,U_14847] :
      ( ? [U_14845] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14848,U_14847)),hAPP(hAPP(c_Product__Type_OPair(U_14848,U_14847),sK382(U_14850,U_14849,U_14848,U_14847)),U_14845)),U_14850))
          & U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),U_14845),sK382(U_14850,U_14849,U_14848,U_14847)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14847,U_14848)),U_14849),hAPP(c_Relation_Oconverse(U_14848,U_14847),U_14850))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_14846,sK382(U_14850,U_14849,U_14848,U_14847))],[f_3742_2]) ).

fof(f_3742_4,plain,
    ! [U_14850,U_14849,U_14848,U_14847] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14848,U_14847)),hAPP(hAPP(c_Product__Type_OPair(U_14848,U_14847),sK382(U_14850,U_14849,U_14848,U_14847)),sK383(U_14850,U_14849,U_14848,U_14847))),U_14850))
        & U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),sK383(U_14850,U_14849,U_14848,U_14847)),sK382(U_14850,U_14849,U_14848,U_14847)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14847,U_14848)),U_14849),hAPP(c_Relation_Oconverse(U_14848,U_14847),U_14850))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_14845,sK383(U_14850,U_14849,U_14848,U_14847))],[f_3742_3]) ).

cnf(f_3742_5,plain,
    ( U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),sK383(U_14850,U_14849,U_14848,U_14847)),sK382(U_14850,U_14849,U_14848,U_14847))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14847,U_14848)),U_14849),hAPP(c_Relation_Oconverse(U_14848,U_14847),U_14850))) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

cnf(f_3742_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14848,U_14847)),hAPP(hAPP(c_Product__Type_OPair(U_14848,U_14847),sK382(U_14850,U_14849,U_14848,U_14847)),sK383(U_14850,U_14849,U_14848,U_14847))),U_14850))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14847,U_14848)),U_14849),hAPP(c_Relation_Oconverse(U_14848,U_14847),U_14850))) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

fof(f_3743_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_3743_2,plain,
    ! [U_14859,U_14858,U_14857,U_14856,U_14855,U_14854] :
      ( ? [U_14853,U_14852,U_14851] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),U_14852),U_14851)),U_14859))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),U_14853),U_14852)),U_14858))
          & U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),U_14853),U_14851) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

fof(f_3743_3,plain,
    ! [U_14859,U_14858,U_14857,U_14856,U_14855,U_14854] :
      ( ? [U_14852,U_14851] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),U_14852),U_14851)),U_14859))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),U_14852)),U_14858))
          & U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),U_14851) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_14853,sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3743_2]) ).

fof(f_3743_4,plain,
    ! [U_14859,U_14858,U_14857,U_14856,U_14855,U_14854] :
      ( ? [U_14851] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),U_14851)),U_14859))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))),U_14858))
          & U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),U_14851) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_14852,sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3743_3]) ).

fof(f_3743_5,plain,
    ! [U_14859,U_14858,U_14857,U_14856,U_14855,U_14854] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK386(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))),U_14859))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))),U_14858))
        & U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK386(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_14851,sK386(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3743_4]) ).

cnf(f_3743_6,plain,
    ( U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK386(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(clausify,[status(thm)],[f_3743_5]) ).

cnf(f_3743_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),sK384(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))),U_14858))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(clausify,[status(thm)],[f_3743_5]) ).

cnf(f_3743_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),sK385(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK386(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))),U_14859))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14855)),U_14856),hAPP(hAPP(c_Relation_Orel__comp(U_14854,U_14857,U_14855),U_14858),U_14859))) ),
    inference(clausify,[status(thm)],[f_3743_5]) ).

fof(f_3744_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_3744_2,plain,
    ! [U_14862,U_14861,U_14860] : c_Nitpick_Oplus__frac(U_14860,U_14861,U_14862) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_14860),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_14860),U_14861),hAPP(c_Nitpick_Odenom(U_14860),U_14862))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_14860),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_14860),tc_Int_Oint),c_Nitpick_Ofrac(U_14860)),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_14860),U_14861))),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_14860),U_14861))))),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_14860),U_14862))),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_14860),U_14862)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

cnf(f_3744_3,plain,
    c_Nitpick_Oplus__frac(U_14860,U_14861,U_14862) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_14860),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_14860),U_14861),hAPP(c_Nitpick_Odenom(U_14860),U_14862))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_14860),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_14860),tc_Int_Oint),c_Nitpick_Ofrac(U_14860)),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_14860),U_14861))),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_14860),U_14861))))),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_14860),U_14862))),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_14860),U_14862)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3744_2]) ).

fof(f_3745_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_3745_2,plain,
    ! [U_14865,U_14864,U_14863] : c_Nitpick_Otimes__frac(U_14863,U_14864,U_14865) = hAPP(hAPP(c_Nitpick_Ofrac(U_14863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14863),U_14864)),hAPP(c_Nitpick_Onum(U_14863),U_14865))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_14863),U_14864)),hAPP(c_Nitpick_Odenom(U_14863),U_14865))),
    inference(variable_rename,[status(thm)],[f_3745_1]) ).

cnf(f_3745_3,plain,
    c_Nitpick_Otimes__frac(U_14863,U_14864,U_14865) = hAPP(hAPP(c_Nitpick_Ofrac(U_14863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14863),U_14864)),hAPP(c_Nitpick_Onum(U_14863),U_14865))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_14863),U_14864)),hAPP(c_Nitpick_Odenom(U_14863),U_14865))),
    inference(clausify,[status(thm)],[f_3745_2]) ).

fof(f_3746_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_3746_2,plain,
    ! [U_14868,U_14867,U_14866] :
      ( c_Nitpick_Oof__frac(U_14867,U_14866,U_14868) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_14866),hAPP(c_Int_Oring__1__class_Oof__int(U_14866),hAPP(c_Nitpick_Onum(U_14867),U_14868))),hAPP(c_Int_Oring__1__class_Oof__int(U_14866),hAPP(c_Nitpick_Odenom(U_14867),U_14868)))
      | ~ class_Rings_Oring__1(U_14866)
      | ~ class_Rings_Oinverse(U_14866) ),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

cnf(f_3746_3,plain,
    ( c_Nitpick_Oof__frac(U_14867,U_14866,U_14868) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_14866),hAPP(c_Int_Oring__1__class_Oof__int(U_14866),hAPP(c_Nitpick_Onum(U_14867),U_14868))),hAPP(c_Int_Oring__1__class_Oof__int(U_14866),hAPP(c_Nitpick_Odenom(U_14867),U_14868)))
    | ~ class_Rings_Oring__1(U_14866)
    | ~ class_Rings_Oinverse(U_14866) ),
    inference(clausify,[status(thm)],[f_3746_2]) ).

fof(f_3747_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_3747_2,plain,
    ! [U_14870,U_14869] : c_Nitpick_Oinverse__frac(U_14869,U_14870) = hAPP(hAPP(c_Nitpick_Ofrac(U_14869),hAPP(c_Nitpick_Odenom(U_14869),U_14870)),hAPP(c_Nitpick_Onum(U_14869),U_14870)),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

cnf(f_3747_3,plain,
    c_Nitpick_Oinverse__frac(U_14869,U_14870) = hAPP(hAPP(c_Nitpick_Ofrac(U_14869),hAPP(c_Nitpick_Odenom(U_14869),U_14870)),hAPP(c_Nitpick_Onum(U_14869),U_14870)),
    inference(clausify,[status(thm)],[f_3747_2]) ).

fof(f_3748_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_3748_2,plain,
    ! [U_14872,U_14871] : c_Nitpick_Ouminus__frac(U_14871,U_14872) = c_Nitpick_OAbs__Frac(U_14871,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_14871),U_14872))),hAPP(c_Nitpick_Odenom(U_14871),U_14872))),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

cnf(f_3748_3,plain,
    c_Nitpick_Ouminus__frac(U_14871,U_14872) = c_Nitpick_OAbs__Frac(U_14871,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_14871),U_14872))),hAPP(c_Nitpick_Odenom(U_14871),U_14872))),
    inference(clausify,[status(thm)],[f_3748_2]) ).

fof(f_3749_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_3749_2,plain,
    ! [U_14875,U_14874,U_14873] :
      ( ( c_Nitpick_Oless__frac(U_14873,U_14874,U_14875)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14873),c_Nitpick_Oplus__frac(U_14873,U_14874,c_Nitpick_Ouminus__frac(U_14873,U_14875)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14873),c_Nitpick_Oplus__frac(U_14873,U_14874,c_Nitpick_Ouminus__frac(U_14873,U_14875)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_14873,U_14874,U_14875) ) ),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ( ! [U_14881,U_14879,U_14877] :
        ( c_Nitpick_Oless__frac(U_14877,U_14879,U_14881)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14877),c_Nitpick_Oplus__frac(U_14877,U_14879,c_Nitpick_Ouminus__frac(U_14877,U_14881)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_14880,U_14878,U_14876] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14876),c_Nitpick_Oplus__frac(U_14876,U_14878,c_Nitpick_Ouminus__frac(U_14876,U_14880)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_14876,U_14878,U_14880) ) ),
    inference(miniscope,[status(thm)],[f_3749_2]) ).

cnf(f_3749_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14876),c_Nitpick_Oplus__frac(U_14876,U_14878,c_Nitpick_Ouminus__frac(U_14876,U_14880)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_14876,U_14878,U_14880) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

cnf(f_3749_5,plain,
    ( c_Nitpick_Oless__frac(U_14877,U_14879,U_14881)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14877),c_Nitpick_Oplus__frac(U_14877,U_14879,c_Nitpick_Ouminus__frac(U_14877,U_14881)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_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_3750_2,plain,
    ! [U_14884,U_14883,U_14882] :
      ( ( c_Nitpick_Oless__eq__frac(U_14882,U_14883,U_14884)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14882),c_Nitpick_Oplus__frac(U_14882,U_14883,c_Nitpick_Ouminus__frac(U_14882,U_14884)))),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_14882),c_Nitpick_Oplus__frac(U_14882,U_14883,c_Nitpick_Ouminus__frac(U_14882,U_14884)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_14882,U_14883,U_14884) ) ),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ( ! [U_14890,U_14888,U_14886] :
        ( c_Nitpick_Oless__eq__frac(U_14886,U_14888,U_14890)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14886),c_Nitpick_Oplus__frac(U_14886,U_14888,c_Nitpick_Ouminus__frac(U_14886,U_14890)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_14889,U_14887,U_14885] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14885),c_Nitpick_Oplus__frac(U_14885,U_14887,c_Nitpick_Ouminus__frac(U_14885,U_14889)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_14885,U_14887,U_14889) ) ),
    inference(miniscope,[status(thm)],[f_3750_2]) ).

cnf(f_3750_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14885),c_Nitpick_Oplus__frac(U_14885,U_14887,c_Nitpick_Ouminus__frac(U_14885,U_14889)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_14885,U_14887,U_14889) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_5,plain,
    ( c_Nitpick_Oless__eq__frac(U_14886,U_14888,U_14890)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14886),c_Nitpick_Oplus__frac(U_14886,U_14888,c_Nitpick_Ouminus__frac(U_14886,U_14890)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_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_3751_2,plain,
    ! [U_14891] : c_Nitpick_Onum(U_14891) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14891,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14891)),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

cnf(f_3751_3,plain,
    c_Nitpick_Onum(U_14891) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14891,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14891)),
    inference(clausify,[status(thm)],[f_3751_2]) ).

fof(f_3752_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_3752_2,plain,
    ! [U_14892] : c_Nitpick_Odenom(U_14892) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14892,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14892)),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

cnf(f_3752_3,plain,
    c_Nitpick_Odenom(U_14892) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14892,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14892)),
    inference(clausify,[status(thm)],[f_3752_2]) ).

fof(f_3753_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_3753_2,plain,
    ! [U_14895,U_14894,U_14893] : c_Product__Type_Ointernal__split(U_14893,U_14894,U_14895) = c_Product__Type_Oprod_Oprod__case(U_14893,U_14894,U_14895),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

cnf(f_3753_3,plain,
    c_Product__Type_Ointernal__split(U_14893,U_14894,U_14895) = c_Product__Type_Oprod_Oprod__case(U_14893,U_14894,U_14895),
    inference(clausify,[status(thm)],[f_3753_2]) ).

fof(f_3754_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_3754_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3754_1]) ).

fof(f_3755_1,plain,
    ! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).

fof(f_3755_2,plain,
    ! [U_14901,U_14900,U_14899,U_14898,U_14897,U_14896] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_14896,U_14897,U_14898),U_14899),hAPP(hAPP(c_Product__Type_OPair(U_14896,U_14897),U_14900),U_14901)) = hAPP(hAPP(U_14899,U_14900),U_14901),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

cnf(f_3755_3,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_14896,U_14897,U_14898),U_14899),hAPP(hAPP(c_Product__Type_OPair(U_14896,U_14897),U_14900),U_14901)) = hAPP(hAPP(U_14899,U_14900),U_14901),
    inference(clausify,[status(thm)],[f_3755_2]) ).

fof(f_3756_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_3756_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3756_1]) ).

fof(f_3757_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_3757_2,plain,
    ! [U_14904,U_14903] :
      ( 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_14903)),U_14904))))
      | ? [U_14902] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14902),hAPP(U_14903,U_14902))) ),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

fof(f_3757_3,plain,
    ! [U_14904,U_14903] :
      ( 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_14903)),U_14904))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK387(U_14904,U_14903)),hAPP(U_14903,sK387(U_14904,U_14903)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_14902,sK387(U_14904,U_14903))],[f_3757_2]) ).

cnf(f_3757_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_14903)),U_14904))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK387(U_14904,U_14903)),hAPP(U_14903,sK387(U_14904,U_14903)))) ),
    inference(clausify,[status(thm)],[f_3757_3]) ).

fof(f_3758_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_3758_2,plain,
    ! [U_14906,U_14905] : c_List_Olenlex(U_14905,U_14906) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905)),tc_List_Olist(U_14905)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_14905),c_Wellfounded_Oless__than,c_List_Olex(U_14905,U_14906))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14905),tc_List_Olist(U_14905),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_14905),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905))),tc_List_Olist(U_14905)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_14905))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14905)))),c_COMBI(tc_List_Olist(U_14905)))),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

cnf(f_3758_3,plain,
    c_List_Olenlex(U_14905,U_14906) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905)),tc_List_Olist(U_14905)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_14905),c_Wellfounded_Oless__than,c_List_Olex(U_14905,U_14906))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14905),tc_List_Olist(U_14905),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_14905),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14905))),tc_List_Olist(U_14905)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_14905))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14905)))),c_COMBI(tc_List_Olist(U_14905)))),
    inference(clausify,[status(thm)],[f_3758_2]) ).

fof(f_3759_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_3759_2,plain,
    ! [U_14911,U_14910,U_14909,U_14908,U_14907] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14907)),U_14909) = U_14911
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14907)),U_14908) = U_14911 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14907),tc_List_Olist(U_14907))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14907),tc_List_Olist(U_14907)),U_14908),U_14909)),hAPP(c_List_Olexn(U_14907,U_14910),U_14911))) ),
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

cnf(f_3759_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14907)),U_14908) = U_14911
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14907),tc_List_Olist(U_14907))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14907),tc_List_Olist(U_14907)),U_14908),U_14909)),hAPP(c_List_Olexn(U_14907,U_14910),U_14911))) ),
    inference(clausify,[status(thm)],[f_3759_2]) ).

cnf(f_3759_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14907)),U_14909) = U_14911
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14907),tc_List_Olist(U_14907))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14907),tc_List_Olist(U_14907)),U_14908),U_14909)),hAPP(c_List_Olexn(U_14907,U_14910),U_14911))) ),
    inference(clausify,[status(thm)],[f_3759_2]) ).

fof(f_3760_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_3760_2,plain,
    ! [U_14914,U_14913,U_14912] :
      ( U_14913 != U_14914
      | 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_3760_1]) ).

fof(f_3760_3,plain,
    ! [U_14914,U_14913] :
      ( ! [U_14912] : 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)
      | U_14913 != U_14914 ),
    inference(miniscope,[status(thm)],[f_3760_2]) ).

cnf(f_3760_4,plain,
    ( 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)
    | U_14913 != U_14914 ),
    inference(clausify,[status(thm)],[f_3760_3]) ).

fof(f_3761_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_3761_2,plain,
    ! [U_14916,U_14915] : c_List_Olenlex(U_14915,U_14916) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14915),tc_List_Olist(U_14915),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBS(tc_List_Olist(U_14915),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14915))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14915)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBS(tc_List_Olist(U_14915),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14915))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_14915)),c_member(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))))),c_Product__Type_OPair(tc_List_Olist(U_14915),tc_List_Olist(U_14915))))),c_List_Olex(U_14915,U_14916)))))),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

cnf(f_3761_3,plain,
    c_List_Olenlex(U_14915,U_14916) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14915),tc_List_Olist(U_14915),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBS(tc_List_Olist(U_14915),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14915))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14915)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBS(tc_List_Olist(U_14915),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14915),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14915))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14915)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14915)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14915),tc_HOL_Obool)),tc_List_Olist(U_14915)),c_COMBC(tc_List_Olist(U_14915),tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14915),tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))),tc_fun(tc_List_Olist(U_14915),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_14915)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_14915)),c_member(tc_prod(tc_List_Olist(U_14915),tc_List_Olist(U_14915))))),c_Product__Type_OPair(tc_List_Olist(U_14915),tc_List_Olist(U_14915))))),c_List_Olex(U_14915,U_14916)))))),
    inference(clausify,[status(thm)],[f_3761_2]) ).

fof(f_3762_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_3762_2,plain,
    ! [U_14919,U_14918,U_14917] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14917)),c_List_Osublist(U_14917,U_14918,U_14919)) = 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_14917)),U_14918)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_14919)))),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

cnf(f_3762_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14917)),c_List_Osublist(U_14917,U_14918,U_14919)) = 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_14917)),U_14918)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_14919)))),
    inference(clausify,[status(thm)],[f_3762_2]) ).

fof(f_3763_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_3763_2,plain,
    ! [U_14922,U_14921,U_14920] : hAPP(c_List_Olexn(U_14920,U_14921),hAPP(c_Nat_OSuc,U_14922)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_14920,tc_List_Olist(U_14920)),tc_prod(U_14920,tc_List_Olist(U_14920))),tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_Product__Type_Omap__pair(tc_prod(U_14920,tc_List_Olist(U_14920)),tc_List_Olist(U_14920),tc_prod(U_14920,tc_List_Olist(U_14920)),tc_List_Olist(U_14920),hAPP(c_Product__Type_Oprod_Oprod__case(U_14920,tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_List_Olist_OCons(U_14920)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14920,tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_List_Olist_OCons(U_14920)))),c_Wellfounded_Olex__prod(U_14920,tc_List_Olist(U_14920),U_14921,hAPP(c_List_Olexn(U_14920,U_14921),U_14922)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14920),tc_List_Olist(U_14920),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool)),tc_List_Olist(U_14920)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14920))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14920)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),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_14920)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14920)))),hAPP(c_Nat_OSuc,U_14922))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),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_14920)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14920)))),hAPP(c_Nat_OSuc,U_14922)))))),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

cnf(f_3763_3,plain,
    hAPP(c_List_Olexn(U_14920,U_14921),hAPP(c_Nat_OSuc,U_14922)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_14920,tc_List_Olist(U_14920)),tc_prod(U_14920,tc_List_Olist(U_14920))),tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_Product__Type_Omap__pair(tc_prod(U_14920,tc_List_Olist(U_14920)),tc_List_Olist(U_14920),tc_prod(U_14920,tc_List_Olist(U_14920)),tc_List_Olist(U_14920),hAPP(c_Product__Type_Oprod_Oprod__case(U_14920,tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_List_Olist_OCons(U_14920)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14920,tc_List_Olist(U_14920),tc_List_Olist(U_14920)),c_List_Olist_OCons(U_14920)))),c_Wellfounded_Olex__prod(U_14920,tc_List_Olist(U_14920),U_14921,hAPP(c_List_Olexn(U_14920,U_14921),U_14922)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14920),tc_List_Olist(U_14920))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14920),tc_List_Olist(U_14920),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14920),tc_HOL_Obool)),tc_List_Olist(U_14920)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14920))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14920)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),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_14920)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14920)))),hAPP(c_Nat_OSuc,U_14922))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14920),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_14920)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14920)))),hAPP(c_Nat_OSuc,U_14922)))))),
    inference(clausify,[status(thm)],[f_3763_2]) ).

fof(f_3764_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_3764_2,plain,
    ! [U_14926,U_14925,U_14924,U_14923] :
      ( U_14924 != hAPP(hAPP(c_List_Olist_OCons(U_14923),U_14926),U_14925)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14923)),U_14924)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14923)),U_14925))) ),
    inference(variable_rename,[status(thm)],[f_3764_1]) ).

cnf(f_3764_3,plain,
    ( U_14924 != hAPP(hAPP(c_List_Olist_OCons(U_14923),U_14926),U_14925)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14923)),U_14924)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14923)),U_14925))) ),
    inference(clausify,[status(thm)],[f_3764_2]) ).

fof(f_3765_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_3765_2,plain,
    ! [U_14931,U_14930,U_14929,U_14928,U_14927] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_14927),U_14928),U_14929) = hAPP(hAPP(c_List_Olist_OCons(U_14927),U_14930),U_14931)
        | U_14929 != U_14931
        | U_14928 != U_14930 )
      & ( ( U_14929 = U_14931
          & U_14928 = U_14930 )
        | hAPP(hAPP(c_List_Olist_OCons(U_14927),U_14928),U_14929) != hAPP(hAPP(c_List_Olist_OCons(U_14927),U_14930),U_14931) ) ),
    inference(variable_rename,[status(thm)],[f_3765_1]) ).

fof(f_3765_3,plain,
    ( ! [U_14941,U_14939,U_14937,U_14935] :
        ( ! [U_14933] : hAPP(hAPP(c_List_Olist_OCons(U_14933),U_14935),U_14937) = hAPP(hAPP(c_List_Olist_OCons(U_14933),U_14939),U_14941)
        | U_14937 != U_14941
        | U_14935 != U_14939 )
    & ! [U_14940,U_14938,U_14936,U_14934] :
        ( ! [U_14932] : hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14934),U_14936) != hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14938),U_14940)
        | ( U_14936 = U_14940
          & U_14934 = U_14938 ) ) ),
    inference(miniscope,[status(thm)],[f_3765_2]) ).

cnf(f_3765_4,plain,
    ( U_14934 = U_14938
    | hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14934),U_14936) != hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14938),U_14940) ),
    inference(clausify,[status(thm)],[f_3765_3]) ).

cnf(f_3765_5,plain,
    ( U_14936 = U_14940
    | hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14934),U_14936) != hAPP(hAPP(c_List_Olist_OCons(U_14932),U_14938),U_14940) ),
    inference(clausify,[status(thm)],[f_3765_3]) ).

cnf(f_3765_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_14933),U_14935),U_14937) = hAPP(hAPP(c_List_Olist_OCons(U_14933),U_14939),U_14941)
    | U_14937 != U_14941
    | U_14935 != U_14939 ),
    inference(clausify,[status(thm)],[f_3765_3]) ).

fof(f_3766_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_3766_2,plain,
    ! [U_14944,U_14943,U_14942] : hAPP(hAPP(c_List_Olist_OCons(U_14942),U_14943),U_14944) != U_14944,
    inference(variable_rename,[status(thm)],[f_3766_1]) ).

cnf(f_3766_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_14942),U_14943),U_14944) != U_14944,
    inference(clausify,[status(thm)],[f_3766_2]) ).

fof(f_3767_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_3767_2,plain,
    ! [U_14947,U_14946,U_14945] : U_14945 != hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14947),U_14945),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

cnf(f_3767_3,plain,
    U_14945 != hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14947),U_14945),
    inference(clausify,[status(thm)],[f_3767_2]) ).

fof(f_3768_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_3768_2,plain,
    ! [U_14950,U_14949,U_14948] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14948)),hAPP(hAPP(c_List_Olist_OCons(U_14948),U_14949),U_14950)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14948)),U_14950)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

cnf(f_3768_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14948)),hAPP(hAPP(c_List_Olist_OCons(U_14948),U_14949),U_14950)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14948)),U_14950)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3768_2]) ).

fof(f_3769_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_3769_2,plain,
    ! [U_14956,U_14955,U_14954,U_14953,U_14952,U_14951] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14951),tc_List_Olist(U_14951))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14951),tc_List_Olist(U_14951)),hAPP(hAPP(c_List_Olist_OCons(U_14951),U_14952),U_14953)),hAPP(hAPP(c_List_Olist_OCons(U_14951),U_14954),U_14955))),c_List_Olex(U_14951,U_14956)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14951),tc_List_Olist(U_14951))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14951),tc_List_Olist(U_14951)),U_14953),U_14955)),c_List_Olex(U_14951,U_14956)))
            | U_14952 != U_14954 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14951)),U_14953) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14951)),U_14955)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14951,U_14951)),hAPP(hAPP(c_Product__Type_OPair(U_14951,U_14951),U_14952),U_14954)),U_14956)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14951),tc_List_Olist(U_14951))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14951),tc_List_Olist(U_14951)),U_14953),U_14955)),c_List_Olex(U_14951,U_14956)))
          & U_14952 = U_14954 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14951)),U_14953) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14951)),U_14955)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14951,U_14951)),hAPP(hAPP(c_Product__Type_OPair(U_14951,U_14951),U_14952),U_14954)),U_14956)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14951),tc_List_Olist(U_14951))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14951),tc_List_Olist(U_14951)),hAPP(hAPP(c_List_Olist_OCons(U_14951),U_14952),U_14953)),hAPP(hAPP(c_List_Olist_OCons(U_14951),U_14954),U_14955))),c_List_Olex(U_14951,U_14956))) ) ),
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

fof(f_3769_3,plain,
    ( ! [U_14968,U_14966,U_14964,U_14962,U_14960,U_14958] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14960),U_14962)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14964),U_14966))),c_List_Olex(U_14958,U_14968)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),U_14962),U_14966)),c_List_Olex(U_14958,U_14968)))
            | U_14960 != U_14964 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14958)),U_14962) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14958)),U_14966)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14958,U_14958)),hAPP(hAPP(c_Product__Type_OPair(U_14958,U_14958),U_14960),U_14964)),U_14968)) ) ) )
    & ! [U_14967,U_14965,U_14963,U_14961,U_14959,U_14957] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),U_14961),U_14965)),c_List_Olex(U_14957,U_14967)))
          & U_14959 = U_14963 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14965)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14957,U_14957)),hAPP(hAPP(c_Product__Type_OPair(U_14957,U_14957),U_14959),U_14963)),U_14967)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14959),U_14961)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14963),U_14965))),c_List_Olex(U_14957,U_14967))) ) ),
    inference(miniscope,[status(thm)],[f_3769_2]) ).

cnf(f_3769_4,plain,
    ( U_14959 = U_14963
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14957,U_14957)),hAPP(hAPP(c_Product__Type_OPair(U_14957,U_14957),U_14959),U_14963)),U_14967))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14959),U_14961)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14963),U_14965))),c_List_Olex(U_14957,U_14967))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

cnf(f_3769_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),U_14961),U_14965)),c_List_Olex(U_14957,U_14967)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14957,U_14957)),hAPP(hAPP(c_Product__Type_OPair(U_14957,U_14957),U_14959),U_14963)),U_14967))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14959),U_14961)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14963),U_14965))),c_List_Olex(U_14957,U_14967))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

cnf(f_3769_6,plain,
    ( U_14959 = U_14963
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14965)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14959),U_14961)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14963),U_14965))),c_List_Olex(U_14957,U_14967))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

cnf(f_3769_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),U_14961),U_14965)),c_List_Olex(U_14957,U_14967)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14957)),U_14965)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14957),tc_List_Olist(U_14957))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14957),tc_List_Olist(U_14957)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14959),U_14961)),hAPP(hAPP(c_List_Olist_OCons(U_14957),U_14963),U_14965))),c_List_Olex(U_14957,U_14967))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

cnf(f_3769_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14958)),U_14962) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14958)),U_14966)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14958,U_14958)),hAPP(hAPP(c_Product__Type_OPair(U_14958,U_14958),U_14960),U_14964)),U_14968))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14960),U_14962)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14964),U_14966))),c_List_Olex(U_14958,U_14968))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

cnf(f_3769_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),U_14962),U_14966)),c_List_Olex(U_14958,U_14968)))
    | U_14960 != U_14964
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14960),U_14962)),hAPP(hAPP(c_List_Olist_OCons(U_14958),U_14964),U_14966))),c_List_Olex(U_14958,U_14968))) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

fof(f_3770_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_3770_2,plain,
    ! [U_14971,U_14970,U_14969] : c_List_Oset__Cons(U_14969,U_14970,U_14971) = hAPP(c_Set_OCollect(tc_List_Olist(U_14969)),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_14969)),c_HOL_OEx(U_14969)),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_HOL_Obool),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_HOL_Obool,U_14969),c_HOL_OEx(tc_List_Olist(U_14969)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_fun(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),c_COMBS(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14969,tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),U_14969),c_COMBS(tc_List_Olist(U_14969),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14969)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969))),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969))),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),U_14969)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_List_Olist(U_14969)),c_COMBB(tc_List_Olist(U_14969),tc_HOL_Obool,tc_List_Olist(U_14969))),c_fequal))),c_List_Olist_OCons(U_14969)))))),hAPP(hAPP(c_COMBC(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),U_14969),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14969))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14969),c_fconj),hAPP(hAPP(c_COMBC(U_14969,tc_fun(U_14969,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14969)),U_14970)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_14969))),U_14971)))))),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

cnf(f_3770_3,plain,
    c_List_Oset__Cons(U_14969,U_14970,U_14971) = hAPP(c_Set_OCollect(tc_List_Olist(U_14969)),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_14969)),c_HOL_OEx(U_14969)),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_HOL_Obool),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_HOL_Obool,U_14969),c_HOL_OEx(tc_List_Olist(U_14969)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_fun(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),c_COMBS(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14969,tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),U_14969),c_COMBS(tc_List_Olist(U_14969),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_14969)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14969)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969))),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_fun(tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969))),tc_fun(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool))),tc_List_Olist(U_14969)),c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),U_14969)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_List_Olist(U_14969)),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),tc_List_Olist(U_14969)),c_COMBB(tc_List_Olist(U_14969),tc_HOL_Obool,tc_List_Olist(U_14969))),c_fequal))),c_List_Olist_OCons(U_14969)))))),hAPP(hAPP(c_COMBC(U_14969,tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool)),U_14969),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14969))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14969),c_fconj),hAPP(hAPP(c_COMBC(U_14969,tc_fun(U_14969,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14969)),U_14970)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14969),tc_fun(tc_List_Olist(U_14969),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_14969))),U_14971)))))),
    inference(clausify,[status(thm)],[f_3770_2]) ).

fof(f_3771_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_3771_2,plain,
    ! [U_14975,U_14974,U_14973,U_14972] :
      ( ( hAPP(c_Random_Opick(U_14973,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14973)),U_14974),U_14975)),U_14972) = hAPP(c_Random_Opick(U_14973,U_14975),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14972),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14973),U_14974)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14972),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14973),U_14974))) )
      & ( hAPP(c_Random_Opick(U_14973,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14973)),U_14974),U_14975)),U_14972) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14973),U_14974)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14972),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14973),U_14974))) ) ),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

fof(f_3771_3,plain,
    ( ! [U_14983,U_14981,U_14979,U_14977] :
        ( hAPP(c_Random_Opick(U_14979,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14979)),U_14981),U_14983)),U_14977) = hAPP(c_Random_Opick(U_14979,U_14983),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14977),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14979),U_14981)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14977),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14979),U_14981))) )
    & ! [U_14982,U_14980,U_14978,U_14976] :
        ( hAPP(c_Random_Opick(U_14978,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14978)),U_14980),U_14982)),U_14976) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14978),U_14980)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14976),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14978),U_14980))) ) ),
    inference(miniscope,[status(thm)],[f_3771_2]) ).

cnf(f_3771_4,plain,
    ( hAPP(c_Random_Opick(U_14978,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14978)),U_14980),U_14982)),U_14976) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14978),U_14980)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14976),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14978),U_14980))) ),
    inference(clausify,[status(thm)],[f_3771_3]) ).

cnf(f_3771_5,plain,
    ( hAPP(c_Random_Opick(U_14979,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14979)),U_14981),U_14983)),U_14977) = hAPP(c_Random_Opick(U_14979,U_14983),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14977),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14979),U_14981)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14977),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14979),U_14981))) ),
    inference(clausify,[status(thm)],[f_3771_3]) ).

fof(f_3772_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_3772_2,plain,
    ! [U_14986,U_14985,U_14984] : c_Random_Oselect__weight(U_14984,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14984)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_14984),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14985)),U_14986)) = c_Random_Oselect__weight(U_14984,U_14986),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

cnf(f_3772_3,plain,
    c_Random_Oselect__weight(U_14984,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14984)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_14984),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14985)),U_14986)) = c_Random_Oselect__weight(U_14984,U_14986),
    inference(clausify,[status(thm)],[f_3772_2]) ).

fof(f_3773_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_3773_2,plain,
    ! [U_14992,U_14991,U_14990,U_14989,U_14988,U_14987] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14987),tc_List_Olist(U_14987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14987),tc_List_Olist(U_14987)),hAPP(hAPP(c_List_Olist_OCons(U_14987),U_14988),U_14989)),hAPP(hAPP(c_List_Olist_OCons(U_14987),U_14990),U_14991))),c_List_Olexord(U_14987,U_14992)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14987),tc_List_Olist(U_14987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14987),tc_List_Olist(U_14987)),U_14989),U_14991)),c_List_Olexord(U_14987,U_14992)))
            | U_14988 != U_14990 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14987,U_14987)),hAPP(hAPP(c_Product__Type_OPair(U_14987,U_14987),U_14988),U_14990)),U_14992)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14987),tc_List_Olist(U_14987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14987),tc_List_Olist(U_14987)),U_14989),U_14991)),c_List_Olexord(U_14987,U_14992)))
          & U_14988 = U_14990 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14987,U_14987)),hAPP(hAPP(c_Product__Type_OPair(U_14987,U_14987),U_14988),U_14990)),U_14992))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14987),tc_List_Olist(U_14987))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14987),tc_List_Olist(U_14987)),hAPP(hAPP(c_List_Olist_OCons(U_14987),U_14988),U_14989)),hAPP(hAPP(c_List_Olist_OCons(U_14987),U_14990),U_14991))),c_List_Olexord(U_14987,U_14992))) ) ),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

fof(f_3773_3,plain,
    ( ! [U_15004,U_15002,U_15000,U_14998,U_14996,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)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_14996),U_14998)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_15000),U_15002))),c_List_Olexord(U_14994,U_15004)))
        | ( ( ~ 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_14998),U_15002)),c_List_Olexord(U_14994,U_15004)))
            | U_14996 != U_15000 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14996),U_15000)),U_15004)) ) )
    & ! [U_15003,U_15001,U_14999,U_14997,U_14995,U_14993] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14993),tc_List_Olist(U_14993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14993),tc_List_Olist(U_14993)),U_14997),U_15001)),c_List_Olexord(U_14993,U_15003)))
          & U_14995 = U_14999 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14993,U_14993)),hAPP(hAPP(c_Product__Type_OPair(U_14993,U_14993),U_14995),U_14999)),U_15003))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14993),tc_List_Olist(U_14993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14993),tc_List_Olist(U_14993)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14995),U_14997)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14999),U_15001))),c_List_Olexord(U_14993,U_15003))) ) ),
    inference(miniscope,[status(thm)],[f_3773_2]) ).

cnf(f_3773_4,plain,
    ( U_14995 = U_14999
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14993,U_14993)),hAPP(hAPP(c_Product__Type_OPair(U_14993,U_14993),U_14995),U_14999)),U_15003))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14993),tc_List_Olist(U_14993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14993),tc_List_Olist(U_14993)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14995),U_14997)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14999),U_15001))),c_List_Olexord(U_14993,U_15003))) ),
    inference(clausify,[status(thm)],[f_3773_3]) ).

cnf(f_3773_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14993),tc_List_Olist(U_14993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14993),tc_List_Olist(U_14993)),U_14997),U_15001)),c_List_Olexord(U_14993,U_15003)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14993,U_14993)),hAPP(hAPP(c_Product__Type_OPair(U_14993,U_14993),U_14995),U_14999)),U_15003))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14993),tc_List_Olist(U_14993))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14993),tc_List_Olist(U_14993)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14995),U_14997)),hAPP(hAPP(c_List_Olist_OCons(U_14993),U_14999),U_15001))),c_List_Olexord(U_14993,U_15003))) ),
    inference(clausify,[status(thm)],[f_3773_3]) ).

cnf(f_3773_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14996),U_15000)),U_15004))
    | 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)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_14996),U_14998)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_15000),U_15002))),c_List_Olexord(U_14994,U_15004))) ),
    inference(clausify,[status(thm)],[f_3773_3]) ).

cnf(f_3773_7,plain,
    ( ~ 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_14998),U_15002)),c_List_Olexord(U_14994,U_15004)))
    | U_14996 != U_15000
    | 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)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_14996),U_14998)),hAPP(hAPP(c_List_Olist_OCons(U_14994),U_15000),U_15002))),c_List_Olexord(U_14994,U_15004))) ),
    inference(clausify,[status(thm)],[f_3773_3]) ).

fof(f_3774_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_3774_2,plain,
    ! [U_15008,U_15007,U_15006,U_15005] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15005),tc_List_Olist(U_15005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15005),tc_List_Olist(U_15005)),U_15006),U_15007)),c_List_Olex(U_15005,U_15008)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15005)),U_15006) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15005)),U_15007)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15005),tc_List_Olist(U_15005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15005),tc_List_Olist(U_15005)),U_15006),U_15007)),c_List_Olexord(U_15005,U_15008))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15005)),U_15006) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15005)),U_15007)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15005),tc_List_Olist(U_15005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15005),tc_List_Olist(U_15005)),U_15006),U_15007)),c_List_Olexord(U_15005,U_15008))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15005),tc_List_Olist(U_15005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15005),tc_List_Olist(U_15005)),U_15006),U_15007)),c_List_Olex(U_15005,U_15008))) ) ),
    inference(variable_rename,[status(thm)],[f_3774_1]) ).

fof(f_3774_3,plain,
    ( ! [U_15016,U_15014,U_15012,U_15010] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15010),tc_List_Olist(U_15010))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15010),tc_List_Olist(U_15010)),U_15012),U_15014)),c_List_Olex(U_15010,U_15016)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15010)),U_15012) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15010)),U_15014)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15010),tc_List_Olist(U_15010))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15010),tc_List_Olist(U_15010)),U_15012),U_15014)),c_List_Olexord(U_15010,U_15016))) )
    & ! [U_15015,U_15013,U_15011,U_15009] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15009)),U_15011) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15009)),U_15013)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15009),tc_List_Olist(U_15009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15009),tc_List_Olist(U_15009)),U_15011),U_15013)),c_List_Olexord(U_15009,U_15015))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15009),tc_List_Olist(U_15009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15009),tc_List_Olist(U_15009)),U_15011),U_15013)),c_List_Olex(U_15009,U_15015))) ) ),
    inference(miniscope,[status(thm)],[f_3774_2]) ).

cnf(f_3774_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15009),tc_List_Olist(U_15009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15009),tc_List_Olist(U_15009)),U_15011),U_15013)),c_List_Olexord(U_15009,U_15015)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15009),tc_List_Olist(U_15009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15009),tc_List_Olist(U_15009)),U_15011),U_15013)),c_List_Olex(U_15009,U_15015))) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

cnf(f_3774_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15009)),U_15011) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15009)),U_15013)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15009),tc_List_Olist(U_15009))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15009),tc_List_Olist(U_15009)),U_15011),U_15013)),c_List_Olex(U_15009,U_15015))) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

cnf(f_3774_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15010),tc_List_Olist(U_15010))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15010),tc_List_Olist(U_15010)),U_15012),U_15014)),c_List_Olex(U_15010,U_15016)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15010)),U_15012) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15010)),U_15014)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15010),tc_List_Olist(U_15010))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15010),tc_List_Olist(U_15010)),U_15012),U_15014)),c_List_Olexord(U_15010,U_15016))) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

fof(f_3775_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_3775_2,plain,
    ! [U_15022,U_15021,U_15020,U_15019,U_15018,U_15017] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15017),tc_List_Olist(U_15017))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15017),tc_List_Olist(U_15017)),hAPP(hAPP(c_List_Olist_OCons(U_15017),U_15018),U_15021)),hAPP(hAPP(c_List_Olist_OCons(U_15017),U_15019),U_15022))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15017),c_List_Olistrel1(U_15017,U_15020))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15017),tc_List_Olist(U_15017))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15017),tc_List_Olist(U_15017)),U_15021),U_15022)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15017),c_List_Olistrel1(U_15017,U_15020))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15017,U_15017)),hAPP(hAPP(c_Product__Type_OPair(U_15017,U_15017),U_15018),U_15019)),c_Transitive__Closure_Ortrancl(U_15017,U_15020))) ),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

cnf(f_3775_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15017),tc_List_Olist(U_15017))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15017),tc_List_Olist(U_15017)),hAPP(hAPP(c_List_Olist_OCons(U_15017),U_15018),U_15021)),hAPP(hAPP(c_List_Olist_OCons(U_15017),U_15019),U_15022))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15017),c_List_Olistrel1(U_15017,U_15020))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15017),tc_List_Olist(U_15017))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15017),tc_List_Olist(U_15017)),U_15021),U_15022)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15017),c_List_Olistrel1(U_15017,U_15020))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15017,U_15017)),hAPP(hAPP(c_Product__Type_OPair(U_15017,U_15017),U_15018),U_15019)),c_Transitive__Closure_Ortrancl(U_15017,U_15020))) ),
    inference(clausify,[status(thm)],[f_3775_2]) ).

fof(f_3776_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_3776_2,plain,
    ! [U_15026,U_15025,U_15024,U_15023] : c_List_Olist_Olist__size(U_15023,U_15024,hAPP(hAPP(c_List_Olist_OCons(U_15023),U_15025),U_15026)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15024,U_15025)),c_List_Olist_Olist__size(U_15023,U_15024,U_15026))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3776_1]) ).

cnf(f_3776_3,plain,
    c_List_Olist_Olist__size(U_15023,U_15024,hAPP(hAPP(c_List_Olist_OCons(U_15023),U_15025),U_15026)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15024,U_15025)),c_List_Olist_Olist__size(U_15023,U_15024,U_15026))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3776_2]) ).

fof(f_3777_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_3777_2,plain,
    ! [U_15030,U_15029,U_15028,U_15027] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15027)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15028),U_15030)),c_Wellfounded_Oacc(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15029))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15027)),U_15030),c_Wellfounded_Oacc(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15029))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15027),U_15028),c_Wellfounded_Oacc(U_15027,U_15029))) ),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

cnf(f_3777_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15027)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15028),U_15030)),c_Wellfounded_Oacc(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15029))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15027)),U_15030),c_Wellfounded_Oacc(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15029))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15027),U_15028),c_Wellfounded_Oacc(U_15027,U_15029))) ),
    inference(clausify,[status(thm)],[f_3777_2]) ).

fof(f_3778_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_3778_2,plain,
    ! [U_15033,U_15032,U_15031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15031),tc_List_Olist(U_15031)),tc_HOL_Obool)),c_List_Olistrel1(U_15031,U_15032)),c_List_Olistrel1(U_15031,U_15033)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15031,U_15031),tc_HOL_Obool)),U_15032),U_15033)) ),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

cnf(f_3778_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15031),tc_List_Olist(U_15031)),tc_HOL_Obool)),c_List_Olistrel1(U_15031,U_15032)),c_List_Olistrel1(U_15031,U_15033)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15031,U_15031),tc_HOL_Obool)),U_15032),U_15033)) ),
    inference(clausify,[status(thm)],[f_3778_2]) ).

fof(f_3779_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_3779_2,plain,
    ! [U_15035,U_15034] : c_List_Olistrel1(U_15034,hAPP(c_Relation_Oconverse(U_15034,U_15034),U_15035)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15034),tc_List_Olist(U_15034)),c_List_Olistrel1(U_15034,U_15035)),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

cnf(f_3779_3,plain,
    c_List_Olistrel1(U_15034,hAPP(c_Relation_Oconverse(U_15034,U_15034),U_15035)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15034),tc_List_Olist(U_15034)),c_List_Olistrel1(U_15034,U_15035)),
    inference(clausify,[status(thm)],[f_3779_2]) ).

fof(f_3780_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_3780_2,plain,
    ! [U_15037,U_15036] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15036),tc_List_Olist(U_15036)),tc_HOL_Obool)),c_List_Olistrel1(U_15036,c_Transitive__Closure_Ortrancl(U_15036,U_15037))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15036),c_List_Olistrel1(U_15036,U_15037)))),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

cnf(f_3780_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15036),tc_List_Olist(U_15036)),tc_HOL_Obool)),c_List_Olistrel1(U_15036,c_Transitive__Closure_Ortrancl(U_15036,U_15037))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15036),c_List_Olistrel1(U_15036,U_15037)))),
    inference(clausify,[status(thm)],[f_3780_2]) ).

fof(f_3781_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_3781_2,plain,
    ! [U_15042,U_15041,U_15040,U_15039,U_15038] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15038),tc_List_Olist(U_15038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15038),tc_List_Olist(U_15038)),hAPP(hAPP(c_List_Olist_OCons(U_15038),U_15042),U_15039)),hAPP(hAPP(c_List_Olist_OCons(U_15038),U_15042),U_15040))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15038),c_List_Olistrel1(U_15038,U_15041))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15038),tc_List_Olist(U_15038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15038),tc_List_Olist(U_15038)),U_15039),U_15040)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15038),c_List_Olistrel1(U_15038,U_15041)))) ),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

cnf(f_3781_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15038),tc_List_Olist(U_15038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15038),tc_List_Olist(U_15038)),hAPP(hAPP(c_List_Olist_OCons(U_15038),U_15042),U_15039)),hAPP(hAPP(c_List_Olist_OCons(U_15038),U_15042),U_15040))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15038),c_List_Olistrel1(U_15038,U_15041))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15038),tc_List_Olist(U_15038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15038),tc_List_Olist(U_15038)),U_15039),U_15040)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15038),c_List_Olistrel1(U_15038,U_15041)))) ),
    inference(clausify,[status(thm)],[f_3781_2]) ).

fof(f_3782_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_3782_2,plain,
    ! [U_15047,U_15046,U_15045,U_15044,U_15043] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15043),tc_List_Olist(U_15043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15043),tc_List_Olist(U_15043)),hAPP(hAPP(c_List_Olist_OCons(U_15043),U_15047),U_15044)),hAPP(hAPP(c_List_Olist_OCons(U_15043),U_15047),U_15045))),c_List_Olistrel1(U_15043,U_15046)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15043),tc_List_Olist(U_15043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15043),tc_List_Olist(U_15043)),U_15044),U_15045)),c_List_Olistrel1(U_15043,U_15046))) ),
    inference(variable_rename,[status(thm)],[f_3782_1]) ).

cnf(f_3782_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15043),tc_List_Olist(U_15043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15043),tc_List_Olist(U_15043)),hAPP(hAPP(c_List_Olist_OCons(U_15043),U_15047),U_15044)),hAPP(hAPP(c_List_Olist_OCons(U_15043),U_15047),U_15045))),c_List_Olistrel1(U_15043,U_15046)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15043),tc_List_Olist(U_15043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15043),tc_List_Olist(U_15043)),U_15044),U_15045)),c_List_Olistrel1(U_15043,U_15046))) ),
    inference(clausify,[status(thm)],[f_3782_2]) ).

fof(f_3783_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_3783_2,plain,
    ! [U_15051,U_15050,U_15049,U_15048] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15048)),U_15049) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15048)),U_15050)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15048),tc_List_Olist(U_15048))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15048),tc_List_Olist(U_15048)),U_15049),U_15050)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15048),c_List_Olistrel1(U_15048,U_15051)))) ),
    inference(variable_rename,[status(thm)],[f_3783_1]) ).

cnf(f_3783_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15048)),U_15049) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15048)),U_15050)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15048),tc_List_Olist(U_15048))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15048),tc_List_Olist(U_15048)),U_15049),U_15050)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15048),c_List_Olistrel1(U_15048,U_15051)))) ),
    inference(clausify,[status(thm)],[f_3783_2]) ).

fof(f_3784_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_3784_2,plain,
    ! [U_15055,U_15054,U_15053,U_15052] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15052)),U_15053) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15052)),U_15054)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15052),tc_List_Olist(U_15052))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15052),tc_List_Olist(U_15052)),U_15053),U_15054)),c_List_Olistrel1(U_15052,U_15055))) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

cnf(f_3784_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15052)),U_15053) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15052)),U_15054)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15052),tc_List_Olist(U_15052))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15052),tc_List_Olist(U_15052)),U_15053),U_15054)),c_List_Olistrel1(U_15052,U_15055))) ),
    inference(clausify,[status(thm)],[f_3784_2]) ).

fof(f_3785_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_3785_2,plain,
    ! [U_15059,U_15058,U_15057,U_15056] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15056),tc_List_Olist(U_15056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),U_15057),U_15058)),c_List_Olistrel1(U_15056,hAPP(c_Relation_Oconverse(U_15056,U_15056),U_15059))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15056),tc_List_Olist(U_15056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),U_15057),U_15058)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),c_List_Olistrel1(U_15056,U_15059)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15056),tc_List_Olist(U_15056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),U_15057),U_15058)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),c_List_Olistrel1(U_15056,U_15059))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15056),tc_List_Olist(U_15056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15056),tc_List_Olist(U_15056)),U_15057),U_15058)),c_List_Olistrel1(U_15056,hAPP(c_Relation_Oconverse(U_15056,U_15056),U_15059)))) ) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

fof(f_3785_3,plain,
    ( ! [U_15067,U_15065,U_15063,U_15061] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15061),tc_List_Olist(U_15061))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),U_15063),U_15065)),c_List_Olistrel1(U_15061,hAPP(c_Relation_Oconverse(U_15061,U_15061),U_15067))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15061),tc_List_Olist(U_15061))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),U_15063),U_15065)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),c_List_Olistrel1(U_15061,U_15067)))) )
    & ! [U_15066,U_15064,U_15062,U_15060] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15060),tc_List_Olist(U_15060))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),U_15062),U_15064)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),c_List_Olistrel1(U_15060,U_15066))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15060),tc_List_Olist(U_15060))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),U_15062),U_15064)),c_List_Olistrel1(U_15060,hAPP(c_Relation_Oconverse(U_15060,U_15060),U_15066)))) ) ),
    inference(miniscope,[status(thm)],[f_3785_2]) ).

cnf(f_3785_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15060),tc_List_Olist(U_15060))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),U_15062),U_15064)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),c_List_Olistrel1(U_15060,U_15066))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15060),tc_List_Olist(U_15060))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15060),tc_List_Olist(U_15060)),U_15062),U_15064)),c_List_Olistrel1(U_15060,hAPP(c_Relation_Oconverse(U_15060,U_15060),U_15066)))) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

cnf(f_3785_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15061),tc_List_Olist(U_15061))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),U_15063),U_15065)),c_List_Olistrel1(U_15061,hAPP(c_Relation_Oconverse(U_15061,U_15061),U_15067))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15061),tc_List_Olist(U_15061))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),U_15063),U_15065)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15061),tc_List_Olist(U_15061)),c_List_Olistrel1(U_15061,U_15067)))) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

fof(f_3786_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_3786_2,plain,
    ! [U_15073,U_15072,U_15071,U_15070,U_15069,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)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15069),U_15070)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15071),U_15072))),c_List_Olistrel1(U_15068,U_15073)))
        | ( ( ~ 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_15070),U_15072)),c_List_Olistrel1(U_15068,U_15073)))
            | U_15069 != U_15071 )
          & ( U_15070 != U_15072
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15069),U_15071)),U_15073)) ) ) )
      & ( ( 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_15070),U_15072)),c_List_Olistrel1(U_15068,U_15073)))
          & U_15069 = U_15071 )
        | ( U_15070 = U_15072
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15069),U_15071)),U_15073)) )
        | ~ 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_15069),U_15070)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15071),U_15072))),c_List_Olistrel1(U_15068,U_15073))) ) ),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

fof(f_3786_3,plain,
    ( ! [U_15085,U_15083,U_15081,U_15079,U_15077,U_15075] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15075),tc_List_Olist(U_15075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15075),tc_List_Olist(U_15075)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15077),U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15081),U_15083))),c_List_Olistrel1(U_15075,U_15085)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15075),tc_List_Olist(U_15075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15075),tc_List_Olist(U_15075)),U_15079),U_15083)),c_List_Olistrel1(U_15075,U_15085)))
            | U_15077 != U_15081 )
          & ( U_15079 != U_15083
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15075,U_15075)),hAPP(hAPP(c_Product__Type_OPair(U_15075,U_15075),U_15077),U_15081)),U_15085)) ) ) )
    & ! [U_15084,U_15082,U_15080,U_15078,U_15076,U_15074] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),U_15078),U_15082)),c_List_Olistrel1(U_15074,U_15084)))
          & U_15076 = U_15080 )
        | ( U_15078 = U_15082
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15074,U_15074)),hAPP(hAPP(c_Product__Type_OPair(U_15074,U_15074),U_15076),U_15080)),U_15084)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15076),U_15078)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15080),U_15082))),c_List_Olistrel1(U_15074,U_15084))) ) ),
    inference(miniscope,[status(thm)],[f_3786_2]) ).

cnf(f_3786_4,plain,
    ( U_15076 = U_15080
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15074,U_15074)),hAPP(hAPP(c_Product__Type_OPair(U_15074,U_15074),U_15076),U_15080)),U_15084))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15076),U_15078)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15080),U_15082))),c_List_Olistrel1(U_15074,U_15084))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

cnf(f_3786_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),U_15078),U_15082)),c_List_Olistrel1(U_15074,U_15084)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15074,U_15074)),hAPP(hAPP(c_Product__Type_OPair(U_15074,U_15074),U_15076),U_15080)),U_15084))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15076),U_15078)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15080),U_15082))),c_List_Olistrel1(U_15074,U_15084))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

cnf(f_3786_6,plain,
    ( U_15076 = U_15080
    | U_15078 = U_15082
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15076),U_15078)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15080),U_15082))),c_List_Olistrel1(U_15074,U_15084))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

cnf(f_3786_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),U_15078),U_15082)),c_List_Olistrel1(U_15074,U_15084)))
    | U_15078 = U_15082
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15074),tc_List_Olist(U_15074))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15074),tc_List_Olist(U_15074)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15076),U_15078)),hAPP(hAPP(c_List_Olist_OCons(U_15074),U_15080),U_15082))),c_List_Olistrel1(U_15074,U_15084))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

cnf(f_3786_8,plain,
    ( U_15079 != U_15083
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15075,U_15075)),hAPP(hAPP(c_Product__Type_OPair(U_15075,U_15075),U_15077),U_15081)),U_15085))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15075),tc_List_Olist(U_15075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15075),tc_List_Olist(U_15075)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15077),U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15081),U_15083))),c_List_Olistrel1(U_15075,U_15085))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

cnf(f_3786_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15075),tc_List_Olist(U_15075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15075),tc_List_Olist(U_15075)),U_15079),U_15083)),c_List_Olistrel1(U_15075,U_15085)))
    | U_15077 != U_15081
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15075),tc_List_Olist(U_15075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15075),tc_List_Olist(U_15075)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15077),U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15075),U_15081),U_15083))),c_List_Olistrel1(U_15075,U_15085))) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

fof(f_3787_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_3787_2,plain,
    ! [U_15090,U_15089,U_15088,U_15087,U_15086] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15086),tc_List_Olist(U_15086))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15086),tc_List_Olist(U_15086)),hAPP(hAPP(c_List_Olist_OCons(U_15086),U_15087),U_15090)),hAPP(hAPP(c_List_Olist_OCons(U_15086),U_15088),U_15090))),c_List_Olistrel1(U_15086,U_15089)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15086,U_15086)),hAPP(hAPP(c_Product__Type_OPair(U_15086,U_15086),U_15087),U_15088)),U_15089)) ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

cnf(f_3787_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15086),tc_List_Olist(U_15086))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15086),tc_List_Olist(U_15086)),hAPP(hAPP(c_List_Olist_OCons(U_15086),U_15087),U_15090)),hAPP(hAPP(c_List_Olist_OCons(U_15086),U_15088),U_15090))),c_List_Olistrel1(U_15086,U_15089)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15086,U_15086)),hAPP(hAPP(c_Product__Type_OPair(U_15086,U_15086),U_15087),U_15088)),U_15089)) ),
    inference(clausify,[status(thm)],[f_3787_2]) ).

fof(f_3788_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_3788_2,plain,
    ! [U_15094,U_15093,U_15092,U_15091] : hAPP(c_Relation_OImage(tc_List_Olist(U_15091),tc_List_Olist(U_15091),c_List_Olistrel(U_15091,U_15092)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15091)),hAPP(hAPP(c_List_Olist_OCons(U_15091),U_15093),U_15094)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15091),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15091,hAPP(c_Relation_OImage(U_15091,U_15091,U_15092),hAPP(hAPP(c_Set_Oinsert(U_15091),U_15093),c_Orderings_Obot__class_Obot(tc_fun(U_15091,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15091),tc_List_Olist(U_15091),c_List_Olistrel(U_15091,U_15092)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15091)),U_15094),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15091),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

cnf(f_3788_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_15091),tc_List_Olist(U_15091),c_List_Olistrel(U_15091,U_15092)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15091)),hAPP(hAPP(c_List_Olist_OCons(U_15091),U_15093),U_15094)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15091),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15091,hAPP(c_Relation_OImage(U_15091,U_15091,U_15092),hAPP(hAPP(c_Set_Oinsert(U_15091),U_15093),c_Orderings_Obot__class_Obot(tc_fun(U_15091,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15091),tc_List_Olist(U_15091),c_List_Olistrel(U_15091,U_15092)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15091)),U_15094),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15091),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3788_2]) ).

fof(f_3789_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_3789_2,plain,
    ! [U_15100,U_15099,U_15098,U_15097] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
      | U_15099 = U_15100
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098)))
      | ? [U_15096,U_15095] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),U_15095),U_15096)),U_15098))
          & U_15096 != U_15095
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),U_15096),U_15095)),U_15098)) ) ),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

fof(f_3789_3,plain,
    ! [U_15100,U_15099,U_15098,U_15097] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
      | U_15099 = U_15100
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098)))
      | ? [U_15095] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),U_15095),sK388(U_15100,U_15099,U_15098,U_15097))),U_15098))
          & sK388(U_15100,U_15099,U_15098,U_15097) != U_15095
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),sK388(U_15100,U_15099,U_15098,U_15097)),U_15095)),U_15098)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_15096,sK388(U_15100,U_15099,U_15098,U_15097))],[f_3789_2]) ).

fof(f_3789_4,plain,
    ! [U_15100,U_15099,U_15098,U_15097] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
      | U_15099 = U_15100
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),sK389(U_15100,U_15099,U_15098,U_15097)),sK388(U_15100,U_15099,U_15098,U_15097))),U_15098))
        & sK388(U_15100,U_15099,U_15098,U_15097) != sK389(U_15100,U_15099,U_15098,U_15097)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),sK388(U_15100,U_15099,U_15098,U_15097)),sK389(U_15100,U_15099,U_15098,U_15097))),U_15098)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_15095,sK389(U_15100,U_15099,U_15098,U_15097))],[f_3789_3]) ).

cnf(f_3789_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),sK388(U_15100,U_15099,U_15098,U_15097)),sK389(U_15100,U_15099,U_15098,U_15097))),U_15098))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
    | U_15099 = U_15100
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098))) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_6,plain,
    ( sK388(U_15100,U_15099,U_15098,U_15097) != sK389(U_15100,U_15099,U_15098,U_15097)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
    | U_15099 = U_15100
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098))) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),hAPP(hAPP(c_Product__Type_OPair(U_15097,U_15097),sK389(U_15100,U_15099,U_15098,U_15097)),sK388(U_15100,U_15099,U_15098,U_15097))),U_15098))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15100),U_15099)),c_List_Olexord(U_15097,U_15098)))
    | U_15099 = U_15100
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15097),tc_List_Olist(U_15097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15097),tc_List_Olist(U_15097)),U_15099),U_15100)),c_List_Olexord(U_15097,U_15098))) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

fof(f_3790_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_3790_2,plain,
    ! [U_15103,U_15102,U_15101] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15101),tc_List_Olist(U_15101))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15101),tc_List_Olist(U_15101)),U_15102),U_15102)),c_List_Olistrel(U_15101,c_Transitive__Closure_Ortrancl(U_15101,U_15103)))),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

cnf(f_3790_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15101),tc_List_Olist(U_15101))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15101),tc_List_Olist(U_15101)),U_15102),U_15102)),c_List_Olistrel(U_15101,c_Transitive__Closure_Ortrancl(U_15101,U_15103)))),
    inference(clausify,[status(thm)],[f_3790_2]) ).

fof(f_3791_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_3791_2,plain,
    ! [U_15106,U_15105,U_15104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15104),tc_List_Olist(U_15104)),tc_HOL_Obool)),c_List_Olistrel(U_15104,U_15105)),c_List_Olistrel(U_15104,U_15106)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)),U_15105),U_15106)) ),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

cnf(f_3791_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15104),tc_List_Olist(U_15104)),tc_HOL_Obool)),c_List_Olistrel(U_15104,U_15105)),c_List_Olistrel(U_15104,U_15106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)),U_15105),U_15106)) ),
    inference(clausify,[status(thm)],[f_3791_2]) ).

fof(f_3792_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_3792_2,plain,
    ! [U_15108,U_15107] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),tc_HOL_Obool)),c_List_Olistrel(U_15107,U_15108)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15107),c_List_Olistrel1(U_15107,U_15108)))),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

cnf(f_3792_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),tc_HOL_Obool)),c_List_Olistrel(U_15107,U_15108)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15107),c_List_Olistrel1(U_15107,U_15108)))),
    inference(clausify,[status(thm)],[f_3792_2]) ).

fof(f_3793_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_3793_2,plain,
    ! [U_15112,U_15111,U_15110,U_15109] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15109)),U_15110) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15109)),U_15111)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15109),tc_List_Olist(U_15109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15109),tc_List_Olist(U_15109)),U_15110),U_15111)),c_List_Olistrel(U_15109,U_15112))) ),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

cnf(f_3793_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15109)),U_15110) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15109)),U_15111)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15109),tc_List_Olist(U_15109))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15109),tc_List_Olist(U_15109)),U_15110),U_15111)),c_List_Olistrel(U_15109,U_15112))) ),
    inference(clausify,[status(thm)],[f_3793_2]) ).

fof(f_3794_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_3794_2,plain,
    ! [U_15117,U_15116,U_15115,U_15114,U_15113] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15114),U_15117)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15115),U_15117)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15114),U_15115)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116)))) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

cnf(f_3794_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15114),U_15117)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15115),U_15117)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15113),tc_List_Olist(U_15113))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15113),tc_List_Olist(U_15113)),U_15114),U_15115)),c_List_Olistrel(U_15113,c_Transitive__Closure_Ortrancl(U_15113,U_15116)))) ),
    inference(clausify,[status(thm)],[f_3794_2]) ).

fof(f_3795_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_3795_2,plain,
    ! [U_15119,U_15118] : c_List_Olistrel(U_15118,c_Transitive__Closure_Ortrancl(U_15118,U_15119)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15118),c_List_Olistrel1(U_15118,U_15119)),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

cnf(f_3795_3,plain,
    c_List_Olistrel(U_15118,c_Transitive__Closure_Ortrancl(U_15118,U_15119)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15118),c_List_Olistrel1(U_15118,U_15119)),
    inference(clausify,[status(thm)],[f_3795_2]) ).

fof(f_3796_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_3796_2,plain,
    ! [U_15123,U_15122,U_15121,U_15120] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15120),tc_List_Olist(U_15120))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15120),tc_List_Olist(U_15120)),U_15121),U_15122)),c_List_Olistrel(U_15120,c_Transitive__Closure_Ortrancl(U_15120,U_15123))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15120),tc_List_Olist(U_15120))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15120),tc_List_Olist(U_15120)),U_15121),U_15122)),c_List_Olistrel1(U_15120,U_15123))) ),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

cnf(f_3796_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15120),tc_List_Olist(U_15120))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15120),tc_List_Olist(U_15120)),U_15121),U_15122)),c_List_Olistrel(U_15120,c_Transitive__Closure_Ortrancl(U_15120,U_15123))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15120),tc_List_Olist(U_15120))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15120),tc_List_Olist(U_15120)),U_15121),U_15122)),c_List_Olistrel1(U_15120,U_15123))) ),
    inference(clausify,[status(thm)],[f_3796_2]) ).

fof(f_3797_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_3797_2,plain,
    ! [U_15126,U_15125,U_15124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15124),tc_List_Olist(U_15124)),tc_HOL_Obool)),c_List_Olistrel1(U_15124,U_15125)),c_List_Olistrel(U_15124,U_15126)))
      | ~ c_Relation_Orefl__on(U_15124,c_Orderings_Otop__class_Otop(tc_fun(U_15124,tc_HOL_Obool)),U_15126)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool)),U_15125),U_15126)) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

cnf(f_3797_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15124),tc_List_Olist(U_15124)),tc_HOL_Obool)),c_List_Olistrel1(U_15124,U_15125)),c_List_Olistrel(U_15124,U_15126)))
    | ~ c_Relation_Orefl__on(U_15124,c_Orderings_Otop__class_Otop(tc_fun(U_15124,tc_HOL_Obool)),U_15126)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool)),U_15125),U_15126)) ),
    inference(clausify,[status(thm)],[f_3797_2]) ).

fof(f_3798_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_3798_2,plain,
    ! [U_15130,U_15129,U_15128,U_15127] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15127),tc_List_Olist(U_15127))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15127),tc_List_Olist(U_15127)),U_15128),U_15129)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15127),c_List_Olistrel1(U_15127,U_15130))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15127),tc_List_Olist(U_15127))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15127),tc_List_Olist(U_15127)),U_15128),U_15129)),c_List_Olistrel(U_15127,U_15130))) ),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

cnf(f_3798_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15127),tc_List_Olist(U_15127))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15127),tc_List_Olist(U_15127)),U_15128),U_15129)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15127),c_List_Olistrel1(U_15127,U_15130))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15127),tc_List_Olist(U_15127))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15127),tc_List_Olist(U_15127)),U_15128),U_15129)),c_List_Olistrel(U_15127,U_15130))) ),
    inference(clausify,[status(thm)],[f_3798_2]) ).

fof(f_3799_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_3799_2,plain,
    ! [U_15136,U_15135,U_15134,U_15133,U_15132,U_15131] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15131),tc_List_Olist(U_15131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15131),tc_List_Olist(U_15131)),hAPP(hAPP(c_List_Olist_OCons(U_15131),U_15132),U_15135)),hAPP(hAPP(c_List_Olist_OCons(U_15131),U_15133),U_15136))),c_List_Olistrel(U_15131,U_15134)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15131),tc_List_Olist(U_15131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15131),tc_List_Olist(U_15131)),U_15135),U_15136)),c_List_Olistrel(U_15131,U_15134)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15131,U_15131)),hAPP(hAPP(c_Product__Type_OPair(U_15131,U_15131),U_15132),U_15133)),U_15134)) ),
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

cnf(f_3799_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15131),tc_List_Olist(U_15131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15131),tc_List_Olist(U_15131)),hAPP(hAPP(c_List_Olist_OCons(U_15131),U_15132),U_15135)),hAPP(hAPP(c_List_Olist_OCons(U_15131),U_15133),U_15136))),c_List_Olistrel(U_15131,U_15134)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15131),tc_List_Olist(U_15131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15131),tc_List_Olist(U_15131)),U_15135),U_15136)),c_List_Olistrel(U_15131,U_15134)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15131,U_15131)),hAPP(hAPP(c_Product__Type_OPair(U_15131,U_15131),U_15132),U_15133)),U_15134)) ),
    inference(clausify,[status(thm)],[f_3799_2]) ).

fof(f_3800_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_3800_2,plain,
    ! [U_15140,U_15139,U_15138,U_15137] :
      ( ( c_List_Olistrelp(U_15137,hAPP(hAPP(c_COMBC(U_15137,tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_fun(U_15137,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15137,tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_fun(U_15137,tc_HOL_Obool)),U_15137),c_COMBC(U_15137,tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15137,tc_prod(U_15137,U_15137)),tc_fun(U_15137,tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),U_15137),hAPP(c_COMBB(tc_prod(U_15137,U_15137),tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool),U_15137),c_member(tc_prod(U_15137,U_15137)))),c_Product__Type_OPair(U_15137,U_15137)))),U_15138),U_15139,U_15140)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15137),tc_List_Olist(U_15137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15137),tc_List_Olist(U_15137)),U_15139),U_15140)),c_List_Olistrel(U_15137,U_15138))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15137),tc_List_Olist(U_15137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15137),tc_List_Olist(U_15137)),U_15139),U_15140)),c_List_Olistrel(U_15137,U_15138)))
        | ~ c_List_Olistrelp(U_15137,hAPP(hAPP(c_COMBC(U_15137,tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_fun(U_15137,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15137,tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_fun(U_15137,tc_HOL_Obool)),U_15137),c_COMBC(U_15137,tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15137,tc_prod(U_15137,U_15137)),tc_fun(U_15137,tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool)),U_15137),hAPP(c_COMBB(tc_prod(U_15137,U_15137),tc_fun(tc_fun(tc_prod(U_15137,U_15137),tc_HOL_Obool),tc_HOL_Obool),U_15137),c_member(tc_prod(U_15137,U_15137)))),c_Product__Type_OPair(U_15137,U_15137)))),U_15138),U_15139,U_15140) ) ),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

fof(f_3800_3,plain,
    ( ! [U_15148,U_15146,U_15144,U_15142] :
        ( c_List_Olistrelp(U_15142,hAPP(hAPP(c_COMBC(U_15142,tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_fun(U_15142,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15142,tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_fun(U_15142,tc_HOL_Obool)),U_15142),c_COMBC(U_15142,tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15142,tc_prod(U_15142,U_15142)),tc_fun(U_15142,tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),U_15142),hAPP(c_COMBB(tc_prod(U_15142,U_15142),tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool),U_15142),c_member(tc_prod(U_15142,U_15142)))),c_Product__Type_OPair(U_15142,U_15142)))),U_15144),U_15146,U_15148)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15142),tc_List_Olist(U_15142))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15142),tc_List_Olist(U_15142)),U_15146),U_15148)),c_List_Olistrel(U_15142,U_15144))) )
    & ! [U_15147,U_15145,U_15143,U_15141] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15141),tc_List_Olist(U_15141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15141),tc_List_Olist(U_15141)),U_15145),U_15147)),c_List_Olistrel(U_15141,U_15143)))
        | ~ c_List_Olistrelp(U_15141,hAPP(hAPP(c_COMBC(U_15141,tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_fun(U_15141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15141,tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_fun(U_15141,tc_HOL_Obool)),U_15141),c_COMBC(U_15141,tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15141,tc_prod(U_15141,U_15141)),tc_fun(U_15141,tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),U_15141),hAPP(c_COMBB(tc_prod(U_15141,U_15141),tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool),U_15141),c_member(tc_prod(U_15141,U_15141)))),c_Product__Type_OPair(U_15141,U_15141)))),U_15143),U_15145,U_15147) ) ),
    inference(miniscope,[status(thm)],[f_3800_2]) ).

cnf(f_3800_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15141),tc_List_Olist(U_15141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15141),tc_List_Olist(U_15141)),U_15145),U_15147)),c_List_Olistrel(U_15141,U_15143)))
    | ~ c_List_Olistrelp(U_15141,hAPP(hAPP(c_COMBC(U_15141,tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_fun(U_15141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15141,tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_fun(U_15141,tc_HOL_Obool)),U_15141),c_COMBC(U_15141,tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15141,tc_prod(U_15141,U_15141)),tc_fun(U_15141,tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool)),U_15141),hAPP(c_COMBB(tc_prod(U_15141,U_15141),tc_fun(tc_fun(tc_prod(U_15141,U_15141),tc_HOL_Obool),tc_HOL_Obool),U_15141),c_member(tc_prod(U_15141,U_15141)))),c_Product__Type_OPair(U_15141,U_15141)))),U_15143),U_15145,U_15147) ),
    inference(clausify,[status(thm)],[f_3800_3]) ).

cnf(f_3800_5,plain,
    ( c_List_Olistrelp(U_15142,hAPP(hAPP(c_COMBC(U_15142,tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_fun(U_15142,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15142,tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_fun(U_15142,tc_HOL_Obool)),U_15142),c_COMBC(U_15142,tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15142,tc_prod(U_15142,U_15142)),tc_fun(U_15142,tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool)),U_15142),hAPP(c_COMBB(tc_prod(U_15142,U_15142),tc_fun(tc_fun(tc_prod(U_15142,U_15142),tc_HOL_Obool),tc_HOL_Obool),U_15142),c_member(tc_prod(U_15142,U_15142)))),c_Product__Type_OPair(U_15142,U_15142)))),U_15144),U_15146,U_15148)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15142),tc_List_Olist(U_15142))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15142),tc_List_Olist(U_15142)),U_15146),U_15148)),c_List_Olistrel(U_15142,U_15144))) ),
    inference(clausify,[status(thm)],[f_3800_3]) ).

fof(f_3801_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_3801_2,plain,
    ! [U_15155,U_15154,U_15153,U_15152,U_15151] :
      ( ? [U_15150,U_15149] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),U_15153),U_15149)),c_List_Olistrel(U_15151,U_15155)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15151,U_15151)),hAPP(hAPP(c_Product__Type_OPair(U_15151,U_15151),U_15152),U_15150)),U_15155))
          & U_15154 = hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15150),U_15149) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(variable_rename,[status(thm)],[f_3801_1]) ).

fof(f_3801_3,plain,
    ! [U_15155,U_15154,U_15153,U_15152,U_15151] :
      ( ? [U_15149] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),U_15153),U_15149)),c_List_Olistrel(U_15151,U_15155)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15151,U_15151)),hAPP(hAPP(c_Product__Type_OPair(U_15151,U_15151),U_15152),sK390(U_15155,U_15154,U_15153,U_15152,U_15151))),U_15155))
          & U_15154 = hAPP(hAPP(c_List_Olist_OCons(U_15151),sK390(U_15155,U_15154,U_15153,U_15152,U_15151)),U_15149) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_15150,sK390(U_15155,U_15154,U_15153,U_15152,U_15151))],[f_3801_2]) ).

fof(f_3801_4,plain,
    ! [U_15155,U_15154,U_15153,U_15152,U_15151] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),U_15153),sK391(U_15155,U_15154,U_15153,U_15152,U_15151))),c_List_Olistrel(U_15151,U_15155)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15151,U_15151)),hAPP(hAPP(c_Product__Type_OPair(U_15151,U_15151),U_15152),sK390(U_15155,U_15154,U_15153,U_15152,U_15151))),U_15155))
        & U_15154 = hAPP(hAPP(c_List_Olist_OCons(U_15151),sK390(U_15155,U_15154,U_15153,U_15152,U_15151)),sK391(U_15155,U_15154,U_15153,U_15152,U_15151)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_15149,sK391(U_15155,U_15154,U_15153,U_15152,U_15151))],[f_3801_3]) ).

cnf(f_3801_5,plain,
    ( U_15154 = hAPP(hAPP(c_List_Olist_OCons(U_15151),sK390(U_15155,U_15154,U_15153,U_15152,U_15151)),sK391(U_15155,U_15154,U_15153,U_15152,U_15151))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(clausify,[status(thm)],[f_3801_4]) ).

cnf(f_3801_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15151,U_15151)),hAPP(hAPP(c_Product__Type_OPair(U_15151,U_15151),U_15152),sK390(U_15155,U_15154,U_15153,U_15152,U_15151))),U_15155))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(clausify,[status(thm)],[f_3801_4]) ).

cnf(f_3801_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),U_15153),sK391(U_15155,U_15154,U_15153,U_15152,U_15151))),c_List_Olistrel(U_15151,U_15155)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15151),tc_List_Olist(U_15151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15151),tc_List_Olist(U_15151)),hAPP(hAPP(c_List_Olist_OCons(U_15151),U_15152),U_15153)),U_15154)),c_List_Olistrel(U_15151,U_15155))) ),
    inference(clausify,[status(thm)],[f_3801_4]) ).

fof(f_3802_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_3802_2,plain,
    ! [U_15161,U_15160,U_15159,U_15158,U_15157,U_15156] :
      ( ( c_List_Olistrelp(U_15156,U_15157,hAPP(hAPP(c_List_Olist_OCons(U_15156),U_15158),U_15159),hAPP(hAPP(c_List_Olist_OCons(U_15156),U_15160),U_15161))
        | ~ c_List_Olistrelp(U_15156,U_15157,U_15159,U_15161)
        | ~ hBOOL(hAPP(hAPP(U_15157,U_15158),U_15160)) )
      & ( ( c_List_Olistrelp(U_15156,U_15157,U_15159,U_15161)
          & hBOOL(hAPP(hAPP(U_15157,U_15158),U_15160)) )
        | ~ c_List_Olistrelp(U_15156,U_15157,hAPP(hAPP(c_List_Olist_OCons(U_15156),U_15158),U_15159),hAPP(hAPP(c_List_Olist_OCons(U_15156),U_15160),U_15161)) ) ),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

fof(f_3802_3,plain,
    ( ! [U_15173,U_15171,U_15169,U_15167,U_15165,U_15163] :
        ( c_List_Olistrelp(U_15163,U_15165,hAPP(hAPP(c_List_Olist_OCons(U_15163),U_15167),U_15169),hAPP(hAPP(c_List_Olist_OCons(U_15163),U_15171),U_15173))
        | ~ c_List_Olistrelp(U_15163,U_15165,U_15169,U_15173)
        | ~ hBOOL(hAPP(hAPP(U_15165,U_15167),U_15171)) )
    & ! [U_15172,U_15170,U_15168,U_15166,U_15164,U_15162] :
        ( ( c_List_Olistrelp(U_15162,U_15164,U_15168,U_15172)
          & hBOOL(hAPP(hAPP(U_15164,U_15166),U_15170)) )
        | ~ c_List_Olistrelp(U_15162,U_15164,hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15166),U_15168),hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15170),U_15172)) ) ),
    inference(miniscope,[status(thm)],[f_3802_2]) ).

cnf(f_3802_4,plain,
    ( hBOOL(hAPP(hAPP(U_15164,U_15166),U_15170))
    | ~ c_List_Olistrelp(U_15162,U_15164,hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15166),U_15168),hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15170),U_15172)) ),
    inference(clausify,[status(thm)],[f_3802_3]) ).

cnf(f_3802_5,plain,
    ( c_List_Olistrelp(U_15162,U_15164,U_15168,U_15172)
    | ~ c_List_Olistrelp(U_15162,U_15164,hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15166),U_15168),hAPP(hAPP(c_List_Olist_OCons(U_15162),U_15170),U_15172)) ),
    inference(clausify,[status(thm)],[f_3802_3]) ).

cnf(f_3802_6,plain,
    ( c_List_Olistrelp(U_15163,U_15165,hAPP(hAPP(c_List_Olist_OCons(U_15163),U_15167),U_15169),hAPP(hAPP(c_List_Olist_OCons(U_15163),U_15171),U_15173))
    | ~ c_List_Olistrelp(U_15163,U_15165,U_15169,U_15173)
    | ~ hBOOL(hAPP(hAPP(U_15165,U_15167),U_15171)) ),
    inference(clausify,[status(thm)],[f_3802_3]) ).

fof(f_3803_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_3803_2,plain,
    ! [U_15179,U_15178,U_15177,U_15176,U_15175,U_15174] :
      ( c_List_Olistrelp(U_15177,U_15174,hAPP(hAPP(c_List_Olist_OCons(U_15177),U_15175),U_15178),hAPP(hAPP(c_List_Olist_OCons(U_15177),U_15176),U_15179))
      | ~ c_List_Olistrelp(U_15177,U_15174,U_15178,U_15179)
      | ~ hBOOL(hAPP(hAPP(U_15174,U_15175),U_15176)) ),
    inference(variable_rename,[status(thm)],[f_3803_1]) ).

cnf(f_3803_3,plain,
    ( c_List_Olistrelp(U_15177,U_15174,hAPP(hAPP(c_List_Olist_OCons(U_15177),U_15175),U_15178),hAPP(hAPP(c_List_Olist_OCons(U_15177),U_15176),U_15179))
    | ~ c_List_Olistrelp(U_15177,U_15174,U_15178,U_15179)
    | ~ hBOOL(hAPP(hAPP(U_15174,U_15175),U_15176)) ),
    inference(clausify,[status(thm)],[f_3803_2]) ).

fof(f_3804_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_3804_2,plain,
    ! [U_15186,U_15185,U_15184,U_15183,U_15182] :
      ( ? [U_15181,U_15180] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15180),U_15185)),c_List_Olistrel(U_15182,U_15186)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15182,U_15182)),hAPP(hAPP(c_Product__Type_OPair(U_15182,U_15182),U_15181),U_15184)),U_15186))
          & U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15181),U_15180) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

fof(f_3804_3,plain,
    ! [U_15186,U_15185,U_15184,U_15183,U_15182] :
      ( ? [U_15180] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15180),U_15185)),c_List_Olistrel(U_15182,U_15186)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15182,U_15182)),hAPP(hAPP(c_Product__Type_OPair(U_15182,U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15184)),U_15186))
          & U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15180) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_15181,sK392(U_15186,U_15185,U_15184,U_15183,U_15182))],[f_3804_2]) ).

fof(f_3804_4,plain,
    ! [U_15186,U_15185,U_15184,U_15183,U_15182] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),sK393(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15185)),c_List_Olistrel(U_15182,U_15186)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15182,U_15182)),hAPP(hAPP(c_Product__Type_OPair(U_15182,U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15184)),U_15186))
        & U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),sK393(U_15186,U_15185,U_15184,U_15183,U_15182)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_15180,sK393(U_15186,U_15185,U_15184,U_15183,U_15182))],[f_3804_3]) ).

cnf(f_3804_5,plain,
    ( U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),sK393(U_15186,U_15185,U_15184,U_15183,U_15182))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(clausify,[status(thm)],[f_3804_4]) ).

cnf(f_3804_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15182,U_15182)),hAPP(hAPP(c_Product__Type_OPair(U_15182,U_15182),sK392(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15184)),U_15186))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(clausify,[status(thm)],[f_3804_4]) ).

cnf(f_3804_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),sK393(U_15186,U_15185,U_15184,U_15183,U_15182)),U_15185)),c_List_Olistrel(U_15182,U_15186)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15182),tc_List_Olist(U_15182))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15182),tc_List_Olist(U_15182)),U_15183),hAPP(hAPP(c_List_Olist_OCons(U_15182),U_15184),U_15185))),c_List_Olistrel(U_15182,U_15186))) ),
    inference(clausify,[status(thm)],[f_3804_4]) ).

fof(f_3805_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_3805_2,plain,
    ! [U_15189,U_15188,U_15187] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15187),tc_List_Olist(U_15187)),tc_HOL_Obool)),c_List_Olistrel(U_15187,U_15188)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15187),tc_List_Olist(U_15187)),c_List_Olists(U_15187,U_15189)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15187),tc_HOL_Obool),tc_List_Olist(U_15187)),c_List_Olists(U_15187,U_15189)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15187,U_15187),tc_HOL_Obool)),U_15188),hAPP(hAPP(c_Product__Type_OSigma(U_15187,U_15187),U_15189),hAPP(c_COMBK(tc_fun(U_15187,tc_HOL_Obool),U_15187),U_15189)))) ),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

cnf(f_3805_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15187),tc_List_Olist(U_15187)),tc_HOL_Obool)),c_List_Olistrel(U_15187,U_15188)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15187),tc_List_Olist(U_15187)),c_List_Olists(U_15187,U_15189)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15187),tc_HOL_Obool),tc_List_Olist(U_15187)),c_List_Olists(U_15187,U_15189)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15187,U_15187),tc_HOL_Obool)),U_15188),hAPP(hAPP(c_Product__Type_OSigma(U_15187,U_15187),U_15189),hAPP(c_COMBK(tc_fun(U_15187,tc_HOL_Obool),U_15187),U_15189)))) ),
    inference(clausify,[status(thm)],[f_3805_2]) ).

fof(f_3806_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_3806_2,plain,
    ! [U_15190] : c_List_Olists(U_15190,c_Orderings_Otop__class_Otop(tc_fun(U_15190,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15190),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

cnf(f_3806_3,plain,
    c_List_Olists(U_15190,c_Orderings_Otop__class_Otop(tc_fun(U_15190,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15190),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3806_2]) ).

fof(f_3807_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_3807_2,plain,
    ! [U_15193,U_15192,U_15191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15191),tc_HOL_Obool)),c_List_Olists(U_15191,U_15192)),c_List_Olists(U_15191,U_15193)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15191,tc_HOL_Obool)),U_15192),U_15193)) ),
    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_List_Olist(U_15191),tc_HOL_Obool)),c_List_Olists(U_15191,U_15192)),c_List_Olists(U_15191,U_15193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15191,tc_HOL_Obool)),U_15192),U_15193)) ),
    inference(clausify,[status(thm)],[f_3807_2]) ).

fof(f_3808_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_3808_2,plain,
    ! [U_15196,U_15195,U_15194] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15194),c_List_Olists(U_15194,U_15195),c_List_Olistrel(U_15194,U_15196))
      | ~ c_Equiv__Relations_Oequiv(U_15194,U_15195,U_15196) ),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

cnf(f_3808_3,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15194),c_List_Olists(U_15194,U_15195),c_List_Olistrel(U_15194,U_15196))
    | ~ c_Equiv__Relations_Oequiv(U_15194,U_15195,U_15196) ),
    inference(clausify,[status(thm)],[f_3808_2]) ).

fof(f_3809_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_3809_2,plain,
    ! [U_15199,U_15198,U_15197] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_15197),c_List_Olists(U_15197,U_15198),c_List_Olistrel(U_15197,U_15199))
      | ~ c_Relation_Orefl__on(U_15197,U_15198,U_15199) ),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

cnf(f_3809_3,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_15197),c_List_Olists(U_15197,U_15198),c_List_Olistrel(U_15197,U_15199))
    | ~ c_Relation_Orefl__on(U_15197,U_15198,U_15199) ),
    inference(clausify,[status(thm)],[f_3809_2]) ).

fof(f_3810_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_3810_2,plain,
    ! [U_15203,U_15202,U_15201,U_15200] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15200)),hAPP(hAPP(c_List_Olist_OCons(U_15200),U_15201),U_15202)),c_List_Olists(U_15200,U_15203)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15200)),U_15202),c_List_Olists(U_15200,U_15203)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15200),U_15201),U_15203)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15200)),U_15202),c_List_Olists(U_15200,U_15203)))
          & hBOOL(hAPP(hAPP(c_member(U_15200),U_15201),U_15203)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15200)),hAPP(hAPP(c_List_Olist_OCons(U_15200),U_15201),U_15202)),c_List_Olists(U_15200,U_15203))) ) ),
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

fof(f_3810_3,plain,
    ( ! [U_15211,U_15209,U_15207,U_15205] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15205)),hAPP(hAPP(c_List_Olist_OCons(U_15205),U_15207),U_15209)),c_List_Olists(U_15205,U_15211)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15205)),U_15209),c_List_Olists(U_15205,U_15211)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15205),U_15207),U_15211)) )
    & ! [U_15210,U_15208,U_15206,U_15204] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15204)),U_15208),c_List_Olists(U_15204,U_15210)))
          & hBOOL(hAPP(hAPP(c_member(U_15204),U_15206),U_15210)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15204)),hAPP(hAPP(c_List_Olist_OCons(U_15204),U_15206),U_15208)),c_List_Olists(U_15204,U_15210))) ) ),
    inference(miniscope,[status(thm)],[f_3810_2]) ).

cnf(f_3810_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15204),U_15206),U_15210))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15204)),hAPP(hAPP(c_List_Olist_OCons(U_15204),U_15206),U_15208)),c_List_Olists(U_15204,U_15210))) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

cnf(f_3810_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15204)),U_15208),c_List_Olists(U_15204,U_15210)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15204)),hAPP(hAPP(c_List_Olist_OCons(U_15204),U_15206),U_15208)),c_List_Olists(U_15204,U_15210))) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

cnf(f_3810_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15205)),hAPP(hAPP(c_List_Olist_OCons(U_15205),U_15207),U_15209)),c_List_Olists(U_15205,U_15211)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15205)),U_15209),c_List_Olists(U_15205,U_15211)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15205),U_15207),U_15211)) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

fof(f_3811_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_3811_2,plain,
    ! [U_15214,U_15213,U_15212] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15212)),U_15213),c_Wellfounded_Oacc(tc_List_Olist(U_15212),c_List_Olistrel1(U_15212,U_15214))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15212)),U_15213),c_List_Olists(U_15212,c_Wellfounded_Oacc(U_15212,U_15214)))) ),
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

cnf(f_3811_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15212)),U_15213),c_Wellfounded_Oacc(tc_List_Olist(U_15212),c_List_Olistrel1(U_15212,U_15214))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15212)),U_15213),c_List_Olists(U_15212,c_Wellfounded_Oacc(U_15212,U_15214)))) ),
    inference(clausify,[status(thm)],[f_3811_2]) ).

fof(f_3812_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_3812_2,plain,
    ! [U_15217,U_15216,U_15215] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15215)),U_15216),c_List_Olists(U_15215,c_Wellfounded_Oacc(U_15215,U_15217))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15215)),U_15216),c_Wellfounded_Oacc(tc_List_Olist(U_15215),c_List_Olistrel1(U_15215,U_15217)))) ),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

cnf(f_3812_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15215)),U_15216),c_List_Olists(U_15215,c_Wellfounded_Oacc(U_15215,U_15217))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15215)),U_15216),c_Wellfounded_Oacc(tc_List_Olist(U_15215),c_List_Olistrel1(U_15215,U_15217)))) ),
    inference(clausify,[status(thm)],[f_3812_2]) ).

fof(f_3813_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_3813_2,plain,
    ! [U_15223,U_15222,U_15221,U_15220] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15220),tc_List_Olist(U_15220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15220),tc_List_Olist(U_15220)),U_15221),U_15222)),c_List_Olistrel(U_15220,U_15223)))
        | ? [U_15219] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),hAPP(hAPP(c_List_Onth(U_15220),U_15221),U_15219)),hAPP(hAPP(c_List_Onth(U_15220),U_15222),U_15219))),U_15223))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15219),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15221))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15221) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15222) )
      & ( ( ! [U_15218] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),hAPP(hAPP(c_List_Onth(U_15220),U_15221),U_15218)),hAPP(hAPP(c_List_Onth(U_15220),U_15222),U_15218))),U_15223))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15221))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15221) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15220)),U_15222) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15220),tc_List_Olist(U_15220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15220),tc_List_Olist(U_15220)),U_15221),U_15222)),c_List_Olistrel(U_15220,U_15223))) ) ),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

fof(f_3813_3,plain,
    ( ! [U_15231,U_15229,U_15227,U_15225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15225),tc_List_Olist(U_15225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15225),tc_List_Olist(U_15225)),U_15227),U_15229)),c_List_Olistrel(U_15225,U_15231)))
        | ? [U_15219] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15225,U_15225)),hAPP(hAPP(c_Product__Type_OPair(U_15225,U_15225),hAPP(hAPP(c_List_Onth(U_15225),U_15227),U_15219)),hAPP(hAPP(c_List_Onth(U_15225),U_15229),U_15219))),U_15231))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15219),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15229) )
    & ! [U_15230,U_15228,U_15226,U_15224] :
        ( ( ! [U_15218] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),hAPP(hAPP(c_List_Onth(U_15224),U_15226),U_15218)),hAPP(hAPP(c_List_Onth(U_15224),U_15228),U_15218))),U_15230))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15228) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),U_15226),U_15228)),c_List_Olistrel(U_15224,U_15230))) ) ),
    inference(miniscope,[status(thm)],[f_3813_2]) ).

fof(f_3813_4,plain,
    ( ! [U_15231,U_15229,U_15227,U_15225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15225),tc_List_Olist(U_15225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15225),tc_List_Olist(U_15225)),U_15227),U_15229)),c_List_Olistrel(U_15225,U_15231)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15225,U_15225)),hAPP(hAPP(c_Product__Type_OPair(U_15225,U_15225),hAPP(hAPP(c_List_Onth(U_15225),U_15227),sK394(U_15231,U_15229,U_15227,U_15225))),hAPP(hAPP(c_List_Onth(U_15225),U_15229),sK394(U_15231,U_15229,U_15227,U_15225)))),U_15231))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK394(U_15231,U_15229,U_15227,U_15225)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15229) )
    & ! [U_15230,U_15228,U_15226,U_15224] :
        ( ( ! [U_15218] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),hAPP(hAPP(c_List_Onth(U_15224),U_15226),U_15218)),hAPP(hAPP(c_List_Onth(U_15224),U_15228),U_15218))),U_15230))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15228) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),U_15226),U_15228)),c_List_Olistrel(U_15224,U_15230))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_15219,sK394(U_15231,U_15229,U_15227,U_15225))],[f_3813_3]) ).

cnf(f_3813_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15228)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),U_15226),U_15228)),c_List_Olistrel(U_15224,U_15230))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15224,U_15224)),hAPP(hAPP(c_Product__Type_OPair(U_15224,U_15224),hAPP(hAPP(c_List_Onth(U_15224),U_15226),U_15218)),hAPP(hAPP(c_List_Onth(U_15224),U_15228),U_15218))),U_15230))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15218),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15224)),U_15226)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),U_15226),U_15228)),c_List_Olistrel(U_15224,U_15230))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK394(U_15231,U_15229,U_15227,U_15225)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15229)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15225),tc_List_Olist(U_15225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15225),tc_List_Olist(U_15225)),U_15227),U_15229)),c_List_Olistrel(U_15225,U_15231))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15225,U_15225)),hAPP(hAPP(c_Product__Type_OPair(U_15225,U_15225),hAPP(hAPP(c_List_Onth(U_15225),U_15227),sK394(U_15231,U_15229,U_15227,U_15225))),hAPP(hAPP(c_List_Onth(U_15225),U_15229),sK394(U_15231,U_15229,U_15227,U_15225)))),U_15231))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15227) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15225)),U_15229)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15225),tc_List_Olist(U_15225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15225),tc_List_Olist(U_15225)),U_15227),U_15229)),c_List_Olistrel(U_15225,U_15231))) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

fof(f_3814_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_3814_2,plain,
    ! [U_15235,U_15234,U_15233] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15233),tc_List_Olist(U_15233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15233),tc_List_Olist(U_15233)),U_15235),U_15235)),c_List_Olexord(U_15233,U_15234)))
      | ? [U_15232] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15233,U_15233)),hAPP(hAPP(c_Product__Type_OPair(U_15233,U_15233),U_15232),U_15232)),U_15234)) ),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

fof(f_3814_3,plain,
    ! [U_15235,U_15234,U_15233] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15233),tc_List_Olist(U_15233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15233),tc_List_Olist(U_15233)),U_15235),U_15235)),c_List_Olexord(U_15233,U_15234)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15233,U_15233)),hAPP(hAPP(c_Product__Type_OPair(U_15233,U_15233),sK395(U_15235,U_15234,U_15233)),sK395(U_15235,U_15234,U_15233))),U_15234)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_15232,sK395(U_15235,U_15234,U_15233))],[f_3814_2]) ).

cnf(f_3814_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15233),tc_List_Olist(U_15233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15233),tc_List_Olist(U_15233)),U_15235),U_15235)),c_List_Olexord(U_15233,U_15234)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15233,U_15233)),hAPP(hAPP(c_Product__Type_OPair(U_15233,U_15233),sK395(U_15235,U_15234,U_15233)),sK395(U_15235,U_15234,U_15233))),U_15234)) ),
    inference(clausify,[status(thm)],[f_3814_3]) ).

fof(f_3815_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_3815_2,plain,
    ! [U_15236] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15236)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15236),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

cnf(f_3815_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15236)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15236),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3815_2]) ).

fof(f_3816_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_3816_2,plain,
    ! [U_15241,U_15240,U_15239] :
      ( ( U_15239 = U_15240
        | ? [U_15238] :
            ( hAPP(hAPP(c_List_Onth(U_15241),U_15239),U_15238) != hAPP(hAPP(c_List_Onth(U_15241),U_15240),U_15238)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15238),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15239))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15239) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15240) )
      & ( ( ! [U_15237] :
              ( hAPP(hAPP(c_List_Onth(U_15241),U_15239),U_15237) = hAPP(hAPP(c_List_Onth(U_15241),U_15240),U_15237)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15239))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15241)),U_15240) )
        | U_15239 != U_15240 ) ),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

fof(f_3816_3,plain,
    ( ! [U_15247,U_15245,U_15243] :
        ( U_15243 = U_15245
        | ? [U_15238] :
            ( hAPP(hAPP(c_List_Onth(U_15247),U_15243),U_15238) != hAPP(hAPP(c_List_Onth(U_15247),U_15245),U_15238)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15238),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15245) )
    & ! [U_15246,U_15244,U_15242] :
        ( ( ! [U_15237] :
              ( hAPP(hAPP(c_List_Onth(U_15246),U_15242),U_15237) = hAPP(hAPP(c_List_Onth(U_15246),U_15244),U_15237)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15244) )
        | U_15242 != U_15244 ) ),
    inference(miniscope,[status(thm)],[f_3816_2]) ).

fof(f_3816_4,plain,
    ( ! [U_15247,U_15245,U_15243] :
        ( U_15243 = U_15245
        | ( hAPP(hAPP(c_List_Onth(U_15247),U_15243),sK396(U_15247,U_15245,U_15243)) != hAPP(hAPP(c_List_Onth(U_15247),U_15245),sK396(U_15247,U_15245,U_15243))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK396(U_15247,U_15245,U_15243)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15245) )
    & ! [U_15246,U_15244,U_15242] :
        ( ( ! [U_15237] :
              ( hAPP(hAPP(c_List_Onth(U_15246),U_15242),U_15237) = hAPP(hAPP(c_List_Onth(U_15246),U_15244),U_15237)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15244) )
        | U_15242 != U_15244 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_15238,sK396(U_15247,U_15245,U_15243))],[f_3816_3]) ).

cnf(f_3816_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15244)
    | U_15242 != U_15244 ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

cnf(f_3816_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15246),U_15242),U_15237) = hAPP(hAPP(c_List_Onth(U_15246),U_15244),U_15237)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15246)),U_15242)))
    | U_15242 != U_15244 ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

cnf(f_3816_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK396(U_15247,U_15245,U_15243)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15245)
    | U_15243 = U_15245 ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

cnf(f_3816_8,plain,
    ( hAPP(hAPP(c_List_Onth(U_15247),U_15243),sK396(U_15247,U_15245,U_15243)) != hAPP(hAPP(c_List_Onth(U_15247),U_15245),sK396(U_15247,U_15245,U_15243))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15243) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15247)),U_15245)
    | U_15243 = U_15245 ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

fof(f_3817_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_3817_2,plain,
    ! [U_15251,U_15250,U_15249,U_15248] : hAPP(hAPP(c_List_Onth(U_15248),hAPP(hAPP(c_List_Olist_OCons(U_15248),U_15249),U_15250)),hAPP(c_Nat_OSuc,U_15251)) = hAPP(hAPP(c_List_Onth(U_15248),U_15250),U_15251),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

cnf(f_3817_3,plain,
    hAPP(hAPP(c_List_Onth(U_15248),hAPP(hAPP(c_List_Olist_OCons(U_15248),U_15249),U_15250)),hAPP(c_Nat_OSuc,U_15251)) = hAPP(hAPP(c_List_Onth(U_15248),U_15250),U_15251),
    inference(clausify,[status(thm)],[f_3817_2]) ).

fof(f_3818_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_3818_2,plain,
    ! [U_15254,U_15253,U_15252] : hAPP(hAPP(c_List_Onth(U_15252),hAPP(hAPP(c_List_Olist_OCons(U_15252),U_15253),U_15254)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15253,
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

cnf(f_3818_3,plain,
    hAPP(hAPP(c_List_Onth(U_15252),hAPP(hAPP(c_List_Olist_OCons(U_15252),U_15253),U_15254)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15253,
    inference(clausify,[status(thm)],[f_3818_2]) ).

fof(f_3819_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_3819_2,plain,
    ! [U_15258,U_15257,U_15256,U_15255] : hAPP(hAPP(c_List_Onth(U_15255),hAPP(hAPP(c_List_Olist_OCons(U_15255),U_15256),U_15257)),U_15258) = c_Nat_Onat_Onat__case(U_15255,U_15256,hAPP(c_List_Onth(U_15255),U_15257),U_15258),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

cnf(f_3819_3,plain,
    hAPP(hAPP(c_List_Onth(U_15255),hAPP(hAPP(c_List_Olist_OCons(U_15255),U_15256),U_15257)),U_15258) = c_Nat_Onat_Onat__case(U_15255,U_15256,hAPP(c_List_Onth(U_15255),U_15257),U_15258),
    inference(clausify,[status(thm)],[f_3819_2]) ).

fof(f_3820_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_3820_2,plain,
    ! [U_15262,U_15261,U_15260,U_15259] :
      ( ( hAPP(hAPP(c_List_Onth(U_15260),hAPP(hAPP(c_List_Olist_OCons(U_15260),U_15261),U_15262)),U_15259) = hAPP(hAPP(c_List_Onth(U_15260),U_15262),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15259),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15260),hAPP(hAPP(c_List_Olist_OCons(U_15260),U_15261),U_15262)),U_15259) = U_15261
        | U_15259 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

fof(f_3820_3,plain,
    ( ! [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)),U_15264) = hAPP(hAPP(c_List_Onth(U_15266),U_15270),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15264),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15269,U_15267,U_15265,U_15263] :
        ( hAPP(hAPP(c_List_Onth(U_15265),hAPP(hAPP(c_List_Olist_OCons(U_15265),U_15267),U_15269)),U_15263) = U_15267
        | U_15263 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3820_2]) ).

cnf(f_3820_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15265),hAPP(hAPP(c_List_Olist_OCons(U_15265),U_15267),U_15269)),U_15263) = U_15267
    | U_15263 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

cnf(f_3820_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15266),hAPP(hAPP(c_List_Olist_OCons(U_15266),U_15268),U_15270)),U_15264) = hAPP(hAPP(c_List_Onth(U_15266),U_15270),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15264),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_15264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

fof(f_3821_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_3821_2,plain,
    ! [U_15274,U_15273,U_15272,U_15271] :
      ( ( hAPP(hAPP(c_List_Onth(U_15272),hAPP(hAPP(c_List_Olist_OCons(U_15272),U_15273),U_15274)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15271)) = hAPP(hAPP(c_List_Onth(U_15272),U_15274),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15271)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15271) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15272),hAPP(hAPP(c_List_Olist_OCons(U_15272),U_15273),U_15274)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15271)) = U_15273
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15271) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

fof(f_3821_3,plain,
    ( ! [U_15282,U_15280,U_15278,U_15276] :
        ( hAPP(hAPP(c_List_Onth(U_15278),hAPP(hAPP(c_List_Olist_OCons(U_15278),U_15280),U_15282)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276)) = hAPP(hAPP(c_List_Onth(U_15278),U_15282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15281,U_15279,U_15277,U_15275] :
        ( hAPP(hAPP(c_List_Onth(U_15277),hAPP(hAPP(c_List_Olist_OCons(U_15277),U_15279),U_15281)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15275)) = U_15279
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15275) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3821_2]) ).

cnf(f_3821_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15277),hAPP(hAPP(c_List_Olist_OCons(U_15277),U_15279),U_15281)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15275)) = U_15279
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15275) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3821_3]) ).

cnf(f_3821_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15278),hAPP(hAPP(c_List_Olist_OCons(U_15278),U_15280),U_15282)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276)) = hAPP(hAPP(c_List_Onth(U_15278),U_15282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3821_3]) ).

fof(f_3822_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_3822_2,plain,
    ! [U_15288,U_15287,U_15286,U_15285] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15285),tc_List_Olist(U_15285))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15285),tc_List_Olist(U_15285)),U_15286),U_15287)),c_List_Olexord(U_15285,U_15288)))
        | ( ! [U_15284] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15285,U_15285)),hAPP(hAPP(c_Product__Type_OPair(U_15285,U_15285),hAPP(hAPP(c_List_Onth(U_15285),U_15286),U_15284)),hAPP(hAPP(c_List_Onth(U_15285),U_15287),U_15284))),U_15288))
              | hAPP(hAPP(c_List_Otake(U_15285),U_15284),U_15286) != hAPP(hAPP(c_List_Otake(U_15285),U_15284),U_15287)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15284),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15287)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15285),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),U_15287) != U_15286
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15287))) ) ) )
      & ( ? [U_15283] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15285,U_15285)),hAPP(hAPP(c_Product__Type_OPair(U_15285,U_15285),hAPP(hAPP(c_List_Onth(U_15285),U_15286),U_15283)),hAPP(hAPP(c_List_Onth(U_15285),U_15287),U_15283))),U_15288))
            & hAPP(hAPP(c_List_Otake(U_15285),U_15283),U_15286) = hAPP(hAPP(c_List_Otake(U_15285),U_15283),U_15287)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15283),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15287)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15285),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),U_15287) = U_15286
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15286)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15285)),U_15287))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15285),tc_List_Olist(U_15285))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15285),tc_List_Olist(U_15285)),U_15286),U_15287)),c_List_Olexord(U_15285,U_15288))) ) ),
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

fof(f_3822_3,plain,
    ( ! [U_15296,U_15294,U_15292,U_15290] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15290),tc_List_Olist(U_15290))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15290),tc_List_Olist(U_15290)),U_15292),U_15294)),c_List_Olexord(U_15290,U_15296)))
        | ( ! [U_15284] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15290,U_15290)),hAPP(hAPP(c_Product__Type_OPair(U_15290,U_15290),hAPP(hAPP(c_List_Onth(U_15290),U_15292),U_15284)),hAPP(hAPP(c_List_Onth(U_15290),U_15294),U_15284))),U_15296))
              | hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15292) != hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15294)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15284),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),U_15294) != U_15292
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294))) ) ) )
    & ! [U_15295,U_15293,U_15291,U_15289] :
        ( ? [U_15283] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15289,U_15289)),hAPP(hAPP(c_Product__Type_OPair(U_15289,U_15289),hAPP(hAPP(c_List_Onth(U_15289),U_15291),U_15283)),hAPP(hAPP(c_List_Onth(U_15289),U_15293),U_15283))),U_15295))
            & hAPP(hAPP(c_List_Otake(U_15289),U_15283),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),U_15283),U_15293)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15283),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),U_15293) = U_15291
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ) ),
    inference(miniscope,[status(thm)],[f_3822_2]) ).

fof(f_3822_4,plain,
    ( ! [U_15296,U_15294,U_15292,U_15290] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15290),tc_List_Olist(U_15290))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15290),tc_List_Olist(U_15290)),U_15292),U_15294)),c_List_Olexord(U_15290,U_15296)))
        | ( ! [U_15284] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15290,U_15290)),hAPP(hAPP(c_Product__Type_OPair(U_15290,U_15290),hAPP(hAPP(c_List_Onth(U_15290),U_15292),U_15284)),hAPP(hAPP(c_List_Onth(U_15290),U_15294),U_15284))),U_15296))
              | hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15292) != hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15294)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15284),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),U_15294) != U_15292
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294))) ) ) )
    & ! [U_15295,U_15293,U_15291,U_15289] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15289,U_15289)),hAPP(hAPP(c_Product__Type_OPair(U_15289,U_15289),hAPP(hAPP(c_List_Onth(U_15289),U_15291),sK397(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK397(U_15295,U_15293,U_15291,U_15289)))),U_15295))
          & hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15293)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK397(U_15295,U_15293,U_15291,U_15289)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),U_15293) = U_15291
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_15283,sK397(U_15295,U_15293,U_15291,U_15289))],[f_3822_3]) ).

cnf(f_3822_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK397(U_15295,U_15293,U_15291,U_15289)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15293)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15289,U_15289)),hAPP(hAPP(c_Product__Type_OPair(U_15289,U_15289),hAPP(hAPP(c_List_Onth(U_15289),U_15291),sK397(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK397(U_15295,U_15293,U_15291,U_15289)))),U_15295))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK397(U_15295,U_15293,U_15291,U_15289)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15293))))
    | hAPP(hAPP(c_List_Otake(U_15289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),U_15293) = U_15291
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK397(U_15295,U_15293,U_15291,U_15289)),U_15293)
    | hAPP(hAPP(c_List_Otake(U_15289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),U_15293) = U_15291
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15289,U_15289)),hAPP(hAPP(c_Product__Type_OPair(U_15289,U_15289),hAPP(hAPP(c_List_Onth(U_15289),U_15291),sK397(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK397(U_15295,U_15293,U_15291,U_15289)))),U_15295))
    | hAPP(hAPP(c_List_Otake(U_15289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15289)),U_15291)),U_15293) = U_15291
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15289),tc_List_Olist(U_15289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15289),tc_List_Olist(U_15289)),U_15291),U_15293)),c_List_Olexord(U_15289,U_15295))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_15290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),U_15294) != U_15292
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15290),tc_List_Olist(U_15290))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15290),tc_List_Olist(U_15290)),U_15292),U_15294)),c_List_Olexord(U_15290,U_15296))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

cnf(f_3822_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15290,U_15290)),hAPP(hAPP(c_Product__Type_OPair(U_15290,U_15290),hAPP(hAPP(c_List_Onth(U_15290),U_15292),U_15284)),hAPP(hAPP(c_List_Onth(U_15290),U_15294),U_15284))),U_15296))
    | hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15292) != hAPP(hAPP(c_List_Otake(U_15290),U_15284),U_15294)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15284),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15292)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15290)),U_15294))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15290),tc_List_Olist(U_15290))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15290),tc_List_Olist(U_15290)),U_15292),U_15294)),c_List_Olexord(U_15290,U_15296))) ),
    inference(clausify,[status(thm)],[f_3822_4]) ).

fof(f_3823_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_3823_2,plain,
    ! [U_15299,U_15298,U_15297] : hAPP(c_List_Oset(U_15297),c_List_Osublist(U_15297,U_15298,U_15299)) = hAPP(c_Set_OCollect(U_15297),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15297),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15297,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_15297),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_15297),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15297,tc_fun(tc_Nat_Onat,U_15297),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15297,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15297),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15297),c_COMBB(U_15297,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15297),U_15298))))),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_15297)),U_15298)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15299))))),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

cnf(f_3823_3,plain,
    hAPP(c_List_Oset(U_15297),c_List_Osublist(U_15297,U_15298,U_15299)) = hAPP(c_Set_OCollect(U_15297),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15297),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15297,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_15297),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_15297),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15297,tc_fun(tc_Nat_Onat,U_15297),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15297,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15297),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15297),c_COMBB(U_15297,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15297),U_15298))))),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_15297)),U_15298)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15299))))),
    inference(clausify,[status(thm)],[f_3823_2]) ).

fof(f_3824_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_3824_2,plain,
    ! [U_15301,U_15300] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_15300),hAPP(c_List_Oset(U_15300),U_15301))),
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

cnf(f_3824_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_15300),hAPP(c_List_Oset(U_15300),U_15301))),
    inference(clausify,[status(thm)],[f_3824_2]) ).

fof(f_3825_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_3825_2,plain,
    ! [U_15304,U_15303,U_15302] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15302,tc_HOL_Obool)),hAPP(c_List_Oset(U_15302),U_15303)),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Olist_OCons(U_15302),U_15304),U_15303)))),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

cnf(f_3825_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15302,tc_HOL_Obool)),hAPP(c_List_Oset(U_15302),U_15303)),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Olist_OCons(U_15302),U_15304),U_15303)))),
    inference(clausify,[status(thm)],[f_3825_2]) ).

fof(f_3826_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_3826_2,plain,
    ! [U_15307,U_15306,U_15305] :
      ( hAPP(hAPP(c_List_Otake(U_15305),U_15307),U_15306) = U_15306
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15305)),U_15306)),U_15307)) ),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

cnf(f_3826_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_15305),U_15307),U_15306) = U_15306
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15305)),U_15306)),U_15307)) ),
    inference(clausify,[status(thm)],[f_3826_2]) ).

fof(f_3827_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_3827_2,plain,
    ! [U_15310,U_15309,U_15308] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15308,tc_HOL_Obool)),hAPP(c_List_Oset(U_15308),hAPP(hAPP(c_List_Otake(U_15308),U_15309),U_15310))),hAPP(c_List_Oset(U_15308),U_15310))),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

cnf(f_3827_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15308,tc_HOL_Obool)),hAPP(c_List_Oset(U_15308),hAPP(hAPP(c_List_Otake(U_15308),U_15309),U_15310))),hAPP(c_List_Oset(U_15308),U_15310))),
    inference(clausify,[status(thm)],[f_3827_2]) ).

fof(f_3828_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_3828_2,plain,
    ! [U_15314,U_15313,U_15312,U_15311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15313,tc_HOL_Obool)),hAPP(c_List_Oset(U_15313),hAPP(hAPP(c_List_Otake(U_15313),U_15311),U_15314))),hAPP(c_List_Oset(U_15313),hAPP(hAPP(c_List_Otake(U_15313),U_15312),U_15314))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15311),U_15312)) ),
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

cnf(f_3828_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15313,tc_HOL_Obool)),hAPP(c_List_Oset(U_15313),hAPP(hAPP(c_List_Otake(U_15313),U_15311),U_15314))),hAPP(c_List_Oset(U_15313),hAPP(hAPP(c_List_Otake(U_15313),U_15312),U_15314))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15311),U_15312)) ),
    inference(clausify,[status(thm)],[f_3828_2]) ).

fof(f_3829_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_3829_2,plain,
    ! [U_15317,U_15316,U_15315] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15315,tc_HOL_Obool)),hAPP(c_List_Oset(U_15315),c_List_Osublist(U_15315,U_15316,U_15317))),hAPP(c_List_Oset(U_15315),U_15316))),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

cnf(f_3829_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15315,tc_HOL_Obool)),hAPP(c_List_Oset(U_15315),c_List_Osublist(U_15315,U_15316,U_15317))),hAPP(c_List_Oset(U_15315),U_15316))),
    inference(clausify,[status(thm)],[f_3829_2]) ).

fof(f_3830_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_3830_2,plain,
    ! [U_15321,U_15320,U_15319,U_15318] :
      ( hAPP(hAPP(c_List_Onth(U_15320),hAPP(hAPP(c_List_Otake(U_15320),U_15319),U_15321)),U_15318) = hAPP(hAPP(c_List_Onth(U_15320),U_15321),U_15318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15318),U_15319)) ),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

cnf(f_3830_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15320),hAPP(hAPP(c_List_Otake(U_15320),U_15319),U_15321)),U_15318) = hAPP(hAPP(c_List_Onth(U_15320),U_15321),U_15318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15318),U_15319)) ),
    inference(clausify,[status(thm)],[f_3830_2]) ).

fof(f_3831_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_3831_2,plain,
    ! [U_15325,U_15324,U_15323,U_15322] :
      ( hBOOL(hAPP(hAPP(c_member(U_15322),U_15323),hAPP(c_List_Oset(U_15322),U_15325)))
      | U_15323 = U_15324
      | ~ hBOOL(hAPP(hAPP(c_member(U_15322),U_15323),hAPP(c_List_Oset(U_15322),hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),U_15325)))) ),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

cnf(f_3831_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15322),U_15323),hAPP(c_List_Oset(U_15322),U_15325)))
    | U_15323 = U_15324
    | ~ hBOOL(hAPP(hAPP(c_member(U_15322),U_15323),hAPP(c_List_Oset(U_15322),hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),U_15325)))) ),
    inference(clausify,[status(thm)],[f_3831_2]) ).

fof(f_3832_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_3832_2,plain,
    ! [U_15329,U_15328,U_15327,U_15326] :
      ( hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),U_15328)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),c_List_Osublist(U_15326,U_15328,U_15329)))) ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

cnf(f_3832_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),U_15328)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),c_List_Osublist(U_15326,U_15328,U_15329)))) ),
    inference(clausify,[status(thm)],[f_3832_2]) ).

fof(f_3833_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_3833_2,plain,
    ! [U_15333,U_15332,U_15331,U_15330] :
      ( hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),U_15333)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),hAPP(hAPP(c_List_Otake(U_15330),U_15332),U_15333)))) ),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

cnf(f_3833_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),U_15333)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),hAPP(hAPP(c_List_Otake(U_15330),U_15332),U_15333)))) ),
    inference(clausify,[status(thm)],[f_3833_2]) ).

fof(f_3834_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_3834_2,plain,
    ! [U_15337,U_15336,U_15335,U_15334] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),c_List_Osublist(U_15334,U_15336,U_15337))))
      | hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),U_15336))) ),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

cnf(f_3834_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),c_List_Osublist(U_15334,U_15336,U_15337))))
    | hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),U_15336))) ),
    inference(clausify,[status(thm)],[f_3834_2]) ).

fof(f_3835_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_3835_2,plain,
    ! [U_15341,U_15340,U_15339,U_15338] : hAPP(hAPP(c_List_Otake(U_15338),hAPP(c_Nat_OSuc,U_15339)),hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15340),U_15341)) = hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15340),hAPP(hAPP(c_List_Otake(U_15338),U_15339),U_15341)),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

cnf(f_3835_3,plain,
    hAPP(hAPP(c_List_Otake(U_15338),hAPP(c_Nat_OSuc,U_15339)),hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15340),U_15341)) = hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15340),hAPP(hAPP(c_List_Otake(U_15338),U_15339),U_15341)),
    inference(clausify,[status(thm)],[f_3835_2]) ).

fof(f_3836_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_3836_2,plain,
    ! [U_15344,U_15343,U_15342] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15342)),hAPP(hAPP(c_List_Otake(U_15342),U_15343),U_15344)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15342)),U_15344)),U_15343),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

cnf(f_3836_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15342)),hAPP(hAPP(c_List_Otake(U_15342),U_15343),U_15344)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15342)),U_15344)),U_15343),
    inference(clausify,[status(thm)],[f_3836_2]) ).

fof(f_3837_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_3837_2,plain,
    ! [U_15348,U_15347,U_15346,U_15345] : hAPP(hAPP(c_List_Otake(U_15345),U_15346),hAPP(hAPP(c_List_Otake(U_15345),U_15347),U_15348)) = hAPP(hAPP(c_List_Otake(U_15345),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15346),U_15347)),U_15348),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

cnf(f_3837_3,plain,
    hAPP(hAPP(c_List_Otake(U_15345),U_15346),hAPP(hAPP(c_List_Otake(U_15345),U_15347),U_15348)) = hAPP(hAPP(c_List_Otake(U_15345),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15346),U_15347)),U_15348),
    inference(clausify,[status(thm)],[f_3837_2]) ).

fof(f_3838_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_3838_2,plain,
    ! [U_15351,U_15350,U_15349] : hAPP(c_List_Oset(U_15349),hAPP(hAPP(c_List_Olist_OCons(U_15349),U_15350),U_15351)) = hAPP(hAPP(c_Set_Oinsert(U_15349),U_15350),hAPP(c_List_Oset(U_15349),U_15351)),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

cnf(f_3838_3,plain,
    hAPP(c_List_Oset(U_15349),hAPP(hAPP(c_List_Olist_OCons(U_15349),U_15350),U_15351)) = hAPP(hAPP(c_Set_Oinsert(U_15349),U_15350),hAPP(c_List_Oset(U_15349),U_15351)),
    inference(clausify,[status(thm)],[f_3838_2]) ).

fof(f_3839_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_3839_2,plain,
    ! [U_15354,U_15353,U_15352] : c_List_Osublist(U_15352,U_15353,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15354)) = hAPP(hAPP(c_List_Otake(U_15352),U_15354),U_15353),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

cnf(f_3839_3,plain,
    c_List_Osublist(U_15352,U_15353,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15354)) = hAPP(hAPP(c_List_Otake(U_15352),U_15354),U_15353),
    inference(clausify,[status(thm)],[f_3839_2]) ).

fof(f_3840_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_3840_2,plain,
    ! [U_15356,U_15355] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15355),hAPP(c_List_Oset(U_15355),U_15356))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15355)),U_15356))),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

cnf(f_3840_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15355),hAPP(c_List_Oset(U_15355),U_15356))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15355)),U_15356))),
    inference(clausify,[status(thm)],[f_3840_2]) ).

fof(f_3841_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_3841_2,plain,
    ! [U_15363,U_15362,U_15361] :
      ( ( ! [U_15360] :
            ( hBOOL(hAPP(U_15363,U_15360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15361),U_15360),hAPP(c_List_Oset(U_15361),U_15362))) )
        | ? [U_15359] :
            ( ~ hBOOL(hAPP(U_15363,hAPP(hAPP(c_List_Onth(U_15361),U_15362),U_15359)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15361)),U_15362))) ) )
      & ( ! [U_15358] :
            ( hBOOL(hAPP(U_15363,hAPP(hAPP(c_List_Onth(U_15361),U_15362),U_15358)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15361)),U_15362))) )
        | ? [U_15357] :
            ( ~ hBOOL(hAPP(U_15363,U_15357))
            & hBOOL(hAPP(hAPP(c_member(U_15361),U_15357),hAPP(c_List_Oset(U_15361),U_15362))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

fof(f_3841_3,plain,
    ( ! [U_15369,U_15367,U_15365] :
        ( ! [U_15360] :
            ( hBOOL(hAPP(U_15369,U_15360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15365),U_15360),hAPP(c_List_Oset(U_15365),U_15367))) )
        | ? [U_15359] :
            ( ~ hBOOL(hAPP(U_15369,hAPP(hAPP(c_List_Onth(U_15365),U_15367),U_15359)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15365)),U_15367))) ) )
    & ! [U_15368,U_15366,U_15364] :
        ( ! [U_15358] :
            ( hBOOL(hAPP(U_15368,hAPP(hAPP(c_List_Onth(U_15364),U_15366),U_15358)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15364)),U_15366))) )
        | ? [U_15357] :
            ( ~ hBOOL(hAPP(U_15368,U_15357))
            & hBOOL(hAPP(hAPP(c_member(U_15364),U_15357),hAPP(c_List_Oset(U_15364),U_15366))) ) ) ),
    inference(miniscope,[status(thm)],[f_3841_2]) ).

fof(f_3841_4,plain,
    ( ! [U_15369,U_15367,U_15365] :
        ( ! [U_15360] :
            ( hBOOL(hAPP(U_15369,U_15360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15365),U_15360),hAPP(c_List_Oset(U_15365),U_15367))) )
        | ? [U_15359] :
            ( ~ hBOOL(hAPP(U_15369,hAPP(hAPP(c_List_Onth(U_15365),U_15367),U_15359)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15365)),U_15367))) ) )
    & ! [U_15368,U_15366,U_15364] :
        ( ! [U_15358] :
            ( hBOOL(hAPP(U_15368,hAPP(hAPP(c_List_Onth(U_15364),U_15366),U_15358)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15364)),U_15366))) )
        | ( ~ hBOOL(hAPP(U_15368,sK398(U_15368,U_15366,U_15364)))
          & hBOOL(hAPP(hAPP(c_member(U_15364),sK398(U_15368,U_15366,U_15364)),hAPP(c_List_Oset(U_15364),U_15366))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_15357,sK398(U_15368,U_15366,U_15364))],[f_3841_3]) ).

fof(f_3841_5,plain,
    ( ! [U_15369,U_15367,U_15365] :
        ( ! [U_15360] :
            ( hBOOL(hAPP(U_15369,U_15360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15365),U_15360),hAPP(c_List_Oset(U_15365),U_15367))) )
        | ( ~ hBOOL(hAPP(U_15369,hAPP(hAPP(c_List_Onth(U_15365),U_15367),sK399(U_15369,U_15367,U_15365))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK399(U_15369,U_15367,U_15365)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15365)),U_15367))) ) )
    & ! [U_15368,U_15366,U_15364] :
        ( ! [U_15358] :
            ( hBOOL(hAPP(U_15368,hAPP(hAPP(c_List_Onth(U_15364),U_15366),U_15358)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15364)),U_15366))) )
        | ( ~ hBOOL(hAPP(U_15368,sK398(U_15368,U_15366,U_15364)))
          & hBOOL(hAPP(hAPP(c_member(U_15364),sK398(U_15368,U_15366,U_15364)),hAPP(c_List_Oset(U_15364),U_15366))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_15359,sK399(U_15369,U_15367,U_15365))],[f_3841_4]) ).

cnf(f_3841_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15364),sK398(U_15368,U_15366,U_15364)),hAPP(c_List_Oset(U_15364),U_15366)))
    | hBOOL(hAPP(U_15368,hAPP(hAPP(c_List_Onth(U_15364),U_15366),U_15358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15364)),U_15366))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

cnf(f_3841_7,plain,
    ( ~ hBOOL(hAPP(U_15368,sK398(U_15368,U_15366,U_15364)))
    | hBOOL(hAPP(U_15368,hAPP(hAPP(c_List_Onth(U_15364),U_15366),U_15358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15364)),U_15366))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

cnf(f_3841_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK399(U_15369,U_15367,U_15365)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15365)),U_15367)))
    | hBOOL(hAPP(U_15369,U_15360))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15365),U_15360),hAPP(c_List_Oset(U_15365),U_15367))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

cnf(f_3841_9,plain,
    ( ~ hBOOL(hAPP(U_15369,hAPP(hAPP(c_List_Onth(U_15365),U_15367),sK399(U_15369,U_15367,U_15365))))
    | hBOOL(hAPP(U_15369,U_15360))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15365),U_15360),hAPP(c_List_Oset(U_15365),U_15367))) ),
    inference(clausify,[status(thm)],[f_3841_5]) ).

fof(f_3842_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_3842_2,plain,
    ! [U_15374,U_15373,U_15372,U_15371,U_15370] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15373),c_List_Olist_Olist__size(U_15370,U_15374,U_15372)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15373),hAPP(U_15374,U_15371)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15370),U_15371),hAPP(c_List_Oset(U_15370),U_15372))) ),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

cnf(f_3842_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15373),c_List_Olist_Olist__size(U_15370,U_15374,U_15372)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15373),hAPP(U_15374,U_15371)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15370),U_15371),hAPP(c_List_Oset(U_15370),U_15372))) ),
    inference(clausify,[status(thm)],[f_3842_2]) ).

fof(f_3843_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_3843_2,plain,
    ! [U_15379,U_15378,U_15377,U_15376,U_15375] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15378),c_List_Olist_Olist__size(U_15375,U_15379,U_15377)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15378),hAPP(U_15379,U_15376)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15375),U_15376),hAPP(c_List_Oset(U_15375),U_15377))) ),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

cnf(f_3843_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15378),c_List_Olist_Olist__size(U_15375,U_15379,U_15377)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15378),hAPP(U_15379,U_15376)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15375),U_15376),hAPP(c_List_Oset(U_15375),U_15377))) ),
    inference(clausify,[status(thm)],[f_3843_2]) ).

fof(f_3844_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_3844_2,plain,
    ! [U_15384,U_15383,U_15382] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15382)),U_15383),c_List_Olists(U_15382,U_15384)))
        | ? [U_15381] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15382),U_15381),U_15384))
            & hBOOL(hAPP(hAPP(c_member(U_15382),U_15381),hAPP(c_List_Oset(U_15382),U_15383))) ) )
      & ( ! [U_15380] :
            ( hBOOL(hAPP(hAPP(c_member(U_15382),U_15380),U_15384))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15382),U_15380),hAPP(c_List_Oset(U_15382),U_15383))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15382)),U_15383),c_List_Olists(U_15382,U_15384))) ) ),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

fof(f_3844_3,plain,
    ( ! [U_15390,U_15388,U_15386] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15386)),U_15388),c_List_Olists(U_15386,U_15390)))
        | ? [U_15381] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15386),U_15381),U_15390))
            & hBOOL(hAPP(hAPP(c_member(U_15386),U_15381),hAPP(c_List_Oset(U_15386),U_15388))) ) )
    & ! [U_15389,U_15387,U_15385] :
        ( ! [U_15380] :
            ( hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),U_15389))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),hAPP(c_List_Oset(U_15385),U_15387))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15385)),U_15387),c_List_Olists(U_15385,U_15389))) ) ),
    inference(miniscope,[status(thm)],[f_3844_2]) ).

fof(f_3844_4,plain,
    ( ! [U_15390,U_15388,U_15386] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15386)),U_15388),c_List_Olists(U_15386,U_15390)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_15386),sK400(U_15390,U_15388,U_15386)),U_15390))
          & hBOOL(hAPP(hAPP(c_member(U_15386),sK400(U_15390,U_15388,U_15386)),hAPP(c_List_Oset(U_15386),U_15388))) ) )
    & ! [U_15389,U_15387,U_15385] :
        ( ! [U_15380] :
            ( hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),U_15389))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),hAPP(c_List_Oset(U_15385),U_15387))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15385)),U_15387),c_List_Olists(U_15385,U_15389))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_15381,sK400(U_15390,U_15388,U_15386))],[f_3844_3]) ).

cnf(f_3844_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),U_15389))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15385),U_15380),hAPP(c_List_Oset(U_15385),U_15387)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15385)),U_15387),c_List_Olists(U_15385,U_15389))) ),
    inference(clausify,[status(thm)],[f_3844_4]) ).

cnf(f_3844_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15386),sK400(U_15390,U_15388,U_15386)),hAPP(c_List_Oset(U_15386),U_15388)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15386)),U_15388),c_List_Olists(U_15386,U_15390))) ),
    inference(clausify,[status(thm)],[f_3844_4]) ).

cnf(f_3844_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15386),sK400(U_15390,U_15388,U_15386)),U_15390))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15386)),U_15388),c_List_Olists(U_15386,U_15390))) ),
    inference(clausify,[status(thm)],[f_3844_4]) ).

fof(f_3845_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_3845_2,plain,
    ! [U_15393,U_15392,U_15391] :
      ( 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_15391)),U_15393)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15392),hAPP(c_List_Oset(U_15391),U_15393))) ),
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

cnf(f_3845_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_15391)),U_15393)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15392),hAPP(c_List_Oset(U_15391),U_15393))) ),
    inference(clausify,[status(thm)],[f_3845_2]) ).

fof(f_3846_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_3846_2,plain,
    ! [U_15396,U_15395,U_15394] :
      ( hBOOL(hAPP(hAPP(c_member(U_15395),hAPP(hAPP(c_List_Onth(U_15395),U_15396),U_15394)),hAPP(c_List_Oset(U_15395),U_15396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15395)),U_15396))) ),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

cnf(f_3846_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15395),hAPP(hAPP(c_List_Onth(U_15395),U_15396),U_15394)),hAPP(c_List_Oset(U_15395),U_15396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15394),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15395)),U_15396))) ),
    inference(clausify,[status(thm)],[f_3846_2]) ).

fof(f_3847_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_3847_2,plain,
    ! [U_15401,U_15400,U_15399] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15399),U_15400),hAPP(c_List_Oset(U_15399),U_15401)))
        | ! [U_15398] :
            ( hAPP(hAPP(c_List_Onth(U_15399),U_15401),U_15398) != U_15400
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15399)),U_15401))) ) )
      & ( ? [U_15397] :
            ( hAPP(hAPP(c_List_Onth(U_15399),U_15401),U_15397) = U_15400
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15397),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15399)),U_15401))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15400),hAPP(c_List_Oset(U_15399),U_15401))) ) ),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

fof(f_3847_3,plain,
    ( ! [U_15407,U_15405,U_15403] :
        ( hBOOL(hAPP(hAPP(c_member(U_15403),U_15405),hAPP(c_List_Oset(U_15403),U_15407)))
        | ! [U_15398] :
            ( hAPP(hAPP(c_List_Onth(U_15403),U_15407),U_15398) != U_15405
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15403)),U_15407))) ) )
    & ! [U_15406,U_15404,U_15402] :
        ( ? [U_15397] :
            ( hAPP(hAPP(c_List_Onth(U_15402),U_15406),U_15397) = U_15404
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15397),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15402)),U_15406))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15404),hAPP(c_List_Oset(U_15402),U_15406))) ) ),
    inference(miniscope,[status(thm)],[f_3847_2]) ).

fof(f_3847_4,plain,
    ( ! [U_15407,U_15405,U_15403] :
        ( hBOOL(hAPP(hAPP(c_member(U_15403),U_15405),hAPP(c_List_Oset(U_15403),U_15407)))
        | ! [U_15398] :
            ( hAPP(hAPP(c_List_Onth(U_15403),U_15407),U_15398) != U_15405
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15403)),U_15407))) ) )
    & ! [U_15406,U_15404,U_15402] :
        ( ( hAPP(hAPP(c_List_Onth(U_15402),U_15406),sK401(U_15406,U_15404,U_15402)) = U_15404
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK401(U_15406,U_15404,U_15402)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15402)),U_15406))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15404),hAPP(c_List_Oset(U_15402),U_15406))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15397,sK401(U_15406,U_15404,U_15402))],[f_3847_3]) ).

cnf(f_3847_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK401(U_15406,U_15404,U_15402)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15402)),U_15406)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15404),hAPP(c_List_Oset(U_15402),U_15406))) ),
    inference(clausify,[status(thm)],[f_3847_4]) ).

cnf(f_3847_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15402),U_15406),sK401(U_15406,U_15404,U_15402)) = U_15404
    | ~ hBOOL(hAPP(hAPP(c_member(U_15402),U_15404),hAPP(c_List_Oset(U_15402),U_15406))) ),
    inference(clausify,[status(thm)],[f_3847_4]) ).

cnf(f_3847_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15403),U_15405),hAPP(c_List_Oset(U_15403),U_15407)))
    | hAPP(hAPP(c_List_Onth(U_15403),U_15407),U_15398) != U_15405
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15403)),U_15407))) ),
    inference(clausify,[status(thm)],[f_3847_4]) ).

fof(f_3848_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_3848_2,plain,
    ! [U_15409,U_15408] : c_List_Olists(U_15408,U_15409) = hAPP(c_Set_OCollect(tc_List_Olist(U_15408)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15408),tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15408,tc_HOL_Obool),tc_fun(tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15408)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15408,tc_HOL_Obool))),c_List_Oset(U_15408))),U_15409)),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

cnf(f_3848_3,plain,
    c_List_Olists(U_15408,U_15409) = hAPP(c_Set_OCollect(tc_List_Olist(U_15408)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15408),tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15408,tc_HOL_Obool),tc_fun(tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15408)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15408,tc_HOL_Obool))),c_List_Oset(U_15408))),U_15409)),
    inference(clausify,[status(thm)],[f_3848_2]) ).

fof(f_3849_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_3849_2,plain,
    ! [U_15411,U_15410] : hAPP(c_List_Oset(U_15410),U_15411) = hAPP(c_Set_OCollect(U_15410),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15410),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15410,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_15410),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_15410),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15410,tc_fun(tc_Nat_Onat,U_15410),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15410,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15410),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15410),c_COMBB(U_15410,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15410),U_15411))))),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_15410)),U_15411))))),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

cnf(f_3849_3,plain,
    hAPP(c_List_Oset(U_15410),U_15411) = hAPP(c_Set_OCollect(U_15410),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15410),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15410,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_15410),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_15410),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15410,tc_fun(tc_Nat_Onat,U_15410),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15410,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15410),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15410),c_COMBB(U_15410,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15410),U_15411))))),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_15410)),U_15411))))),
    inference(clausify,[status(thm)],[f_3849_2]) ).

fof(f_3850_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_3850_2,plain,
    ! [U_15414,U_15413,U_15412] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15412)),hAPP(c_Set_OCollect(tc_List_Olist(U_15412)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15412),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_15412)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15412),tc_fun(U_15412,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_HOL_Obool),tc_fun(tc_fun(U_15412,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15412)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15412,tc_HOL_Obool))),c_List_Oset(U_15412))),U_15413))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15412),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_15412)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15412)))),U_15414)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15412),U_15413)) ),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

cnf(f_3850_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15412)),hAPP(c_Set_OCollect(tc_List_Olist(U_15412)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15412),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_15412)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15412),tc_fun(U_15412,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_HOL_Obool),tc_fun(tc_fun(U_15412,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15412)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15412,tc_HOL_Obool))),c_List_Oset(U_15412))),U_15413))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15412),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_15412)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15412)))),U_15414)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15412),U_15413)) ),
    inference(clausify,[status(thm)],[f_3850_2]) ).

fof(f_3851_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_3851_2,plain,
    ! [U_15417,U_15416,U_15415] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15415)),hAPP(c_Set_OCollect(tc_List_Olist(U_15415)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15415),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_15415)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15415),tc_fun(U_15415,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_HOL_Obool),tc_fun(tc_fun(U_15415,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15415)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15415,tc_HOL_Obool))),c_List_Oset(U_15415))),U_15416))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15415),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_15415)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15415)))),U_15417)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15415),U_15416)) ),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

cnf(f_3851_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15415)),hAPP(c_Set_OCollect(tc_List_Olist(U_15415)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15415),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_15415)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15415),tc_fun(U_15415,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_HOL_Obool),tc_fun(tc_fun(U_15415,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15415)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15415,tc_HOL_Obool))),c_List_Oset(U_15415))),U_15416))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15415),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_15415)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15415)))),U_15417)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15415),U_15416)) ),
    inference(clausify,[status(thm)],[f_3851_2]) ).

fof(f_3852_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_3852_2,plain,
    ! [U_15423,U_15422,U_15421,U_15420] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15420),tc_List_Olist(U_15420))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15420),tc_List_Olist(U_15420)),U_15421),U_15422)),c_List_Olistrel(U_15420,U_15423)))
        | ? [U_15419] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15420,U_15420,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15420,tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_fun(U_15420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15420,tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_fun(U_15420,tc_HOL_Obool)),U_15420),c_COMBC(U_15420,tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15420,tc_prod(U_15420,U_15420)),tc_fun(U_15420,tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),U_15420),hAPP(c_COMBB(tc_prod(U_15420,U_15420),tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool),U_15420),c_member(tc_prod(U_15420,U_15420)))),c_Product__Type_OPair(U_15420,U_15420)))),U_15423)),U_15419))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15420)),U_15419),hAPP(c_List_Oset(tc_prod(U_15420,U_15420)),hAPP(hAPP(c_List_Ozip(U_15420,U_15420),U_15421),U_15422)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15420)),U_15421) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15420)),U_15422) )
      & ( ( ! [U_15418] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15420,U_15420,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15420,tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_fun(U_15420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15420,tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_fun(U_15420,tc_HOL_Obool)),U_15420),c_COMBC(U_15420,tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15420,tc_prod(U_15420,U_15420)),tc_fun(U_15420,tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool)),U_15420),hAPP(c_COMBB(tc_prod(U_15420,U_15420),tc_fun(tc_fun(tc_prod(U_15420,U_15420),tc_HOL_Obool),tc_HOL_Obool),U_15420),c_member(tc_prod(U_15420,U_15420)))),c_Product__Type_OPair(U_15420,U_15420)))),U_15423)),U_15418))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15420,U_15420)),U_15418),hAPP(c_List_Oset(tc_prod(U_15420,U_15420)),hAPP(hAPP(c_List_Ozip(U_15420,U_15420),U_15421),U_15422)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15420)),U_15421) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15420)),U_15422) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15420),tc_List_Olist(U_15420))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15420),tc_List_Olist(U_15420)),U_15421),U_15422)),c_List_Olistrel(U_15420,U_15423))) ) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

fof(f_3852_3,plain,
    ( ! [U_15431,U_15429,U_15427,U_15425] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15425),tc_List_Olist(U_15425))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15425),tc_List_Olist(U_15425)),U_15427),U_15429)),c_List_Olistrel(U_15425,U_15431)))
        | ? [U_15419] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15425,U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_prod(U_15425,U_15425)),tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15425),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool),U_15425),c_member(tc_prod(U_15425,U_15425)))),c_Product__Type_OPair(U_15425,U_15425)))),U_15431)),U_15419))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15425)),U_15419),hAPP(c_List_Oset(tc_prod(U_15425,U_15425)),hAPP(hAPP(c_List_Ozip(U_15425,U_15425),U_15427),U_15429)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15427) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15429) )
    & ! [U_15430,U_15428,U_15426,U_15424] :
        ( ( ! [U_15418] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15424,U_15424,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),U_15424),c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_prod(U_15424,U_15424)),tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),U_15424),hAPP(c_COMBB(tc_prod(U_15424,U_15424),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool),U_15424),c_member(tc_prod(U_15424,U_15424)))),c_Product__Type_OPair(U_15424,U_15424)))),U_15430)),U_15418))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15424,U_15424)),U_15418),hAPP(c_List_Oset(tc_prod(U_15424,U_15424)),hAPP(hAPP(c_List_Ozip(U_15424,U_15424),U_15426),U_15428)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15426) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15428) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15424),tc_List_Olist(U_15424))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15424),tc_List_Olist(U_15424)),U_15426),U_15428)),c_List_Olistrel(U_15424,U_15430))) ) ),
    inference(miniscope,[status(thm)],[f_3852_2]) ).

fof(f_3852_4,plain,
    ( ! [U_15431,U_15429,U_15427,U_15425] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15425),tc_List_Olist(U_15425))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15425),tc_List_Olist(U_15425)),U_15427),U_15429)),c_List_Olistrel(U_15425,U_15431)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15425,U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_prod(U_15425,U_15425)),tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15425),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool),U_15425),c_member(tc_prod(U_15425,U_15425)))),c_Product__Type_OPair(U_15425,U_15425)))),U_15431)),sK402(U_15431,U_15429,U_15427,U_15425)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15425)),sK402(U_15431,U_15429,U_15427,U_15425)),hAPP(c_List_Oset(tc_prod(U_15425,U_15425)),hAPP(hAPP(c_List_Ozip(U_15425,U_15425),U_15427),U_15429)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15427) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15429) )
    & ! [U_15430,U_15428,U_15426,U_15424] :
        ( ( ! [U_15418] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15424,U_15424,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),U_15424),c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_prod(U_15424,U_15424)),tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),U_15424),hAPP(c_COMBB(tc_prod(U_15424,U_15424),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool),U_15424),c_member(tc_prod(U_15424,U_15424)))),c_Product__Type_OPair(U_15424,U_15424)))),U_15430)),U_15418))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15424,U_15424)),U_15418),hAPP(c_List_Oset(tc_prod(U_15424,U_15424)),hAPP(hAPP(c_List_Ozip(U_15424,U_15424),U_15426),U_15428)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15426) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15428) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15424),tc_List_Olist(U_15424))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15424),tc_List_Olist(U_15424)),U_15426),U_15428)),c_List_Olistrel(U_15424,U_15430))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15419,sK402(U_15431,U_15429,U_15427,U_15425))],[f_3852_3]) ).

cnf(f_3852_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15426) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15424)),U_15428)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15424),tc_List_Olist(U_15424))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15424),tc_List_Olist(U_15424)),U_15426),U_15428)),c_List_Olistrel(U_15424,U_15430))) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

cnf(f_3852_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15424,U_15424,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_fun(U_15424,tc_HOL_Obool)),U_15424),c_COMBC(U_15424,tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15424,tc_prod(U_15424,U_15424)),tc_fun(U_15424,tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool)),U_15424),hAPP(c_COMBB(tc_prod(U_15424,U_15424),tc_fun(tc_fun(tc_prod(U_15424,U_15424),tc_HOL_Obool),tc_HOL_Obool),U_15424),c_member(tc_prod(U_15424,U_15424)))),c_Product__Type_OPair(U_15424,U_15424)))),U_15430)),U_15418))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15424,U_15424)),U_15418),hAPP(c_List_Oset(tc_prod(U_15424,U_15424)),hAPP(hAPP(c_List_Ozip(U_15424,U_15424),U_15426),U_15428))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15424),tc_List_Olist(U_15424))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15424),tc_List_Olist(U_15424)),U_15426),U_15428)),c_List_Olistrel(U_15424,U_15430))) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

cnf(f_3852_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15425)),sK402(U_15431,U_15429,U_15427,U_15425)),hAPP(c_List_Oset(tc_prod(U_15425,U_15425)),hAPP(hAPP(c_List_Ozip(U_15425,U_15425),U_15427),U_15429))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15427) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15429)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15425),tc_List_Olist(U_15425))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15425),tc_List_Olist(U_15425)),U_15427),U_15429)),c_List_Olistrel(U_15425,U_15431))) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

cnf(f_3852_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15425,U_15425,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_fun(U_15425,tc_HOL_Obool)),U_15425),c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15425,tc_prod(U_15425,U_15425)),tc_fun(U_15425,tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15425),tc_fun(tc_fun(tc_prod(U_15425,U_15425),tc_HOL_Obool),tc_HOL_Obool),U_15425),c_member(tc_prod(U_15425,U_15425)))),c_Product__Type_OPair(U_15425,U_15425)))),U_15431)),sK402(U_15431,U_15429,U_15427,U_15425)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15427) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15425)),U_15429)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15425),tc_List_Olist(U_15425))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15425),tc_List_Olist(U_15425)),U_15427),U_15429)),c_List_Olistrel(U_15425,U_15431))) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

fof(f_3853_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_3853_2,plain,
    ! [U_15435,U_15434,U_15433,U_15432] : hAPP(c_List_Oset(tc_prod(U_15432,U_15433)),hAPP(hAPP(c_List_Ozip(U_15432,U_15433),U_15434),U_15435)) = hAPP(c_Set_OCollect(tc_prod(U_15432,U_15433)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_15432,U_15433)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_15432,U_15433),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_15432,U_15433)),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_15432,U_15433)),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_15432,U_15433),tc_fun(tc_Nat_Onat,tc_prod(U_15432,U_15433)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15432,U_15433),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_15432,U_15433)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15432,U_15433)),c_COMBB(tc_prod(U_15432,U_15433),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_15433,tc_prod(U_15432,U_15433)),hAPP(hAPP(c_COMBB(U_15432,tc_fun(U_15433,tc_prod(U_15432,U_15433)),tc_Nat_Onat),c_Product__Type_OPair(U_15432,U_15433)),hAPP(c_List_Onth(U_15432),U_15434))),hAPP(c_List_Onth(U_15433),U_15435)))))),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_15432)),U_15434)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15433)),U_15435)))))),
    inference(variable_rename,[status(thm)],[f_3853_1]) ).

cnf(f_3853_3,plain,
    hAPP(c_List_Oset(tc_prod(U_15432,U_15433)),hAPP(hAPP(c_List_Ozip(U_15432,U_15433),U_15434),U_15435)) = hAPP(c_Set_OCollect(tc_prod(U_15432,U_15433)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_15432,U_15433)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_15432,U_15433),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_15432,U_15433)),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_15432,U_15433)),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_15432,U_15433),tc_fun(tc_Nat_Onat,tc_prod(U_15432,U_15433)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15432,U_15433),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_15432,U_15433)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15432,U_15433)),c_COMBB(tc_prod(U_15432,U_15433),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_15433,tc_prod(U_15432,U_15433)),hAPP(hAPP(c_COMBB(U_15432,tc_fun(U_15433,tc_prod(U_15432,U_15433)),tc_Nat_Onat),c_Product__Type_OPair(U_15432,U_15433)),hAPP(c_List_Onth(U_15432),U_15434))),hAPP(c_List_Onth(U_15433),U_15435)))))),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_15432)),U_15434)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15433)),U_15435)))))),
    inference(clausify,[status(thm)],[f_3853_2]) ).

fof(f_3854_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_3854_2,plain,
    ! [U_15440,U_15439,U_15438,U_15437,U_15436] : hAPP(hAPP(c_List_Otake(tc_prod(U_15436,U_15437)),U_15438),hAPP(hAPP(c_List_Ozip(U_15436,U_15437),U_15439),U_15440)) = hAPP(hAPP(c_List_Ozip(U_15436,U_15437),hAPP(hAPP(c_List_Otake(U_15436),U_15438),U_15439)),hAPP(hAPP(c_List_Otake(U_15437),U_15438),U_15440)),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

cnf(f_3854_3,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_15436,U_15437)),U_15438),hAPP(hAPP(c_List_Ozip(U_15436,U_15437),U_15439),U_15440)) = hAPP(hAPP(c_List_Ozip(U_15436,U_15437),hAPP(hAPP(c_List_Otake(U_15436),U_15438),U_15439)),hAPP(hAPP(c_List_Otake(U_15437),U_15438),U_15440)),
    inference(clausify,[status(thm)],[f_3854_2]) ).

fof(f_3855_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_3855_2,plain,
    ! [U_15444,U_15443,U_15442,U_15441] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_15441,U_15442))),hAPP(hAPP(c_List_Ozip(U_15441,U_15442),U_15443),U_15444)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15441)),U_15443)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15442)),U_15444)),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

cnf(f_3855_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_15441,U_15442))),hAPP(hAPP(c_List_Ozip(U_15441,U_15442),U_15443),U_15444)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15441)),U_15443)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15442)),U_15444)),
    inference(clausify,[status(thm)],[f_3855_2]) ).

fof(f_3856_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_3856_2,plain,
    ! [U_15450,U_15449,U_15448,U_15447,U_15446,U_15445] : hAPP(hAPP(c_List_Ozip(U_15445,U_15446),hAPP(hAPP(c_List_Olist_OCons(U_15445),U_15447),U_15448)),hAPP(hAPP(c_List_Olist_OCons(U_15446),U_15449),U_15450)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_15445,U_15446)),hAPP(hAPP(c_Product__Type_OPair(U_15445,U_15446),U_15447),U_15449)),hAPP(hAPP(c_List_Ozip(U_15445,U_15446),U_15448),U_15450)),
    inference(variable_rename,[status(thm)],[f_3856_1]) ).

cnf(f_3856_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15445,U_15446),hAPP(hAPP(c_List_Olist_OCons(U_15445),U_15447),U_15448)),hAPP(hAPP(c_List_Olist_OCons(U_15446),U_15449),U_15450)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_15445,U_15446)),hAPP(hAPP(c_Product__Type_OPair(U_15445,U_15446),U_15447),U_15449)),hAPP(hAPP(c_List_Ozip(U_15445,U_15446),U_15448),U_15450)),
    inference(clausify,[status(thm)],[f_3856_2]) ).

fof(f_3857_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_3857_2,plain,
    ! [U_15455,U_15454,U_15453] :
      ( ( U_15453 = U_15454
        | ? [U_15452] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15455,U_15455,tc_HOL_Obool),c_fequal),U_15452))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),U_15452),hAPP(c_List_Oset(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_List_Ozip(U_15455,U_15455),U_15453),U_15454)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15455)),U_15453) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15455)),U_15454) )
      & ( ( ! [U_15451] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15455,U_15455,tc_HOL_Obool),c_fequal),U_15451))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),U_15451),hAPP(c_List_Oset(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_List_Ozip(U_15455,U_15455),U_15453),U_15454)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15455)),U_15453) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15455)),U_15454) )
        | U_15453 != U_15454 ) ),
    inference(variable_rename,[status(thm)],[f_3857_1]) ).

fof(f_3857_3,plain,
    ( ! [U_15461,U_15459,U_15457] :
        ( U_15457 = U_15459
        | ? [U_15452] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15461,U_15461,tc_HOL_Obool),c_fequal),U_15452))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),U_15452),hAPP(c_List_Oset(tc_prod(U_15461,U_15461)),hAPP(hAPP(c_List_Ozip(U_15461,U_15461),U_15457),U_15459)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15457) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15459) )
    & ! [U_15460,U_15458,U_15456] :
        ( ( ! [U_15451] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15460,U_15460,tc_HOL_Obool),c_fequal),U_15451))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15460,U_15460)),U_15451),hAPP(c_List_Oset(tc_prod(U_15460,U_15460)),hAPP(hAPP(c_List_Ozip(U_15460,U_15460),U_15456),U_15458)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15456) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15458) )
        | U_15456 != U_15458 ) ),
    inference(miniscope,[status(thm)],[f_3857_2]) ).

fof(f_3857_4,plain,
    ( ! [U_15461,U_15459,U_15457] :
        ( U_15457 = U_15459
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15461,U_15461,tc_HOL_Obool),c_fequal),sK403(U_15461,U_15459,U_15457)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),sK403(U_15461,U_15459,U_15457)),hAPP(c_List_Oset(tc_prod(U_15461,U_15461)),hAPP(hAPP(c_List_Ozip(U_15461,U_15461),U_15457),U_15459)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15457) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15459) )
    & ! [U_15460,U_15458,U_15456] :
        ( ( ! [U_15451] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15460,U_15460,tc_HOL_Obool),c_fequal),U_15451))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15460,U_15460)),U_15451),hAPP(c_List_Oset(tc_prod(U_15460,U_15460)),hAPP(hAPP(c_List_Ozip(U_15460,U_15460),U_15456),U_15458)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15456) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15458) )
        | U_15456 != U_15458 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15452,sK403(U_15461,U_15459,U_15457))],[f_3857_3]) ).

cnf(f_3857_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15456) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15460)),U_15458)
    | U_15456 != U_15458 ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15460,U_15460,tc_HOL_Obool),c_fequal),U_15451))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15460,U_15460)),U_15451),hAPP(c_List_Oset(tc_prod(U_15460,U_15460)),hAPP(hAPP(c_List_Ozip(U_15460,U_15460),U_15456),U_15458))))
    | U_15456 != U_15458 ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),sK403(U_15461,U_15459,U_15457)),hAPP(c_List_Oset(tc_prod(U_15461,U_15461)),hAPP(hAPP(c_List_Ozip(U_15461,U_15461),U_15457),U_15459))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15457) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15459)
    | U_15457 = U_15459 ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15461,U_15461,tc_HOL_Obool),c_fequal),sK403(U_15461,U_15459,U_15457)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15457) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15461)),U_15459)
    | U_15457 = U_15459 ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

fof(f_3858_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_3858_2,plain,
    ! [U_15467,U_15466,U_15465,U_15464,U_15463,U_15462] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15463),U_15465),hAPP(c_List_Oset(U_15463),U_15467)))
        & hBOOL(hAPP(hAPP(c_member(U_15462),U_15464),hAPP(c_List_Oset(U_15462),U_15466))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15462,U_15463)),hAPP(hAPP(c_Product__Type_OPair(U_15462,U_15463),U_15464),U_15465)),hAPP(c_List_Oset(tc_prod(U_15462,U_15463)),hAPP(hAPP(c_List_Ozip(U_15462,U_15463),U_15466),U_15467)))) ),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

cnf(f_3858_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15462),U_15464),hAPP(c_List_Oset(U_15462),U_15466)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15462,U_15463)),hAPP(hAPP(c_Product__Type_OPair(U_15462,U_15463),U_15464),U_15465)),hAPP(c_List_Oset(tc_prod(U_15462,U_15463)),hAPP(hAPP(c_List_Ozip(U_15462,U_15463),U_15466),U_15467)))) ),
    inference(clausify,[status(thm)],[f_3858_2]) ).

cnf(f_3858_4,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_15462,U_15463)),hAPP(hAPP(c_Product__Type_OPair(U_15462,U_15463),U_15464),U_15465)),hAPP(c_List_Oset(tc_prod(U_15462,U_15463)),hAPP(hAPP(c_List_Ozip(U_15462,U_15463),U_15466),U_15467)))) ),
    inference(clausify,[status(thm)],[f_3858_2]) ).

fof(f_3859_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_3859_2,plain,
    ! [U_15473,U_15472,U_15471,U_15470,U_15469,U_15468] :
      ( hBOOL(hAPP(hAPP(c_member(U_15469),U_15471),hAPP(c_List_Oset(U_15469),U_15473)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_Product__Type_OPair(U_15468,U_15469),U_15470),U_15471)),hAPP(c_List_Oset(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_List_Ozip(U_15468,U_15469),U_15472),U_15473)))) ),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

fof(f_3859_3,plain,
    ! [U_15473,U_15472,U_15471,U_15470,U_15469] :
      ( ! [U_15468] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_Product__Type_OPair(U_15468,U_15469),U_15470),U_15471)),hAPP(c_List_Oset(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_List_Ozip(U_15468,U_15469),U_15472),U_15473))))
      | hBOOL(hAPP(hAPP(c_member(U_15469),U_15471),hAPP(c_List_Oset(U_15469),U_15473))) ),
    inference(miniscope,[status(thm)],[f_3859_2]) ).

cnf(f_3859_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_Product__Type_OPair(U_15468,U_15469),U_15470),U_15471)),hAPP(c_List_Oset(tc_prod(U_15468,U_15469)),hAPP(hAPP(c_List_Ozip(U_15468,U_15469),U_15472),U_15473))))
    | hBOOL(hAPP(hAPP(c_member(U_15469),U_15471),hAPP(c_List_Oset(U_15469),U_15473))) ),
    inference(clausify,[status(thm)],[f_3859_3]) ).

fof(f_3860_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_3860_2,plain,
    ! [U_15479,U_15478,U_15477,U_15476,U_15475,U_15474] :
      ( hBOOL(hAPP(hAPP(c_member(U_15474),U_15476),hAPP(c_List_Oset(U_15474),U_15478)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15474,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15474,U_15475),U_15476),U_15477)),hAPP(c_List_Oset(tc_prod(U_15474,U_15475)),hAPP(hAPP(c_List_Ozip(U_15474,U_15475),U_15478),U_15479)))) ),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

cnf(f_3860_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15474),U_15476),hAPP(c_List_Oset(U_15474),U_15478)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15474,U_15475)),hAPP(hAPP(c_Product__Type_OPair(U_15474,U_15475),U_15476),U_15477)),hAPP(c_List_Oset(tc_prod(U_15474,U_15475)),hAPP(hAPP(c_List_Ozip(U_15474,U_15475),U_15478),U_15479)))) ),
    inference(clausify,[status(thm)],[f_3860_2]) ).

fof(f_3861_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_3861_2,plain,
    ! [U_15483,U_15482,U_15481,U_15480] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15482)),hAPP(c_List_Oset(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_List_Ozip(U_15480,U_15480),U_15483),U_15483))))
        | U_15481 != U_15482
        | ~ hBOOL(hAPP(hAPP(c_member(U_15480),U_15481),hAPP(c_List_Oset(U_15480),U_15483))) )
      & ( ( U_15481 = U_15482
          & hBOOL(hAPP(hAPP(c_member(U_15480),U_15481),hAPP(c_List_Oset(U_15480),U_15483))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15480),U_15481),U_15482)),hAPP(c_List_Oset(tc_prod(U_15480,U_15480)),hAPP(hAPP(c_List_Ozip(U_15480,U_15480),U_15483),U_15483)))) ) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

fof(f_3861_3,plain,
    ( ! [U_15491,U_15489,U_15487,U_15485] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15487),U_15489)),hAPP(c_List_Oset(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_List_Ozip(U_15485,U_15485),U_15491),U_15491))))
        | U_15487 != U_15489
        | ~ hBOOL(hAPP(hAPP(c_member(U_15485),U_15487),hAPP(c_List_Oset(U_15485),U_15491))) )
    & ! [U_15490,U_15488,U_15486,U_15484] :
        ( ( U_15486 = U_15488
          & hBOOL(hAPP(hAPP(c_member(U_15484),U_15486),hAPP(c_List_Oset(U_15484),U_15490))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_Product__Type_OPair(U_15484,U_15484),U_15486),U_15488)),hAPP(c_List_Oset(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_List_Ozip(U_15484,U_15484),U_15490),U_15490)))) ) ),
    inference(miniscope,[status(thm)],[f_3861_2]) ).

cnf(f_3861_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15484),U_15486),hAPP(c_List_Oset(U_15484),U_15490)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_Product__Type_OPair(U_15484,U_15484),U_15486),U_15488)),hAPP(c_List_Oset(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_List_Ozip(U_15484,U_15484),U_15490),U_15490)))) ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

cnf(f_3861_5,plain,
    ( U_15486 = U_15488
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_Product__Type_OPair(U_15484,U_15484),U_15486),U_15488)),hAPP(c_List_Oset(tc_prod(U_15484,U_15484)),hAPP(hAPP(c_List_Ozip(U_15484,U_15484),U_15490),U_15490)))) ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

cnf(f_3861_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_Product__Type_OPair(U_15485,U_15485),U_15487),U_15489)),hAPP(c_List_Oset(tc_prod(U_15485,U_15485)),hAPP(hAPP(c_List_Ozip(U_15485,U_15485),U_15491),U_15491))))
    | U_15487 != U_15489
    | ~ hBOOL(hAPP(hAPP(c_member(U_15485),U_15487),hAPP(c_List_Oset(U_15485),U_15491))) ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

fof(f_3862_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_3862_2,plain,
    ! [U_15496,U_15495,U_15494,U_15493,U_15492] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_15493,U_15495)),hAPP(hAPP(c_List_Ozip(U_15493,U_15495),U_15494),U_15496)),U_15492) = hAPP(hAPP(c_Product__Type_OPair(U_15493,U_15495),hAPP(hAPP(c_List_Onth(U_15493),U_15494),U_15492)),hAPP(hAPP(c_List_Onth(U_15495),U_15496),U_15492))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15495)),U_15496)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15493)),U_15494))) ),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

cnf(f_3862_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_15493,U_15495)),hAPP(hAPP(c_List_Ozip(U_15493,U_15495),U_15494),U_15496)),U_15492) = hAPP(hAPP(c_Product__Type_OPair(U_15493,U_15495),hAPP(hAPP(c_List_Onth(U_15493),U_15494),U_15492)),hAPP(hAPP(c_List_Onth(U_15495),U_15496),U_15492))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15495)),U_15496)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15493)),U_15494))) ),
    inference(clausify,[status(thm)],[f_3862_2]) ).

fof(f_3863_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_3863_2,plain,
    ! [U_15498,U_15497] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_15497,U_15498) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15497),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15498),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

cnf(f_3863_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_15497,U_15498) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15497),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15498),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3863_2]) ).

fof(f_3864_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_3864_2,plain,
    ! [U_15500,U_15499] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15499),U_15500) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_15499),hAPP(c_List_Onth(U_15499),U_15500)),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_15499)),U_15500)))
      | ~ class_Groups_Ocomm__monoid__add(U_15499) ),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

cnf(f_3864_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15499),U_15500) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_15499),hAPP(c_List_Onth(U_15499),U_15500)),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_15499)),U_15500)))
    | ~ class_Groups_Ocomm__monoid__add(U_15499) ),
    inference(clausify,[status(thm)],[f_3864_2]) ).

fof(f_3865_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_3865_2,plain,
    ! [U_15503] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15503) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_15502] :
            ( U_15502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15502),hAPP(c_List_Oset(tc_Nat_Onat),U_15503))) ) )
      & ( ! [U_15501] :
            ( U_15501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15501),hAPP(c_List_Oset(tc_Nat_Onat),U_15503))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15503) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

fof(f_3865_3,plain,
    ( ! [U_15505] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_15502] :
            ( U_15502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15502),hAPP(c_List_Oset(tc_Nat_Onat),U_15505))) ) )
    & ! [U_15504] :
        ( ! [U_15501] :
            ( U_15501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15501),hAPP(c_List_Oset(tc_Nat_Onat),U_15504))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3865_2]) ).

fof(f_3865_4,plain,
    ( ! [U_15505] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK404(U_15505) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK404(U_15505)),hAPP(c_List_Oset(tc_Nat_Onat),U_15505))) ) )
    & ! [U_15504] :
        ( ! [U_15501] :
            ( U_15501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15501),hAPP(c_List_Oset(tc_Nat_Onat),U_15504))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15502,sK404(U_15505))],[f_3865_3]) ).

cnf(f_3865_5,plain,
    ( U_15501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15501),hAPP(c_List_Oset(tc_Nat_Onat),U_15504)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15504) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

cnf(f_3865_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK404(U_15505)),hAPP(c_List_Oset(tc_Nat_Onat),U_15505)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

cnf(f_3865_7,plain,
    ( sK404(U_15505) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

fof(f_3866_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_3866_2,plain,
    ! [U_15507,U_15506] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15506,U_15507) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15506,U_15507)),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

cnf(f_3866_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15506,U_15507) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15506,U_15507)),
    inference(clausify,[status(thm)],[f_3866_2]) ).

fof(f_3867_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_3867_2,plain,
    ! [U_15509,U_15508] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15508,U_15509)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15508,U_15509),
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

cnf(f_3867_3,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15508,U_15509)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15508,U_15509),
    inference(clausify,[status(thm)],[f_3867_2]) ).

fof(f_3868_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_3868_2,plain,
    ! [U_15511,U_15510] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15511),U_15510)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15511)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15510),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15511))) ),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

cnf(f_3868_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15511),U_15510)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15511)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15510),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15511))) ),
    inference(clausify,[status(thm)],[f_3868_2]) ).

fof(f_3869_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_3869_2,plain,
    ! [U_15514,U_15513,U_15512] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15512),hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15513),U_15514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15512),U_15513),hAPP(c_List_Omonoid__add__class_Olistsum(U_15512),U_15514))
      | ~ class_Groups_Omonoid__add(U_15512) ),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

cnf(f_3869_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15512),hAPP(hAPP(c_List_Olist_OCons(U_15512),U_15513),U_15514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15512),U_15513),hAPP(c_List_Omonoid__add__class_Olistsum(U_15512),U_15514))
    | ~ class_Groups_Omonoid__add(U_15512) ),
    inference(clausify,[status(thm)],[f_3869_2]) ).

fof(f_3870_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_3870_2,plain,
    ! [U_15516,U_15515] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_15515),U_15516) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15515,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15516),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

cnf(f_3870_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_15515),U_15516) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15515,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15516),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3870_2]) ).

fof(f_3871_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_3871_2,plain,
    ! [U_15518,U_15517] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_15517,U_15518) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15517),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15518)),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

cnf(f_3871_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_15517,U_15518) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15517),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15518)),
    inference(clausify,[status(thm)],[f_3871_2]) ).

fof(f_3872_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_3872_2,plain,
    ! [U_15519] :
      ( ( c_List_Onat__list(U_15519)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15519)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15519))
        | ~ c_List_Onat__list(U_15519) ) ),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

fof(f_3872_3,plain,
    ( ! [U_15521] :
        ( c_List_Onat__list(U_15521)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15521)) )
    & ! [U_15520] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15520))
        | ~ c_List_Onat__list(U_15520) ) ),
    inference(miniscope,[status(thm)],[f_3872_2]) ).

cnf(f_3872_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15520))
    | ~ c_List_Onat__list(U_15520) ),
    inference(clausify,[status(thm)],[f_3872_3]) ).

cnf(f_3872_5,plain,
    ( c_List_Onat__list(U_15521)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15521)) ),
    inference(clausify,[status(thm)],[f_3872_3]) ).

fof(f_3873_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_3873_2,plain,
    ! [U_15526,U_15525,U_15524,U_15523] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15523,U_15525,U_15524)),c_List_Olist_Olist__size(U_15523,U_15526,U_15524)))
      | ? [U_15522] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15525,U_15522)),hAPP(U_15526,U_15522)))
          & hBOOL(hAPP(hAPP(c_member(U_15523),U_15522),hAPP(c_List_Oset(U_15523),U_15524))) ) ),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

fof(f_3873_3,plain,
    ! [U_15526,U_15525,U_15524,U_15523] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15523,U_15525,U_15524)),c_List_Olist_Olist__size(U_15523,U_15526,U_15524)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15525,sK405(U_15526,U_15525,U_15524,U_15523))),hAPP(U_15526,sK405(U_15526,U_15525,U_15524,U_15523))))
        & hBOOL(hAPP(hAPP(c_member(U_15523),sK405(U_15526,U_15525,U_15524,U_15523)),hAPP(c_List_Oset(U_15523),U_15524))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_15522,sK405(U_15526,U_15525,U_15524,U_15523))],[f_3873_2]) ).

cnf(f_3873_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15523),sK405(U_15526,U_15525,U_15524,U_15523)),hAPP(c_List_Oset(U_15523),U_15524)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15523,U_15525,U_15524)),c_List_Olist_Olist__size(U_15523,U_15526,U_15524))) ),
    inference(clausify,[status(thm)],[f_3873_3]) ).

cnf(f_3873_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15525,sK405(U_15526,U_15525,U_15524,U_15523))),hAPP(U_15526,sK405(U_15526,U_15525,U_15524,U_15523))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15523,U_15525,U_15524)),c_List_Olist_Olist__size(U_15523,U_15526,U_15524))) ),
    inference(clausify,[status(thm)],[f_3873_3]) ).

fof(f_3874_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_3874_2,plain,
    ! [U_15529,U_15528,U_15527] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_15528),U_15527),U_15529)) = 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_15528)),U_15529)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15528),U_15527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15528))) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

cnf(f_3874_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_15528),U_15527),U_15529)) = 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_15528)),U_15529)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15528),U_15527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15528))) ),
    inference(clausify,[status(thm)],[f_3874_2]) ).

fof(f_3875_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_3875_2,plain,
    ! [U_15532,U_15531,U_15530] :
      ( c_List_Obutlast(U_15531,hAPP(hAPP(c_List_Otake(U_15531),U_15530),U_15532)) = hAPP(hAPP(c_List_Otake(U_15531),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15530),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15531)),U_15532))) ),
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

cnf(f_3875_3,plain,
    ( c_List_Obutlast(U_15531,hAPP(hAPP(c_List_Otake(U_15531),U_15530),U_15532)) = hAPP(hAPP(c_List_Otake(U_15531),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15530),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15532)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15531)),U_15532))) ),
    inference(clausify,[status(thm)],[f_3875_2]) ).

fof(f_3876_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_3876_2,plain,
    ! [U_15536,U_15535,U_15534,U_15533] :
      ( hAPP(hAPP(c_List_Olist__update(U_15533,U_15534),U_15535),U_15536) = U_15534
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15533)),U_15534)),U_15535)) ),
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

cnf(f_3876_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15533,U_15534),U_15535),U_15536) = U_15534
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15533)),U_15534)),U_15535)) ),
    inference(clausify,[status(thm)],[f_3876_2]) ).

fof(f_3877_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_3877_2,plain,
    ! [U_15539,U_15538,U_15537] : hAPP(hAPP(c_List_Olist__update(U_15537,U_15538),U_15539),hAPP(hAPP(c_List_Onth(U_15537),U_15538),U_15539)) = U_15538,
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

cnf(f_3877_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15537,U_15538),U_15539),hAPP(hAPP(c_List_Onth(U_15537),U_15538),U_15539)) = U_15538,
    inference(clausify,[status(thm)],[f_3877_2]) ).

fof(f_3878_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_3878_2,plain,
    ! [U_15544,U_15543,U_15542,U_15541,U_15540] :
      ( hAPP(hAPP(c_List_Onth(U_15542),hAPP(hAPP(c_List_Olist__update(U_15542,U_15543),U_15540),U_15544)),U_15541) = hAPP(hAPP(c_List_Onth(U_15542),U_15543),U_15541)
      | U_15540 = U_15541 ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

cnf(f_3878_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15542),hAPP(hAPP(c_List_Olist__update(U_15542,U_15543),U_15540),U_15544)),U_15541) = hAPP(hAPP(c_List_Onth(U_15542),U_15543),U_15541)
    | U_15540 = U_15541 ),
    inference(clausify,[status(thm)],[f_3878_2]) ).

fof(f_3879_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_3879_2,plain,
    ! [U_15548,U_15547,U_15546,U_15545] :
      ( ( c_List_Obutlast(U_15546,hAPP(hAPP(c_List_Olist__update(U_15546,U_15547),U_15545),U_15548)) = hAPP(hAPP(c_List_Olist__update(U_15546,c_List_Obutlast(U_15546,U_15547)),U_15545),U_15548)
        | U_15545 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15546)),U_15547)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_15546,hAPP(hAPP(c_List_Olist__update(U_15546,U_15547),U_15545),U_15548)) = c_List_Obutlast(U_15546,U_15547)
        | U_15545 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15546)),U_15547)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

fof(f_3879_3,plain,
    ( ! [U_15556,U_15554,U_15552,U_15550] :
        ( c_List_Obutlast(U_15552,hAPP(hAPP(c_List_Olist__update(U_15552,U_15554),U_15550),U_15556)) = hAPP(hAPP(c_List_Olist__update(U_15552,c_List_Obutlast(U_15552,U_15554)),U_15550),U_15556)
        | U_15550 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15552)),U_15554)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_15555,U_15553,U_15551,U_15549] :
        ( c_List_Obutlast(U_15551,hAPP(hAPP(c_List_Olist__update(U_15551,U_15553),U_15549),U_15555)) = c_List_Obutlast(U_15551,U_15553)
        | U_15549 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15551)),U_15553)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_3879_2]) ).

cnf(f_3879_4,plain,
    ( c_List_Obutlast(U_15551,hAPP(hAPP(c_List_Olist__update(U_15551,U_15553),U_15549),U_15555)) = c_List_Obutlast(U_15551,U_15553)
    | U_15549 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15551)),U_15553)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3879_3]) ).

cnf(f_3879_5,plain,
    ( c_List_Obutlast(U_15552,hAPP(hAPP(c_List_Olist__update(U_15552,U_15554),U_15550),U_15556)) = hAPP(hAPP(c_List_Olist__update(U_15552,c_List_Obutlast(U_15552,U_15554)),U_15550),U_15556)
    | U_15550 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15552)),U_15554)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3879_3]) ).

fof(f_3880_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_3880_2,plain,
    ! [U_15560,U_15559,U_15558,U_15557] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15557)),hAPP(hAPP(c_List_Olist__update(U_15557,U_15558),U_15559),U_15560)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15557)),U_15558),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

cnf(f_3880_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15557)),hAPP(hAPP(c_List_Olist__update(U_15557,U_15558),U_15559),U_15560)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15557)),U_15558),
    inference(clausify,[status(thm)],[f_3880_2]) ).

fof(f_3881_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_3881_2,plain,
    ! [U_15567,U_15566,U_15565,U_15564,U_15563,U_15562,U_15561] : hAPP(hAPP(c_List_Ozip(U_15561,U_15562),hAPP(hAPP(c_List_Olist__update(U_15561,U_15563),U_15564),U_15565)),hAPP(hAPP(c_List_Olist__update(U_15562,U_15566),U_15564),U_15567)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_15561,U_15562),hAPP(hAPP(c_List_Ozip(U_15561,U_15562),U_15563),U_15566)),U_15564),hAPP(hAPP(c_Product__Type_OPair(U_15561,U_15562),U_15565),U_15567)),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

cnf(f_3881_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15561,U_15562),hAPP(hAPP(c_List_Olist__update(U_15561,U_15563),U_15564),U_15565)),hAPP(hAPP(c_List_Olist__update(U_15562,U_15566),U_15564),U_15567)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_15561,U_15562),hAPP(hAPP(c_List_Ozip(U_15561,U_15562),U_15563),U_15566)),U_15564),hAPP(hAPP(c_Product__Type_OPair(U_15561,U_15562),U_15565),U_15567)),
    inference(clausify,[status(thm)],[f_3881_2]) ).

fof(f_3882_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_3882_2,plain,
    ! [U_15573,U_15572,U_15571,U_15570,U_15569,U_15568] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_15568,U_15569),hAPP(hAPP(c_List_Ozip(U_15568,U_15569),U_15570),U_15571)),U_15572),U_15573) = hAPP(hAPP(c_List_Ozip(U_15568,U_15569),hAPP(hAPP(c_List_Olist__update(U_15568,U_15570),U_15572),hAPP(c_Product__Type_Ofst(U_15568,U_15569),U_15573))),hAPP(hAPP(c_List_Olist__update(U_15569,U_15571),U_15572),hAPP(c_Product__Type_Osnd(U_15568,U_15569),U_15573))),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

cnf(f_3882_3,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_15568,U_15569),hAPP(hAPP(c_List_Ozip(U_15568,U_15569),U_15570),U_15571)),U_15572),U_15573) = hAPP(hAPP(c_List_Ozip(U_15568,U_15569),hAPP(hAPP(c_List_Olist__update(U_15568,U_15570),U_15572),hAPP(c_Product__Type_Ofst(U_15568,U_15569),U_15573))),hAPP(hAPP(c_List_Olist__update(U_15569,U_15571),U_15572),hAPP(c_Product__Type_Osnd(U_15568,U_15569),U_15573))),
    inference(clausify,[status(thm)],[f_3882_2]) ).

fof(f_3883_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_3883_2,plain,
    ! [U_15579,U_15578,U_15577,U_15576,U_15575,U_15574] :
      ( hAPP(hAPP(c_List_Olist__update(U_15576,hAPP(hAPP(c_List_Olist__update(U_15576,U_15577),U_15574),U_15578)),U_15575),U_15579) = hAPP(hAPP(c_List_Olist__update(U_15576,hAPP(hAPP(c_List_Olist__update(U_15576,U_15577),U_15575),U_15579)),U_15574),U_15578)
      | U_15574 = U_15575 ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

cnf(f_3883_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15576,hAPP(hAPP(c_List_Olist__update(U_15576,U_15577),U_15574),U_15578)),U_15575),U_15579) = hAPP(hAPP(c_List_Olist__update(U_15576,hAPP(hAPP(c_List_Olist__update(U_15576,U_15577),U_15575),U_15579)),U_15574),U_15578)
    | U_15574 = U_15575 ),
    inference(clausify,[status(thm)],[f_3883_2]) ).

fof(f_3884_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_3884_2,plain,
    ! [U_15584,U_15583,U_15582,U_15581,U_15580] : hAPP(hAPP(c_List_Olist__update(U_15580,hAPP(hAPP(c_List_Olist__update(U_15580,U_15581),U_15582),U_15583)),U_15582),U_15584) = hAPP(hAPP(c_List_Olist__update(U_15580,U_15581),U_15582),U_15584),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

cnf(f_3884_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15580,hAPP(hAPP(c_List_Olist__update(U_15580,U_15581),U_15582),U_15583)),U_15582),U_15584) = hAPP(hAPP(c_List_Olist__update(U_15580,U_15581),U_15582),U_15584),
    inference(clausify,[status(thm)],[f_3884_2]) ).

fof(f_3885_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_3885_2,plain,
    ! [U_15589,U_15588,U_15587,U_15586,U_15585] : hAPP(hAPP(c_List_Olist__update(U_15585,hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15586),U_15587)),hAPP(c_Nat_OSuc,U_15588)),U_15589) = hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15586),hAPP(hAPP(c_List_Olist__update(U_15585,U_15587),U_15588),U_15589)),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

cnf(f_3885_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15585,hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15586),U_15587)),hAPP(c_Nat_OSuc,U_15588)),U_15589) = hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15586),hAPP(hAPP(c_List_Olist__update(U_15585,U_15587),U_15588),U_15589)),
    inference(clausify,[status(thm)],[f_3885_2]) ).

fof(f_3886_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_3886_2,plain,
    ! [U_15593,U_15592,U_15591,U_15590] : hAPP(hAPP(c_List_Olist__update(U_15590,hAPP(hAPP(c_List_Olist_OCons(U_15590),U_15591),U_15592)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15593) = hAPP(hAPP(c_List_Olist_OCons(U_15590),U_15593),U_15592),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

cnf(f_3886_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15590,hAPP(hAPP(c_List_Olist_OCons(U_15590),U_15591),U_15592)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15593) = hAPP(hAPP(c_List_Olist_OCons(U_15590),U_15593),U_15592),
    inference(clausify,[status(thm)],[f_3886_2]) ).

fof(f_3887_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_3887_2,plain,
    ! [U_15598,U_15597,U_15596,U_15595,U_15594] : hAPP(hAPP(c_List_Olist__update(U_15594,hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15595),U_15596)),U_15597),U_15598) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15594),hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15598),U_15596),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15594),tc_List_Olist(U_15594),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15594),U_15595)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15594,tc_List_Olist(U_15594)),c_List_Olist__update(U_15594,U_15596)),U_15598)),U_15597),
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

cnf(f_3887_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15594,hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15595),U_15596)),U_15597),U_15598) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15594),hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15598),U_15596),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15594),tc_List_Olist(U_15594),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15594),U_15595)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15594,tc_List_Olist(U_15594)),c_List_Olist__update(U_15594,U_15596)),U_15598)),U_15597),
    inference(clausify,[status(thm)],[f_3887_2]) ).

fof(f_3888_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_3888_2,plain,
    ! [U_15601,U_15600,U_15599] :
      ( hBOOL(hAPP(hAPP(c_member(U_15599),U_15600),hAPP(c_List_Oset(U_15599),U_15601)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15599),U_15600),hAPP(c_List_Oset(U_15599),c_List_Obutlast(U_15599,U_15601)))) ),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

cnf(f_3888_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15599),U_15600),hAPP(c_List_Oset(U_15599),U_15601)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15599),U_15600),hAPP(c_List_Oset(U_15599),c_List_Obutlast(U_15599,U_15601)))) ),
    inference(clausify,[status(thm)],[f_3888_2]) ).

fof(f_3889_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_3889_2,plain,
    ! [U_15606,U_15605,U_15604,U_15603,U_15602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15602,tc_HOL_Obool)),hAPP(c_List_Oset(U_15602),hAPP(hAPP(c_List_Olist__update(U_15602,U_15603),U_15606),U_15605))),U_15604))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15602),U_15605),U_15604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15602,tc_HOL_Obool)),hAPP(c_List_Oset(U_15602),U_15603)),U_15604)) ),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

cnf(f_3889_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15602,tc_HOL_Obool)),hAPP(c_List_Oset(U_15602),hAPP(hAPP(c_List_Olist__update(U_15602,U_15603),U_15606),U_15605))),U_15604))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15602),U_15605),U_15604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15602,tc_HOL_Obool)),hAPP(c_List_Oset(U_15602),U_15603)),U_15604)) ),
    inference(clausify,[status(thm)],[f_3889_2]) ).

fof(f_3890_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_3890_2,plain,
    ! [U_15610,U_15609,U_15608,U_15607] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15607,tc_HOL_Obool)),hAPP(c_List_Oset(U_15607),hAPP(hAPP(c_List_Olist__update(U_15607,U_15608),U_15609),U_15610))),hAPP(hAPP(c_Set_Oinsert(U_15607),U_15610),hAPP(c_List_Oset(U_15607),U_15608)))),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

cnf(f_3890_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15607,tc_HOL_Obool)),hAPP(c_List_Oset(U_15607),hAPP(hAPP(c_List_Olist__update(U_15607,U_15608),U_15609),U_15610))),hAPP(hAPP(c_Set_Oinsert(U_15607),U_15610),hAPP(c_List_Oset(U_15607),U_15608)))),
    inference(clausify,[status(thm)],[f_3890_2]) ).

fof(f_3891_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_3891_2,plain,
    ! [U_15614,U_15613,U_15612,U_15611] :
      ( hAPP(hAPP(c_List_Onth(U_15612),hAPP(hAPP(c_List_Olist__update(U_15612,U_15613),U_15611),U_15614)),U_15611) = U_15614
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15611),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15612)),U_15613))) ),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

cnf(f_3891_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15612),hAPP(hAPP(c_List_Olist__update(U_15612,U_15613),U_15611),U_15614)),U_15611) = U_15614
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15611),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15612)),U_15613))) ),
    inference(clausify,[status(thm)],[f_3891_2]) ).

fof(f_3892_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_3892_2,plain,
    ! [U_15618,U_15617,U_15616,U_15615] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_15616,U_15617),U_15615),U_15618) = U_15617
          | hAPP(hAPP(c_List_Onth(U_15616),U_15617),U_15615) != U_15618 )
        & ( hAPP(hAPP(c_List_Onth(U_15616),U_15617),U_15615) = U_15618
          | hAPP(hAPP(c_List_Olist__update(U_15616,U_15617),U_15615),U_15618) != U_15617 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15615),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),U_15617))) ),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

cnf(f_3892_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15616),U_15617),U_15615) = U_15618
    | hAPP(hAPP(c_List_Olist__update(U_15616,U_15617),U_15615),U_15618) != U_15617
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15615),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),U_15617))) ),
    inference(clausify,[status(thm)],[f_3892_2]) ).

cnf(f_3892_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15616,U_15617),U_15615),U_15618) = U_15617
    | hAPP(hAPP(c_List_Onth(U_15616),U_15617),U_15615) != U_15618
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15615),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),U_15617))) ),
    inference(clausify,[status(thm)],[f_3892_2]) ).

fof(f_3893_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_3893_2,plain,
    ! [U_15623,U_15622,U_15621,U_15620,U_15619] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_15620),hAPP(hAPP(c_List_Olist__update(U_15620,U_15621),U_15619),U_15623)),U_15622) = hAPP(hAPP(c_List_Onth(U_15620),U_15621),U_15622)
          | U_15619 = U_15622 )
        & ( hAPP(hAPP(c_List_Onth(U_15620),hAPP(hAPP(c_List_Olist__update(U_15620,U_15621),U_15619),U_15623)),U_15622) = U_15623
          | U_15619 != U_15622 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15619),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15620)),U_15621))) ),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

cnf(f_3893_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15620),hAPP(hAPP(c_List_Olist__update(U_15620,U_15621),U_15619),U_15623)),U_15622) = U_15623
    | U_15619 != U_15622
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15619),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15620)),U_15621))) ),
    inference(clausify,[status(thm)],[f_3893_2]) ).

cnf(f_3893_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15620),hAPP(hAPP(c_List_Olist__update(U_15620,U_15621),U_15619),U_15623)),U_15622) = hAPP(hAPP(c_List_Onth(U_15620),U_15621),U_15622)
    | U_15619 = U_15622
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15619),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15620)),U_15621))) ),
    inference(clausify,[status(thm)],[f_3893_2]) ).

fof(f_3894_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_3894_2,plain,
    ! [U_15626,U_15625,U_15624] :
      ( hAPP(hAPP(c_List_Otake(U_15625),U_15624),c_List_Obutlast(U_15625,U_15626)) = hAPP(hAPP(c_List_Otake(U_15625),U_15624),U_15626)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15625)),U_15626))) ),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

cnf(f_3894_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_15625),U_15624),c_List_Obutlast(U_15625,U_15626)) = hAPP(hAPP(c_List_Otake(U_15625),U_15624),U_15626)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15625)),U_15626))) ),
    inference(clausify,[status(thm)],[f_3894_2]) ).

fof(f_3895_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_3895_2,plain,
    ! [U_15628,U_15627] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),c_List_Obutlast(U_15627,U_15628)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15628)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

cnf(f_3895_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),c_List_Obutlast(U_15627,U_15628)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15627)),U_15628)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_3895_2]) ).

fof(f_3896_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_3896_2,plain,
    ! [U_15632,U_15631,U_15630,U_15629] :
      ( hBOOL(hAPP(hAPP(c_member(U_15630),U_15632),hAPP(c_List_Oset(U_15630),hAPP(hAPP(c_List_Olist__update(U_15630,U_15631),U_15629),U_15632))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15629),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15630)),U_15631))) ),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

cnf(f_3896_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15630),U_15632),hAPP(c_List_Oset(U_15630),hAPP(hAPP(c_List_Olist__update(U_15630,U_15631),U_15629),U_15632))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15629),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15630)),U_15631))) ),
    inference(clausify,[status(thm)],[f_3896_2]) ).

fof(f_3897_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_3897_2,plain,
    ! [U_15634,U_15633] : c_List_Obutlast(U_15633,U_15634) = hAPP(hAPP(c_List_Otake(U_15633),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15634)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15634),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

cnf(f_3897_3,plain,
    c_List_Obutlast(U_15633,U_15634) = hAPP(hAPP(c_List_Otake(U_15633),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15634)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15634),
    inference(clausify,[status(thm)],[f_3897_2]) ).

fof(f_3898_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_3898_2,plain,
    ! [U_15642,U_15641,U_15640,U_15639] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15640),U_15641)),c_List_Olistrel1(U_15639,U_15642)))
        | ! [U_15638,U_15637] :
            ( U_15641 != hAPP(hAPP(c_List_Olist__update(U_15639,U_15640),U_15637),U_15638)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15639)),U_15640)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15639,U_15639)),hAPP(hAPP(c_Product__Type_OPair(U_15639,U_15639),hAPP(hAPP(c_List_Onth(U_15639),U_15640),U_15637)),U_15638)),U_15642)) ) )
      & ( ? [U_15636,U_15635] :
            ( U_15641 = hAPP(hAPP(c_List_Olist__update(U_15639,U_15640),U_15635),U_15636)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15635),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15639)),U_15640)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15639,U_15639)),hAPP(hAPP(c_Product__Type_OPair(U_15639,U_15639),hAPP(hAPP(c_List_Onth(U_15639),U_15640),U_15635)),U_15636)),U_15642)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15639),tc_List_Olist(U_15639))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15639),tc_List_Olist(U_15639)),U_15640),U_15641)),c_List_Olistrel1(U_15639,U_15642))) ) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

fof(f_3898_3,plain,
    ( ! [U_15650,U_15648,U_15646,U_15644] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15644),tc_List_Olist(U_15644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15644),tc_List_Olist(U_15644)),U_15646),U_15648)),c_List_Olistrel1(U_15644,U_15650)))
        | ! [U_15638,U_15637] :
            ( U_15648 != hAPP(hAPP(c_List_Olist__update(U_15644,U_15646),U_15637),U_15638)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15644)),U_15646)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15644,U_15644)),hAPP(hAPP(c_Product__Type_OPair(U_15644,U_15644),hAPP(hAPP(c_List_Onth(U_15644),U_15646),U_15637)),U_15638)),U_15650)) ) )
    & ! [U_15649,U_15647,U_15645,U_15643] :
        ( ? [U_15636,U_15635] :
            ( U_15647 = hAPP(hAPP(c_List_Olist__update(U_15643,U_15645),U_15635),U_15636)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15635),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15643)),U_15645)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15643,U_15643)),hAPP(hAPP(c_Product__Type_OPair(U_15643,U_15643),hAPP(hAPP(c_List_Onth(U_15643),U_15645),U_15635)),U_15636)),U_15649)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ) ),
    inference(miniscope,[status(thm)],[f_3898_2]) ).

fof(f_3898_4,plain,
    ( ! [U_15650,U_15648,U_15646,U_15644] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15644),tc_List_Olist(U_15644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15644),tc_List_Olist(U_15644)),U_15646),U_15648)),c_List_Olistrel1(U_15644,U_15650)))
        | ! [U_15638,U_15637] :
            ( U_15648 != hAPP(hAPP(c_List_Olist__update(U_15644,U_15646),U_15637),U_15638)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15644)),U_15646)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15644,U_15644)),hAPP(hAPP(c_Product__Type_OPair(U_15644,U_15644),hAPP(hAPP(c_List_Onth(U_15644),U_15646),U_15637)),U_15638)),U_15650)) ) )
    & ! [U_15649,U_15647,U_15645,U_15643] :
        ( ? [U_15635] :
            ( U_15647 = hAPP(hAPP(c_List_Olist__update(U_15643,U_15645),U_15635),sK406(U_15649,U_15647,U_15645,U_15643))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15635),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15643)),U_15645)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15643,U_15643)),hAPP(hAPP(c_Product__Type_OPair(U_15643,U_15643),hAPP(hAPP(c_List_Onth(U_15643),U_15645),U_15635)),sK406(U_15649,U_15647,U_15645,U_15643))),U_15649)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_15636,sK406(U_15649,U_15647,U_15645,U_15643))],[f_3898_3]) ).

fof(f_3898_5,plain,
    ( ! [U_15650,U_15648,U_15646,U_15644] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15644),tc_List_Olist(U_15644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15644),tc_List_Olist(U_15644)),U_15646),U_15648)),c_List_Olistrel1(U_15644,U_15650)))
        | ! [U_15638,U_15637] :
            ( U_15648 != hAPP(hAPP(c_List_Olist__update(U_15644,U_15646),U_15637),U_15638)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15644)),U_15646)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15644,U_15644)),hAPP(hAPP(c_Product__Type_OPair(U_15644,U_15644),hAPP(hAPP(c_List_Onth(U_15644),U_15646),U_15637)),U_15638)),U_15650)) ) )
    & ! [U_15649,U_15647,U_15645,U_15643] :
        ( ( U_15647 = hAPP(hAPP(c_List_Olist__update(U_15643,U_15645),sK407(U_15649,U_15647,U_15645,U_15643)),sK406(U_15649,U_15647,U_15645,U_15643))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK407(U_15649,U_15647,U_15645,U_15643)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15643)),U_15645)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15643,U_15643)),hAPP(hAPP(c_Product__Type_OPair(U_15643,U_15643),hAPP(hAPP(c_List_Onth(U_15643),U_15645),sK407(U_15649,U_15647,U_15645,U_15643))),sK406(U_15649,U_15647,U_15645,U_15643))),U_15649)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_15635,sK407(U_15649,U_15647,U_15645,U_15643))],[f_3898_4]) ).

cnf(f_3898_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15643,U_15643)),hAPP(hAPP(c_Product__Type_OPair(U_15643,U_15643),hAPP(hAPP(c_List_Onth(U_15643),U_15645),sK407(U_15649,U_15647,U_15645,U_15643))),sK406(U_15649,U_15647,U_15645,U_15643))),U_15649))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ),
    inference(clausify,[status(thm)],[f_3898_5]) ).

cnf(f_3898_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK407(U_15649,U_15647,U_15645,U_15643)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15643)),U_15645)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ),
    inference(clausify,[status(thm)],[f_3898_5]) ).

cnf(f_3898_8,plain,
    ( U_15647 = hAPP(hAPP(c_List_Olist__update(U_15643,U_15645),sK407(U_15649,U_15647,U_15645,U_15643)),sK406(U_15649,U_15647,U_15645,U_15643))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15643),tc_List_Olist(U_15643))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15643),tc_List_Olist(U_15643)),U_15645),U_15647)),c_List_Olistrel1(U_15643,U_15649))) ),
    inference(clausify,[status(thm)],[f_3898_5]) ).

cnf(f_3898_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15644),tc_List_Olist(U_15644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15644),tc_List_Olist(U_15644)),U_15646),U_15648)),c_List_Olistrel1(U_15644,U_15650)))
    | U_15648 != hAPP(hAPP(c_List_Olist__update(U_15644,U_15646),U_15637),U_15638)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15644)),U_15646)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15644,U_15644)),hAPP(hAPP(c_Product__Type_OPair(U_15644,U_15644),hAPP(hAPP(c_List_Onth(U_15644),U_15646),U_15637)),U_15638)),U_15650)) ),
    inference(clausify,[status(thm)],[f_3898_5]) ).

fof(f_3899_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_3899_2,plain,
    ! [U_15654,U_15653,U_15652,U_15651] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15651),hAPP(hAPP(c_List_Olist__update(U_15651,U_15652),U_15654),U_15653)))
      | hBOOL(hAPP(hAPP(c_member(U_15651),U_15653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15651,tc_HOL_Obool)),hAPP(c_List_Oset(U_15651),U_15652)),hAPP(hAPP(c_Set_Oinsert(U_15651),hAPP(hAPP(c_List_Onth(U_15651),U_15652),U_15654)),c_Orderings_Obot__class_Obot(tc_fun(U_15651,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15651),U_15652)) ),
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

cnf(f_3899_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15651),hAPP(hAPP(c_List_Olist__update(U_15651,U_15652),U_15654),U_15653)))
    | hBOOL(hAPP(hAPP(c_member(U_15651),U_15653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15651,tc_HOL_Obool)),hAPP(c_List_Oset(U_15651),U_15652)),hAPP(hAPP(c_Set_Oinsert(U_15651),hAPP(hAPP(c_List_Onth(U_15651),U_15652),U_15654)),c_Orderings_Obot__class_Obot(tc_fun(U_15651,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15651),U_15652)) ),
    inference(clausify,[status(thm)],[f_3899_2]) ).

fof(f_3900_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_3900_2,plain,
    ! [U_15656,U_15655] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_15655,U_15656))),
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

cnf(f_3900_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_15655,U_15656))),
    inference(clausify,[status(thm)],[f_3900_2]) ).

fof(f_3901_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_3901_2,plain,
    ! [U_15659,U_15658,U_15657] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15657),hAPP(hAPP(c_List_Otake(U_15657),U_15659),U_15658)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15657),U_15658)) ),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

cnf(f_3901_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15657),hAPP(hAPP(c_List_Otake(U_15657),U_15659),U_15658)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15657),U_15658)) ),
    inference(clausify,[status(thm)],[f_3901_2]) ).

fof(f_3902_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_3902_2,plain,
    ! [U_15662,U_15661,U_15660] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15660),c_List_Osublist(U_15660,U_15661,U_15662)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15660),U_15661)) ),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

cnf(f_3902_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15660),c_List_Osublist(U_15660,U_15661,U_15662)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15660),U_15661)) ),
    inference(clausify,[status(thm)],[f_3902_2]) ).

fof(f_3903_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_3903_2,plain,
    ! [U_15666,U_15665,U_15664,U_15663] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15665,U_15663)),hAPP(hAPP(c_List_Ozip(U_15665,U_15663),U_15666),U_15664)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15663),U_15664)) ),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

cnf(f_3903_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15665,U_15663)),hAPP(hAPP(c_List_Ozip(U_15665,U_15663),U_15666),U_15664)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15663),U_15664)) ),
    inference(clausify,[status(thm)],[f_3903_2]) ).

fof(f_3904_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_3904_2,plain,
    ! [U_15670,U_15669,U_15668,U_15667] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15667,U_15669)),hAPP(hAPP(c_List_Ozip(U_15667,U_15669),U_15668),U_15670)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15667),U_15668)) ),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

cnf(f_3904_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15667,U_15669)),hAPP(hAPP(c_List_Ozip(U_15667,U_15669),U_15668),U_15670)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15667),U_15668)) ),
    inference(clausify,[status(thm)],[f_3904_2]) ).

fof(f_3905_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_3905_2,plain,
    ! [U_15673,U_15672,U_15671] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_15671),hAPP(hAPP(c_List_Olist_OCons(U_15671),U_15672),U_15673)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15671),U_15673))
        | hBOOL(hAPP(hAPP(c_member(U_15671),U_15672),hAPP(c_List_Oset(U_15671),U_15673))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_15671),U_15673))
          & ~ hBOOL(hAPP(hAPP(c_member(U_15671),U_15672),hAPP(c_List_Oset(U_15671),U_15673))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15671),hAPP(hAPP(c_List_Olist_OCons(U_15671),U_15672),U_15673))) ) ),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

fof(f_3905_3,plain,
    ( ! [U_15679,U_15677,U_15675] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15675),hAPP(hAPP(c_List_Olist_OCons(U_15675),U_15677),U_15679)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15675),U_15679))
        | hBOOL(hAPP(hAPP(c_member(U_15675),U_15677),hAPP(c_List_Oset(U_15675),U_15679))) )
    & ! [U_15678,U_15676,U_15674] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_15674),U_15678))
          & ~ hBOOL(hAPP(hAPP(c_member(U_15674),U_15676),hAPP(c_List_Oset(U_15674),U_15678))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15674),hAPP(hAPP(c_List_Olist_OCons(U_15674),U_15676),U_15678))) ) ),
    inference(miniscope,[status(thm)],[f_3905_2]) ).

cnf(f_3905_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15674),U_15676),hAPP(c_List_Oset(U_15674),U_15678)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15674),hAPP(hAPP(c_List_Olist_OCons(U_15674),U_15676),U_15678))) ),
    inference(clausify,[status(thm)],[f_3905_3]) ).

cnf(f_3905_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15674),U_15678))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15674),hAPP(hAPP(c_List_Olist_OCons(U_15674),U_15676),U_15678))) ),
    inference(clausify,[status(thm)],[f_3905_3]) ).

cnf(f_3905_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15675),hAPP(hAPP(c_List_Olist_OCons(U_15675),U_15677),U_15679)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15675),U_15679))
    | hBOOL(hAPP(hAPP(c_member(U_15675),U_15677),hAPP(c_List_Oset(U_15675),U_15679))) ),
    inference(clausify,[status(thm)],[f_3905_3]) ).

fof(f_3906_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_3906_2,plain,
    ! [U_15681,U_15680] :
      ( hAPP(c_Finite__Set_Ocard(U_15680),hAPP(c_List_Oset(U_15680),U_15681)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15681)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15680),U_15681)) ),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

cnf(f_3906_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_15680),hAPP(c_List_Oset(U_15680),U_15681)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15681)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15680),U_15681)) ),
    inference(clausify,[status(thm)],[f_3906_2]) ).

fof(f_3907_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_3907_2,plain,
    ! [U_15683,U_15682] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15682),U_15683))
      | hAPP(c_Finite__Set_Ocard(U_15682),hAPP(c_List_Oset(U_15682),U_15683)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15682)),U_15683) ),
    inference(variable_rename,[status(thm)],[f_3907_1]) ).

cnf(f_3907_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15682),U_15683))
    | hAPP(c_Finite__Set_Ocard(U_15682),hAPP(c_List_Oset(U_15682),U_15683)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15682)),U_15683) ),
    inference(clausify,[status(thm)],[f_3907_2]) ).

fof(f_3908_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_3908_2,plain,
    ! [U_15687,U_15686,U_15685,U_15684] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15686) = hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15687)
          | U_15686 != U_15687 )
        & ( U_15686 = U_15687
          | hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15686) != hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15687) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15687),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15684),U_15685)) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

cnf(f_3908_3,plain,
    ( U_15686 = U_15687
    | hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15686) != hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15687)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15687),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15684),U_15685)) ),
    inference(clausify,[status(thm)],[f_3908_2]) ).

cnf(f_3908_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15686) = hAPP(hAPP(c_List_Onth(U_15684),U_15685),U_15687)
    | U_15686 != U_15687
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15687),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15684)),U_15685)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15684),U_15685)) ),
    inference(clausify,[status(thm)],[f_3908_2]) ).

fof(f_3909_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_3909_2,plain,
    ! [U_15693,U_15692] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_15692),U_15693))
        | ? [U_15691] :
            ( ? [U_15690] :
                ( hAPP(hAPP(c_List_Onth(U_15692),U_15693),U_15691) = hAPP(hAPP(c_List_Onth(U_15692),U_15693),U_15690)
                & U_15691 != U_15690
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15690),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15692)),U_15693))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15692)),U_15693))) ) )
      & ( ! [U_15689] :
            ( ! [U_15688] :
                ( hAPP(hAPP(c_List_Onth(U_15692),U_15693),U_15689) != hAPP(hAPP(c_List_Onth(U_15692),U_15693),U_15688)
                | U_15689 = U_15688
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15692)),U_15693))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15692)),U_15693))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15692),U_15693)) ) ),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

fof(f_3909_3,plain,
    ( ! [U_15697,U_15695] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697))
        | ? [U_15691] :
            ( ? [U_15690] :
                ( hAPP(hAPP(c_List_Onth(U_15695),U_15697),U_15691) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),U_15690)
                & U_15691 != U_15690
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15690),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697))) ) )
    & ! [U_15696,U_15694] :
        ( ! [U_15689] :
            ( ! [U_15688] :
                ( hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15689) != hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15688)
                | U_15689 = U_15688
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15694),U_15696)) ) ),
    inference(miniscope,[status(thm)],[f_3909_2]) ).

fof(f_3909_4,plain,
    ( ! [U_15697,U_15695] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697))
        | ( ? [U_15690] :
              ( hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK408(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),U_15690)
              & sK408(U_15697,U_15695) != U_15690
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15690),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK408(U_15697,U_15695)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697))) ) )
    & ! [U_15696,U_15694] :
        ( ! [U_15689] :
            ( ! [U_15688] :
                ( hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15689) != hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15688)
                | U_15689 = U_15688
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15694),U_15696)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_15691,sK408(U_15697,U_15695))],[f_3909_3]) ).

fof(f_3909_5,plain,
    ( ! [U_15697,U_15695] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697))
        | ( hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK408(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK409(U_15697,U_15695))
          & sK408(U_15697,U_15695) != sK409(U_15697,U_15695)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(U_15697,U_15695)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK408(U_15697,U_15695)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697))) ) )
    & ! [U_15696,U_15694] :
        ( ! [U_15689] :
            ( ! [U_15688] :
                ( hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15689) != hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15688)
                | U_15689 = U_15688
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15694),U_15696)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_15690,sK409(U_15697,U_15695))],[f_3909_4]) ).

cnf(f_3909_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15689) != hAPP(hAPP(c_List_Onth(U_15694),U_15696),U_15688)
    | U_15689 = U_15688
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15694)),U_15696)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15694),U_15696)) ),
    inference(clausify,[status(thm)],[f_3909_5]) ).

cnf(f_3909_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK408(U_15697,U_15695)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697)))
    | hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
    inference(clausify,[status(thm)],[f_3909_5]) ).

cnf(f_3909_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(U_15697,U_15695)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15695)),U_15697)))
    | hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
    inference(clausify,[status(thm)],[f_3909_5]) ).

cnf(f_3909_9,plain,
    ( sK408(U_15697,U_15695) != sK409(U_15697,U_15695)
    | hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
    inference(clausify,[status(thm)],[f_3909_5]) ).

cnf(f_3909_10,plain,
    ( hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK408(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK409(U_15697,U_15695))
    | hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
    inference(clausify,[status(thm)],[f_3909_5]) ).

fof(f_3910_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_3910_2,plain,
    ! [U_15699,U_15698] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15698),U_15699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15698,U_15698),c_COMBI(U_15698)),hAPP(c_List_Oset(U_15698),U_15699))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15698),U_15699))
      | ~ class_Groups_Ocomm__monoid__add(U_15698) ),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

cnf(f_3910_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15698),U_15699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15698,U_15698),c_COMBI(U_15698)),hAPP(c_List_Oset(U_15698),U_15699))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15698),U_15699))
    | ~ class_Groups_Ocomm__monoid__add(U_15698) ),
    inference(clausify,[status(thm)],[f_3910_2]) ).

fof(f_3911_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_3911_2,plain,
    ! [U_15701,U_15700] :
      ( ( c_Nitpick_Ocard_H(U_15700,U_15701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15700),U_15701)) )
      & ( c_Nitpick_Ocard_H(U_15700,U_15701) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15700)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15700),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15700),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_15700)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15700),tc_fun(U_15700,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15700,tc_HOL_Obool),tc_fun(tc_fun(U_15700,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15700)),c_fequal),c_List_Oset(U_15700))),U_15701))),c_List_Odistinct(U_15700))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15700),U_15701)) ) ),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

fof(f_3911_3,plain,
    ( ! [U_15705,U_15703] :
        ( c_Nitpick_Ocard_H(U_15703,U_15705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15703),U_15705)) )
    & ! [U_15704,U_15702] :
        ( c_Nitpick_Ocard_H(U_15702,U_15704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15702)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15702),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15702),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_15702)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15702),tc_fun(U_15702,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15702,tc_HOL_Obool),tc_fun(tc_fun(U_15702,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15702)),c_fequal),c_List_Oset(U_15702))),U_15704))),c_List_Odistinct(U_15702))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15702),U_15704)) ) ),
    inference(miniscope,[status(thm)],[f_3911_2]) ).

cnf(f_3911_4,plain,
    ( c_Nitpick_Ocard_H(U_15702,U_15704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15702)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15702),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15702),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_15702)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15702),tc_fun(U_15702,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15702,tc_HOL_Obool),tc_fun(tc_fun(U_15702,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15702)),c_fequal),c_List_Oset(U_15702))),U_15704))),c_List_Odistinct(U_15702))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15702),U_15704)) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

cnf(f_3911_5,plain,
    ( c_Nitpick_Ocard_H(U_15703,U_15705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15703),U_15705)) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

fof(f_3912_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_3912_2,plain,
    ! [U_15710,U_15709,U_15708,U_15707] :
      ( hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15709) = hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15710)
      | ? [U_15706] :
          ( hAPP(hAPP(c_List_Onth(U_15708),U_15709),U_15706) != hAPP(hAPP(c_List_Onth(U_15708),U_15710),U_15706)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15706),U_15707)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15710)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15709))) ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

fof(f_3912_3,plain,
    ! [U_15710,U_15709,U_15708,U_15707] :
      ( hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15709) = hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15710)
      | ( hAPP(hAPP(c_List_Onth(U_15708),U_15709),sK410(U_15710,U_15709,U_15708,U_15707)) != hAPP(hAPP(c_List_Onth(U_15708),U_15710),sK410(U_15710,U_15709,U_15708,U_15707))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK410(U_15710,U_15709,U_15708,U_15707)),U_15707)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15710)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15709))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_15706,sK410(U_15710,U_15709,U_15708,U_15707))],[f_3912_2]) ).

cnf(f_3912_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK410(U_15710,U_15709,U_15708,U_15707)),U_15707))
    | hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15709) = hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15710)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15709))) ),
    inference(clausify,[status(thm)],[f_3912_3]) ).

cnf(f_3912_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15708),U_15709),sK410(U_15710,U_15709,U_15708,U_15707)) != hAPP(hAPP(c_List_Onth(U_15708),U_15710),sK410(U_15710,U_15709,U_15708,U_15707))
    | hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15709) = hAPP(hAPP(c_List_Otake(U_15708),U_15707),U_15710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15710)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15707),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15708)),U_15709))) ),
    inference(clausify,[status(thm)],[f_3912_3]) ).

fof(f_3913_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_3913_2,plain,
    ! [U_15713,U_15712,U_15711] :
      ( hAPP(c_List_Oset(U_15711),c_List_Oremove1(U_15711,U_15713,U_15712)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15711,tc_HOL_Obool)),hAPP(c_List_Oset(U_15711),U_15712)),hAPP(hAPP(c_Set_Oinsert(U_15711),U_15713),c_Orderings_Obot__class_Obot(tc_fun(U_15711,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15711),U_15712)) ),
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

cnf(f_3913_3,plain,
    ( hAPP(c_List_Oset(U_15711),c_List_Oremove1(U_15711,U_15713,U_15712)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15711,tc_HOL_Obool)),hAPP(c_List_Oset(U_15711),U_15712)),hAPP(hAPP(c_Set_Oinsert(U_15711),U_15713),c_Orderings_Obot__class_Obot(tc_fun(U_15711,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15711),U_15712)) ),
    inference(clausify,[status(thm)],[f_3913_2]) ).

fof(f_3914_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_3914_2,plain,
    ! [U_15717,U_15716,U_15715,U_15714] :
      ( ( hAPP(hAPP(c_List_Otake(U_15715),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15714)),hAPP(hAPP(c_List_Olist_OCons(U_15715),U_15716),U_15717)) = hAPP(hAPP(c_List_Olist_OCons(U_15715),U_15716),hAPP(hAPP(c_List_Otake(U_15715),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15714)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15717))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15714) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_15715),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15714)),hAPP(hAPP(c_List_Olist_OCons(U_15715),U_15716),U_15717)) = c_List_Olist_ONil(U_15715)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15714) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

fof(f_3914_3,plain,
    ( ! [U_15725,U_15723,U_15721,U_15719] :
        ( hAPP(hAPP(c_List_Otake(U_15721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719)),hAPP(hAPP(c_List_Olist_OCons(U_15721),U_15723),U_15725)) = hAPP(hAPP(c_List_Olist_OCons(U_15721),U_15723),hAPP(hAPP(c_List_Otake(U_15721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15725))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15724,U_15722,U_15720,U_15718] :
        ( hAPP(hAPP(c_List_Otake(U_15720),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15718)),hAPP(hAPP(c_List_Olist_OCons(U_15720),U_15722),U_15724)) = c_List_Olist_ONil(U_15720)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3914_2]) ).

cnf(f_3914_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_15720),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15718)),hAPP(hAPP(c_List_Olist_OCons(U_15720),U_15722),U_15724)) = c_List_Olist_ONil(U_15720)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3914_3]) ).

cnf(f_3914_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_15721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719)),hAPP(hAPP(c_List_Olist_OCons(U_15721),U_15723),U_15725)) = hAPP(hAPP(c_List_Olist_OCons(U_15721),U_15723),hAPP(hAPP(c_List_Otake(U_15721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15725))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3914_3]) ).

fof(f_3915_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_3915_2,plain,
    ! [U_15727,U_15726] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15726)),c_List_Olist_ONil(U_15726)),c_List_Olists(U_15726,U_15727))),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

cnf(f_3915_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15726)),c_List_Olist_ONil(U_15726)),c_List_Olists(U_15726,U_15727))),
    inference(clausify,[status(thm)],[f_3915_2]) ).

fof(f_3916_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_3916_2,plain,
    ! [U_15730,U_15729,U_15728] :
      ( U_15729 = c_List_Olist_ONil(U_15728)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),c_List_Olist_ONil(U_15728))),c_List_Olistrel(U_15728,U_15730))) ),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

cnf(f_3916_3,plain,
    ( U_15729 = c_List_Olist_ONil(U_15728)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15728),tc_List_Olist(U_15728))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15728),tc_List_Olist(U_15728)),U_15729),c_List_Olist_ONil(U_15728))),c_List_Olistrel(U_15728,U_15730))) ),
    inference(clausify,[status(thm)],[f_3916_2]) ).

fof(f_3917_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_3917_2,plain,
    ! [U_15733,U_15732,U_15731] :
      ( U_15732 = c_List_Olist_ONil(U_15731)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15731),tc_List_Olist(U_15731))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15731),tc_List_Olist(U_15731)),c_List_Olist_ONil(U_15731)),U_15732)),c_List_Olistrel(U_15731,U_15733))) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

cnf(f_3917_3,plain,
    ( U_15732 = c_List_Olist_ONil(U_15731)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15731),tc_List_Olist(U_15731))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15731),tc_List_Olist(U_15731)),c_List_Olist_ONil(U_15731)),U_15732)),c_List_Olistrel(U_15731,U_15733))) ),
    inference(clausify,[status(thm)],[f_3917_2]) ).

fof(f_3918_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_3918_2,plain,
    ! [U_15735,U_15734] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15735),c_List_Obutlast(U_15735,U_15734)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15735),U_15734))
      | U_15734 = c_List_Olist_ONil(U_15735) ),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

cnf(f_3918_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15735),c_List_Obutlast(U_15735,U_15734)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15735),U_15734))
    | U_15734 = c_List_Olist_ONil(U_15735) ),
    inference(clausify,[status(thm)],[f_3918_2]) ).

fof(f_3919_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_3919_2,plain,
    ! [U_15736] : hBOOL(hAPP(c_List_Odistinct(U_15736),c_List_Olist_ONil(U_15736))),
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

cnf(f_3919_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_15736),c_List_Olist_ONil(U_15736))),
    inference(clausify,[status(thm)],[f_3919_2]) ).

fof(f_3920_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_3920_2,plain,
    ! [U_15739,U_15738,U_15737] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15737),c_List_Oremove1(U_15737,U_15739,U_15738)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15737),U_15738)) ),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

cnf(f_3920_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15737),c_List_Oremove1(U_15737,U_15739,U_15738)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15737),U_15738)) ),
    inference(clausify,[status(thm)],[f_3920_2]) ).

fof(f_3921_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_3921_2,plain,
    ! [U_15740] : c_List_Obutlast(U_15740,c_List_Olist_ONil(U_15740)) = c_List_Olist_ONil(U_15740),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

cnf(f_3921_3,plain,
    c_List_Obutlast(U_15740,c_List_Olist_ONil(U_15740)) = c_List_Olist_ONil(U_15740),
    inference(clausify,[status(thm)],[f_3921_2]) ).

fof(f_3922_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_3922_2,plain,
    ! [U_15743,U_15742,U_15741] :
      ( ( c_List_Obutlast(U_15742,hAPP(hAPP(c_List_Olist_OCons(U_15742),U_15743),U_15741)) = hAPP(hAPP(c_List_Olist_OCons(U_15742),U_15743),c_List_Obutlast(U_15742,U_15741))
        | U_15741 = c_List_Olist_ONil(U_15742) )
      & ( c_List_Obutlast(U_15742,hAPP(hAPP(c_List_Olist_OCons(U_15742),U_15743),U_15741)) = c_List_Olist_ONil(U_15742)
        | U_15741 != c_List_Olist_ONil(U_15742) ) ),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ( ! [U_15749,U_15747,U_15745] :
        ( c_List_Obutlast(U_15747,hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15749),U_15745)) = hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15749),c_List_Obutlast(U_15747,U_15745))
        | U_15745 = c_List_Olist_ONil(U_15747) )
    & ! [U_15748,U_15746,U_15744] :
        ( c_List_Obutlast(U_15746,hAPP(hAPP(c_List_Olist_OCons(U_15746),U_15748),U_15744)) = c_List_Olist_ONil(U_15746)
        | U_15744 != c_List_Olist_ONil(U_15746) ) ),
    inference(miniscope,[status(thm)],[f_3922_2]) ).

cnf(f_3922_4,plain,
    ( c_List_Obutlast(U_15746,hAPP(hAPP(c_List_Olist_OCons(U_15746),U_15748),U_15744)) = c_List_Olist_ONil(U_15746)
    | U_15744 != c_List_Olist_ONil(U_15746) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

cnf(f_3922_5,plain,
    ( c_List_Obutlast(U_15747,hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15749),U_15745)) = hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15749),c_List_Obutlast(U_15747,U_15745))
    | U_15745 = c_List_Olist_ONil(U_15747) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_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_3923_2,plain,
    ! [U_15753,U_15752,U_15751,U_15750] :
      ( ( c_List_Oremove1(U_15752,U_15750,hAPP(hAPP(c_List_Olist_OCons(U_15752),U_15751),U_15753)) = hAPP(hAPP(c_List_Olist_OCons(U_15752),U_15751),c_List_Oremove1(U_15752,U_15750,U_15753))
        | U_15750 = U_15751 )
      & ( c_List_Oremove1(U_15752,U_15750,hAPP(hAPP(c_List_Olist_OCons(U_15752),U_15751),U_15753)) = U_15753
        | U_15750 != U_15751 ) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

fof(f_3923_3,plain,
    ( ! [U_15761,U_15759,U_15757,U_15755] :
        ( c_List_Oremove1(U_15759,U_15755,hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15757),U_15761)) = hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15757),c_List_Oremove1(U_15759,U_15755,U_15761))
        | U_15755 = U_15757 )
    & ! [U_15760,U_15758,U_15756,U_15754] :
        ( c_List_Oremove1(U_15758,U_15754,hAPP(hAPP(c_List_Olist_OCons(U_15758),U_15756),U_15760)) = U_15760
        | U_15754 != U_15756 ) ),
    inference(miniscope,[status(thm)],[f_3923_2]) ).

cnf(f_3923_4,plain,
    ( c_List_Oremove1(U_15758,U_15754,hAPP(hAPP(c_List_Olist_OCons(U_15758),U_15756),U_15760)) = U_15760
    | U_15754 != U_15756 ),
    inference(clausify,[status(thm)],[f_3923_3]) ).

cnf(f_3923_5,plain,
    ( c_List_Oremove1(U_15759,U_15755,hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15757),U_15761)) = hAPP(hAPP(c_List_Olist_OCons(U_15759),U_15757),c_List_Oremove1(U_15759,U_15755,U_15761))
    | U_15755 = U_15757 ),
    inference(clausify,[status(thm)],[f_3923_3]) ).

fof(f_3924_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_3924_2,plain,
    ! [U_15764,U_15763,U_15762] : hAPP(hAPP(c_List_Olist_OCons(U_15762),U_15763),U_15764) != c_List_Olist_ONil(U_15762),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

cnf(f_3924_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_15762),U_15763),U_15764) != c_List_Olist_ONil(U_15762),
    inference(clausify,[status(thm)],[f_3924_2]) ).

fof(f_3925_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_3925_2,plain,
    ! [U_15767,U_15766,U_15765] : c_List_Olist_ONil(U_15765) != hAPP(hAPP(c_List_Olist_OCons(U_15765),U_15766),U_15767),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

cnf(f_3925_3,plain,
    c_List_Olist_ONil(U_15765) != hAPP(hAPP(c_List_Olist_OCons(U_15765),U_15766),U_15767),
    inference(clausify,[status(thm)],[f_3925_2]) ).

fof(f_3926_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_3926_2,plain,
    ! [U_15769,U_15768] :
      ( c_List_Oupto(U_15769,U_15768) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_15768),U_15769)) ),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

cnf(f_3926_3,plain,
    ( c_List_Oupto(U_15769,U_15768) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_15768),U_15769)) ),
    inference(clausify,[status(thm)],[f_3926_2]) ).

fof(f_3927_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_3927_2,plain,
    ! [U_15771,U_15770] : hAPP(hAPP(c_List_Otake(U_15770),U_15771),c_List_Olist_ONil(U_15770)) = c_List_Olist_ONil(U_15770),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

cnf(f_3927_3,plain,
    hAPP(hAPP(c_List_Otake(U_15770),U_15771),c_List_Olist_ONil(U_15770)) = c_List_Olist_ONil(U_15770),
    inference(clausify,[status(thm)],[f_3927_2]) ).

fof(f_3928_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_3928_2,plain,
    ! [U_15773,U_15772] : hAPP(hAPP(c_List_Otake(U_15772),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15773) = c_List_Olist_ONil(U_15772),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

cnf(f_3928_3,plain,
    hAPP(hAPP(c_List_Otake(U_15772),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15773) = c_List_Olist_ONil(U_15772),
    inference(clausify,[status(thm)],[f_3928_2]) ).

fof(f_3929_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_3929_2,plain,
    ! [U_15776,U_15775,U_15774] :
      ( ( hAPP(hAPP(c_List_Otake(U_15774),U_15775),U_15776) = c_List_Olist_ONil(U_15774)
        | ( U_15776 != c_List_Olist_ONil(U_15774)
          & U_15775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_15776 = c_List_Olist_ONil(U_15774)
        | U_15775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_15774),U_15775),U_15776) != c_List_Olist_ONil(U_15774) ) ),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

fof(f_3929_3,plain,
    ( ! [U_15782,U_15780,U_15778] :
        ( hAPP(hAPP(c_List_Otake(U_15778),U_15780),U_15782) = c_List_Olist_ONil(U_15778)
        | ( U_15782 != c_List_Olist_ONil(U_15778)
          & U_15780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_15781,U_15779,U_15777] :
        ( U_15781 = c_List_Olist_ONil(U_15777)
        | U_15779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_15777),U_15779),U_15781) != c_List_Olist_ONil(U_15777) ) ),
    inference(miniscope,[status(thm)],[f_3929_2]) ).

cnf(f_3929_4,plain,
    ( U_15781 = c_List_Olist_ONil(U_15777)
    | U_15779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_15777),U_15779),U_15781) != c_List_Olist_ONil(U_15777) ),
    inference(clausify,[status(thm)],[f_3929_3]) ).

cnf(f_3929_5,plain,
    ( U_15780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_15778),U_15780),U_15782) = c_List_Olist_ONil(U_15778) ),
    inference(clausify,[status(thm)],[f_3929_3]) ).

cnf(f_3929_6,plain,
    ( U_15782 != c_List_Olist_ONil(U_15778)
    | hAPP(hAPP(c_List_Otake(U_15778),U_15780),U_15782) = c_List_Olist_ONil(U_15778) ),
    inference(clausify,[status(thm)],[f_3929_3]) ).

fof(f_3930_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_3930_2,plain,
    ! [U_15784,U_15783] : c_List_Osublist(U_15783,c_List_Olist_ONil(U_15783),U_15784) = c_List_Olist_ONil(U_15783),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

cnf(f_3930_3,plain,
    c_List_Osublist(U_15783,c_List_Olist_ONil(U_15783),U_15784) = c_List_Olist_ONil(U_15783),
    inference(clausify,[status(thm)],[f_3930_2]) ).

fof(f_3931_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_3931_2,plain,
    ! [U_15786,U_15785] : c_List_Oremove1(U_15785,U_15786,c_List_Olist_ONil(U_15785)) = c_List_Olist_ONil(U_15785),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

cnf(f_3931_3,plain,
    c_List_Oremove1(U_15785,U_15786,c_List_Olist_ONil(U_15785)) = c_List_Olist_ONil(U_15785),
    inference(clausify,[status(thm)],[f_3931_2]) ).

fof(f_3932_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_3932_2,plain,
    ! [U_15790,U_15789,U_15788,U_15787] : c_List_Oremove1(U_15787,U_15788,c_List_Oremove1(U_15787,U_15789,U_15790)) = c_List_Oremove1(U_15787,U_15789,c_List_Oremove1(U_15787,U_15788,U_15790)),
    inference(variable_rename,[status(thm)],[f_3932_1]) ).

cnf(f_3932_3,plain,
    c_List_Oremove1(U_15787,U_15788,c_List_Oremove1(U_15787,U_15789,U_15790)) = c_List_Oremove1(U_15787,U_15789,c_List_Oremove1(U_15787,U_15788,U_15790)),
    inference(clausify,[status(thm)],[f_3932_2]) ).

fof(f_3933_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_3933_2,plain,
    ! [U_15792,U_15791] : c_List_Olistrelp(U_15791,U_15792,c_List_Olist_ONil(U_15791),c_List_Olist_ONil(U_15791)),
    inference(variable_rename,[status(thm)],[f_3933_1]) ).

cnf(f_3933_3,plain,
    c_List_Olistrelp(U_15791,U_15792,c_List_Olist_ONil(U_15791),c_List_Olist_ONil(U_15791)),
    inference(clausify,[status(thm)],[f_3933_2]) ).

fof(f_3934_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_3934_2,plain,
    ! [U_15794,U_15793] : c_List_Olistrelp(U_15793,U_15794,c_List_Olist_ONil(U_15793),c_List_Olist_ONil(U_15793)),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

cnf(f_3934_3,plain,
    c_List_Olistrelp(U_15793,U_15794,c_List_Olist_ONil(U_15793),c_List_Olist_ONil(U_15793)),
    inference(clausify,[status(thm)],[f_3934_2]) ).

fof(f_3935_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_3935_2,plain,
    ! [U_15797,U_15796,U_15795] : hAPP(hAPP(c_List_Ozip(U_15795,U_15796),U_15797),c_List_Olist_ONil(U_15796)) = c_List_Olist_ONil(tc_prod(U_15795,U_15796)),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

cnf(f_3935_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15795,U_15796),U_15797),c_List_Olist_ONil(U_15796)) = c_List_Olist_ONil(tc_prod(U_15795,U_15796)),
    inference(clausify,[status(thm)],[f_3935_2]) ).

fof(f_3936_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_3936_2,plain,
    ! [U_15800,U_15799,U_15798] : hAPP(hAPP(c_List_Ozip(U_15798,U_15799),c_List_Olist_ONil(U_15798)),U_15800) = c_List_Olist_ONil(tc_prod(U_15798,U_15799)),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

cnf(f_3936_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15798,U_15799),c_List_Olist_ONil(U_15798)),U_15800) = c_List_Olist_ONil(tc_prod(U_15798,U_15799)),
    inference(clausify,[status(thm)],[f_3936_2]) ).

fof(f_3937_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_3937_2,plain,
    ! [U_15801] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15801),c_List_Olist_ONil(U_15801)) = c_Groups_Ozero__class_Ozero(U_15801)
      | ~ class_Groups_Omonoid__add(U_15801) ),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

cnf(f_3937_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15801),c_List_Olist_ONil(U_15801)) = c_Groups_Ozero__class_Ozero(U_15801)
    | ~ class_Groups_Omonoid__add(U_15801) ),
    inference(clausify,[status(thm)],[f_3937_2]) ).

fof(f_3938_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_3938_2,plain,
    ! [U_15803,U_15802] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_15803 != c_List_Olist_ONil(U_15802) )
      & ( U_15803 = c_List_Olist_ONil(U_15802)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15802)),U_15803) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

fof(f_3938_3,plain,
    ( ! [U_15807,U_15805] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15805)),U_15807) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_15807 != c_List_Olist_ONil(U_15805) )
    & ! [U_15806,U_15804] :
        ( U_15806 = c_List_Olist_ONil(U_15804)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15804)),U_15806) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3938_2]) ).

cnf(f_3938_4,plain,
    ( U_15806 = c_List_Olist_ONil(U_15804)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15804)),U_15806) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

cnf(f_3938_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15805)),U_15807) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_15807 != c_List_Olist_ONil(U_15805) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

fof(f_3939_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_3939_2,plain,
    ! [U_15808] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15808)),c_List_Olist_ONil(U_15808)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

cnf(f_3939_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15808)),c_List_Olist_ONil(U_15808)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3939_2]) ).

fof(f_3940_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_3940_2,plain,
    ! [U_15810,U_15809] :
      ( ( hAPP(c_List_Oset(U_15809),U_15810) = c_Orderings_Obot__class_Obot(tc_fun(U_15809,tc_HOL_Obool))
        | U_15810 != c_List_Olist_ONil(U_15809) )
      & ( U_15810 = c_List_Olist_ONil(U_15809)
        | hAPP(c_List_Oset(U_15809),U_15810) != c_Orderings_Obot__class_Obot(tc_fun(U_15809,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

fof(f_3940_3,plain,
    ( ! [U_15814,U_15812] :
        ( hAPP(c_List_Oset(U_15812),U_15814) = c_Orderings_Obot__class_Obot(tc_fun(U_15812,tc_HOL_Obool))
        | U_15814 != c_List_Olist_ONil(U_15812) )
    & ! [U_15813,U_15811] :
        ( U_15813 = c_List_Olist_ONil(U_15811)
        | hAPP(c_List_Oset(U_15811),U_15813) != c_Orderings_Obot__class_Obot(tc_fun(U_15811,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3940_2]) ).

cnf(f_3940_4,plain,
    ( U_15813 = c_List_Olist_ONil(U_15811)
    | hAPP(c_List_Oset(U_15811),U_15813) != c_Orderings_Obot__class_Obot(tc_fun(U_15811,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3940_3]) ).

cnf(f_3940_5,plain,
    ( hAPP(c_List_Oset(U_15812),U_15814) = c_Orderings_Obot__class_Obot(tc_fun(U_15812,tc_HOL_Obool))
    | U_15814 != c_List_Olist_ONil(U_15812) ),
    inference(clausify,[status(thm)],[f_3940_3]) ).

fof(f_3941_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_3941_2,plain,
    ! [U_15816,U_15815] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_15815,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15815),U_15816)
        | U_15816 != c_List_Olist_ONil(U_15815) )
      & ( U_15816 = c_List_Olist_ONil(U_15815)
        | c_Orderings_Obot__class_Obot(tc_fun(U_15815,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15815),U_15816) ) ),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

fof(f_3941_3,plain,
    ( ! [U_15820,U_15818] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_15818,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15818),U_15820)
        | U_15820 != c_List_Olist_ONil(U_15818) )
    & ! [U_15819,U_15817] :
        ( U_15819 = c_List_Olist_ONil(U_15817)
        | c_Orderings_Obot__class_Obot(tc_fun(U_15817,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15817),U_15819) ) ),
    inference(miniscope,[status(thm)],[f_3941_2]) ).

cnf(f_3941_4,plain,
    ( U_15819 = c_List_Olist_ONil(U_15817)
    | c_Orderings_Obot__class_Obot(tc_fun(U_15817,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15817),U_15819) ),
    inference(clausify,[status(thm)],[f_3941_3]) ).

cnf(f_3941_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_15818,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15818),U_15820)
    | U_15820 != c_List_Olist_ONil(U_15818) ),
    inference(clausify,[status(thm)],[f_3941_3]) ).

fof(f_3942_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_3942_2,plain,
    ! [U_15821] : hAPP(c_List_Oset(U_15821),c_List_Olist_ONil(U_15821)) = c_Orderings_Obot__class_Obot(tc_fun(U_15821,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

cnf(f_3942_3,plain,
    hAPP(c_List_Oset(U_15821),c_List_Olist_ONil(U_15821)) = c_Orderings_Obot__class_Obot(tc_fun(U_15821,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3942_2]) ).

fof(f_3943_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_3943_2,plain,
    ! [U_15823,U_15822] : c_List_Olist_Olist__size(U_15822,U_15823,c_List_Olist_ONil(U_15822)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

cnf(f_3943_3,plain,
    c_List_Olist_Olist__size(U_15822,U_15823,c_List_Olist_ONil(U_15822)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3943_2]) ).

fof(f_3944_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_3944_2,plain,
    ! [U_15827,U_15826,U_15825,U_15824] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_15824,U_15825),U_15826),U_15827) = c_List_Olist_ONil(U_15824)
        | U_15825 != c_List_Olist_ONil(U_15824) )
      & ( U_15825 = c_List_Olist_ONil(U_15824)
        | hAPP(hAPP(c_List_Olist__update(U_15824,U_15825),U_15826),U_15827) != c_List_Olist_ONil(U_15824) ) ),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

fof(f_3944_3,plain,
    ( ! [U_15835,U_15833,U_15831,U_15829] :
        ( hAPP(hAPP(c_List_Olist__update(U_15829,U_15831),U_15833),U_15835) = c_List_Olist_ONil(U_15829)
        | U_15831 != c_List_Olist_ONil(U_15829) )
    & ! [U_15834,U_15832,U_15830,U_15828] :
        ( U_15830 = c_List_Olist_ONil(U_15828)
        | hAPP(hAPP(c_List_Olist__update(U_15828,U_15830),U_15832),U_15834) != c_List_Olist_ONil(U_15828) ) ),
    inference(miniscope,[status(thm)],[f_3944_2]) ).

cnf(f_3944_4,plain,
    ( U_15830 = c_List_Olist_ONil(U_15828)
    | hAPP(hAPP(c_List_Olist__update(U_15828,U_15830),U_15832),U_15834) != c_List_Olist_ONil(U_15828) ),
    inference(clausify,[status(thm)],[f_3944_3]) ).

cnf(f_3944_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15829,U_15831),U_15833),U_15835) = c_List_Olist_ONil(U_15829)
    | U_15831 != c_List_Olist_ONil(U_15829) ),
    inference(clausify,[status(thm)],[f_3944_3]) ).

fof(f_3945_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_3945_2,plain,
    ! [U_15838,U_15837,U_15836] : hAPP(hAPP(c_List_Olist__update(U_15836,c_List_Olist_ONil(U_15836)),U_15837),U_15838) = c_List_Olist_ONil(U_15836),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

cnf(f_3945_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15836,c_List_Olist_ONil(U_15836)),U_15837),U_15838) = c_List_Olist_ONil(U_15836),
    inference(clausify,[status(thm)],[f_3945_2]) ).

fof(f_3946_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_3946_2,plain,
    ! [U_15841,U_15840,U_15839] : hAPP(hAPP(c_List_Olist__update(U_15839,c_List_Olist_ONil(U_15839)),U_15840),U_15841) = c_List_Olist_ONil(U_15839),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

cnf(f_3946_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15839,c_List_Olist_ONil(U_15839)),U_15840),U_15841) = c_List_Olist_ONil(U_15839),
    inference(clausify,[status(thm)],[f_3946_2]) ).

fof(f_3947_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_3947_2,plain,
    ! [U_15845,U_15844,U_15843,U_15842] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15843,U_15845))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),U_15845))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),U_15845)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15843,U_15845)))) ) )
      | U_15842 = U_15843 ),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

cnf(f_3947_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),U_15845)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15843,U_15845))))
    | U_15842 = U_15843 ),
    inference(clausify,[status(thm)],[f_3947_2]) ).

cnf(f_3947_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15843,U_15845))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15844),U_15842),hAPP(c_List_Oset(U_15844),U_15845)))
    | U_15842 = U_15843 ),
    inference(clausify,[status(thm)],[f_3947_2]) ).

fof(f_3948_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_3948_2,plain,
    ! [U_15849,U_15848,U_15847,U_15846] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15846),U_15847),hAPP(c_List_Oset(U_15846),c_List_Oremove1(U_15846,U_15849,U_15848))))
      | hBOOL(hAPP(hAPP(c_member(U_15846),U_15847),hAPP(c_List_Oset(U_15846),U_15848))) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

cnf(f_3948_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15846),U_15847),hAPP(c_List_Oset(U_15846),c_List_Oremove1(U_15846,U_15849,U_15848))))
    | hBOOL(hAPP(hAPP(c_member(U_15846),U_15847),hAPP(c_List_Oset(U_15846),U_15848))) ),
    inference(clausify,[status(thm)],[f_3948_2]) ).

fof(f_3949_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_3949_2,plain,
    ! [U_15852,U_15851,U_15850] :
      ( c_List_Oremove1(U_15850,U_15851,U_15852) = U_15852
      | hBOOL(hAPP(hAPP(c_member(U_15850),U_15851),hAPP(c_List_Oset(U_15850),U_15852))) ),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

cnf(f_3949_3,plain,
    ( c_List_Oremove1(U_15850,U_15851,U_15852) = U_15852
    | hBOOL(hAPP(hAPP(c_member(U_15850),U_15851),hAPP(c_List_Oset(U_15850),U_15852))) ),
    inference(clausify,[status(thm)],[f_3949_2]) ).

fof(f_3950_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_3950_2,plain,
    ! [U_15854,U_15853] : c_List_Osublist(U_15853,U_15854,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_15853),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

cnf(f_3950_3,plain,
    c_List_Osublist(U_15853,U_15854,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_15853),
    inference(clausify,[status(thm)],[f_3950_2]) ).

fof(f_3951_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_3951_2,plain,
    ! [U_15857,U_15856,U_15855] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15855,tc_HOL_Obool)),hAPP(c_List_Oset(U_15855),c_List_Oremove1(U_15855,U_15856,U_15857))),hAPP(c_List_Oset(U_15855),U_15857))),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

cnf(f_3951_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15855,tc_HOL_Obool)),hAPP(c_List_Oset(U_15855),c_List_Oremove1(U_15855,U_15856,U_15857))),hAPP(c_List_Oset(U_15855),U_15857))),
    inference(clausify,[status(thm)],[f_3951_2]) ).

fof(f_3952_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_3952_2,plain,
    ! [U_15859,U_15858] :
      ( ( 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_15858)),U_15859)))
        | U_15859 = c_List_Olist_ONil(U_15858) )
      & ( U_15859 != c_List_Olist_ONil(U_15858)
        | ~ 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_15858)),U_15859))) ) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

fof(f_3952_3,plain,
    ( ! [U_15863,U_15861] :
        ( 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_15861)),U_15863)))
        | U_15863 = c_List_Olist_ONil(U_15861) )
    & ! [U_15862,U_15860] :
        ( U_15862 != c_List_Olist_ONil(U_15860)
        | ~ 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_15860)),U_15862))) ) ),
    inference(miniscope,[status(thm)],[f_3952_2]) ).

cnf(f_3952_4,plain,
    ( U_15862 != c_List_Olist_ONil(U_15860)
    | ~ 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_15860)),U_15862))) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

cnf(f_3952_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_15861)),U_15863)))
    | U_15863 = c_List_Olist_ONil(U_15861) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

fof(f_3953_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_3953_2,plain,
    ! [U_15866,U_15865,U_15864] : hAPP(hAPP(c_List_Otake(U_15864),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_15864),U_15865),U_15866)) = hAPP(hAPP(c_List_Olist_OCons(U_15864),U_15865),c_List_Olist_ONil(U_15864)),
    inference(variable_rename,[status(thm)],[f_3953_1]) ).

cnf(f_3953_3,plain,
    hAPP(hAPP(c_List_Otake(U_15864),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_15864),U_15865),U_15866)) = hAPP(hAPP(c_List_Olist_OCons(U_15864),U_15865),c_List_Olist_ONil(U_15864)),
    inference(clausify,[status(thm)],[f_3953_2]) ).

fof(f_3954_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_3954_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)),U_15868),c_List_Olist_ONil(U_15867))),c_List_Olistrel1(U_15867,U_15869))),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

cnf(f_3954_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)),U_15868),c_List_Olist_ONil(U_15867))),c_List_Olistrel1(U_15867,U_15869))),
    inference(clausify,[status(thm)],[f_3954_2]) ).

fof(f_3955_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_3955_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)),c_List_Olist_ONil(U_15870)),U_15871)),c_List_Olistrel1(U_15870,U_15872))),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

cnf(f_3955_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)),c_List_Olist_ONil(U_15870)),U_15871)),c_List_Olistrel1(U_15870,U_15872))),
    inference(clausify,[status(thm)],[f_3955_2]) ).

fof(f_3956_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_3956_2,plain,
    ! [U_15874,U_15873] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15873),tc_List_Olist(U_15873))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15873),tc_List_Olist(U_15873)),c_List_Olist_ONil(U_15873)),c_List_Olist_ONil(U_15873))),c_List_Olistrel(U_15873,U_15874))),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

cnf(f_3956_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15873),tc_List_Olist(U_15873))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15873),tc_List_Olist(U_15873)),c_List_Olist_ONil(U_15873)),c_List_Olist_ONil(U_15873))),c_List_Olistrel(U_15873,U_15874))),
    inference(clausify,[status(thm)],[f_3956_2]) ).

fof(f_3957_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_3957_2,plain,
    ! [U_15877,U_15876,U_15875] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15875),tc_List_Olist(U_15875))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15875),tc_List_Olist(U_15875)),U_15876),c_List_Olist_ONil(U_15875))),c_List_Olexord(U_15875,U_15877))),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

cnf(f_3957_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15875),tc_List_Olist(U_15875))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15875),tc_List_Olist(U_15875)),U_15876),c_List_Olist_ONil(U_15875))),c_List_Olexord(U_15875,U_15877))),
    inference(clausify,[status(thm)],[f_3957_2]) ).

fof(f_3958_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_3958_2,plain,
    ! [U_15880,U_15879,U_15878] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15878),tc_List_Olist(U_15878))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15878),tc_List_Olist(U_15878)),U_15879),c_List_Olist_ONil(U_15878))),c_List_Olex(U_15878,U_15880))),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

cnf(f_3958_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15878),tc_List_Olist(U_15878))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15878),tc_List_Olist(U_15878)),U_15879),c_List_Olist_ONil(U_15878))),c_List_Olex(U_15878,U_15880))),
    inference(clausify,[status(thm)],[f_3958_2]) ).

fof(f_3959_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_3959_2,plain,
    ! [U_15883,U_15882,U_15881] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15881),tc_List_Olist(U_15881))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15881),tc_List_Olist(U_15881)),c_List_Olist_ONil(U_15881)),U_15882)),c_List_Olex(U_15881,U_15883))),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

cnf(f_3959_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15881),tc_List_Olist(U_15881))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15881),tc_List_Olist(U_15881)),c_List_Olist_ONil(U_15881)),U_15882)),c_List_Olex(U_15881,U_15883))),
    inference(clausify,[status(thm)],[f_3959_2]) ).

fof(f_3960_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_3960_2,plain,
    ! [U_15887,U_15886,U_15885,U_15884] : hAPP(hAPP(c_List_Otake(U_15884),U_15885),hAPP(hAPP(c_List_Olist_OCons(U_15884),U_15886),U_15887)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15884),c_List_Olist_ONil(U_15884),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15884),tc_List_Olist(U_15884),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15884),U_15886)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_15884),tc_List_Olist(U_15884)),c_List_Otake(U_15884)),U_15887)),U_15885),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

cnf(f_3960_3,plain,
    hAPP(hAPP(c_List_Otake(U_15884),U_15885),hAPP(hAPP(c_List_Olist_OCons(U_15884),U_15886),U_15887)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15884),c_List_Olist_ONil(U_15884),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15884),tc_List_Olist(U_15884),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15884),U_15886)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_15884),tc_List_Olist(U_15884)),c_List_Otake(U_15884)),U_15887)),U_15885),
    inference(clausify,[status(thm)],[f_3960_2]) ).

fof(f_3961_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_3961_2,plain,
    ! [U_15889,U_15888] :
      ( ( c_List_Oupto(U_15888,U_15889) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15888),U_15889)) )
      & ( c_List_Oupto(U_15888,U_15889) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15888),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15888),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15889))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15888),U_15889)) ) ),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

fof(f_3961_3,plain,
    ( ! [U_15893,U_15891] :
        ( c_List_Oupto(U_15891,U_15893) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15891),U_15893)) )
    & ! [U_15892,U_15890] :
        ( c_List_Oupto(U_15890,U_15892) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15890),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15890),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15892))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15890),U_15892)) ) ),
    inference(miniscope,[status(thm)],[f_3961_2]) ).

cnf(f_3961_4,plain,
    ( c_List_Oupto(U_15890,U_15892) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15890),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15890),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15892))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15890),U_15892)) ),
    inference(clausify,[status(thm)],[f_3961_3]) ).

cnf(f_3961_5,plain,
    ( c_List_Oupto(U_15891,U_15893) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15891),U_15893)) ),
    inference(clausify,[status(thm)],[f_3961_3]) ).

fof(f_3962_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_3962_2,plain,
    ! [U_15896,U_15895,U_15894] :
      ( ( c_List_Osublist(U_15895,hAPP(hAPP(c_List_Olist_OCons(U_15895),U_15896),c_List_Olist_ONil(U_15895)),U_15894) = c_List_Olist_ONil(U_15895)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15894)) )
      & ( c_List_Osublist(U_15895,hAPP(hAPP(c_List_Olist_OCons(U_15895),U_15896),c_List_Olist_ONil(U_15895)),U_15894) = hAPP(hAPP(c_List_Olist_OCons(U_15895),U_15896),c_List_Olist_ONil(U_15895))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15894)) ) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

fof(f_3962_3,plain,
    ( ! [U_15902,U_15900,U_15898] :
        ( c_List_Osublist(U_15900,hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),c_List_Olist_ONil(U_15900)),U_15898) = c_List_Olist_ONil(U_15900)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15898)) )
    & ! [U_15901,U_15899,U_15897] :
        ( c_List_Osublist(U_15899,hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),c_List_Olist_ONil(U_15899)),U_15897) = hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),c_List_Olist_ONil(U_15899))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15897)) ) ),
    inference(miniscope,[status(thm)],[f_3962_2]) ).

cnf(f_3962_4,plain,
    ( c_List_Osublist(U_15899,hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),c_List_Olist_ONil(U_15899)),U_15897) = hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),c_List_Olist_ONil(U_15899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15897)) ),
    inference(clausify,[status(thm)],[f_3962_3]) ).

cnf(f_3962_5,plain,
    ( c_List_Osublist(U_15900,hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),c_List_Olist_ONil(U_15900)),U_15898) = c_List_Olist_ONil(U_15900)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15898)) ),
    inference(clausify,[status(thm)],[f_3962_3]) ).

fof(f_3963_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_3963_2,plain,
    ! [U_15903] : c_List_Olists(U_15903,c_Orderings_Obot__class_Obot(tc_fun(U_15903,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15903)),c_List_Olist_ONil(U_15903)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15903),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

cnf(f_3963_3,plain,
    c_List_Olists(U_15903,c_Orderings_Obot__class_Obot(tc_fun(U_15903,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15903)),c_List_Olist_ONil(U_15903)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15903),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3963_2]) ).

fof(f_3964_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_3964_2,plain,
    ! [U_15907,U_15906,U_15905,U_15904] :
      ( ( hAPP(hAPP(c_List_Otake(U_15905),U_15904),hAPP(hAPP(c_List_Olist_OCons(U_15905),U_15906),U_15907)) = hAPP(hAPP(c_List_Olist_OCons(U_15905),U_15906),hAPP(hAPP(c_List_Otake(U_15905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15904),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15907))
        | U_15904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_15905),U_15904),hAPP(hAPP(c_List_Olist_OCons(U_15905),U_15906),U_15907)) = c_List_Olist_ONil(U_15905)
        | U_15904 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

fof(f_3964_3,plain,
    ( ! [U_15915,U_15913,U_15911,U_15909] :
        ( hAPP(hAPP(c_List_Otake(U_15911),U_15909),hAPP(hAPP(c_List_Olist_OCons(U_15911),U_15913),U_15915)) = hAPP(hAPP(c_List_Olist_OCons(U_15911),U_15913),hAPP(hAPP(c_List_Otake(U_15911),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15909),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15915))
        | U_15909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15914,U_15912,U_15910,U_15908] :
        ( hAPP(hAPP(c_List_Otake(U_15910),U_15908),hAPP(hAPP(c_List_Olist_OCons(U_15910),U_15912),U_15914)) = c_List_Olist_ONil(U_15910)
        | U_15908 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3964_2]) ).

cnf(f_3964_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_15910),U_15908),hAPP(hAPP(c_List_Olist_OCons(U_15910),U_15912),U_15914)) = c_List_Olist_ONil(U_15910)
    | U_15908 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3964_3]) ).

cnf(f_3964_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_15911),U_15909),hAPP(hAPP(c_List_Olist_OCons(U_15911),U_15913),U_15915)) = hAPP(hAPP(c_List_Olist_OCons(U_15911),U_15913),hAPP(hAPP(c_List_Otake(U_15911),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15909),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15915))
    | U_15909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3964_3]) ).

fof(f_3965_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_3965_2,plain,
    ! [U_15917,U_15916] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15916),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15917)) = 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_15916)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15917))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15916),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15917)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15916)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15916)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15917)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15916)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15917))) ) ),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

fof(f_3965_3,plain,
    ( ! [U_15921,U_15919] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15919),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15921)) = 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_15919)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15921))) )
    & ! [U_15920,U_15918] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920))) ) ),
    inference(miniscope,[status(thm)],[f_3965_2]) ).

cnf(f_3965_4,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15918)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15920))) ),
    inference(clausify,[status(thm)],[f_3965_3]) ).

cnf(f_3965_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15919),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15921)) = 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_15919)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15921))) ),
    inference(clausify,[status(thm)],[f_3965_3]) ).

fof(f_3966_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_3966_2,plain,
    ! [U_15923,U_15922] : hAPP(c_Relation_OImage(tc_List_Olist(U_15922),tc_List_Olist(U_15922),c_List_Olistrel(U_15922,U_15923)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15922)),c_List_Olist_ONil(U_15922)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15922),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15922)),c_List_Olist_ONil(U_15922)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15922),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

cnf(f_3966_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_15922),tc_List_Olist(U_15922),c_List_Olistrel(U_15922,U_15923)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15922)),c_List_Olist_ONil(U_15922)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15922),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15922)),c_List_Olist_ONil(U_15922)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15922),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3966_2]) ).

fof(f_3967_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_3967_2,plain,
    ! [U_15925,U_15924] : c_List_Oset__Cons(U_15924,U_15925,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15924)),c_List_Olist_ONil(U_15924)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15924),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_15924,tc_List_Olist(U_15924),hAPP(hAPP(c_COMBC(U_15924,tc_List_Olist(U_15924),tc_List_Olist(U_15924)),c_List_Olist_OCons(U_15924)),c_List_Olist_ONil(U_15924))),U_15925),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

cnf(f_3967_3,plain,
    c_List_Oset__Cons(U_15924,U_15925,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15924)),c_List_Olist_ONil(U_15924)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15924),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_15924,tc_List_Olist(U_15924),hAPP(hAPP(c_COMBC(U_15924,tc_List_Olist(U_15924),tc_List_Olist(U_15924)),c_List_Olist_OCons(U_15924)),c_List_Olist_ONil(U_15924))),U_15925),
    inference(clausify,[status(thm)],[f_3967_2]) ).

fof(f_3968_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_3968_2,plain,
    ! [U_15928,U_15927,U_15926] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15926)),c_List_Oremove1(U_15926,U_15927,U_15928)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15926)),U_15928)
        | hBOOL(hAPP(hAPP(c_member(U_15926),U_15927),hAPP(c_List_Oset(U_15926),U_15928))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15926)),c_List_Oremove1(U_15926,U_15927,U_15928)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15926)),U_15928)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15926),U_15927),hAPP(c_List_Oset(U_15926),U_15928))) ) ),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

fof(f_3968_3,plain,
    ( ! [U_15934,U_15932,U_15930] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15930)),c_List_Oremove1(U_15930,U_15932,U_15934)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15930)),U_15934)
        | hBOOL(hAPP(hAPP(c_member(U_15930),U_15932),hAPP(c_List_Oset(U_15930),U_15934))) )
    & ! [U_15933,U_15931,U_15929] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15929)),c_List_Oremove1(U_15929,U_15931,U_15933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15929)),U_15933)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15929),U_15931),hAPP(c_List_Oset(U_15929),U_15933))) ) ),
    inference(miniscope,[status(thm)],[f_3968_2]) ).

cnf(f_3968_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15929)),c_List_Oremove1(U_15929,U_15931,U_15933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15929)),U_15933)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15929),U_15931),hAPP(c_List_Oset(U_15929),U_15933))) ),
    inference(clausify,[status(thm)],[f_3968_3]) ).

cnf(f_3968_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15930)),c_List_Oremove1(U_15930,U_15932,U_15934)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15930)),U_15934)
    | hBOOL(hAPP(hAPP(c_member(U_15930),U_15932),hAPP(c_List_Oset(U_15930),U_15934))) ),
    inference(clausify,[status(thm)],[f_3968_3]) ).

fof(f_3969_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_3969_2,plain,
    ! [U_15936,U_15935] :
      ( ( ( c_List_Oupto(U_15935,U_15936) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15935),U_15936)) )
        & ( c_List_Oupto(U_15935,U_15936) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15935),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15935),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15936))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15935),U_15936)) ) )
      | ~ 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_15935),U_15936))) ),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

cnf(f_3969_3,plain,
    ( c_List_Oupto(U_15935,U_15936) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15935),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15935),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15936))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15935),U_15936))
    | ~ 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_15935),U_15936))) ),
    inference(clausify,[status(thm)],[f_3969_2]) ).

cnf(f_3969_4,plain,
    ( c_List_Oupto(U_15935,U_15936) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15935),U_15936))
    | ~ 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_15935),U_15936))) ),
    inference(clausify,[status(thm)],[f_3969_2]) ).

fof(f_3970_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_3970_2,plain,
    ! [U_15939,U_15938,U_15937] :
      ( hBOOL(hAPP(hAPP(c_member(U_15938),hAPP(c_Product__Type_Ofst(U_15938,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_15938,U_15937),U_15939))),hAPP(c_List_Oset(U_15938),U_15937)))
      | U_15937 = c_List_Olist_ONil(U_15938) ),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

cnf(f_3970_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15938),hAPP(c_Product__Type_Ofst(U_15938,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_15938,U_15937),U_15939))),hAPP(c_List_Oset(U_15938),U_15937)))
    | U_15937 = c_List_Olist_ONil(U_15938) ),
    inference(clausify,[status(thm)],[f_3970_2]) ).

fof(f_3971_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_3971_2,plain,
    ! [U_15940] : c_List_Olistset(U_15940,c_List_Olist_ONil(tc_fun(U_15940,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15940)),c_List_Olist_ONil(U_15940)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15940),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

cnf(f_3971_3,plain,
    c_List_Olistset(U_15940,c_List_Olist_ONil(tc_fun(U_15940,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15940)),c_List_Olist_ONil(U_15940)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15940),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3971_2]) ).

fof(f_3972_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_3972_2,plain,
    ! [U_15945,U_15944,U_15943,U_15942,U_15941] : hAPP(hAPP(c_List_Ozip(U_15941,U_15942),U_15943),hAPP(hAPP(c_List_Olist_OCons(U_15942),U_15944),U_15945)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15941,U_15942)),U_15941,c_List_Olist_ONil(tc_prod(U_15941,U_15942)),hAPP(hAPP(c_COMBC(U_15941,tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942)))),U_15941),c_COMBB(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(U_15941))),hAPP(hAPP(c_COMBB(tc_prod(U_15941,U_15942),tc_fun(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942))),U_15941),c_List_Olist_OCons(tc_prod(U_15941,U_15942))),hAPP(hAPP(c_COMBC(U_15941,U_15942,tc_prod(U_15941,U_15942)),c_Product__Type_OPair(U_15941,U_15942)),U_15944)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15941),tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),c_List_Ozip(U_15941,U_15942)),U_15945))),U_15943),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

cnf(f_3972_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15941,U_15942),U_15943),hAPP(hAPP(c_List_Olist_OCons(U_15942),U_15944),U_15945)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15941,U_15942)),U_15941,c_List_Olist_ONil(tc_prod(U_15941,U_15942)),hAPP(hAPP(c_COMBC(U_15941,tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15941),tc_List_Olist(tc_prod(U_15941,U_15942)))),U_15941),c_COMBB(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(U_15941))),hAPP(hAPP(c_COMBB(tc_prod(U_15941,U_15942),tc_fun(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942))),U_15941),c_List_Olist_OCons(tc_prod(U_15941,U_15942))),hAPP(hAPP(c_COMBC(U_15941,U_15942,tc_prod(U_15941,U_15942)),c_Product__Type_OPair(U_15941,U_15942)),U_15944)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15941),tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),c_List_Ozip(U_15941,U_15942)),U_15945))),U_15943),
    inference(clausify,[status(thm)],[f_3972_2]) ).

fof(f_3973_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_3973_2,plain,
    ! [U_15951,U_15950,U_15949,U_15948,U_15947,U_15946] : hAPP(c_List_Olist_Olist__case(U_15946,U_15947,U_15948,U_15949),hAPP(hAPP(c_List_Olist_OCons(U_15947),U_15950),U_15951)) = hAPP(hAPP(U_15949,U_15950),U_15951),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

cnf(f_3973_3,plain,
    hAPP(c_List_Olist_Olist__case(U_15946,U_15947,U_15948,U_15949),hAPP(hAPP(c_List_Olist_OCons(U_15947),U_15950),U_15951)) = hAPP(hAPP(U_15949,U_15950),U_15951),
    inference(clausify,[status(thm)],[f_3973_2]) ).

fof(f_3974_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_3974_2,plain,
    ! [U_15955,U_15954,U_15953,U_15952] : hAPP(c_List_Olist_Olist__case(U_15952,U_15953,U_15954,U_15955),c_List_Olist_ONil(U_15953)) = U_15954,
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

cnf(f_3974_3,plain,
    hAPP(c_List_Olist_Olist__case(U_15952,U_15953,U_15954,U_15955),c_List_Olist_ONil(U_15953)) = U_15954,
    inference(clausify,[status(thm)],[f_3974_2]) ).

fof(f_3975_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_3975_2,plain,
    ! [U_15958,U_15957,U_15956] : c_List_Olistset(U_15956,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_15956,tc_HOL_Obool)),U_15957),U_15958)) = c_List_Oset__Cons(U_15956,U_15957,c_List_Olistset(U_15956,U_15958)),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

cnf(f_3975_3,plain,
    c_List_Olistset(U_15956,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_15956,tc_HOL_Obool)),U_15957),U_15958)) = c_List_Oset__Cons(U_15956,U_15957,c_List_Olistset(U_15956,U_15958)),
    inference(clausify,[status(thm)],[f_3975_2]) ).

fof(f_3976_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_3976_2,plain,
    ! [U_15963,U_15962,U_15961,U_15960,U_15959] : hAPP(hAPP(c_List_Ozip(U_15959,U_15960),hAPP(hAPP(c_List_Olist_OCons(U_15959),U_15961),U_15962)),U_15963) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15959,U_15960)),U_15960,c_List_Olist_ONil(tc_prod(U_15959,U_15960)),hAPP(hAPP(c_COMBC(U_15960,tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960)))),U_15960),c_COMBB(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(U_15960))),hAPP(hAPP(c_COMBB(tc_prod(U_15959,U_15960),tc_fun(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960))),U_15960),c_List_Olist_OCons(tc_prod(U_15959,U_15960))),hAPP(c_Product__Type_OPair(U_15959,U_15960),U_15961)))),hAPP(c_List_Ozip(U_15959,U_15960),U_15962))),U_15963),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

cnf(f_3976_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15959,U_15960),hAPP(hAPP(c_List_Olist_OCons(U_15959),U_15961),U_15962)),U_15963) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15959,U_15960)),U_15960,c_List_Olist_ONil(tc_prod(U_15959,U_15960)),hAPP(hAPP(c_COMBC(U_15960,tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960)))),U_15960),c_COMBB(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(U_15960))),hAPP(hAPP(c_COMBB(tc_prod(U_15959,U_15960),tc_fun(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960))),U_15960),c_List_Olist_OCons(tc_prod(U_15959,U_15960))),hAPP(c_Product__Type_OPair(U_15959,U_15960),U_15961)))),hAPP(c_List_Ozip(U_15959,U_15960),U_15962))),U_15963),
    inference(clausify,[status(thm)],[f_3976_2]) ).

fof(f_3977_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_3977_2,plain,
    ! [U_15966,U_15965,U_15964] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_15964,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15964,tc_HOL_Obool)),U_15965),hAPP(hAPP(c_Set_Oinsert(U_15964),U_15966),c_Orderings_Obot__class_Obot(tc_fun(U_15964,tc_HOL_Obool))))) = c_List_Oremove1(U_15964,U_15966,c_List_Olinorder__class_Osorted__list__of__set(U_15964,U_15965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15964),U_15965))
      | ~ class_Orderings_Olinorder(U_15964) ),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

cnf(f_3977_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_15964,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15964,tc_HOL_Obool)),U_15965),hAPP(hAPP(c_Set_Oinsert(U_15964),U_15966),c_Orderings_Obot__class_Obot(tc_fun(U_15964,tc_HOL_Obool))))) = c_List_Oremove1(U_15964,U_15966,c_List_Olinorder__class_Osorted__list__of__set(U_15964,U_15965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15964),U_15965))
    | ~ class_Orderings_Olinorder(U_15964) ),
    inference(clausify,[status(thm)],[f_3977_2]) ).

fof(f_3978_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_3978_2,plain,
    ! [U_15971,U_15970,U_15969] :
      ( hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
      | ? [U_15968,U_15967] :
          ( ~ hBOOL(hAPP(hAPP(U_15971,U_15968),U_15967))
          & ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15968),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_15967))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15968),U_15967)) )
          & 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_15968),U_15967))) )
      | ~ 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_15969),U_15970))) ),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

fof(f_3978_3,plain,
    ! [U_15971,U_15970,U_15969] :
      ( hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
      | ? [U_15967] :
          ( ~ hBOOL(hAPP(hAPP(U_15971,sK411(U_15971,U_15970,U_15969)),U_15967))
          & ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_15967))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),U_15967)) )
          & 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),sK411(U_15971,U_15970,U_15969)),U_15967))) )
      | ~ 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_15969),U_15970))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_15968,sK411(U_15971,U_15970,U_15969))],[f_3978_2]) ).

fof(f_3978_4,plain,
    ! [U_15971,U_15970,U_15969] :
      ( hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
      | ( ~ hBOOL(hAPP(hAPP(U_15971,sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969)))
        & ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK412(U_15971,U_15970,U_15969)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969))) )
        & 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),sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969)))) )
      | ~ 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_15969),U_15970))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_15967,sK412(U_15971,U_15970,U_15969))],[f_3978_3]) ).

cnf(f_3978_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),sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969))))
    | hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
    | ~ 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_15969),U_15970))) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

cnf(f_3978_6,plain,
    ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK412(U_15971,U_15970,U_15969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969)))
    | hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
    | ~ 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_15969),U_15970))) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

cnf(f_3978_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_15971,sK411(U_15971,U_15970,U_15969)),sK412(U_15971,U_15970,U_15969)))
    | hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
    | ~ 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_15969),U_15970))) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

fof(f_3979_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_3979_2,plain,
    ! [U_15972] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_15972,c_Orderings_Obot__class_Obot(tc_fun(U_15972,tc_HOL_Obool))) = c_List_Olist_ONil(U_15972)
      | ~ class_Orderings_Olinorder(U_15972) ),
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

cnf(f_3979_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_15972,c_Orderings_Obot__class_Obot(tc_fun(U_15972,tc_HOL_Obool))) = c_List_Olist_ONil(U_15972)
    | ~ class_Orderings_Olinorder(U_15972) ),
    inference(clausify,[status(thm)],[f_3979_2]) ).

fof(f_3980_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_3980_2,plain,
    ! [U_15977,U_15976,U_15975,U_15974,U_15973] :
      ( ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15974,U_15975,U_15976),U_15973),U_15977) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15975),U_15974),tc_prod(U_15975,U_15974),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15975),U_15974),c_List_Olist_ONil(U_15975)),U_15977),hAPP(c_Product__Type_Oprod_Oprod__case(U_15975,U_15974,tc_prod(tc_List_Olist(U_15975),U_15974)),hAPP(hAPP(c_COMBC(U_15975,tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974)),tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15975),U_15974),tc_prod(tc_List_Olist(U_15975),U_15974)),tc_fun(tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974)),tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974))),U_15975),c_COMBB(tc_prod(tc_List_Olist(U_15975),U_15974),tc_prod(tc_List_Olist(U_15975),U_15974),U_15974)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15975),tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974))),tc_fun(tc_prod(tc_List_Olist(U_15975),U_15974),tc_prod(tc_List_Olist(U_15975),U_15974)),U_15975),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15975),U_15974,tc_prod(tc_List_Olist(U_15975),U_15974))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15975),tc_List_Olist(U_15975)),tc_fun(tc_List_Olist(U_15975),tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974))),U_15975),hAPP(c_COMBB(tc_List_Olist(U_15975),tc_fun(U_15974,tc_prod(tc_List_Olist(U_15975),U_15974)),tc_List_Olist(U_15975)),c_Product__Type_OPair(tc_List_Olist(U_15975),U_15974))),c_List_Olist_OCons(U_15975))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15974,U_15975,U_15976),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15973),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15976,U_15977))
        | U_15973 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15974,U_15975,U_15976),U_15973),U_15977) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15975),U_15974),c_List_Olist_ONil(U_15975)),U_15977)
        | U_15973 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

fof(f_3980_3,plain,
    ( ! [U_15987,U_15985,U_15983,U_15981,U_15979] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15981,U_15983,U_15985),U_15979),U_15987) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(U_15983,U_15981),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15983),U_15981),c_List_Olist_ONil(U_15983)),U_15987),hAPP(c_Product__Type_Oprod_Oprod__case(U_15983,U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),hAPP(hAPP(c_COMBC(U_15983,tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),U_15983),c_COMBB(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981),U_15981)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),tc_fun(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981)),U_15983),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15983),U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15983),tc_List_Olist(U_15983)),tc_fun(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),U_15983),hAPP(c_COMBB(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_List_Olist(U_15983)),c_Product__Type_OPair(tc_List_Olist(U_15983),U_15981))),c_List_Olist_OCons(U_15983))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15981,U_15983,U_15985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15979),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15985,U_15987))
        | U_15979 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_15986,U_15984,U_15982,U_15980,U_15978] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15980,U_15982,U_15984),U_15978),U_15986) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15982),U_15980),c_List_Olist_ONil(U_15982)),U_15986)
        | U_15978 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3980_2]) ).

cnf(f_3980_4,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15980,U_15982,U_15984),U_15978),U_15986) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15982),U_15980),c_List_Olist_ONil(U_15982)),U_15986)
    | U_15978 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3980_3]) ).

cnf(f_3980_5,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15981,U_15983,U_15985),U_15979),U_15987) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(U_15983,U_15981),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15983),U_15981),c_List_Olist_ONil(U_15983)),U_15987),hAPP(c_Product__Type_Oprod_Oprod__case(U_15983,U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),hAPP(hAPP(c_COMBC(U_15983,tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),U_15983),c_COMBB(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981),U_15981)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),tc_fun(tc_prod(tc_List_Olist(U_15983),U_15981),tc_prod(tc_List_Olist(U_15983),U_15981)),U_15983),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15983),U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15983),tc_List_Olist(U_15983)),tc_fun(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981))),U_15983),hAPP(c_COMBB(tc_List_Olist(U_15983),tc_fun(U_15981,tc_prod(tc_List_Olist(U_15983),U_15981)),tc_List_Olist(U_15983)),c_Product__Type_OPair(tc_List_Olist(U_15983),U_15981))),c_List_Olist_OCons(U_15983))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15981,U_15983,U_15985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15979),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15985,U_15987))
    | U_15979 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3980_3]) ).

fof(f_3981_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_3981_2,plain,
    ! [U_15991,U_15990,U_15989,U_15988] : c_List_Osublist(U_15988,hAPP(hAPP(c_List_Olist_OCons(U_15988),U_15989),U_15990),U_15991) = hAPP(hAPP(c_List_Oappend(U_15988),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_15988)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15991)),hAPP(hAPP(c_List_Olist_OCons(U_15988),U_15989),c_List_Olist_ONil(U_15988))),c_List_Olist_ONil(U_15988))),c_List_Osublist(U_15988,U_15990,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_15991)))),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

cnf(f_3981_3,plain,
    c_List_Osublist(U_15988,hAPP(hAPP(c_List_Olist_OCons(U_15988),U_15989),U_15990),U_15991) = hAPP(hAPP(c_List_Oappend(U_15988),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_15988)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15991)),hAPP(hAPP(c_List_Olist_OCons(U_15988),U_15989),c_List_Olist_ONil(U_15988))),c_List_Olist_ONil(U_15988))),c_List_Osublist(U_15988,U_15990,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_15991)))),
    inference(clausify,[status(thm)],[f_3981_2]) ).

fof(f_3982_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_3982_2,plain,
    ! [U_15996,U_15995,U_15994,U_15993,U_15992] :
      ( ( hAPP(hAPP(c_List_Oappend(U_15992),U_15993),hAPP(hAPP(c_List_Olist_OCons(U_15992),U_15994),c_List_Olist_ONil(U_15992))) = hAPP(hAPP(c_List_Oappend(U_15992),U_15995),hAPP(hAPP(c_List_Olist_OCons(U_15992),U_15996),c_List_Olist_ONil(U_15992)))
        | U_15994 != U_15996
        | U_15993 != U_15995 )
      & ( ( U_15994 = U_15996
          & U_15993 = U_15995 )
        | hAPP(hAPP(c_List_Oappend(U_15992),U_15993),hAPP(hAPP(c_List_Olist_OCons(U_15992),U_15994),c_List_Olist_ONil(U_15992))) != hAPP(hAPP(c_List_Oappend(U_15992),U_15995),hAPP(hAPP(c_List_Olist_OCons(U_15992),U_15996),c_List_Olist_ONil(U_15992))) ) ),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

fof(f_3982_3,plain,
    ( ! [U_16006,U_16004,U_16002,U_16000] :
        ( ! [U_15998] : hAPP(hAPP(c_List_Oappend(U_15998),U_16000),hAPP(hAPP(c_List_Olist_OCons(U_15998),U_16002),c_List_Olist_ONil(U_15998))) = hAPP(hAPP(c_List_Oappend(U_15998),U_16004),hAPP(hAPP(c_List_Olist_OCons(U_15998),U_16006),c_List_Olist_ONil(U_15998)))
        | U_16002 != U_16006
        | U_16000 != U_16004 )
    & ! [U_16005,U_16003,U_16001,U_15999] :
        ( ! [U_15997] : hAPP(hAPP(c_List_Oappend(U_15997),U_15999),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16001),c_List_Olist_ONil(U_15997))) != hAPP(hAPP(c_List_Oappend(U_15997),U_16003),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16005),c_List_Olist_ONil(U_15997)))
        | ( U_16001 = U_16005
          & U_15999 = U_16003 ) ) ),
    inference(miniscope,[status(thm)],[f_3982_2]) ).

cnf(f_3982_4,plain,
    ( U_15999 = U_16003
    | hAPP(hAPP(c_List_Oappend(U_15997),U_15999),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16001),c_List_Olist_ONil(U_15997))) != hAPP(hAPP(c_List_Oappend(U_15997),U_16003),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16005),c_List_Olist_ONil(U_15997))) ),
    inference(clausify,[status(thm)],[f_3982_3]) ).

cnf(f_3982_5,plain,
    ( U_16001 = U_16005
    | hAPP(hAPP(c_List_Oappend(U_15997),U_15999),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16001),c_List_Olist_ONil(U_15997))) != hAPP(hAPP(c_List_Oappend(U_15997),U_16003),hAPP(hAPP(c_List_Olist_OCons(U_15997),U_16005),c_List_Olist_ONil(U_15997))) ),
    inference(clausify,[status(thm)],[f_3982_3]) ).

cnf(f_3982_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_15998),U_16000),hAPP(hAPP(c_List_Olist_OCons(U_15998),U_16002),c_List_Olist_ONil(U_15998))) = hAPP(hAPP(c_List_Oappend(U_15998),U_16004),hAPP(hAPP(c_List_Olist_OCons(U_15998),U_16006),c_List_Olist_ONil(U_15998)))
    | U_16002 != U_16006
    | U_16000 != U_16004 ),
    inference(clausify,[status(thm)],[f_3982_3]) ).

fof(f_3983_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_3983_2,plain,
    ! [U_16013,U_16012,U_16011,U_16010,U_16009] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16011) = hAPP(hAPP(c_List_Oappend(U_16009),U_16012),U_16013)
        | ( ! [U_16008] :
              ( U_16011 != hAPP(hAPP(c_List_Oappend(U_16009),U_16008),U_16013)
              | hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16008) != U_16012 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16011) != U_16013
            | U_16012 != c_List_Olist_ONil(U_16009) ) ) )
      & ( ? [U_16007] :
            ( U_16011 = hAPP(hAPP(c_List_Oappend(U_16009),U_16007),U_16013)
            & hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16007) = U_16012 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16011) = U_16013
          & U_16012 = c_List_Olist_ONil(U_16009) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16009),U_16010),U_16011) != hAPP(hAPP(c_List_Oappend(U_16009),U_16012),U_16013) ) ),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

fof(f_3983_3,plain,
    ( ! [U_16023,U_16021,U_16019,U_16017,U_16015] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) = hAPP(hAPP(c_List_Oappend(U_16015),U_16021),U_16023)
        | ( ! [U_16008] :
              ( U_16019 != hAPP(hAPP(c_List_Oappend(U_16015),U_16008),U_16023)
              | hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16008) != U_16021 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) != U_16023
            | U_16021 != c_List_Olist_ONil(U_16015) ) ) )
    & ! [U_16022,U_16020,U_16018,U_16016,U_16014] :
        ( ? [U_16007] :
            ( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),U_16007),U_16022)
            & hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16007) = U_16020 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) = U_16022
          & U_16020 = c_List_Olist_ONil(U_16014) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ) ),
    inference(miniscope,[status(thm)],[f_3983_2]) ).

fof(f_3983_4,plain,
    ( ! [U_16023,U_16021,U_16019,U_16017,U_16015] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) = hAPP(hAPP(c_List_Oappend(U_16015),U_16021),U_16023)
        | ( ! [U_16008] :
              ( U_16019 != hAPP(hAPP(c_List_Oappend(U_16015),U_16008),U_16023)
              | hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16008) != U_16021 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) != U_16023
            | U_16021 != c_List_Olist_ONil(U_16015) ) ) )
    & ! [U_16022,U_16020,U_16018,U_16016,U_16014] :
        ( ( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)),U_16022)
          & hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)) = U_16020 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) = U_16022
          & U_16020 = c_List_Olist_ONil(U_16014) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_16007,sK413(U_16022,U_16020,U_16018,U_16016,U_16014))],[f_3983_3]) ).

cnf(f_3983_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)) = U_16020
    | U_16020 = c_List_Olist_ONil(U_16014)
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_6,plain,
    ( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)),U_16022)
    | U_16020 = c_List_Olist_ONil(U_16014)
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)) = U_16020
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) = U_16022
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_8,plain,
    ( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),sK413(U_16022,U_16020,U_16018,U_16016,U_16014)),U_16022)
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) = U_16022
    | hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),U_16018) != hAPP(hAPP(c_List_Oappend(U_16014),U_16020),U_16022) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) != U_16023
    | U_16021 != c_List_Olist_ONil(U_16015)
    | hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) = hAPP(hAPP(c_List_Oappend(U_16015),U_16021),U_16023) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_10,plain,
    ( U_16019 != hAPP(hAPP(c_List_Oappend(U_16015),U_16008),U_16023)
    | hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16008) != U_16021
    | hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16017),U_16019) = hAPP(hAPP(c_List_Oappend(U_16015),U_16021),U_16023) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

fof(f_3984_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_3984_2,plain,
    ! [U_16030,U_16029,U_16028,U_16027,U_16026] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16026),U_16027),U_16028) = hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16030)
        | ( ! [U_16025] :
              ( hAPP(hAPP(c_List_Oappend(U_16026),U_16025),U_16028) != U_16030
              | U_16027 != hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16025) )
          & ( U_16028 != hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16030)
            | U_16027 != c_List_Olist_ONil(U_16026) ) ) )
      & ( ? [U_16024] :
            ( hAPP(hAPP(c_List_Oappend(U_16026),U_16024),U_16028) = U_16030
            & U_16027 = hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16024) )
        | ( U_16028 = hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16030)
          & U_16027 = c_List_Olist_ONil(U_16026) )
        | hAPP(hAPP(c_List_Oappend(U_16026),U_16027),U_16028) != hAPP(hAPP(c_List_Olist_OCons(U_16026),U_16029),U_16030) ) ),
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

fof(f_3984_3,plain,
    ( ! [U_16040,U_16038,U_16036,U_16034,U_16032] :
        ( hAPP(hAPP(c_List_Oappend(U_16032),U_16034),U_16036) = hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040)
        | ( ! [U_16025] :
              ( hAPP(hAPP(c_List_Oappend(U_16032),U_16025),U_16036) != U_16040
              | U_16034 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16025) )
          & ( U_16036 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040)
            | U_16034 != c_List_Olist_ONil(U_16032) ) ) )
    & ! [U_16039,U_16037,U_16035,U_16033,U_16031] :
        ( ? [U_16024] :
            ( hAPP(hAPP(c_List_Oappend(U_16031),U_16024),U_16035) = U_16039
            & U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16024) )
        | ( U_16035 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039)
          & U_16033 = c_List_Olist_ONil(U_16031) )
        | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ) ),
    inference(miniscope,[status(thm)],[f_3984_2]) ).

fof(f_3984_4,plain,
    ( ! [U_16040,U_16038,U_16036,U_16034,U_16032] :
        ( hAPP(hAPP(c_List_Oappend(U_16032),U_16034),U_16036) = hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040)
        | ( ! [U_16025] :
              ( hAPP(hAPP(c_List_Oappend(U_16032),U_16025),U_16036) != U_16040
              | U_16034 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16025) )
          & ( U_16036 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040)
            | U_16034 != c_List_Olist_ONil(U_16032) ) ) )
    & ! [U_16039,U_16037,U_16035,U_16033,U_16031] :
        ( ( hAPP(hAPP(c_List_Oappend(U_16031),sK414(U_16039,U_16037,U_16035,U_16033,U_16031)),U_16035) = U_16039
          & U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),sK414(U_16039,U_16037,U_16035,U_16033,U_16031)) )
        | ( U_16035 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039)
          & U_16033 = c_List_Olist_ONil(U_16031) )
        | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_16024,sK414(U_16039,U_16037,U_16035,U_16033,U_16031))],[f_3984_3]) ).

cnf(f_3984_5,plain,
    ( U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),sK414(U_16039,U_16037,U_16035,U_16033,U_16031))
    | U_16033 = c_List_Olist_ONil(U_16031)
    | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16031),sK414(U_16039,U_16037,U_16035,U_16033,U_16031)),U_16035) = U_16039
    | U_16033 = c_List_Olist_ONil(U_16031)
    | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_7,plain,
    ( U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),sK414(U_16039,U_16037,U_16035,U_16033,U_16031))
    | U_16035 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039)
    | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16031),sK414(U_16039,U_16037,U_16035,U_16033,U_16031)),U_16035) = U_16039
    | U_16035 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039)
    | hAPP(hAPP(c_List_Oappend(U_16031),U_16033),U_16035) != hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),U_16039) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_9,plain,
    ( U_16036 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040)
    | U_16034 != c_List_Olist_ONil(U_16032)
    | hAPP(hAPP(c_List_Oappend(U_16032),U_16034),U_16036) = hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16032),U_16025),U_16036) != U_16040
    | U_16034 != hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16025)
    | hAPP(hAPP(c_List_Oappend(U_16032),U_16034),U_16036) = hAPP(hAPP(c_List_Olist_OCons(U_16032),U_16038),U_16040) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

fof(f_3985_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_3985_2,plain,
    ! [U_16046,U_16045,U_16044,U_16043,U_16042,U_16041] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_16041),U_16042),U_16045) = hAPP(hAPP(c_List_Oappend(U_16041),U_16044),U_16046)
      | U_16045 != hAPP(hAPP(c_List_Oappend(U_16041),U_16043),U_16046)
      | hAPP(hAPP(c_List_Olist_OCons(U_16041),U_16042),U_16043) != U_16044 ),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

cnf(f_3985_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16041),U_16042),U_16045) = hAPP(hAPP(c_List_Oappend(U_16041),U_16044),U_16046)
    | U_16045 != hAPP(hAPP(c_List_Oappend(U_16041),U_16043),U_16046)
    | hAPP(hAPP(c_List_Olist_OCons(U_16041),U_16042),U_16043) != U_16044 ),
    inference(clausify,[status(thm)],[f_3985_2]) ).

fof(f_3986_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_3986_2,plain,
    ! [U_16050,U_16049,U_16048,U_16047] : hAPP(hAPP(c_List_Oappend(U_16047),hAPP(hAPP(c_List_Olist_OCons(U_16047),U_16048),U_16049)),U_16050) = hAPP(hAPP(c_List_Olist_OCons(U_16047),U_16048),hAPP(hAPP(c_List_Oappend(U_16047),U_16049),U_16050)),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

cnf(f_3986_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16047),hAPP(hAPP(c_List_Olist_OCons(U_16047),U_16048),U_16049)),U_16050) = hAPP(hAPP(c_List_Olist_OCons(U_16047),U_16048),hAPP(hAPP(c_List_Oappend(U_16047),U_16049),U_16050)),
    inference(clausify,[status(thm)],[f_3986_2]) ).

fof(f_3987_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_3987_2,plain,
    ! [U_16054,U_16053,U_16052,U_16051] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),hAPP(hAPP(c_List_Oappend(U_16051),U_16052),U_16053)),c_List_Olists(U_16051,U_16054)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),U_16053),c_List_Olists(U_16051,U_16054)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),U_16052),c_List_Olists(U_16051,U_16054))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),U_16053),c_List_Olists(U_16051,U_16054)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),U_16052),c_List_Olists(U_16051,U_16054))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16051)),hAPP(hAPP(c_List_Oappend(U_16051),U_16052),U_16053)),c_List_Olists(U_16051,U_16054))) ) ),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

fof(f_3987_3,plain,
    ( ! [U_16062,U_16060,U_16058,U_16056] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),hAPP(hAPP(c_List_Oappend(U_16056),U_16058),U_16060)),c_List_Olists(U_16056,U_16062)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),U_16060),c_List_Olists(U_16056,U_16062)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),U_16058),c_List_Olists(U_16056,U_16062))) )
    & ! [U_16061,U_16059,U_16057,U_16055] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),U_16059),c_List_Olists(U_16055,U_16061)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),U_16057),c_List_Olists(U_16055,U_16061))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),hAPP(hAPP(c_List_Oappend(U_16055),U_16057),U_16059)),c_List_Olists(U_16055,U_16061))) ) ),
    inference(miniscope,[status(thm)],[f_3987_2]) ).

cnf(f_3987_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),U_16057),c_List_Olists(U_16055,U_16061)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),hAPP(hAPP(c_List_Oappend(U_16055),U_16057),U_16059)),c_List_Olists(U_16055,U_16061))) ),
    inference(clausify,[status(thm)],[f_3987_3]) ).

cnf(f_3987_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),U_16059),c_List_Olists(U_16055,U_16061)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16055)),hAPP(hAPP(c_List_Oappend(U_16055),U_16057),U_16059)),c_List_Olists(U_16055,U_16061))) ),
    inference(clausify,[status(thm)],[f_3987_3]) ).

cnf(f_3987_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),hAPP(hAPP(c_List_Oappend(U_16056),U_16058),U_16060)),c_List_Olists(U_16056,U_16062)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),U_16060),c_List_Olists(U_16056,U_16062)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16056)),U_16058),c_List_Olists(U_16056,U_16062))) ),
    inference(clausify,[status(thm)],[f_3987_3]) ).

fof(f_3988_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_3988_2,plain,
    ! [U_16066,U_16065,U_16064,U_16063] : hAPP(hAPP(c_List_Oappend(U_16063),hAPP(hAPP(c_List_Oappend(U_16063),U_16064),U_16065)),U_16066) = hAPP(hAPP(c_List_Oappend(U_16063),U_16064),hAPP(hAPP(c_List_Oappend(U_16063),U_16065),U_16066)),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

cnf(f_3988_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16063),hAPP(hAPP(c_List_Oappend(U_16063),U_16064),U_16065)),U_16066) = hAPP(hAPP(c_List_Oappend(U_16063),U_16064),hAPP(hAPP(c_List_Oappend(U_16063),U_16065),U_16066)),
    inference(clausify,[status(thm)],[f_3988_2]) ).

fof(f_3989_1,plain,
    ! [V_ts_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_ts_2)
        | ! [B_us] :
            ( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_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_ts_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_ts_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_ts_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_ts_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).

fof(f_3989_2,plain,
    ! [U_16073,U_16072,U_16071,U_16070,U_16069] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16069),U_16070),U_16071) = hAPP(hAPP(c_List_Oappend(U_16069),U_16072),U_16073)
        | ! [U_16068] :
            ( ( U_16071 != hAPP(hAPP(c_List_Oappend(U_16069),U_16068),U_16073)
              | hAPP(hAPP(c_List_Oappend(U_16069),U_16070),U_16068) != U_16072 )
            & ( hAPP(hAPP(c_List_Oappend(U_16069),U_16068),U_16071) != U_16073
              | U_16070 != hAPP(hAPP(c_List_Oappend(U_16069),U_16072),U_16068) ) ) )
      & ( ? [U_16067] :
            ( ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16069),U_16067),U_16073)
              & hAPP(hAPP(c_List_Oappend(U_16069),U_16070),U_16067) = U_16072 )
            | ( hAPP(hAPP(c_List_Oappend(U_16069),U_16067),U_16071) = U_16073
              & U_16070 = hAPP(hAPP(c_List_Oappend(U_16069),U_16072),U_16067) ) )
        | hAPP(hAPP(c_List_Oappend(U_16069),U_16070),U_16071) != hAPP(hAPP(c_List_Oappend(U_16069),U_16072),U_16073) ) ),
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

fof(f_3989_3,plain,
    ( ! [U_16087,U_16085,U_16083,U_16081,U_16079] :
        ( hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16083) = hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16087)
        | ( ! [U_16077] :
              ( U_16083 != hAPP(hAPP(c_List_Oappend(U_16079),U_16077),U_16087)
              | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16077) != U_16085 )
          & ! [U_16076] :
              ( hAPP(hAPP(c_List_Oappend(U_16079),U_16076),U_16083) != U_16087
              | U_16081 != hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16076) ) ) )
    & ! [U_16086,U_16084,U_16082,U_16080,U_16078] :
        ( ? [U_16075] :
            ( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),U_16075),U_16086)
            & hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16075) = U_16084 )
        | ? [U_16074] :
            ( hAPP(hAPP(c_List_Oappend(U_16078),U_16074),U_16082) = U_16086
            & U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16074) )
        | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ) ),
    inference(miniscope,[status(thm)],[f_3989_2]) ).

fof(f_3989_4,plain,
    ( ! [U_16087,U_16085,U_16083,U_16081,U_16079] :
        ( hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16083) = hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16087)
        | ( ! [U_16077] :
              ( U_16083 != hAPP(hAPP(c_List_Oappend(U_16079),U_16077),U_16087)
              | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16077) != U_16085 )
          & ! [U_16076] :
              ( hAPP(hAPP(c_List_Oappend(U_16079),U_16076),U_16083) != U_16087
              | U_16081 != hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16076) ) ) )
    & ! [U_16086,U_16084,U_16082,U_16080,U_16078] :
        ( ? [U_16075] :
            ( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),U_16075),U_16086)
            & hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16075) = U_16084 )
        | ( hAPP(hAPP(c_List_Oappend(U_16078),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16082) = U_16086
          & U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)) )
        | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_16074,sK415(U_16086,U_16084,U_16082,U_16080,U_16078))],[f_3989_3]) ).

fof(f_3989_5,plain,
    ( ! [U_16087,U_16085,U_16083,U_16081,U_16079] :
        ( hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16083) = hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16087)
        | ( ! [U_16077] :
              ( U_16083 != hAPP(hAPP(c_List_Oappend(U_16079),U_16077),U_16087)
              | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16077) != U_16085 )
          & ! [U_16076] :
              ( hAPP(hAPP(c_List_Oappend(U_16079),U_16076),U_16083) != U_16087
              | U_16081 != hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16076) ) ) )
    & ! [U_16086,U_16084,U_16082,U_16080,U_16078] :
        ( ( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
          & hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084 )
        | ( hAPP(hAPP(c_List_Oappend(U_16078),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16082) = U_16086
          & U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)) )
        | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_16075,sK416(U_16086,U_16084,U_16082,U_16080,U_16078))],[f_3989_4]) ).

cnf(f_3989_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084
    | U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK415(U_16086,U_16084,U_16082,U_16080,U_16078))
    | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

cnf(f_3989_7,plain,
    ( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
    | U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK415(U_16086,U_16084,U_16082,U_16080,U_16078))
    | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

cnf(f_3989_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084
    | hAPP(hAPP(c_List_Oappend(U_16078),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16082) = U_16086
    | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

cnf(f_3989_9,plain,
    ( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),sK416(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
    | hAPP(hAPP(c_List_Oappend(U_16078),sK415(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16082) = U_16086
    | hAPP(hAPP(c_List_Oappend(U_16078),U_16080),U_16082) != hAPP(hAPP(c_List_Oappend(U_16078),U_16084),U_16086) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

cnf(f_3989_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16079),U_16076),U_16083) != U_16087
    | U_16081 != hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16076)
    | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16083) = hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16087) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

cnf(f_3989_11,plain,
    ( U_16083 != hAPP(hAPP(c_List_Oappend(U_16079),U_16077),U_16087)
    | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16077) != U_16085
    | hAPP(hAPP(c_List_Oappend(U_16079),U_16081),U_16083) = hAPP(hAPP(c_List_Oappend(U_16079),U_16085),U_16087) ),
    inference(clausify,[status(thm)],[f_3989_5]) ).

fof(f_3990_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_3990_2,plain,
    ! [U_16091,U_16090,U_16089,U_16088] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16088),U_16089),U_16090) = hAPP(hAPP(c_List_Oappend(U_16088),U_16089),U_16091)
        | U_16090 != U_16091 )
      & ( U_16090 = U_16091
        | hAPP(hAPP(c_List_Oappend(U_16088),U_16089),U_16090) != hAPP(hAPP(c_List_Oappend(U_16088),U_16089),U_16091) ) ),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

fof(f_3990_3,plain,
    ( ! [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_16095),U_16099)
        | U_16097 != U_16099 )
    & ! [U_16098,U_16096] :
        ( ! [U_16094,U_16092] : hAPP(hAPP(c_List_Oappend(U_16092),U_16094),U_16096) != hAPP(hAPP(c_List_Oappend(U_16092),U_16094),U_16098)
        | U_16096 = U_16098 ) ),
    inference(miniscope,[status(thm)],[f_3990_2]) ).

cnf(f_3990_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16092),U_16094),U_16096) != hAPP(hAPP(c_List_Oappend(U_16092),U_16094),U_16098)
    | U_16096 = U_16098 ),
    inference(clausify,[status(thm)],[f_3990_3]) ).

cnf(f_3990_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16093),U_16095),U_16097) = hAPP(hAPP(c_List_Oappend(U_16093),U_16095),U_16099)
    | U_16097 != U_16099 ),
    inference(clausify,[status(thm)],[f_3990_3]) ).

fof(f_3991_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_3991_2,plain,
    ! [U_16103,U_16102,U_16101,U_16100] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16100),U_16101),U_16102) = hAPP(hAPP(c_List_Oappend(U_16100),U_16103),U_16102)
        | U_16101 != U_16103 )
      & ( U_16101 = U_16103
        | hAPP(hAPP(c_List_Oappend(U_16100),U_16101),U_16102) != hAPP(hAPP(c_List_Oappend(U_16100),U_16103),U_16102) ) ),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

fof(f_3991_3,plain,
    ( ! [U_16111,U_16109,U_16107] :
        ( ! [U_16105] : hAPP(hAPP(c_List_Oappend(U_16105),U_16107),U_16109) = hAPP(hAPP(c_List_Oappend(U_16105),U_16111),U_16109)
        | U_16107 != U_16111 )
    & ! [U_16110,U_16108,U_16106] :
        ( ! [U_16104] : hAPP(hAPP(c_List_Oappend(U_16104),U_16106),U_16108) != hAPP(hAPP(c_List_Oappend(U_16104),U_16110),U_16108)
        | U_16106 = U_16110 ) ),
    inference(miniscope,[status(thm)],[f_3991_2]) ).

cnf(f_3991_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16104),U_16106),U_16108) != hAPP(hAPP(c_List_Oappend(U_16104),U_16110),U_16108)
    | U_16106 = U_16110 ),
    inference(clausify,[status(thm)],[f_3991_3]) ).

cnf(f_3991_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16105),U_16107),U_16109) = hAPP(hAPP(c_List_Oappend(U_16105),U_16111),U_16109)
    | U_16107 != U_16111 ),
    inference(clausify,[status(thm)],[f_3991_3]) ).

fof(f_3992_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_3992_2,plain,
    ! [U_16117,U_16116,U_16115,U_16114,U_16113,U_16112] :
      ( hAPP(hAPP(c_List_Oappend(U_16112),U_16113),U_16116) = hAPP(hAPP(c_List_Oappend(U_16112),U_16115),U_16117)
      | U_16116 != hAPP(hAPP(c_List_Oappend(U_16112),U_16114),U_16117)
      | hAPP(hAPP(c_List_Oappend(U_16112),U_16113),U_16114) != U_16115 ),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

cnf(f_3992_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16112),U_16113),U_16116) = hAPP(hAPP(c_List_Oappend(U_16112),U_16115),U_16117)
    | U_16116 != hAPP(hAPP(c_List_Oappend(U_16112),U_16114),U_16117)
    | hAPP(hAPP(c_List_Oappend(U_16112),U_16113),U_16114) != U_16115 ),
    inference(clausify,[status(thm)],[f_3992_2]) ).

fof(f_3993_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_3993_2,plain,
    ! [U_16120,U_16119,U_16118] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),hAPP(hAPP(c_List_Oappend(U_16118),U_16119),U_16120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16118),hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),U_16119)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),U_16120))
      | ~ class_Groups_Omonoid__add(U_16118) ),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

cnf(f_3993_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),hAPP(hAPP(c_List_Oappend(U_16118),U_16119),U_16120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16118),hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),U_16119)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16118),U_16120))
    | ~ class_Groups_Omonoid__add(U_16118) ),
    inference(clausify,[status(thm)],[f_3993_2]) ).

fof(f_3994_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_3994_2,plain,
    ! [U_16123,U_16122,U_16121] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),hAPP(hAPP(c_List_Oappend(U_16121),U_16122),U_16123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),U_16122)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),U_16123)),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

cnf(f_3994_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),hAPP(hAPP(c_List_Oappend(U_16121),U_16122),U_16123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),U_16122)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16121)),U_16123)),
    inference(clausify,[status(thm)],[f_3994_2]) ).

fof(f_3995_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_3995_2,plain,
    ! [U_16129,U_16128,U_16127,U_16126,U_16125,U_16124] :
      ( hAPP(hAPP(c_List_Ozip(U_16124,U_16126),hAPP(hAPP(c_List_Oappend(U_16124),U_16125),U_16128)),hAPP(hAPP(c_List_Oappend(U_16126),U_16127),U_16129)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16124,U_16126)),hAPP(hAPP(c_List_Ozip(U_16124,U_16126),U_16125),U_16127)),hAPP(hAPP(c_List_Ozip(U_16124,U_16126),U_16128),U_16129))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16124)),U_16128) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16126)),U_16129)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16124)),U_16125) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16126)),U_16127) ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

cnf(f_3995_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_16124,U_16126),hAPP(hAPP(c_List_Oappend(U_16124),U_16125),U_16128)),hAPP(hAPP(c_List_Oappend(U_16126),U_16127),U_16129)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16124,U_16126)),hAPP(hAPP(c_List_Ozip(U_16124,U_16126),U_16125),U_16127)),hAPP(hAPP(c_List_Ozip(U_16124,U_16126),U_16128),U_16129))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16124)),U_16128) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16126)),U_16129)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16124)),U_16125) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16126)),U_16127) ),
    inference(clausify,[status(thm)],[f_3995_2]) ).

fof(f_3996_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_3996_2,plain,
    ! [U_16132,U_16131,U_16130] : hAPP(c_List_Oset(U_16130),hAPP(hAPP(c_List_Oappend(U_16130),U_16131),U_16132)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16130,tc_HOL_Obool)),hAPP(c_List_Oset(U_16130),U_16131)),hAPP(c_List_Oset(U_16130),U_16132)),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

cnf(f_3996_3,plain,
    hAPP(c_List_Oset(U_16130),hAPP(hAPP(c_List_Oappend(U_16130),U_16131),U_16132)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16130,tc_HOL_Obool)),hAPP(c_List_Oset(U_16130),U_16131)),hAPP(c_List_Oset(U_16130),U_16132)),
    inference(clausify,[status(thm)],[f_3996_2]) ).

fof(f_3997_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_3997_2,plain,
    ! [U_16135,U_16134,U_16133] :
      ( U_16133 = hAPP(hAPP(c_List_Oappend(U_16135),c_List_Olist_ONil(U_16135)),U_16134)
      | U_16133 != U_16134 ),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

cnf(f_3997_3,plain,
    ( U_16133 = hAPP(hAPP(c_List_Oappend(U_16135),c_List_Olist_ONil(U_16135)),U_16134)
    | U_16133 != U_16134 ),
    inference(clausify,[status(thm)],[f_3997_2]) ).

fof(f_3998_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_3998_2,plain,
    ! [U_16138,U_16137,U_16136] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16136),U_16137),U_16138) = U_16138
        | U_16137 != c_List_Olist_ONil(U_16136) )
      & ( U_16137 = c_List_Olist_ONil(U_16136)
        | hAPP(hAPP(c_List_Oappend(U_16136),U_16137),U_16138) != U_16138 ) ),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

fof(f_3998_3,plain,
    ( ! [U_16144,U_16142,U_16140] :
        ( hAPP(hAPP(c_List_Oappend(U_16140),U_16142),U_16144) = U_16144
        | U_16142 != c_List_Olist_ONil(U_16140) )
    & ! [U_16143,U_16141,U_16139] :
        ( U_16141 = c_List_Olist_ONil(U_16139)
        | hAPP(hAPP(c_List_Oappend(U_16139),U_16141),U_16143) != U_16143 ) ),
    inference(miniscope,[status(thm)],[f_3998_2]) ).

cnf(f_3998_4,plain,
    ( U_16141 = c_List_Olist_ONil(U_16139)
    | hAPP(hAPP(c_List_Oappend(U_16139),U_16141),U_16143) != U_16143 ),
    inference(clausify,[status(thm)],[f_3998_3]) ).

cnf(f_3998_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16140),U_16142),U_16144) = U_16144
    | U_16142 != c_List_Olist_ONil(U_16140) ),
    inference(clausify,[status(thm)],[f_3998_3]) ).

fof(f_3999_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_3999_2,plain,
    ! [U_16147,U_16146,U_16145] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16145),U_16146),U_16147) = U_16146
        | U_16147 != c_List_Olist_ONil(U_16145) )
      & ( U_16147 = c_List_Olist_ONil(U_16145)
        | hAPP(hAPP(c_List_Oappend(U_16145),U_16146),U_16147) != U_16146 ) ),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

fof(f_3999_3,plain,
    ( ! [U_16153,U_16151,U_16149] :
        ( hAPP(hAPP(c_List_Oappend(U_16149),U_16151),U_16153) = U_16151
        | U_16153 != c_List_Olist_ONil(U_16149) )
    & ! [U_16152,U_16150,U_16148] :
        ( U_16152 = c_List_Olist_ONil(U_16148)
        | hAPP(hAPP(c_List_Oappend(U_16148),U_16150),U_16152) != U_16150 ) ),
    inference(miniscope,[status(thm)],[f_3999_2]) ).

cnf(f_3999_4,plain,
    ( U_16152 = c_List_Olist_ONil(U_16148)
    | hAPP(hAPP(c_List_Oappend(U_16148),U_16150),U_16152) != U_16150 ),
    inference(clausify,[status(thm)],[f_3999_3]) ).

cnf(f_3999_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16149),U_16151),U_16153) = U_16151
    | U_16153 != c_List_Olist_ONil(U_16149) ),
    inference(clausify,[status(thm)],[f_3999_3]) ).

fof(f_4000_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_4000_2,plain,
    ! [U_16156,U_16155,U_16154] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16154),U_16155),U_16156) = c_List_Olist_ONil(U_16154)
        | U_16156 != c_List_Olist_ONil(U_16154)
        | U_16155 != c_List_Olist_ONil(U_16154) )
      & ( ( U_16156 = c_List_Olist_ONil(U_16154)
          & U_16155 = c_List_Olist_ONil(U_16154) )
        | hAPP(hAPP(c_List_Oappend(U_16154),U_16155),U_16156) != c_List_Olist_ONil(U_16154) ) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ( ! [U_16162,U_16160,U_16158] :
        ( hAPP(hAPP(c_List_Oappend(U_16158),U_16160),U_16162) = c_List_Olist_ONil(U_16158)
        | U_16162 != c_List_Olist_ONil(U_16158)
        | U_16160 != c_List_Olist_ONil(U_16158) )
    & ! [U_16161,U_16159,U_16157] :
        ( ( U_16161 = c_List_Olist_ONil(U_16157)
          & U_16159 = c_List_Olist_ONil(U_16157) )
        | hAPP(hAPP(c_List_Oappend(U_16157),U_16159),U_16161) != c_List_Olist_ONil(U_16157) ) ),
    inference(miniscope,[status(thm)],[f_4000_2]) ).

cnf(f_4000_4,plain,
    ( U_16159 = c_List_Olist_ONil(U_16157)
    | hAPP(hAPP(c_List_Oappend(U_16157),U_16159),U_16161) != c_List_Olist_ONil(U_16157) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

cnf(f_4000_5,plain,
    ( U_16161 = c_List_Olist_ONil(U_16157)
    | hAPP(hAPP(c_List_Oappend(U_16157),U_16159),U_16161) != c_List_Olist_ONil(U_16157) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

cnf(f_4000_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16158),U_16160),U_16162) = c_List_Olist_ONil(U_16158)
    | U_16162 != c_List_Olist_ONil(U_16158)
    | U_16160 != c_List_Olist_ONil(U_16158) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

fof(f_4001_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_4001_2,plain,
    ! [U_16165,U_16164,U_16163] :
      ( ( U_16163 = hAPP(hAPP(c_List_Oappend(U_16164),U_16165),U_16163)
        | U_16165 != c_List_Olist_ONil(U_16164) )
      & ( U_16165 = c_List_Olist_ONil(U_16164)
        | U_16163 != hAPP(hAPP(c_List_Oappend(U_16164),U_16165),U_16163) ) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

fof(f_4001_3,plain,
    ( ! [U_16171,U_16169] :
        ( ! [U_16167] : U_16167 = hAPP(hAPP(c_List_Oappend(U_16169),U_16171),U_16167)
        | U_16171 != c_List_Olist_ONil(U_16169) )
    & ! [U_16170,U_16168] :
        ( ! [U_16166] : U_16166 != hAPP(hAPP(c_List_Oappend(U_16168),U_16170),U_16166)
        | U_16170 = c_List_Olist_ONil(U_16168) ) ),
    inference(miniscope,[status(thm)],[f_4001_2]) ).

cnf(f_4001_4,plain,
    ( U_16166 != hAPP(hAPP(c_List_Oappend(U_16168),U_16170),U_16166)
    | U_16170 = c_List_Olist_ONil(U_16168) ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

cnf(f_4001_5,plain,
    ( U_16167 = hAPP(hAPP(c_List_Oappend(U_16169),U_16171),U_16167)
    | U_16171 != c_List_Olist_ONil(U_16169) ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

fof(f_4002_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_4002_2,plain,
    ! [U_16174,U_16173,U_16172] :
      ( ( U_16172 = hAPP(hAPP(c_List_Oappend(U_16173),U_16172),U_16174)
        | U_16174 != c_List_Olist_ONil(U_16173) )
      & ( U_16174 = c_List_Olist_ONil(U_16173)
        | U_16172 != hAPP(hAPP(c_List_Oappend(U_16173),U_16172),U_16174) ) ),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

fof(f_4002_3,plain,
    ( ! [U_16180,U_16178] :
        ( ! [U_16176] : U_16176 = hAPP(hAPP(c_List_Oappend(U_16178),U_16176),U_16180)
        | U_16180 != c_List_Olist_ONil(U_16178) )
    & ! [U_16179,U_16177] :
        ( ! [U_16175] : U_16175 != hAPP(hAPP(c_List_Oappend(U_16177),U_16175),U_16179)
        | U_16179 = c_List_Olist_ONil(U_16177) ) ),
    inference(miniscope,[status(thm)],[f_4002_2]) ).

cnf(f_4002_4,plain,
    ( U_16175 != hAPP(hAPP(c_List_Oappend(U_16177),U_16175),U_16179)
    | U_16179 = c_List_Olist_ONil(U_16177) ),
    inference(clausify,[status(thm)],[f_4002_3]) ).

cnf(f_4002_5,plain,
    ( U_16176 = hAPP(hAPP(c_List_Oappend(U_16178),U_16176),U_16180)
    | U_16180 != c_List_Olist_ONil(U_16178) ),
    inference(clausify,[status(thm)],[f_4002_3]) ).

fof(f_4003_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_4003_2,plain,
    ! [U_16182,U_16181] : hAPP(hAPP(c_List_Oappend(U_16181),U_16182),c_List_Olist_ONil(U_16181)) = U_16182,
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

cnf(f_4003_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16181),U_16182),c_List_Olist_ONil(U_16181)) = U_16182,
    inference(clausify,[status(thm)],[f_4003_2]) ).

fof(f_4004_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_4004_2,plain,
    ! [U_16185,U_16184,U_16183] :
      ( ( c_List_Olist_ONil(U_16183) = hAPP(hAPP(c_List_Oappend(U_16183),U_16184),U_16185)
        | U_16185 != c_List_Olist_ONil(U_16183)
        | U_16184 != c_List_Olist_ONil(U_16183) )
      & ( ( U_16185 = c_List_Olist_ONil(U_16183)
          & U_16184 = c_List_Olist_ONil(U_16183) )
        | c_List_Olist_ONil(U_16183) != hAPP(hAPP(c_List_Oappend(U_16183),U_16184),U_16185) ) ),
    inference(variable_rename,[status(thm)],[f_4004_1]) ).

fof(f_4004_3,plain,
    ( ! [U_16191,U_16189,U_16187] :
        ( c_List_Olist_ONil(U_16187) = hAPP(hAPP(c_List_Oappend(U_16187),U_16189),U_16191)
        | U_16191 != c_List_Olist_ONil(U_16187)
        | U_16189 != c_List_Olist_ONil(U_16187) )
    & ! [U_16190,U_16188,U_16186] :
        ( ( U_16190 = c_List_Olist_ONil(U_16186)
          & U_16188 = c_List_Olist_ONil(U_16186) )
        | c_List_Olist_ONil(U_16186) != hAPP(hAPP(c_List_Oappend(U_16186),U_16188),U_16190) ) ),
    inference(miniscope,[status(thm)],[f_4004_2]) ).

cnf(f_4004_4,plain,
    ( U_16188 = c_List_Olist_ONil(U_16186)
    | c_List_Olist_ONil(U_16186) != hAPP(hAPP(c_List_Oappend(U_16186),U_16188),U_16190) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

cnf(f_4004_5,plain,
    ( U_16190 = c_List_Olist_ONil(U_16186)
    | c_List_Olist_ONil(U_16186) != hAPP(hAPP(c_List_Oappend(U_16186),U_16188),U_16190) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

cnf(f_4004_6,plain,
    ( c_List_Olist_ONil(U_16187) = hAPP(hAPP(c_List_Oappend(U_16187),U_16189),U_16191)
    | U_16191 != c_List_Olist_ONil(U_16187)
    | U_16189 != c_List_Olist_ONil(U_16187) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

fof(f_4005_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_4005_2,plain,
    ! [U_16193,U_16192] : hAPP(hAPP(c_List_Oappend(U_16192),c_List_Olist_ONil(U_16192)),U_16193) = U_16193,
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

cnf(f_4005_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16192),c_List_Olist_ONil(U_16192)),U_16193) = U_16193,
    inference(clausify,[status(thm)],[f_4005_2]) ).

fof(f_4006_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_4006_2,plain,
    ! [U_16196,U_16195,U_16194] :
      ( ( c_List_Obutlast(U_16195,hAPP(hAPP(c_List_Oappend(U_16195),U_16196),U_16194)) = hAPP(hAPP(c_List_Oappend(U_16195),U_16196),c_List_Obutlast(U_16195,U_16194))
        | U_16194 = c_List_Olist_ONil(U_16195) )
      & ( c_List_Obutlast(U_16195,hAPP(hAPP(c_List_Oappend(U_16195),U_16196),U_16194)) = c_List_Obutlast(U_16195,U_16196)
        | U_16194 != c_List_Olist_ONil(U_16195) ) ),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

fof(f_4006_3,plain,
    ( ! [U_16202,U_16200,U_16198] :
        ( c_List_Obutlast(U_16200,hAPP(hAPP(c_List_Oappend(U_16200),U_16202),U_16198)) = hAPP(hAPP(c_List_Oappend(U_16200),U_16202),c_List_Obutlast(U_16200,U_16198))
        | U_16198 = c_List_Olist_ONil(U_16200) )
    & ! [U_16201,U_16199,U_16197] :
        ( c_List_Obutlast(U_16199,hAPP(hAPP(c_List_Oappend(U_16199),U_16201),U_16197)) = c_List_Obutlast(U_16199,U_16201)
        | U_16197 != c_List_Olist_ONil(U_16199) ) ),
    inference(miniscope,[status(thm)],[f_4006_2]) ).

cnf(f_4006_4,plain,
    ( c_List_Obutlast(U_16199,hAPP(hAPP(c_List_Oappend(U_16199),U_16201),U_16197)) = c_List_Obutlast(U_16199,U_16201)
    | U_16197 != c_List_Olist_ONil(U_16199) ),
    inference(clausify,[status(thm)],[f_4006_3]) ).

cnf(f_4006_5,plain,
    ( c_List_Obutlast(U_16200,hAPP(hAPP(c_List_Oappend(U_16200),U_16202),U_16198)) = hAPP(hAPP(c_List_Oappend(U_16200),U_16202),c_List_Obutlast(U_16200,U_16198))
    | U_16198 = c_List_Olist_ONil(U_16200) ),
    inference(clausify,[status(thm)],[f_4006_3]) ).

fof(f_4007_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_4007_2,plain,
    ! [U_16206,U_16205,U_16204,U_16203] : hAPP(hAPP(c_List_Onth(U_16203),hAPP(hAPP(c_List_Oappend(U_16203),U_16204),hAPP(hAPP(c_List_Olist_OCons(U_16203),U_16205),U_16206))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16203)),U_16204)) = U_16205,
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

cnf(f_4007_3,plain,
    hAPP(hAPP(c_List_Onth(U_16203),hAPP(hAPP(c_List_Oappend(U_16203),U_16204),hAPP(hAPP(c_List_Olist_OCons(U_16203),U_16205),U_16206))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16203)),U_16204)) = U_16205,
    inference(clausify,[status(thm)],[f_4007_2]) ).

fof(f_4008_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_4008_2,plain,
    ! [U_16210,U_16209,U_16208,U_16207] : hAPP(hAPP(c_List_Onth(U_16207),hAPP(hAPP(c_List_Oappend(U_16207),U_16208),U_16209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16207)),U_16208)),U_16210)) = hAPP(hAPP(c_List_Onth(U_16207),U_16209),U_16210),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

cnf(f_4008_3,plain,
    hAPP(hAPP(c_List_Onth(U_16207),hAPP(hAPP(c_List_Oappend(U_16207),U_16208),U_16209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16207)),U_16208)),U_16210)) = hAPP(hAPP(c_List_Onth(U_16207),U_16209),U_16210),
    inference(clausify,[status(thm)],[f_4008_2]) ).

fof(f_4009_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_4009_2,plain,
    ! [U_16214,U_16213,U_16212,U_16211] : hAPP(hAPP(c_List_Otake(U_16211),U_16212),hAPP(hAPP(c_List_Oappend(U_16211),U_16213),U_16214)) = hAPP(hAPP(c_List_Oappend(U_16211),hAPP(hAPP(c_List_Otake(U_16211),U_16212),U_16213)),hAPP(hAPP(c_List_Otake(U_16211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16211)),U_16213))),U_16214)),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

cnf(f_4009_3,plain,
    hAPP(hAPP(c_List_Otake(U_16211),U_16212),hAPP(hAPP(c_List_Oappend(U_16211),U_16213),U_16214)) = hAPP(hAPP(c_List_Oappend(U_16211),hAPP(hAPP(c_List_Otake(U_16211),U_16212),U_16213)),hAPP(hAPP(c_List_Otake(U_16211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16211)),U_16213))),U_16214)),
    inference(clausify,[status(thm)],[f_4009_2]) ).

fof(f_4010_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_4010_2,plain,
    ! [U_16219,U_16218,U_16217,U_16216,U_16215] :
      ( hAPP(hAPP(c_List_Olist__update(U_16216,hAPP(hAPP(c_List_Oappend(U_16216),U_16217),U_16218)),U_16215),U_16219) = hAPP(hAPP(c_List_Oappend(U_16216),hAPP(hAPP(c_List_Olist__update(U_16216,U_16217),U_16215),U_16219)),U_16218)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16215),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16216)),U_16217))) ),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

cnf(f_4010_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16216,hAPP(hAPP(c_List_Oappend(U_16216),U_16217),U_16218)),U_16215),U_16219) = hAPP(hAPP(c_List_Oappend(U_16216),hAPP(hAPP(c_List_Olist__update(U_16216,U_16217),U_16215),U_16219)),U_16218)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16215),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16216)),U_16217))) ),
    inference(clausify,[status(thm)],[f_4010_2]) ).

fof(f_4011_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_4011_2,plain,
    ! [U_16224,U_16223,U_16222,U_16221,U_16220] : hAPP(hAPP(c_List_Olist__update(U_16220,hAPP(hAPP(c_List_Oappend(U_16220),U_16221),hAPP(hAPP(c_List_Olist_OCons(U_16220),U_16222),U_16223))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16220)),U_16221)),U_16224) = hAPP(hAPP(c_List_Oappend(U_16220),U_16221),hAPP(hAPP(c_List_Olist_OCons(U_16220),U_16224),U_16223)),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

cnf(f_4011_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16220,hAPP(hAPP(c_List_Oappend(U_16220),U_16221),hAPP(hAPP(c_List_Olist_OCons(U_16220),U_16222),U_16223))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16220)),U_16221)),U_16224) = hAPP(hAPP(c_List_Oappend(U_16220),U_16221),hAPP(hAPP(c_List_Olist_OCons(U_16220),U_16224),U_16223)),
    inference(clausify,[status(thm)],[f_4011_2]) ).

fof(f_4012_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_4012_2,plain,
    ! [U_16228,U_16227,U_16226,U_16225] :
      ( ( c_List_Oremove1(U_16225,U_16226,hAPP(hAPP(c_List_Oappend(U_16225),U_16227),U_16228)) = hAPP(hAPP(c_List_Oappend(U_16225),U_16227),c_List_Oremove1(U_16225,U_16226,U_16228))
        | hBOOL(hAPP(hAPP(c_member(U_16225),U_16226),hAPP(c_List_Oset(U_16225),U_16227))) )
      & ( c_List_Oremove1(U_16225,U_16226,hAPP(hAPP(c_List_Oappend(U_16225),U_16227),U_16228)) = hAPP(hAPP(c_List_Oappend(U_16225),c_List_Oremove1(U_16225,U_16226,U_16227)),U_16228)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16225),U_16226),hAPP(c_List_Oset(U_16225),U_16227))) ) ),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

fof(f_4012_3,plain,
    ( ! [U_16236,U_16234,U_16232,U_16230] :
        ( c_List_Oremove1(U_16230,U_16232,hAPP(hAPP(c_List_Oappend(U_16230),U_16234),U_16236)) = hAPP(hAPP(c_List_Oappend(U_16230),U_16234),c_List_Oremove1(U_16230,U_16232,U_16236))
        | hBOOL(hAPP(hAPP(c_member(U_16230),U_16232),hAPP(c_List_Oset(U_16230),U_16234))) )
    & ! [U_16235,U_16233,U_16231,U_16229] :
        ( c_List_Oremove1(U_16229,U_16231,hAPP(hAPP(c_List_Oappend(U_16229),U_16233),U_16235)) = hAPP(hAPP(c_List_Oappend(U_16229),c_List_Oremove1(U_16229,U_16231,U_16233)),U_16235)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16229),U_16231),hAPP(c_List_Oset(U_16229),U_16233))) ) ),
    inference(miniscope,[status(thm)],[f_4012_2]) ).

cnf(f_4012_4,plain,
    ( c_List_Oremove1(U_16229,U_16231,hAPP(hAPP(c_List_Oappend(U_16229),U_16233),U_16235)) = hAPP(hAPP(c_List_Oappend(U_16229),c_List_Oremove1(U_16229,U_16231,U_16233)),U_16235)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16229),U_16231),hAPP(c_List_Oset(U_16229),U_16233))) ),
    inference(clausify,[status(thm)],[f_4012_3]) ).

cnf(f_4012_5,plain,
    ( c_List_Oremove1(U_16230,U_16232,hAPP(hAPP(c_List_Oappend(U_16230),U_16234),U_16236)) = hAPP(hAPP(c_List_Oappend(U_16230),U_16234),c_List_Oremove1(U_16230,U_16232,U_16236))
    | hBOOL(hAPP(hAPP(c_member(U_16230),U_16232),hAPP(c_List_Oset(U_16230),U_16234))) ),
    inference(clausify,[status(thm)],[f_4012_3]) ).

fof(f_4013_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_4013_2,plain,
    ! [U_16240,U_16239,U_16238,U_16237] :
      ( hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,hAPP(hAPP(c_List_Oappend(U_16237),U_16239),U_16240)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,U_16240))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,U_16239)))) ) ),
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

cnf(f_4013_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,U_16239))))
    | hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,hAPP(hAPP(c_List_Oappend(U_16237),U_16239),U_16240))))) ),
    inference(clausify,[status(thm)],[f_4013_2]) ).

cnf(f_4013_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,U_16240))))
    | hBOOL(hAPP(hAPP(c_member(U_16237),U_16238),hAPP(c_List_Oset(U_16237),c_List_Obutlast(U_16237,hAPP(hAPP(c_List_Oappend(U_16237),U_16239),U_16240))))) ),
    inference(clausify,[status(thm)],[f_4013_2]) ).

fof(f_4014_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_4014_2,plain,
    ! [U_16243,U_16242,U_16241] : c_List_Obutlast(U_16241,hAPP(hAPP(c_List_Oappend(U_16241),U_16242),hAPP(hAPP(c_List_Olist_OCons(U_16241),U_16243),c_List_Olist_ONil(U_16241)))) = U_16242,
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

cnf(f_4014_3,plain,
    c_List_Obutlast(U_16241,hAPP(hAPP(c_List_Oappend(U_16241),U_16242),hAPP(hAPP(c_List_Olist_OCons(U_16241),U_16243),c_List_Olist_ONil(U_16241)))) = U_16242,
    inference(clausify,[status(thm)],[f_4014_2]) ).

fof(f_4015_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_4015_2,plain,
    ! [U_16249,U_16248,U_16247,U_16246,U_16245,U_16244] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),hAPP(hAPP(c_List_Oappend(U_16244),U_16245),U_16248)),hAPP(hAPP(c_List_Oappend(U_16244),U_16246),U_16249))),c_List_Olistrel1(U_16244,U_16247)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),U_16248),U_16249)),c_List_Olistrel1(U_16244,U_16247)))
          | U_16245 != U_16246 )
        & ( U_16248 != U_16249
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),U_16245),U_16246)),c_List_Olistrel1(U_16244,U_16247))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

cnf(f_4015_3,plain,
    ( U_16248 != U_16249
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),U_16245),U_16246)),c_List_Olistrel1(U_16244,U_16247)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),hAPP(hAPP(c_List_Oappend(U_16244),U_16245),U_16248)),hAPP(hAPP(c_List_Oappend(U_16244),U_16246),U_16249))),c_List_Olistrel1(U_16244,U_16247))) ),
    inference(clausify,[status(thm)],[f_4015_2]) ).

cnf(f_4015_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),U_16248),U_16249)),c_List_Olistrel1(U_16244,U_16247)))
    | U_16245 != U_16246
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16244),tc_List_Olist(U_16244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16244),tc_List_Olist(U_16244)),hAPP(hAPP(c_List_Oappend(U_16244),U_16245),U_16248)),hAPP(hAPP(c_List_Oappend(U_16244),U_16246),U_16249))),c_List_Olistrel1(U_16244,U_16247))) ),
    inference(clausify,[status(thm)],[f_4015_2]) ).

fof(f_4016_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_4016_2,plain,
    ! [U_16254,U_16253,U_16252,U_16251,U_16250] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16250),tc_List_Olist(U_16250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16250),tc_List_Olist(U_16250)),hAPP(hAPP(c_List_Oappend(U_16250),U_16254),U_16251)),hAPP(hAPP(c_List_Oappend(U_16250),U_16254),U_16252))),c_List_Olexord(U_16250,U_16253)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16250),tc_List_Olist(U_16250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16250),tc_List_Olist(U_16250)),U_16251),U_16252)),c_List_Olexord(U_16250,U_16253))) ),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

cnf(f_4016_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16250),tc_List_Olist(U_16250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16250),tc_List_Olist(U_16250)),hAPP(hAPP(c_List_Oappend(U_16250),U_16254),U_16251)),hAPP(hAPP(c_List_Oappend(U_16250),U_16254),U_16252))),c_List_Olexord(U_16250,U_16253)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16250),tc_List_Olist(U_16250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16250),tc_List_Olist(U_16250)),U_16251),U_16252)),c_List_Olexord(U_16250,U_16253))) ),
    inference(clausify,[status(thm)],[f_4016_2]) ).

fof(f_4017_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_4017_2,plain,
    ! [U_16257,U_16256,U_16255] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16255),hAPP(hAPP(c_List_Oappend(U_16255),U_16256),U_16257)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16255,tc_HOL_Obool)),hAPP(c_List_Oset(U_16255),U_16256)),hAPP(c_List_Oset(U_16255),U_16257)) != c_Orderings_Obot__class_Obot(tc_fun(U_16255,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),U_16257))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),U_16256)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16255,tc_HOL_Obool)),hAPP(c_List_Oset(U_16255),U_16256)),hAPP(c_List_Oset(U_16255),U_16257)) = c_Orderings_Obot__class_Obot(tc_fun(U_16255,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16255),U_16257))
          & hBOOL(hAPP(c_List_Odistinct(U_16255),U_16256)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16255),hAPP(hAPP(c_List_Oappend(U_16255),U_16256),U_16257))) ) ),
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

fof(f_4017_3,plain,
    ( ! [U_16263,U_16261,U_16259] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16259),hAPP(hAPP(c_List_Oappend(U_16259),U_16261),U_16263)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16259,tc_HOL_Obool)),hAPP(c_List_Oset(U_16259),U_16261)),hAPP(c_List_Oset(U_16259),U_16263)) != c_Orderings_Obot__class_Obot(tc_fun(U_16259,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16259),U_16263))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16259),U_16261)) )
    & ! [U_16262,U_16260,U_16258] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16258,tc_HOL_Obool)),hAPP(c_List_Oset(U_16258),U_16260)),hAPP(c_List_Oset(U_16258),U_16262)) = c_Orderings_Obot__class_Obot(tc_fun(U_16258,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16258),U_16262))
          & hBOOL(hAPP(c_List_Odistinct(U_16258),U_16260)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16258),hAPP(hAPP(c_List_Oappend(U_16258),U_16260),U_16262))) ) ),
    inference(miniscope,[status(thm)],[f_4017_2]) ).

cnf(f_4017_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16258),U_16260))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16258),hAPP(hAPP(c_List_Oappend(U_16258),U_16260),U_16262))) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

cnf(f_4017_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16258),U_16262))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16258),hAPP(hAPP(c_List_Oappend(U_16258),U_16260),U_16262))) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

cnf(f_4017_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16258,tc_HOL_Obool)),hAPP(c_List_Oset(U_16258),U_16260)),hAPP(c_List_Oset(U_16258),U_16262)) = c_Orderings_Obot__class_Obot(tc_fun(U_16258,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16258),hAPP(hAPP(c_List_Oappend(U_16258),U_16260),U_16262))) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

cnf(f_4017_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16259),hAPP(hAPP(c_List_Oappend(U_16259),U_16261),U_16263)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16259,tc_HOL_Obool)),hAPP(c_List_Oset(U_16259),U_16261)),hAPP(c_List_Oset(U_16259),U_16263)) != c_Orderings_Obot__class_Obot(tc_fun(U_16259,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16259),U_16263))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16259),U_16261)) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

fof(f_4018_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_4018_2,plain,
    ! [U_16267,U_16266,U_16265,U_16264] :
      ( ( hAPP(hAPP(c_List_Onth(U_16265),hAPP(hAPP(c_List_Oappend(U_16265),U_16266),U_16267)),U_16264) = hAPP(hAPP(c_List_Onth(U_16265),U_16267),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16264),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16264),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266))) )
      & ( hAPP(hAPP(c_List_Onth(U_16265),hAPP(hAPP(c_List_Oappend(U_16265),U_16266),U_16267)),U_16264) = hAPP(hAPP(c_List_Onth(U_16265),U_16266),U_16264)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16264),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16265)),U_16266))) ) ),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

fof(f_4018_3,plain,
    ( ! [U_16275,U_16273,U_16271,U_16269] :
        ( hAPP(hAPP(c_List_Onth(U_16271),hAPP(hAPP(c_List_Oappend(U_16271),U_16273),U_16275)),U_16269) = hAPP(hAPP(c_List_Onth(U_16271),U_16275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16271)),U_16273)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16271)),U_16273))) )
    & ! [U_16274,U_16272,U_16270,U_16268] :
        ( hAPP(hAPP(c_List_Onth(U_16270),hAPP(hAPP(c_List_Oappend(U_16270),U_16272),U_16274)),U_16268) = hAPP(hAPP(c_List_Onth(U_16270),U_16272),U_16268)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16268),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16270)),U_16272))) ) ),
    inference(miniscope,[status(thm)],[f_4018_2]) ).

cnf(f_4018_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_16270),hAPP(hAPP(c_List_Oappend(U_16270),U_16272),U_16274)),U_16268) = hAPP(hAPP(c_List_Onth(U_16270),U_16272),U_16268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16268),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16270)),U_16272))) ),
    inference(clausify,[status(thm)],[f_4018_3]) ).

cnf(f_4018_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_16271),hAPP(hAPP(c_List_Oappend(U_16271),U_16273),U_16275)),U_16269) = hAPP(hAPP(c_List_Onth(U_16271),U_16275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16271)),U_16273)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16269),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16271)),U_16273))) ),
    inference(clausify,[status(thm)],[f_4018_3]) ).

fof(f_4019_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_4019_2,plain,
    ! [U_16280,U_16279,U_16278,U_16277,U_16276] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_16277,hAPP(hAPP(c_List_Oappend(U_16277),U_16278),U_16279)),U_16276),U_16280) = hAPP(hAPP(c_List_Oappend(U_16277),U_16278),hAPP(hAPP(c_List_Olist__update(U_16277,U_16279),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16276),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16277)),U_16278))),U_16280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16276),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16277)),U_16278))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_16277,hAPP(hAPP(c_List_Oappend(U_16277),U_16278),U_16279)),U_16276),U_16280) = hAPP(hAPP(c_List_Oappend(U_16277),hAPP(hAPP(c_List_Olist__update(U_16277,U_16278),U_16276),U_16280)),U_16279)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16276),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16277)),U_16278))) ) ),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

fof(f_4019_3,plain,
    ( ! [U_16290,U_16288,U_16286,U_16284,U_16282] :
        ( hAPP(hAPP(c_List_Olist__update(U_16284,hAPP(hAPP(c_List_Oappend(U_16284),U_16286),U_16288)),U_16282),U_16290) = hAPP(hAPP(c_List_Oappend(U_16284),U_16286),hAPP(hAPP(c_List_Olist__update(U_16284,U_16288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16282),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16284)),U_16286))),U_16290))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16282),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16284)),U_16286))) )
    & ! [U_16289,U_16287,U_16285,U_16283,U_16281] :
        ( hAPP(hAPP(c_List_Olist__update(U_16283,hAPP(hAPP(c_List_Oappend(U_16283),U_16285),U_16287)),U_16281),U_16289) = hAPP(hAPP(c_List_Oappend(U_16283),hAPP(hAPP(c_List_Olist__update(U_16283,U_16285),U_16281),U_16289)),U_16287)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16281),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16283)),U_16285))) ) ),
    inference(miniscope,[status(thm)],[f_4019_2]) ).

cnf(f_4019_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16283,hAPP(hAPP(c_List_Oappend(U_16283),U_16285),U_16287)),U_16281),U_16289) = hAPP(hAPP(c_List_Oappend(U_16283),hAPP(hAPP(c_List_Olist__update(U_16283,U_16285),U_16281),U_16289)),U_16287)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16281),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16283)),U_16285))) ),
    inference(clausify,[status(thm)],[f_4019_3]) ).

cnf(f_4019_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16284,hAPP(hAPP(c_List_Oappend(U_16284),U_16286),U_16288)),U_16282),U_16290) = hAPP(hAPP(c_List_Oappend(U_16284),U_16286),hAPP(hAPP(c_List_Olist__update(U_16284,U_16288),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16282),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16284)),U_16286))),U_16290))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16282),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16284)),U_16286))) ),
    inference(clausify,[status(thm)],[f_4019_3]) ).

fof(f_4020_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_4020_2,plain,
    ! [U_16294,U_16293,U_16292,U_16291] : c_List_Osublist(U_16291,hAPP(hAPP(c_List_Oappend(U_16291),U_16292),U_16293),U_16294) = hAPP(hAPP(c_List_Oappend(U_16291),c_List_Osublist(U_16291,U_16292,U_16294)),c_List_Osublist(U_16291,U_16293,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_16291)),U_16292)))),U_16294)))),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

cnf(f_4020_3,plain,
    c_List_Osublist(U_16291,hAPP(hAPP(c_List_Oappend(U_16291),U_16292),U_16293),U_16294) = hAPP(hAPP(c_List_Oappend(U_16291),c_List_Osublist(U_16291,U_16292,U_16294)),c_List_Osublist(U_16291,U_16293,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_16291)),U_16292)))),U_16294)))),
    inference(clausify,[status(thm)],[f_4020_2]) ).

fof(f_4021_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_4021_2,plain,
    ! [U_16302,U_16301,U_16300,U_16299,U_16298,U_16297,U_16296,U_16295] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16295),tc_List_Olist(U_16295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16295),tc_List_Olist(U_16295)),U_16299),U_16302)),c_List_Olistrel1(U_16295,U_16298)))
      | U_16302 != hAPP(hAPP(c_List_Oappend(U_16295),U_16300),hAPP(hAPP(c_List_Olist_OCons(U_16295),U_16297),U_16301))
      | U_16299 != hAPP(hAPP(c_List_Oappend(U_16295),U_16300),hAPP(hAPP(c_List_Olist_OCons(U_16295),U_16296),U_16301))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16295,U_16295)),hAPP(hAPP(c_Product__Type_OPair(U_16295,U_16295),U_16296),U_16297)),U_16298)) ),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

cnf(f_4021_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16295),tc_List_Olist(U_16295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16295),tc_List_Olist(U_16295)),U_16299),U_16302)),c_List_Olistrel1(U_16295,U_16298)))
    | U_16302 != hAPP(hAPP(c_List_Oappend(U_16295),U_16300),hAPP(hAPP(c_List_Olist_OCons(U_16295),U_16297),U_16301))
    | U_16299 != hAPP(hAPP(c_List_Oappend(U_16295),U_16300),hAPP(hAPP(c_List_Olist_OCons(U_16295),U_16296),U_16301))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16295,U_16295)),hAPP(hAPP(c_Product__Type_OPair(U_16295,U_16295),U_16296),U_16297)),U_16298)) ),
    inference(clausify,[status(thm)],[f_4021_2]) ).

fof(f_4022_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_4022_2,plain,
    ! [U_16309,U_16308,U_16307,U_16306,U_16305,U_16304,U_16303] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16303),tc_List_Olist(U_16303))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16303),tc_List_Olist(U_16303)),hAPP(hAPP(c_List_Oappend(U_16303),U_16307),hAPP(hAPP(c_List_Olist_OCons(U_16303),U_16304),U_16308))),hAPP(hAPP(c_List_Oappend(U_16303),U_16307),hAPP(hAPP(c_List_Olist_OCons(U_16303),U_16305),U_16309)))),c_List_Olexord(U_16303,U_16306)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16303,U_16303)),hAPP(hAPP(c_Product__Type_OPair(U_16303,U_16303),U_16304),U_16305)),U_16306)) ),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

cnf(f_4022_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16303),tc_List_Olist(U_16303))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16303),tc_List_Olist(U_16303)),hAPP(hAPP(c_List_Oappend(U_16303),U_16307),hAPP(hAPP(c_List_Olist_OCons(U_16303),U_16304),U_16308))),hAPP(hAPP(c_List_Oappend(U_16303),U_16307),hAPP(hAPP(c_List_Olist_OCons(U_16303),U_16305),U_16309)))),c_List_Olexord(U_16303,U_16306)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16303,U_16303)),hAPP(hAPP(c_Product__Type_OPair(U_16303,U_16303),U_16304),U_16305)),U_16306)) ),
    inference(clausify,[status(thm)],[f_4022_2]) ).

fof(f_4023_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_4023_2,plain,
    ! [U_16312,U_16311,U_16310] :
      ( hAPP(hAPP(c_List_Otake(U_16311),hAPP(c_Nat_OSuc,U_16310)),U_16312) = hAPP(hAPP(c_List_Oappend(U_16311),hAPP(hAPP(c_List_Otake(U_16311),U_16310),U_16312)),hAPP(hAPP(c_List_Olist_OCons(U_16311),hAPP(hAPP(c_List_Onth(U_16311),U_16312),U_16310)),c_List_Olist_ONil(U_16311)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16310),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16311)),U_16312))) ),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

cnf(f_4023_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16311),hAPP(c_Nat_OSuc,U_16310)),U_16312) = hAPP(hAPP(c_List_Oappend(U_16311),hAPP(hAPP(c_List_Otake(U_16311),U_16310),U_16312)),hAPP(hAPP(c_List_Olist_OCons(U_16311),hAPP(hAPP(c_List_Onth(U_16311),U_16312),U_16310)),c_List_Olist_ONil(U_16311)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16310),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16311)),U_16312))) ),
    inference(clausify,[status(thm)],[f_4023_2]) ).

fof(f_4024_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_4024_2,plain,
    ! [U_16318,U_16317,U_16316,U_16315,U_16314,U_16313] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16313),tc_List_Olist(U_16313))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16313),tc_List_Olist(U_16313)),hAPP(hAPP(c_List_Oappend(U_16313),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16313),U_16315),c_List_Olist_ONil(U_16313)))),hAPP(hAPP(c_List_Oappend(U_16313),U_16316),hAPP(hAPP(c_List_Olist_OCons(U_16313),U_16317),c_List_Olist_ONil(U_16313))))),c_List_Olistrel1(U_16313,U_16318)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16313,U_16313)),hAPP(hAPP(c_Product__Type_OPair(U_16313,U_16313),U_16315),U_16317)),U_16318))
            | U_16314 != U_16316 )
          & ( U_16315 != U_16317
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16313),tc_List_Olist(U_16313))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16313),tc_List_Olist(U_16313)),U_16314),U_16316)),c_List_Olistrel1(U_16313,U_16318))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16313,U_16313)),hAPP(hAPP(c_Product__Type_OPair(U_16313,U_16313),U_16315),U_16317)),U_16318))
          & U_16314 = U_16316 )
        | ( U_16315 = U_16317
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16313),tc_List_Olist(U_16313))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16313),tc_List_Olist(U_16313)),U_16314),U_16316)),c_List_Olistrel1(U_16313,U_16318))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16313),tc_List_Olist(U_16313))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16313),tc_List_Olist(U_16313)),hAPP(hAPP(c_List_Oappend(U_16313),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16313),U_16315),c_List_Olist_ONil(U_16313)))),hAPP(hAPP(c_List_Oappend(U_16313),U_16316),hAPP(hAPP(c_List_Olist_OCons(U_16313),U_16317),c_List_Olist_ONil(U_16313))))),c_List_Olistrel1(U_16313,U_16318))) ) ),
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

fof(f_4024_3,plain,
    ( ! [U_16330,U_16328,U_16326,U_16324,U_16322,U_16320] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16320),tc_List_Olist(U_16320))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16320),tc_List_Olist(U_16320)),hAPP(hAPP(c_List_Oappend(U_16320),U_16322),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16324),c_List_Olist_ONil(U_16320)))),hAPP(hAPP(c_List_Oappend(U_16320),U_16326),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16328),c_List_Olist_ONil(U_16320))))),c_List_Olistrel1(U_16320,U_16330)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16320,U_16320)),hAPP(hAPP(c_Product__Type_OPair(U_16320,U_16320),U_16324),U_16328)),U_16330))
            | U_16322 != U_16326 )
          & ( U_16324 != U_16328
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16320),tc_List_Olist(U_16320))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16320),tc_List_Olist(U_16320)),U_16322),U_16326)),c_List_Olistrel1(U_16320,U_16330))) ) ) )
    & ! [U_16329,U_16327,U_16325,U_16323,U_16321,U_16319] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16319,U_16319)),hAPP(hAPP(c_Product__Type_OPair(U_16319,U_16319),U_16323),U_16327)),U_16329))
          & U_16321 = U_16325 )
        | ( U_16323 = U_16327
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),U_16321),U_16325)),c_List_Olistrel1(U_16319,U_16329))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),hAPP(hAPP(c_List_Oappend(U_16319),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16323),c_List_Olist_ONil(U_16319)))),hAPP(hAPP(c_List_Oappend(U_16319),U_16325),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16327),c_List_Olist_ONil(U_16319))))),c_List_Olistrel1(U_16319,U_16329))) ) ),
    inference(miniscope,[status(thm)],[f_4024_2]) ).

cnf(f_4024_4,plain,
    ( U_16321 = U_16325
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),U_16321),U_16325)),c_List_Olistrel1(U_16319,U_16329)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),hAPP(hAPP(c_List_Oappend(U_16319),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16323),c_List_Olist_ONil(U_16319)))),hAPP(hAPP(c_List_Oappend(U_16319),U_16325),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16327),c_List_Olist_ONil(U_16319))))),c_List_Olistrel1(U_16319,U_16329))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

cnf(f_4024_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16319,U_16319)),hAPP(hAPP(c_Product__Type_OPair(U_16319,U_16319),U_16323),U_16327)),U_16329))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),U_16321),U_16325)),c_List_Olistrel1(U_16319,U_16329)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),hAPP(hAPP(c_List_Oappend(U_16319),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16323),c_List_Olist_ONil(U_16319)))),hAPP(hAPP(c_List_Oappend(U_16319),U_16325),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16327),c_List_Olist_ONil(U_16319))))),c_List_Olistrel1(U_16319,U_16329))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

cnf(f_4024_6,plain,
    ( U_16321 = U_16325
    | U_16323 = U_16327
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),hAPP(hAPP(c_List_Oappend(U_16319),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16323),c_List_Olist_ONil(U_16319)))),hAPP(hAPP(c_List_Oappend(U_16319),U_16325),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16327),c_List_Olist_ONil(U_16319))))),c_List_Olistrel1(U_16319,U_16329))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

cnf(f_4024_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16319,U_16319)),hAPP(hAPP(c_Product__Type_OPair(U_16319,U_16319),U_16323),U_16327)),U_16329))
    | U_16323 = U_16327
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16319),tc_List_Olist(U_16319))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16319),tc_List_Olist(U_16319)),hAPP(hAPP(c_List_Oappend(U_16319),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16323),c_List_Olist_ONil(U_16319)))),hAPP(hAPP(c_List_Oappend(U_16319),U_16325),hAPP(hAPP(c_List_Olist_OCons(U_16319),U_16327),c_List_Olist_ONil(U_16319))))),c_List_Olistrel1(U_16319,U_16329))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

cnf(f_4024_8,plain,
    ( U_16324 != U_16328
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16320),tc_List_Olist(U_16320))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16320),tc_List_Olist(U_16320)),U_16322),U_16326)),c_List_Olistrel1(U_16320,U_16330)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16320),tc_List_Olist(U_16320))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16320),tc_List_Olist(U_16320)),hAPP(hAPP(c_List_Oappend(U_16320),U_16322),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16324),c_List_Olist_ONil(U_16320)))),hAPP(hAPP(c_List_Oappend(U_16320),U_16326),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16328),c_List_Olist_ONil(U_16320))))),c_List_Olistrel1(U_16320,U_16330))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

cnf(f_4024_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16320,U_16320)),hAPP(hAPP(c_Product__Type_OPair(U_16320,U_16320),U_16324),U_16328)),U_16330))
    | U_16322 != U_16326
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16320),tc_List_Olist(U_16320))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16320),tc_List_Olist(U_16320)),hAPP(hAPP(c_List_Oappend(U_16320),U_16322),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16324),c_List_Olist_ONil(U_16320)))),hAPP(hAPP(c_List_Oappend(U_16320),U_16326),hAPP(hAPP(c_List_Olist_OCons(U_16320),U_16328),c_List_Olist_ONil(U_16320))))),c_List_Olistrel1(U_16320,U_16330))) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

fof(f_4025_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_4025_2,plain,
    ! [U_16338,U_16337,U_16336,U_16335] :
      ( ? [U_16334,U_16333] :
          ( ? [U_16332,U_16331] :
              ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),U_16333),U_16331))
              & U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),U_16334),U_16331)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),U_16334),U_16333)),U_16338)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

fof(f_4025_3,plain,
    ! [U_16338,U_16337,U_16336,U_16335] :
      ( ? [U_16333] :
          ( ? [U_16332,U_16331] :
              ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),U_16333),U_16331))
              & U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),U_16331)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),U_16333)),U_16338)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_16334,sK417(U_16338,U_16337,U_16336,U_16335))],[f_4025_2]) ).

fof(f_4025_4,plain,
    ! [U_16338,U_16337,U_16336,U_16335] :
      ( ( ? [U_16332,U_16331] :
            ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK418(U_16338,U_16337,U_16336,U_16335)),U_16331))
            & U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),U_16332),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),U_16331)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK418(U_16338,U_16337,U_16336,U_16335))),U_16338)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_16333,sK418(U_16338,U_16337,U_16336,U_16335))],[f_4025_3]) ).

fof(f_4025_5,plain,
    ! [U_16338,U_16337,U_16336,U_16335] :
      ( ( ? [U_16331] :
            ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK418(U_16338,U_16337,U_16336,U_16335)),U_16331))
            & U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),U_16331)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK418(U_16338,U_16337,U_16336,U_16335))),U_16338)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_16332,sK419(U_16338,U_16337,U_16336,U_16335))],[f_4025_4]) ).

fof(f_4025_6,plain,
    ! [U_16338,U_16337,U_16336,U_16335] :
      ( ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK418(U_16338,U_16337,U_16336,U_16335)),sK420(U_16338,U_16337,U_16336,U_16335)))
        & U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK420(U_16338,U_16337,U_16336,U_16335)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK418(U_16338,U_16337,U_16336,U_16335))),U_16338)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_16331,sK420(U_16338,U_16337,U_16336,U_16335))],[f_4025_5]) ).

cnf(f_4025_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16335,U_16335)),hAPP(hAPP(c_Product__Type_OPair(U_16335,U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK418(U_16338,U_16337,U_16336,U_16335))),U_16338))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(clausify,[status(thm)],[f_4025_6]) ).

cnf(f_4025_8,plain,
    ( U_16336 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK417(U_16338,U_16337,U_16336,U_16335)),sK420(U_16338,U_16337,U_16336,U_16335)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(clausify,[status(thm)],[f_4025_6]) ).

cnf(f_4025_9,plain,
    ( U_16337 = hAPP(hAPP(c_List_Oappend(U_16335),sK419(U_16338,U_16337,U_16336,U_16335)),hAPP(hAPP(c_List_Olist_OCons(U_16335),sK418(U_16338,U_16337,U_16336,U_16335)),sK420(U_16338,U_16337,U_16336,U_16335)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16335),tc_List_Olist(U_16335))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16335),tc_List_Olist(U_16335)),U_16336),U_16337)),c_List_Olistrel1(U_16335,U_16338))) ),
    inference(clausify,[status(thm)],[f_4025_6]) ).

fof(f_4026_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_4026_2,plain,
    ! [U_16344,U_16343,U_16342,U_16341,U_16340] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),U_16342),U_16343)),c_List_Olexord(U_16340,U_16344)))
      | ? [U_16339] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16340,U_16340)),hAPP(hAPP(c_Product__Type_OPair(U_16340,U_16340),U_16339),U_16339)),U_16344))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16342)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16343))),c_List_Olexord(U_16340,U_16344))) ),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

fof(f_4026_3,plain,
    ! [U_16344,U_16343,U_16342,U_16341,U_16340] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),U_16342),U_16343)),c_List_Olexord(U_16340,U_16344)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16340,U_16340)),hAPP(hAPP(c_Product__Type_OPair(U_16340,U_16340),sK421(U_16344,U_16343,U_16342,U_16341,U_16340)),sK421(U_16344,U_16343,U_16342,U_16341,U_16340))),U_16344))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16342)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16343))),c_List_Olexord(U_16340,U_16344))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_16339,sK421(U_16344,U_16343,U_16342,U_16341,U_16340))],[f_4026_2]) ).

cnf(f_4026_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),U_16342),U_16343)),c_List_Olexord(U_16340,U_16344)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16340,U_16340)),hAPP(hAPP(c_Product__Type_OPair(U_16340,U_16340),sK421(U_16344,U_16343,U_16342,U_16341,U_16340)),sK421(U_16344,U_16343,U_16342,U_16341,U_16340))),U_16344))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16340),tc_List_Olist(U_16340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16340),tc_List_Olist(U_16340)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16342)),hAPP(hAPP(c_List_Oappend(U_16340),U_16341),U_16343))),c_List_Olexord(U_16340,U_16344))) ),
    inference(clausify,[status(thm)],[f_4026_3]) ).

fof(f_4027_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_4027_2,plain,
    ! [U_16346,U_16345] : hAPP(c_List_Orotate1(U_16345),U_16346) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16345),U_16345,c_List_Olist_ONil(U_16345),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16345),tc_fun(tc_List_Olist(U_16345),tc_List_Olist(U_16345)),U_16345),hAPP(c_COMBC(tc_List_Olist(U_16345),tc_List_Olist(U_16345),tc_List_Olist(U_16345)),c_List_Oappend(U_16345))),hAPP(hAPP(c_COMBC(U_16345,tc_List_Olist(U_16345),tc_List_Olist(U_16345)),c_List_Olist_OCons(U_16345)),c_List_Olist_ONil(U_16345)))),U_16346),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

cnf(f_4027_3,plain,
    hAPP(c_List_Orotate1(U_16345),U_16346) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16345),U_16345,c_List_Olist_ONil(U_16345),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16345),tc_fun(tc_List_Olist(U_16345),tc_List_Olist(U_16345)),U_16345),hAPP(c_COMBC(tc_List_Olist(U_16345),tc_List_Olist(U_16345),tc_List_Olist(U_16345)),c_List_Oappend(U_16345))),hAPP(hAPP(c_COMBC(U_16345,tc_List_Olist(U_16345),tc_List_Olist(U_16345)),c_List_Olist_OCons(U_16345)),c_List_Olist_ONil(U_16345)))),U_16346),
    inference(clausify,[status(thm)],[f_4027_2]) ).

fof(f_4028_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_4028_2,plain,
    ! [U_16350,U_16349,U_16348,U_16347] :
      ( hAPP(hAPP(c_List_Olist__update(U_16348,U_16349),U_16347),U_16350) = hAPP(hAPP(c_List_Oappend(U_16348),hAPP(hAPP(c_List_Otake(U_16348),U_16347),U_16349)),hAPP(hAPP(c_List_Olist_OCons(U_16348),U_16350),hAPP(hAPP(c_List_Odrop(U_16348),hAPP(c_Nat_OSuc,U_16347)),U_16349)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16348)),U_16349))) ),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

cnf(f_4028_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16348,U_16349),U_16347),U_16350) = hAPP(hAPP(c_List_Oappend(U_16348),hAPP(hAPP(c_List_Otake(U_16348),U_16347),U_16349)),hAPP(hAPP(c_List_Olist_OCons(U_16348),U_16350),hAPP(hAPP(c_List_Odrop(U_16348),hAPP(c_Nat_OSuc,U_16347)),U_16349)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16348)),U_16349))) ),
    inference(clausify,[status(thm)],[f_4028_2]) ).

fof(f_4029_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_4029_2,plain,
    ! [U_16353,U_16352,U_16351] : hAPP(hAPP(c_List_Oappend(U_16351),hAPP(hAPP(c_List_Otake(U_16351),U_16352),U_16353)),hAPP(hAPP(c_List_Odrop(U_16351),U_16352),U_16353)) = U_16353,
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

cnf(f_4029_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16351),hAPP(hAPP(c_List_Otake(U_16351),U_16352),U_16353)),hAPP(hAPP(c_List_Odrop(U_16351),U_16352),U_16353)) = U_16353,
    inference(clausify,[status(thm)],[f_4029_2]) ).

fof(f_4030_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_4030_2,plain,
    ! [U_16357,U_16356,U_16355,U_16354] : hAPP(hAPP(c_List_Odrop(U_16354),hAPP(c_Nat_OSuc,U_16355)),hAPP(hAPP(c_List_Olist_OCons(U_16354),U_16356),U_16357)) = hAPP(hAPP(c_List_Odrop(U_16354),U_16355),U_16357),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

cnf(f_4030_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16354),hAPP(c_Nat_OSuc,U_16355)),hAPP(hAPP(c_List_Olist_OCons(U_16354),U_16356),U_16357)) = hAPP(hAPP(c_List_Odrop(U_16354),U_16355),U_16357),
    inference(clausify,[status(thm)],[f_4030_2]) ).

fof(f_4031_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_4031_2,plain,
    ! [U_16360,U_16359,U_16358] : hAPP(hAPP(c_List_Odrop(U_16358),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16358),U_16359),U_16360)) = U_16360,
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

cnf(f_4031_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16358),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16358),U_16359),U_16360)) = U_16360,
    inference(clausify,[status(thm)],[f_4031_2]) ).

fof(f_4032_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_4032_2,plain,
    ! [U_16365,U_16364,U_16363,U_16362,U_16361] :
      ( hAPP(hAPP(c_List_Onth(U_16361),U_16363),U_16362) = U_16364
      | hAPP(hAPP(c_List_Odrop(U_16361),U_16362),U_16363) != hAPP(hAPP(c_List_Olist_OCons(U_16361),U_16364),U_16365) ),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

cnf(f_4032_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16361),U_16363),U_16362) = U_16364
    | hAPP(hAPP(c_List_Odrop(U_16361),U_16362),U_16363) != hAPP(hAPP(c_List_Olist_OCons(U_16361),U_16364),U_16365) ),
    inference(clausify,[status(thm)],[f_4032_2]) ).

fof(f_4033_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_4033_2,plain,
    ! [U_16367,U_16366] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16366),hAPP(c_List_Orotate1(U_16366),U_16367)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16366),U_16367)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_16366),U_16367))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16366),hAPP(c_List_Orotate1(U_16366),U_16367))) ) ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

fof(f_4033_3,plain,
    ( ! [U_16371,U_16369] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16369),hAPP(c_List_Orotate1(U_16369),U_16371)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16369),U_16371)) )
    & ! [U_16370,U_16368] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16368),U_16370))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16368),hAPP(c_List_Orotate1(U_16368),U_16370))) ) ),
    inference(miniscope,[status(thm)],[f_4033_2]) ).

cnf(f_4033_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16368),U_16370))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16368),hAPP(c_List_Orotate1(U_16368),U_16370))) ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

cnf(f_4033_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16369),hAPP(c_List_Orotate1(U_16369),U_16371)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16369),U_16371)) ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

fof(f_4034_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_4034_2,plain,
    ! [U_16374,U_16373,U_16372] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16372),hAPP(hAPP(c_List_Odrop(U_16372),U_16374),U_16373)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16372),U_16373)) ),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

cnf(f_4034_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16372),hAPP(hAPP(c_List_Odrop(U_16372),U_16374),U_16373)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16372),U_16373)) ),
    inference(clausify,[status(thm)],[f_4034_2]) ).

fof(f_4035_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_4035_2,plain,
    ! [U_16377,U_16376,U_16375] : hAPP(hAPP(c_List_Odrop(U_16375),U_16376),c_List_Obutlast(U_16375,U_16377)) = c_List_Obutlast(U_16375,hAPP(hAPP(c_List_Odrop(U_16375),U_16376),U_16377)),
    inference(variable_rename,[status(thm)],[f_4035_1]) ).

cnf(f_4035_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16375),U_16376),c_List_Obutlast(U_16375,U_16377)) = c_List_Obutlast(U_16375,hAPP(hAPP(c_List_Odrop(U_16375),U_16376),U_16377)),
    inference(clausify,[status(thm)],[f_4035_2]) ).

fof(f_4036_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_4036_2,plain,
    ! [U_16380,U_16379,U_16378] : c_List_Obutlast(U_16378,hAPP(hAPP(c_List_Odrop(U_16378),U_16379),U_16380)) = hAPP(hAPP(c_List_Odrop(U_16378),U_16379),c_List_Obutlast(U_16378,U_16380)),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

cnf(f_4036_3,plain,
    c_List_Obutlast(U_16378,hAPP(hAPP(c_List_Odrop(U_16378),U_16379),U_16380)) = hAPP(hAPP(c_List_Odrop(U_16378),U_16379),c_List_Obutlast(U_16378,U_16380)),
    inference(clausify,[status(thm)],[f_4036_2]) ).

fof(f_4037_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_4037_2,plain,
    ! [U_16384,U_16383,U_16382,U_16381] : hAPP(hAPP(c_List_Odrop(U_16381),U_16382),hAPP(hAPP(c_List_Otake(U_16381),U_16383),U_16384)) = hAPP(hAPP(c_List_Otake(U_16381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16383),U_16382)),hAPP(hAPP(c_List_Odrop(U_16381),U_16382),U_16384)),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

cnf(f_4037_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16381),U_16382),hAPP(hAPP(c_List_Otake(U_16381),U_16383),U_16384)) = hAPP(hAPP(c_List_Otake(U_16381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16383),U_16382)),hAPP(hAPP(c_List_Odrop(U_16381),U_16382),U_16384)),
    inference(clausify,[status(thm)],[f_4037_2]) ).

fof(f_4038_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_4038_2,plain,
    ! [U_16388,U_16387,U_16386,U_16385] : hAPP(hAPP(c_List_Otake(U_16385),U_16386),hAPP(hAPP(c_List_Odrop(U_16385),U_16387),U_16388)) = hAPP(hAPP(c_List_Odrop(U_16385),U_16387),hAPP(hAPP(c_List_Otake(U_16385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16386),U_16387)),U_16388)),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

cnf(f_4038_3,plain,
    hAPP(hAPP(c_List_Otake(U_16385),U_16386),hAPP(hAPP(c_List_Odrop(U_16385),U_16387),U_16388)) = hAPP(hAPP(c_List_Odrop(U_16385),U_16387),hAPP(hAPP(c_List_Otake(U_16385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16386),U_16387)),U_16388)),
    inference(clausify,[status(thm)],[f_4038_2]) ).

fof(f_4039_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_4039_2,plain,
    ! [U_16390,U_16389] : hAPP(hAPP(c_List_Odrop(U_16389),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16390) = U_16390,
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

cnf(f_4039_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16389),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16390) = U_16390,
    inference(clausify,[status(thm)],[f_4039_2]) ).

fof(f_4040_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_4040_2,plain,
    ! [U_16394,U_16393,U_16392,U_16391] : hAPP(hAPP(c_List_Odrop(U_16391),U_16392),hAPP(hAPP(c_List_Odrop(U_16391),U_16393),U_16394)) = hAPP(hAPP(c_List_Odrop(U_16391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16392),U_16393)),U_16394),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

cnf(f_4040_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16391),U_16392),hAPP(hAPP(c_List_Odrop(U_16391),U_16393),U_16394)) = hAPP(hAPP(c_List_Odrop(U_16391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16392),U_16393)),U_16394),
    inference(clausify,[status(thm)],[f_4040_2]) ).

fof(f_4041_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_4041_2,plain,
    ! [U_16399,U_16398,U_16397,U_16396,U_16395] : hAPP(hAPP(c_List_Odrop(tc_prod(U_16395,U_16396)),U_16397),hAPP(hAPP(c_List_Ozip(U_16395,U_16396),U_16398),U_16399)) = hAPP(hAPP(c_List_Ozip(U_16395,U_16396),hAPP(hAPP(c_List_Odrop(U_16395),U_16397),U_16398)),hAPP(hAPP(c_List_Odrop(U_16396),U_16397),U_16399)),
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

cnf(f_4041_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_16395,U_16396)),U_16397),hAPP(hAPP(c_List_Ozip(U_16395,U_16396),U_16398),U_16399)) = hAPP(hAPP(c_List_Ozip(U_16395,U_16396),hAPP(hAPP(c_List_Odrop(U_16395),U_16397),U_16398)),hAPP(hAPP(c_List_Odrop(U_16396),U_16397),U_16399)),
    inference(clausify,[status(thm)],[f_4041_2]) ).

fof(f_4042_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_4042_2,plain,
    ! [U_16401,U_16400] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16400)),hAPP(c_List_Orotate1(U_16400),U_16401)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16400)),U_16401),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

cnf(f_4042_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16400)),hAPP(c_List_Orotate1(U_16400),U_16401)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16400)),U_16401),
    inference(clausify,[status(thm)],[f_4042_2]) ).

fof(f_4043_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_4043_2,plain,
    ! [U_16404,U_16403,U_16402] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16402)),hAPP(hAPP(c_List_Odrop(U_16402),U_16403),U_16404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16402)),U_16404)),U_16403),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

cnf(f_4043_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16402)),hAPP(hAPP(c_List_Odrop(U_16402),U_16403),U_16404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16402)),U_16404)),U_16403),
    inference(clausify,[status(thm)],[f_4043_2]) ).

fof(f_4044_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_4044_2,plain,
    ! [U_16406,U_16405] : hAPP(c_List_Oset(U_16405),hAPP(c_List_Orotate1(U_16405),U_16406)) = hAPP(c_List_Oset(U_16405),U_16406),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

cnf(f_4044_3,plain,
    hAPP(c_List_Oset(U_16405),hAPP(c_List_Orotate1(U_16405),U_16406)) = hAPP(c_List_Oset(U_16405),U_16406),
    inference(clausify,[status(thm)],[f_4044_2]) ).

fof(f_4045_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_4045_2,plain,
    ! [U_16410,U_16409,U_16408,U_16407] :
      ( hBOOL(hAPP(hAPP(c_member(U_16407),U_16408),hAPP(c_List_Oset(U_16407),U_16410)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16407),U_16408),hAPP(c_List_Oset(U_16407),hAPP(hAPP(c_List_Odrop(U_16407),U_16409),U_16410)))) ),
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

cnf(f_4045_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16407),U_16408),hAPP(c_List_Oset(U_16407),U_16410)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16407),U_16408),hAPP(c_List_Oset(U_16407),hAPP(hAPP(c_List_Odrop(U_16407),U_16409),U_16410)))) ),
    inference(clausify,[status(thm)],[f_4045_2]) ).

fof(f_4046_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_4046_2,plain,
    ! [U_16413,U_16412,U_16411] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16411,tc_HOL_Obool)),hAPP(c_List_Oset(U_16411),hAPP(hAPP(c_List_Odrop(U_16411),U_16412),U_16413))),hAPP(c_List_Oset(U_16411),U_16413))),
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

cnf(f_4046_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16411,tc_HOL_Obool)),hAPP(c_List_Oset(U_16411),hAPP(hAPP(c_List_Odrop(U_16411),U_16412),U_16413))),hAPP(c_List_Oset(U_16411),U_16413))),
    inference(clausify,[status(thm)],[f_4046_2]) ).

fof(f_4047_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_4047_2,plain,
    ! [U_16415,U_16414] :
      ( ( hAPP(c_List_Orotate1(U_16414),U_16415) = c_List_Olist_ONil(U_16414)
        | U_16415 != c_List_Olist_ONil(U_16414) )
      & ( U_16415 = c_List_Olist_ONil(U_16414)
        | hAPP(c_List_Orotate1(U_16414),U_16415) != c_List_Olist_ONil(U_16414) ) ),
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

fof(f_4047_3,plain,
    ( ! [U_16419,U_16417] :
        ( hAPP(c_List_Orotate1(U_16417),U_16419) = c_List_Olist_ONil(U_16417)
        | U_16419 != c_List_Olist_ONil(U_16417) )
    & ! [U_16418,U_16416] :
        ( U_16418 = c_List_Olist_ONil(U_16416)
        | hAPP(c_List_Orotate1(U_16416),U_16418) != c_List_Olist_ONil(U_16416) ) ),
    inference(miniscope,[status(thm)],[f_4047_2]) ).

cnf(f_4047_4,plain,
    ( U_16418 = c_List_Olist_ONil(U_16416)
    | hAPP(c_List_Orotate1(U_16416),U_16418) != c_List_Olist_ONil(U_16416) ),
    inference(clausify,[status(thm)],[f_4047_3]) ).

cnf(f_4047_5,plain,
    ( hAPP(c_List_Orotate1(U_16417),U_16419) = c_List_Olist_ONil(U_16417)
    | U_16419 != c_List_Olist_ONil(U_16417) ),
    inference(clausify,[status(thm)],[f_4047_3]) ).

fof(f_4048_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_4048_2,plain,
    ! [U_16421,U_16420] : hAPP(hAPP(c_List_Odrop(U_16420),U_16421),c_List_Olist_ONil(U_16420)) = c_List_Olist_ONil(U_16420),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

cnf(f_4048_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16420),U_16421),c_List_Olist_ONil(U_16420)) = c_List_Olist_ONil(U_16420),
    inference(clausify,[status(thm)],[f_4048_2]) ).

fof(f_4049_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_4049_2,plain,
    ! [U_16425,U_16424,U_16423,U_16422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16424,tc_HOL_Obool)),hAPP(c_List_Oset(U_16424),hAPP(hAPP(c_List_Odrop(U_16424),U_16423),U_16425))),hAPP(c_List_Oset(U_16424),hAPP(hAPP(c_List_Odrop(U_16424),U_16422),U_16425))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16422),U_16423)) ),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

cnf(f_4049_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16424,tc_HOL_Obool)),hAPP(c_List_Oset(U_16424),hAPP(hAPP(c_List_Odrop(U_16424),U_16423),U_16425))),hAPP(c_List_Oset(U_16424),hAPP(hAPP(c_List_Odrop(U_16424),U_16422),U_16425))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16422),U_16423)) ),
    inference(clausify,[status(thm)],[f_4049_2]) ).

fof(f_4050_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_4050_2,plain,
    ! [U_16428,U_16427,U_16426] :
      ( hAPP(hAPP(c_List_Odrop(U_16426),U_16428),U_16427) = c_List_Olist_ONil(U_16426)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16426)),U_16427)),U_16428)) ),
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

cnf(f_4050_3,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16426),U_16428),U_16427) = c_List_Olist_ONil(U_16426)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16426)),U_16427)),U_16428)) ),
    inference(clausify,[status(thm)],[f_4050_2]) ).

fof(f_4051_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_4051_2,plain,
    ! [U_16431,U_16430,U_16429] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16429),U_16430),U_16431) = c_List_Olist_ONil(U_16429)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16429)),U_16431)),U_16430)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16429)),U_16431)),U_16430))
        | hAPP(hAPP(c_List_Odrop(U_16429),U_16430),U_16431) != c_List_Olist_ONil(U_16429) ) ),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

fof(f_4051_3,plain,
    ( ! [U_16437,U_16435,U_16433] :
        ( hAPP(hAPP(c_List_Odrop(U_16433),U_16435),U_16437) = c_List_Olist_ONil(U_16433)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16433)),U_16437)),U_16435)) )
    & ! [U_16436,U_16434,U_16432] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16432)),U_16436)),U_16434))
        | hAPP(hAPP(c_List_Odrop(U_16432),U_16434),U_16436) != c_List_Olist_ONil(U_16432) ) ),
    inference(miniscope,[status(thm)],[f_4051_2]) ).

cnf(f_4051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16432)),U_16436)),U_16434))
    | hAPP(hAPP(c_List_Odrop(U_16432),U_16434),U_16436) != c_List_Olist_ONil(U_16432) ),
    inference(clausify,[status(thm)],[f_4051_3]) ).

cnf(f_4051_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16433),U_16435),U_16437) = c_List_Olist_ONil(U_16433)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16433)),U_16437)),U_16435)) ),
    inference(clausify,[status(thm)],[f_4051_3]) ).

fof(f_4052_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_4052_2,plain,
    ! [U_16441,U_16440,U_16439,U_16438] : hAPP(hAPP(c_List_Odrop(U_16438),U_16439),hAPP(hAPP(c_List_Oappend(U_16438),U_16440),U_16441)) = hAPP(hAPP(c_List_Oappend(U_16438),hAPP(hAPP(c_List_Odrop(U_16438),U_16439),U_16440)),hAPP(hAPP(c_List_Odrop(U_16438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16439),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16438)),U_16440))),U_16441)),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

cnf(f_4052_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16438),U_16439),hAPP(hAPP(c_List_Oappend(U_16438),U_16440),U_16441)) = hAPP(hAPP(c_List_Oappend(U_16438),hAPP(hAPP(c_List_Odrop(U_16438),U_16439),U_16440)),hAPP(hAPP(c_List_Odrop(U_16438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16439),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16438)),U_16440))),U_16441)),
    inference(clausify,[status(thm)],[f_4052_2]) ).

fof(f_4053_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_4053_2,plain,
    ! [U_16445,U_16444,U_16443,U_16442] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16442),U_16443),U_16444) = U_16445
        | U_16444 != hAPP(hAPP(c_List_Odrop(U_16442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16442)),U_16443)),U_16445)
        | U_16443 != hAPP(hAPP(c_List_Otake(U_16442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16442)),U_16443)),U_16445) )
      & ( ( U_16444 = hAPP(hAPP(c_List_Odrop(U_16442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16442)),U_16443)),U_16445)
          & U_16443 = hAPP(hAPP(c_List_Otake(U_16442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16442)),U_16443)),U_16445) )
        | hAPP(hAPP(c_List_Oappend(U_16442),U_16443),U_16444) != U_16445 ) ),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

fof(f_4053_3,plain,
    ( ! [U_16453,U_16451,U_16449,U_16447] :
        ( hAPP(hAPP(c_List_Oappend(U_16447),U_16449),U_16451) = U_16453
        | U_16451 != hAPP(hAPP(c_List_Odrop(U_16447),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16447)),U_16449)),U_16453)
        | U_16449 != hAPP(hAPP(c_List_Otake(U_16447),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16447)),U_16449)),U_16453) )
    & ! [U_16452,U_16450,U_16448,U_16446] :
        ( ( U_16450 = hAPP(hAPP(c_List_Odrop(U_16446),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16446)),U_16448)),U_16452)
          & U_16448 = hAPP(hAPP(c_List_Otake(U_16446),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16446)),U_16448)),U_16452) )
        | hAPP(hAPP(c_List_Oappend(U_16446),U_16448),U_16450) != U_16452 ) ),
    inference(miniscope,[status(thm)],[f_4053_2]) ).

cnf(f_4053_4,plain,
    ( U_16448 = hAPP(hAPP(c_List_Otake(U_16446),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16446)),U_16448)),U_16452)
    | hAPP(hAPP(c_List_Oappend(U_16446),U_16448),U_16450) != U_16452 ),
    inference(clausify,[status(thm)],[f_4053_3]) ).

cnf(f_4053_5,plain,
    ( U_16450 = hAPP(hAPP(c_List_Odrop(U_16446),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16446)),U_16448)),U_16452)
    | hAPP(hAPP(c_List_Oappend(U_16446),U_16448),U_16450) != U_16452 ),
    inference(clausify,[status(thm)],[f_4053_3]) ).

cnf(f_4053_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16447),U_16449),U_16451) = U_16453
    | U_16451 != hAPP(hAPP(c_List_Odrop(U_16447),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16447)),U_16449)),U_16453)
    | U_16449 != hAPP(hAPP(c_List_Otake(U_16447),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16447)),U_16449)),U_16453) ),
    inference(clausify,[status(thm)],[f_4053_3]) ).

fof(f_4054_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_4054_2,plain,
    ! [U_16457,U_16456,U_16455,U_16454] : hAPP(hAPP(c_List_Odrop(U_16454),U_16455),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16457)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16454),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16457),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16454),tc_List_Olist(U_16454)),c_List_Odrop(U_16454)),U_16457),U_16455),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

cnf(f_4054_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16454),U_16455),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16457)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16454),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16457),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16454),tc_List_Olist(U_16454)),c_List_Odrop(U_16454)),U_16457),U_16455),
    inference(clausify,[status(thm)],[f_4054_2]) ).

fof(f_4055_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_4055_2,plain,
    ! [U_16461,U_16460,U_16459,U_16458] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16459),U_16458),hAPP(hAPP(c_List_Olist_OCons(U_16459),U_16460),U_16461)) = hAPP(hAPP(c_List_Odrop(U_16459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16458),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16461)
        | U_16458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_16459),U_16458),hAPP(hAPP(c_List_Olist_OCons(U_16459),U_16460),U_16461)) = hAPP(hAPP(c_List_Olist_OCons(U_16459),U_16460),U_16461)
        | U_16458 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

fof(f_4055_3,plain,
    ( ! [U_16469,U_16467,U_16465,U_16463] :
        ( hAPP(hAPP(c_List_Odrop(U_16465),U_16463),hAPP(hAPP(c_List_Olist_OCons(U_16465),U_16467),U_16469)) = hAPP(hAPP(c_List_Odrop(U_16465),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16463),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16469)
        | U_16463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16468,U_16466,U_16464,U_16462] :
        ( hAPP(hAPP(c_List_Odrop(U_16464),U_16462),hAPP(hAPP(c_List_Olist_OCons(U_16464),U_16466),U_16468)) = hAPP(hAPP(c_List_Olist_OCons(U_16464),U_16466),U_16468)
        | U_16462 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4055_2]) ).

cnf(f_4055_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16464),U_16462),hAPP(hAPP(c_List_Olist_OCons(U_16464),U_16466),U_16468)) = hAPP(hAPP(c_List_Olist_OCons(U_16464),U_16466),U_16468)
    | U_16462 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4055_3]) ).

cnf(f_4055_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16465),U_16463),hAPP(hAPP(c_List_Olist_OCons(U_16465),U_16467),U_16469)) = hAPP(hAPP(c_List_Odrop(U_16465),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16463),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16469)
    | U_16463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4055_3]) ).

fof(f_4056_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_4056_2,plain,
    ! [U_16473,U_16472,U_16471,U_16470] :
      ( hAPP(hAPP(c_List_Onth(U_16472),hAPP(hAPP(c_List_Odrop(U_16472),U_16470),U_16473)),U_16471) = hAPP(hAPP(c_List_Onth(U_16472),U_16473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16470),U_16471))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16470),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16472)),U_16473))) ),
    inference(variable_rename,[status(thm)],[f_4056_1]) ).

cnf(f_4056_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16472),hAPP(hAPP(c_List_Odrop(U_16472),U_16470),U_16473)),U_16471) = hAPP(hAPP(c_List_Onth(U_16472),U_16473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16470),U_16471))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16470),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16472)),U_16473))) ),
    inference(clausify,[status(thm)],[f_4056_2]) ).

fof(f_4057_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_4057_2,plain,
    ! [U_16478,U_16477,U_16476,U_16475,U_16474] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16474),U_16475),U_16476) = hAPP(hAPP(c_List_Oappend(U_16474),U_16477),U_16478)
        | ( ( hAPP(hAPP(c_List_Oappend(U_16474),hAPP(hAPP(c_List_Odrop(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477)),U_16475)),U_16476) != U_16478
            | hAPP(hAPP(c_List_Otake(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477)),U_16475) != U_16477 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477))) )
        | ( ( U_16476 != hAPP(hAPP(c_List_Oappend(U_16474),hAPP(hAPP(c_List_Odrop(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),U_16477)),U_16478)
            | U_16475 != hAPP(hAPP(c_List_Otake(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),U_16477) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_16474),hAPP(hAPP(c_List_Odrop(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477)),U_16475)),U_16476) = U_16478
              & hAPP(hAPP(c_List_Otake(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477)),U_16475) = U_16477 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477))) )
          & ( ( U_16476 = hAPP(hAPP(c_List_Oappend(U_16474),hAPP(hAPP(c_List_Odrop(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),U_16477)),U_16478)
              & U_16475 = hAPP(hAPP(c_List_Otake(U_16474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),U_16477) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16475)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16474)),U_16477))) ) )
        | hAPP(hAPP(c_List_Oappend(U_16474),U_16475),U_16476) != hAPP(hAPP(c_List_Oappend(U_16474),U_16477),U_16478) ) ),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

fof(f_4057_3,plain,
    ( ! [U_16488,U_16486,U_16484,U_16482,U_16480] :
        ( hAPP(hAPP(c_List_Oappend(U_16480),U_16482),U_16484) = hAPP(hAPP(c_List_Oappend(U_16480),U_16486),U_16488)
        | ( ( hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482)),U_16484) != U_16488
            | hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482) != U_16486 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486))) )
        | ( ( U_16484 != hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486)),U_16488)
            | U_16482 != hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486))) ) )
    & ! [U_16487,U_16485,U_16483,U_16481,U_16479] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_16479),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)),U_16481)),U_16483) = U_16487
              & hAPP(hAPP(c_List_Otake(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)),U_16481) = U_16485 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485))) )
          & ( ( U_16483 = hAPP(hAPP(c_List_Oappend(U_16479),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),U_16485)),U_16487)
              & U_16481 = hAPP(hAPP(c_List_Otake(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),U_16485) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485))) ) )
        | hAPP(hAPP(c_List_Oappend(U_16479),U_16481),U_16483) != hAPP(hAPP(c_List_Oappend(U_16479),U_16485),U_16487) ) ),
    inference(miniscope,[status(thm)],[f_4057_2]) ).

cnf(f_4057_4,plain,
    ( U_16481 = hAPP(hAPP(c_List_Otake(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),U_16485)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)))
    | hAPP(hAPP(c_List_Oappend(U_16479),U_16481),U_16483) != hAPP(hAPP(c_List_Oappend(U_16479),U_16485),U_16487) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_5,plain,
    ( U_16483 = hAPP(hAPP(c_List_Oappend(U_16479),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),U_16485)),U_16487)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)))
    | hAPP(hAPP(c_List_Oappend(U_16479),U_16481),U_16483) != hAPP(hAPP(c_List_Oappend(U_16479),U_16485),U_16487) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)),U_16481) = U_16485
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)))
    | hAPP(hAPP(c_List_Oappend(U_16479),U_16481),U_16483) != hAPP(hAPP(c_List_Oappend(U_16479),U_16485),U_16487) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16479),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)),U_16481)),U_16483) = U_16487
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16481)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16485)))
    | hAPP(hAPP(c_List_Oappend(U_16479),U_16481),U_16483) != hAPP(hAPP(c_List_Oappend(U_16479),U_16485),U_16487) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)))
    | hAPP(hAPP(c_List_Oappend(U_16480),U_16482),U_16484) = hAPP(hAPP(c_List_Oappend(U_16480),U_16486),U_16488) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_9,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482)),U_16484) != U_16488
    | hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482) != U_16486
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)))
    | hAPP(hAPP(c_List_Oappend(U_16480),U_16482),U_16484) = hAPP(hAPP(c_List_Oappend(U_16480),U_16486),U_16488) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)))
    | U_16484 != hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486)),U_16488)
    | U_16482 != hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486)
    | hAPP(hAPP(c_List_Oappend(U_16480),U_16482),U_16484) = hAPP(hAPP(c_List_Oappend(U_16480),U_16486),U_16488) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482)),U_16484) != U_16488
    | hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16486)),U_16482) != U_16486
    | U_16484 != hAPP(hAPP(c_List_Oappend(U_16480),hAPP(hAPP(c_List_Odrop(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486)),U_16488)
    | U_16482 != hAPP(hAPP(c_List_Otake(U_16480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16480)),U_16482)),U_16486)
    | hAPP(hAPP(c_List_Oappend(U_16480),U_16482),U_16484) = hAPP(hAPP(c_List_Oappend(U_16480),U_16486),U_16488) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

fof(f_4058_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_4058_2,plain,
    ! [U_16491,U_16490,U_16489] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_16490),hAPP(hAPP(c_List_Onth(U_16490),U_16491),U_16489)),hAPP(hAPP(c_List_Odrop(U_16490),hAPP(c_Nat_OSuc,U_16489)),U_16491)) = hAPP(hAPP(c_List_Odrop(U_16490),U_16489),U_16491)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16489),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16490)),U_16491))) ),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

cnf(f_4058_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16490),hAPP(hAPP(c_List_Onth(U_16490),U_16491),U_16489)),hAPP(hAPP(c_List_Odrop(U_16490),hAPP(c_Nat_OSuc,U_16489)),U_16491)) = hAPP(hAPP(c_List_Odrop(U_16490),U_16489),U_16491)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16489),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16490)),U_16491))) ),
    inference(clausify,[status(thm)],[f_4058_2]) ).

fof(f_4059_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_4059_2,plain,
    ! [U_16495,U_16494,U_16493,U_16492] :
      ( hAPP(c_List_Orotate1(U_16493),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),U_16495)) = hAPP(hAPP(c_List_Oappend(U_16493),U_16495),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),c_List_Olist_ONil(U_16493)))
      & hAPP(c_List_Orotate1(U_16492),c_List_Olist_ONil(U_16492)) = c_List_Olist_ONil(U_16492) ),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

fof(f_4059_3,plain,
    ( ! [U_16495,U_16494,U_16493] : hAPP(c_List_Orotate1(U_16493),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),U_16495)) = hAPP(hAPP(c_List_Oappend(U_16493),U_16495),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),c_List_Olist_ONil(U_16493)))
    & ! [U_16492] : hAPP(c_List_Orotate1(U_16492),c_List_Olist_ONil(U_16492)) = c_List_Olist_ONil(U_16492) ),
    inference(miniscope,[status(thm)],[f_4059_2]) ).

cnf(f_4059_4,plain,
    hAPP(c_List_Orotate1(U_16492),c_List_Olist_ONil(U_16492)) = c_List_Olist_ONil(U_16492),
    inference(clausify,[status(thm)],[f_4059_3]) ).

cnf(f_4059_5,plain,
    hAPP(c_List_Orotate1(U_16493),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),U_16495)) = hAPP(hAPP(c_List_Oappend(U_16493),U_16495),hAPP(hAPP(c_List_Olist_OCons(U_16493),U_16494),c_List_Olist_ONil(U_16493))),
    inference(clausify,[status(thm)],[f_4059_3]) ).

fof(f_4060_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_4060_2,plain,
    ! [U_16499,U_16498,U_16497,U_16496] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16497),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16496)),hAPP(hAPP(c_List_Olist_OCons(U_16497),U_16498),U_16499)) = hAPP(hAPP(c_List_Odrop(U_16497),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16496)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16499)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_16497),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16496)),hAPP(hAPP(c_List_Olist_OCons(U_16497),U_16498),U_16499)) = hAPP(hAPP(c_List_Olist_OCons(U_16497),U_16498),U_16499)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16496) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

fof(f_4060_3,plain,
    ( ! [U_16507,U_16505,U_16503,U_16501] :
        ( hAPP(hAPP(c_List_Odrop(U_16503),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501)),hAPP(hAPP(c_List_Olist_OCons(U_16503),U_16505),U_16507)) = hAPP(hAPP(c_List_Odrop(U_16503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16507)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16506,U_16504,U_16502,U_16500] :
        ( hAPP(hAPP(c_List_Odrop(U_16502),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16500)),hAPP(hAPP(c_List_Olist_OCons(U_16502),U_16504),U_16506)) = hAPP(hAPP(c_List_Olist_OCons(U_16502),U_16504),U_16506)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16500) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4060_2]) ).

cnf(f_4060_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16502),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16500)),hAPP(hAPP(c_List_Olist_OCons(U_16502),U_16504),U_16506)) = hAPP(hAPP(c_List_Olist_OCons(U_16502),U_16504),U_16506)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16500) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4060_3]) ).

cnf(f_4060_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16503),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501)),hAPP(hAPP(c_List_Olist_OCons(U_16503),U_16505),U_16507)) = hAPP(hAPP(c_List_Odrop(U_16503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16507)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16501) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4060_3]) ).

fof(f_4061_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_4061_2,plain,
    ! [U_16511,U_16510,U_16509,U_16508] :
      ( hAPP(hAPP(c_List_Otake(U_16510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16508),U_16509)),U_16511) = hAPP(hAPP(c_List_Oappend(U_16510),hAPP(hAPP(c_List_Otake(U_16510),U_16508),U_16511)),hAPP(hAPP(c_List_Otake(U_16510),U_16509),hAPP(hAPP(c_List_Odrop(U_16510),U_16508),U_16511)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16508),U_16509)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16510)),U_16511))) ),
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

cnf(f_4061_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16508),U_16509)),U_16511) = hAPP(hAPP(c_List_Oappend(U_16510),hAPP(hAPP(c_List_Otake(U_16510),U_16508),U_16511)),hAPP(hAPP(c_List_Otake(U_16510),U_16509),hAPP(hAPP(c_List_Odrop(U_16510),U_16508),U_16511)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16508),U_16509)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16510)),U_16511))) ),
    inference(clausify,[status(thm)],[f_4061_2]) ).

fof(f_4062_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_4062_2,plain,
    ! [U_16513,U_16512] :
      ( hAPP(c_List_Orotate1(U_16512),U_16513) = U_16513
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16512)),U_16513)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

cnf(f_4062_3,plain,
    ( hAPP(c_List_Orotate1(U_16512),U_16513) = U_16513
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16512)),U_16513)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4062_2]) ).

fof(f_4063_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_4063_2,plain,
    ! [U_16518,U_16517,U_16516,U_16515,U_16514] : hAPP(hAPP(c_List_Ozip(U_16514,U_16515),hAPP(hAPP(c_List_Oappend(U_16514),U_16516),U_16517)),U_16518) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16514,U_16515)),hAPP(hAPP(c_List_Ozip(U_16514,U_16515),U_16516),hAPP(hAPP(c_List_Otake(U_16515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16516)),U_16518))),hAPP(hAPP(c_List_Ozip(U_16514,U_16515),U_16517),hAPP(hAPP(c_List_Odrop(U_16515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16516)),U_16518))),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

cnf(f_4063_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16514,U_16515),hAPP(hAPP(c_List_Oappend(U_16514),U_16516),U_16517)),U_16518) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16514,U_16515)),hAPP(hAPP(c_List_Ozip(U_16514,U_16515),U_16516),hAPP(hAPP(c_List_Otake(U_16515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16516)),U_16518))),hAPP(hAPP(c_List_Ozip(U_16514,U_16515),U_16517),hAPP(hAPP(c_List_Odrop(U_16515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16516)),U_16518))),
    inference(clausify,[status(thm)],[f_4063_2]) ).

fof(f_4064_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_4064_2,plain,
    ! [U_16523,U_16522,U_16521,U_16520,U_16519] : hAPP(hAPP(c_List_Ozip(U_16519,U_16520),U_16521),hAPP(hAPP(c_List_Oappend(U_16520),U_16522),U_16523)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16519,U_16520)),hAPP(hAPP(c_List_Ozip(U_16519,U_16520),hAPP(hAPP(c_List_Otake(U_16519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16522)),U_16521)),U_16522)),hAPP(hAPP(c_List_Ozip(U_16519,U_16520),hAPP(hAPP(c_List_Odrop(U_16519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16522)),U_16521)),U_16523)),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

cnf(f_4064_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16519,U_16520),U_16521),hAPP(hAPP(c_List_Oappend(U_16520),U_16522),U_16523)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16519,U_16520)),hAPP(hAPP(c_List_Ozip(U_16519,U_16520),hAPP(hAPP(c_List_Otake(U_16519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16522)),U_16521)),U_16522)),hAPP(hAPP(c_List_Ozip(U_16519,U_16520),hAPP(hAPP(c_List_Odrop(U_16519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16522)),U_16521)),U_16523)),
    inference(clausify,[status(thm)],[f_4064_2]) ).

fof(f_4065_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_4065_2,plain,
    ! [U_16526,U_16525,U_16524] :
      ( U_16526 = hAPP(hAPP(c_List_Oappend(U_16525),hAPP(hAPP(c_List_Otake(U_16525),U_16524),U_16526)),hAPP(hAPP(c_List_Olist_OCons(U_16525),hAPP(hAPP(c_List_Onth(U_16525),U_16526),U_16524)),hAPP(hAPP(c_List_Odrop(U_16525),hAPP(c_Nat_OSuc,U_16524)),U_16526)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16525)),U_16526))) ),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

cnf(f_4065_3,plain,
    ( U_16526 = hAPP(hAPP(c_List_Oappend(U_16525),hAPP(hAPP(c_List_Otake(U_16525),U_16524),U_16526)),hAPP(hAPP(c_List_Olist_OCons(U_16525),hAPP(hAPP(c_List_Onth(U_16525),U_16526),U_16524)),hAPP(hAPP(c_List_Odrop(U_16525),hAPP(c_Nat_OSuc,U_16524)),U_16526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16524),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16525)),U_16526))) ),
    inference(clausify,[status(thm)],[f_4065_2]) ).

fof(f_4066_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_4066_2,plain,
    ! [U_16529,U_16528,U_16527] :
      ( hAPP(hAPP(c_List_Oappend(U_16528),hAPP(hAPP(c_List_Otake(U_16528),U_16527),U_16529)),hAPP(hAPP(c_List_Olist_OCons(U_16528),hAPP(c_List_Ohd(U_16528),hAPP(hAPP(c_List_Odrop(U_16528),U_16527),U_16529))),c_List_Olist_ONil(U_16528))) = hAPP(hAPP(c_List_Otake(U_16528),hAPP(c_Nat_OSuc,U_16527)),U_16529)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16528)),U_16529))) ),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

cnf(f_4066_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16528),hAPP(hAPP(c_List_Otake(U_16528),U_16527),U_16529)),hAPP(hAPP(c_List_Olist_OCons(U_16528),hAPP(c_List_Ohd(U_16528),hAPP(hAPP(c_List_Odrop(U_16528),U_16527),U_16529))),c_List_Olist_ONil(U_16528))) = hAPP(hAPP(c_List_Otake(U_16528),hAPP(c_Nat_OSuc,U_16527)),U_16529)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16528)),U_16529))) ),
    inference(clausify,[status(thm)],[f_4066_2]) ).

fof(f_4067_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_4067_2,plain,
    ! [U_16532,U_16531,U_16530] :
      ( hAPP(c_List_Ohd(U_16531),hAPP(hAPP(c_List_Odrop(U_16531),U_16532),U_16530)) = hAPP(hAPP(c_List_Onth(U_16531),U_16530),U_16532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16532),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16531)),U_16530)))
      | U_16530 = c_List_Olist_ONil(U_16531) ),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

cnf(f_4067_3,plain,
    ( hAPP(c_List_Ohd(U_16531),hAPP(hAPP(c_List_Odrop(U_16531),U_16532),U_16530)) = hAPP(hAPP(c_List_Onth(U_16531),U_16530),U_16532)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16532),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16531)),U_16530)))
    | U_16530 = c_List_Olist_ONil(U_16531) ),
    inference(clausify,[status(thm)],[f_4067_2]) ).

fof(f_4068_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_4068_2,plain,
    ! [U_16535,U_16534,U_16533] : hAPP(c_List_Ohd(U_16533),hAPP(hAPP(c_List_Olist_OCons(U_16533),U_16534),U_16535)) = U_16534,
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

cnf(f_4068_3,plain,
    hAPP(c_List_Ohd(U_16533),hAPP(hAPP(c_List_Olist_OCons(U_16533),U_16534),U_16535)) = U_16534,
    inference(clausify,[status(thm)],[f_4068_2]) ).

fof(f_4069_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_4069_2,plain,
    ! [U_16538,U_16537,U_16536] :
      ( ( hAPP(c_List_Ohd(U_16537),hAPP(hAPP(c_List_Oappend(U_16537),U_16536),U_16538)) = hAPP(c_List_Ohd(U_16537),U_16536)
        | U_16536 = c_List_Olist_ONil(U_16537) )
      & ( hAPP(c_List_Ohd(U_16537),hAPP(hAPP(c_List_Oappend(U_16537),U_16536),U_16538)) = hAPP(c_List_Ohd(U_16537),U_16538)
        | U_16536 != c_List_Olist_ONil(U_16537) ) ),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

fof(f_4069_3,plain,
    ( ! [U_16544,U_16542,U_16540] :
        ( hAPP(c_List_Ohd(U_16542),hAPP(hAPP(c_List_Oappend(U_16542),U_16540),U_16544)) = hAPP(c_List_Ohd(U_16542),U_16540)
        | U_16540 = c_List_Olist_ONil(U_16542) )
    & ! [U_16543,U_16541,U_16539] :
        ( hAPP(c_List_Ohd(U_16541),hAPP(hAPP(c_List_Oappend(U_16541),U_16539),U_16543)) = hAPP(c_List_Ohd(U_16541),U_16543)
        | U_16539 != c_List_Olist_ONil(U_16541) ) ),
    inference(miniscope,[status(thm)],[f_4069_2]) ).

cnf(f_4069_4,plain,
    ( hAPP(c_List_Ohd(U_16541),hAPP(hAPP(c_List_Oappend(U_16541),U_16539),U_16543)) = hAPP(c_List_Ohd(U_16541),U_16543)
    | U_16539 != c_List_Olist_ONil(U_16541) ),
    inference(clausify,[status(thm)],[f_4069_3]) ).

cnf(f_4069_5,plain,
    ( hAPP(c_List_Ohd(U_16542),hAPP(hAPP(c_List_Oappend(U_16542),U_16540),U_16544)) = hAPP(c_List_Ohd(U_16542),U_16540)
    | U_16540 = c_List_Olist_ONil(U_16542) ),
    inference(clausify,[status(thm)],[f_4069_3]) ).

fof(f_4070_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_4070_2,plain,
    ! [U_16547,U_16546,U_16545] :
      ( hAPP(c_List_Ohd(U_16546),hAPP(hAPP(c_List_Oappend(U_16546),U_16545),U_16547)) = hAPP(c_List_Ohd(U_16546),U_16545)
      | U_16545 = c_List_Olist_ONil(U_16546) ),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

cnf(f_4070_3,plain,
    ( hAPP(c_List_Ohd(U_16546),hAPP(hAPP(c_List_Oappend(U_16546),U_16545),U_16547)) = hAPP(c_List_Ohd(U_16546),U_16545)
    | U_16545 = c_List_Olist_ONil(U_16546) ),
    inference(clausify,[status(thm)],[f_4070_2]) ).

fof(f_4071_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_4071_2,plain,
    ! [U_16549,U_16548] :
      ( hBOOL(hAPP(hAPP(c_member(U_16549),hAPP(c_List_Ohd(U_16549),U_16548)),hAPP(c_List_Oset(U_16549),U_16548)))
      | U_16548 = c_List_Olist_ONil(U_16549) ),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

cnf(f_4071_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16549),hAPP(c_List_Ohd(U_16549),U_16548)),hAPP(c_List_Oset(U_16549),U_16548)))
    | U_16548 = c_List_Olist_ONil(U_16549) ),
    inference(clausify,[status(thm)],[f_4071_2]) ).

fof(f_4072_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_4072_2,plain,
    ! [U_16551,U_16550] :
      ( hAPP(c_List_Ohd(U_16551),U_16550) = hAPP(hAPP(c_List_Onth(U_16551),U_16550),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_16550 = c_List_Olist_ONil(U_16551) ),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

cnf(f_4072_3,plain,
    ( hAPP(c_List_Ohd(U_16551),U_16550) = hAPP(hAPP(c_List_Onth(U_16551),U_16550),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_16550 = c_List_Olist_ONil(U_16551) ),
    inference(clausify,[status(thm)],[f_4072_2]) ).

fof(f_4073_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_4073_2,plain,
    ! [U_16553,U_16552] :
      ( hAPP(c_List_Orotate1(U_16553),U_16552) = hAPP(hAPP(c_List_Oappend(U_16553),hAPP(c_List_Otl(U_16553),U_16552)),hAPP(hAPP(c_List_Olist_OCons(U_16553),hAPP(c_List_Ohd(U_16553),U_16552)),c_List_Olist_ONil(U_16553)))
      | U_16552 = c_List_Olist_ONil(U_16553) ),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

cnf(f_4073_3,plain,
    ( hAPP(c_List_Orotate1(U_16553),U_16552) = hAPP(hAPP(c_List_Oappend(U_16553),hAPP(c_List_Otl(U_16553),U_16552)),hAPP(hAPP(c_List_Olist_OCons(U_16553),hAPP(c_List_Ohd(U_16553),U_16552)),c_List_Olist_ONil(U_16553)))
    | U_16552 = c_List_Olist_ONil(U_16553) ),
    inference(clausify,[status(thm)],[f_4073_2]) ).

fof(f_4074_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_4074_2,plain,
    ! [U_16556,U_16555,U_16554] :
      ( hAPP(c_List_Ohd(U_16555),hAPP(c_List_Orotate(U_16555,U_16556),U_16554)) = hAPP(hAPP(c_List_Onth(U_16555),U_16554),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16556,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16555)),U_16554)))
      | U_16554 = c_List_Olist_ONil(U_16555) ),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

cnf(f_4074_3,plain,
    ( hAPP(c_List_Ohd(U_16555),hAPP(c_List_Orotate(U_16555,U_16556),U_16554)) = hAPP(hAPP(c_List_Onth(U_16555),U_16554),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16556,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16555)),U_16554)))
    | U_16554 = c_List_Olist_ONil(U_16555) ),
    inference(clausify,[status(thm)],[f_4074_2]) ).

fof(f_4075_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_4075_2,plain,
    ! [U_16559,U_16558,U_16557] : hAPP(c_List_Otl(U_16557),hAPP(hAPP(c_List_Odrop(U_16557),U_16558),U_16559)) = hAPP(hAPP(c_List_Odrop(U_16557),U_16558),hAPP(c_List_Otl(U_16557),U_16559)),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

cnf(f_4075_3,plain,
    hAPP(c_List_Otl(U_16557),hAPP(hAPP(c_List_Odrop(U_16557),U_16558),U_16559)) = hAPP(hAPP(c_List_Odrop(U_16557),U_16558),hAPP(c_List_Otl(U_16557),U_16559)),
    inference(clausify,[status(thm)],[f_4075_2]) ).

fof(f_4076_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_4076_2,plain,
    ! [U_16562,U_16561,U_16560] : hAPP(hAPP(c_List_Odrop(U_16560),U_16561),hAPP(c_List_Otl(U_16560),U_16562)) = hAPP(c_List_Otl(U_16560),hAPP(hAPP(c_List_Odrop(U_16560),U_16561),U_16562)),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

cnf(f_4076_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16560),U_16561),hAPP(c_List_Otl(U_16560),U_16562)) = hAPP(c_List_Otl(U_16560),hAPP(hAPP(c_List_Odrop(U_16560),U_16561),U_16562)),
    inference(clausify,[status(thm)],[f_4076_2]) ).

fof(f_4077_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_4077_2,plain,
    ! [U_16565,U_16564,U_16563] : hAPP(c_List_Otl(U_16563),hAPP(hAPP(c_List_Olist_OCons(U_16563),U_16564),U_16565)) = U_16565,
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

cnf(f_4077_3,plain,
    hAPP(c_List_Otl(U_16563),hAPP(hAPP(c_List_Olist_OCons(U_16563),U_16564),U_16565)) = U_16565,
    inference(clausify,[status(thm)],[f_4077_2]) ).

fof(f_4078_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_4078_2,plain,
    ! [U_16568,U_16567,U_16566] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16566),hAPP(c_List_Orotate(U_16566,U_16567),U_16568)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16566),U_16568)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_16566),U_16568))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16566),hAPP(c_List_Orotate(U_16566,U_16567),U_16568))) ) ),
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

fof(f_4078_3,plain,
    ( ! [U_16574,U_16572,U_16570] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16570),hAPP(c_List_Orotate(U_16570,U_16572),U_16574)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16570),U_16574)) )
    & ! [U_16573,U_16571,U_16569] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16569),U_16573))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16569),hAPP(c_List_Orotate(U_16569,U_16571),U_16573))) ) ),
    inference(miniscope,[status(thm)],[f_4078_2]) ).

cnf(f_4078_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16569),U_16573))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16569),hAPP(c_List_Orotate(U_16569,U_16571),U_16573))) ),
    inference(clausify,[status(thm)],[f_4078_3]) ).

cnf(f_4078_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16570),hAPP(c_List_Orotate(U_16570,U_16572),U_16574)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16570),U_16574)) ),
    inference(clausify,[status(thm)],[f_4078_3]) ).

fof(f_4079_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_4079_2,plain,
    ! [U_16576,U_16575] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16575),hAPP(c_List_Otl(U_16575),U_16576)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16575),U_16576)) ),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

cnf(f_4079_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16575),hAPP(c_List_Otl(U_16575),U_16576)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16575),U_16576)) ),
    inference(clausify,[status(thm)],[f_4079_2]) ).

fof(f_4080_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_4080_2,plain,
    ! [U_16577] : c_List_Orotate(U_16577,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_16577)),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

cnf(f_4080_3,plain,
    c_List_Orotate(U_16577,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_16577)),
    inference(clausify,[status(thm)],[f_4080_2]) ).

fof(f_4081_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_4081_2,plain,
    ! [U_16581,U_16580,U_16579,U_16578] : hAPP(c_List_Orotate(U_16578,U_16579),hAPP(c_List_Orotate(U_16578,U_16580),U_16581)) = hAPP(c_List_Orotate(U_16578,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16579),U_16580)),U_16581),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

cnf(f_4081_3,plain,
    hAPP(c_List_Orotate(U_16578,U_16579),hAPP(c_List_Orotate(U_16578,U_16580),U_16581)) = hAPP(c_List_Orotate(U_16578,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16579),U_16580)),U_16581),
    inference(clausify,[status(thm)],[f_4081_2]) ).

fof(f_4082_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_4082_2,plain,
    ! [U_16584,U_16583,U_16582] : c_List_Orotate(U_16582,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16583),U_16584)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_16582),tc_List_Olist(U_16582),tc_List_Olist(U_16582),c_List_Orotate(U_16582,U_16583)),c_List_Orotate(U_16582,U_16584)),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

cnf(f_4082_3,plain,
    c_List_Orotate(U_16582,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16583),U_16584)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_16582),tc_List_Olist(U_16582),tc_List_Olist(U_16582),c_List_Orotate(U_16582,U_16583)),c_List_Orotate(U_16582,U_16584)),
    inference(clausify,[status(thm)],[f_4082_2]) ).

fof(f_4083_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_4083_2,plain,
    ! [U_16587,U_16586,U_16585] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16585)),hAPP(c_List_Orotate(U_16585,U_16586),U_16587)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16585)),U_16587),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

cnf(f_4083_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16585)),hAPP(c_List_Orotate(U_16585,U_16586),U_16587)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16585)),U_16587),
    inference(clausify,[status(thm)],[f_4083_2]) ).

fof(f_4084_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_4084_2,plain,
    ! [U_16590,U_16589,U_16588] : hAPP(c_List_Oset(U_16588),hAPP(c_List_Orotate(U_16588,U_16589),U_16590)) = hAPP(c_List_Oset(U_16588),U_16590),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

cnf(f_4084_3,plain,
    hAPP(c_List_Oset(U_16588),hAPP(c_List_Orotate(U_16588,U_16589),U_16590)) = hAPP(c_List_Oset(U_16588),U_16590),
    inference(clausify,[status(thm)],[f_4084_2]) ).

fof(f_4085_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_4085_2,plain,
    ! [U_16593,U_16592,U_16591] :
      ( ( hAPP(c_List_Orotate(U_16591,U_16592),U_16593) = c_List_Olist_ONil(U_16591)
        | U_16593 != c_List_Olist_ONil(U_16591) )
      & ( U_16593 = c_List_Olist_ONil(U_16591)
        | hAPP(c_List_Orotate(U_16591,U_16592),U_16593) != c_List_Olist_ONil(U_16591) ) ),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

fof(f_4085_3,plain,
    ( ! [U_16599,U_16597,U_16595] :
        ( hAPP(c_List_Orotate(U_16595,U_16597),U_16599) = c_List_Olist_ONil(U_16595)
        | U_16599 != c_List_Olist_ONil(U_16595) )
    & ! [U_16598,U_16596,U_16594] :
        ( U_16598 = c_List_Olist_ONil(U_16594)
        | hAPP(c_List_Orotate(U_16594,U_16596),U_16598) != c_List_Olist_ONil(U_16594) ) ),
    inference(miniscope,[status(thm)],[f_4085_2]) ).

cnf(f_4085_4,plain,
    ( U_16598 = c_List_Olist_ONil(U_16594)
    | hAPP(c_List_Orotate(U_16594,U_16596),U_16598) != c_List_Olist_ONil(U_16594) ),
    inference(clausify,[status(thm)],[f_4085_3]) ).

cnf(f_4085_5,plain,
    ( hAPP(c_List_Orotate(U_16595,U_16597),U_16599) = c_List_Olist_ONil(U_16595)
    | U_16599 != c_List_Olist_ONil(U_16595) ),
    inference(clausify,[status(thm)],[f_4085_3]) ).

fof(f_4086_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_4086_2,plain,
    ! [U_16600] : hAPP(c_List_Otl(U_16600),c_List_Olist_ONil(U_16600)) = c_List_Olist_ONil(U_16600),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

cnf(f_4086_3,plain,
    hAPP(c_List_Otl(U_16600),c_List_Olist_ONil(U_16600)) = c_List_Olist_ONil(U_16600),
    inference(clausify,[status(thm)],[f_4086_2]) ).

fof(f_4087_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_4087_2,plain,
    ! [U_16603,U_16602,U_16601] : hAPP(c_List_Orotate1(U_16601),hAPP(c_List_Orotate(U_16601,U_16602),U_16603)) = hAPP(c_List_Orotate(U_16601,U_16602),hAPP(c_List_Orotate1(U_16601),U_16603)),
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

cnf(f_4087_3,plain,
    hAPP(c_List_Orotate1(U_16601),hAPP(c_List_Orotate(U_16601,U_16602),U_16603)) = hAPP(c_List_Orotate(U_16601,U_16602),hAPP(c_List_Orotate1(U_16601),U_16603)),
    inference(clausify,[status(thm)],[f_4087_2]) ).

fof(f_4088_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_4088_2,plain,
    ! [U_16605,U_16604] : c_List_Orotate(U_16604,U_16605) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_16604),tc_List_Olist(U_16604)),U_16605),c_List_Orotate1(U_16604)),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

cnf(f_4088_3,plain,
    c_List_Orotate(U_16604,U_16605) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_16604),tc_List_Olist(U_16604)),U_16605),c_List_Orotate1(U_16604)),
    inference(clausify,[status(thm)],[f_4088_2]) ).

fof(f_4089_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_4089_2,plain,
    ! [U_16608,U_16607,U_16606] :
      ( hAPP(c_List_Otl(U_16607),hAPP(hAPP(c_List_Oappend(U_16607),U_16606),U_16608)) = hAPP(hAPP(c_List_Oappend(U_16607),hAPP(c_List_Otl(U_16607),U_16606)),U_16608)
      | U_16606 = c_List_Olist_ONil(U_16607) ),
    inference(variable_rename,[status(thm)],[f_4089_1]) ).

cnf(f_4089_3,plain,
    ( hAPP(c_List_Otl(U_16607),hAPP(hAPP(c_List_Oappend(U_16607),U_16606),U_16608)) = hAPP(hAPP(c_List_Oappend(U_16607),hAPP(c_List_Otl(U_16607),U_16606)),U_16608)
    | U_16606 = c_List_Olist_ONil(U_16607) ),
    inference(clausify,[status(thm)],[f_4089_2]) ).

fof(f_4090_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_4090_2,plain,
    ! [U_16611,U_16610,U_16609] : hAPP(hAPP(c_List_Otake(U_16609),U_16610),hAPP(c_List_Otl(U_16609),U_16611)) = hAPP(c_List_Otl(U_16609),hAPP(hAPP(c_List_Otake(U_16609),hAPP(c_Nat_OSuc,U_16610)),U_16611)),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

cnf(f_4090_3,plain,
    hAPP(hAPP(c_List_Otake(U_16609),U_16610),hAPP(c_List_Otl(U_16609),U_16611)) = hAPP(c_List_Otl(U_16609),hAPP(hAPP(c_List_Otake(U_16609),hAPP(c_Nat_OSuc,U_16610)),U_16611)),
    inference(clausify,[status(thm)],[f_4090_2]) ).

fof(f_4091_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_4091_2,plain,
    ! [U_16614,U_16613,U_16612] : hAPP(c_List_Orotate(U_16612,U_16613),U_16614) = hAPP(c_List_Orotate(U_16612,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16613,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16612)),U_16614))),U_16614),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

cnf(f_4091_3,plain,
    hAPP(c_List_Orotate(U_16612,U_16613),U_16614) = hAPP(c_List_Orotate(U_16612,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16613,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16612)),U_16614))),U_16614),
    inference(clausify,[status(thm)],[f_4091_2]) ).

fof(f_4092_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_4092_2,plain,
    ! [U_16617,U_16616,U_16615] : hAPP(hAPP(c_List_Odrop(U_16615),hAPP(c_Nat_OSuc,U_16616)),U_16617) = hAPP(hAPP(c_List_Odrop(U_16615),U_16616),hAPP(c_List_Otl(U_16615),U_16617)),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

cnf(f_4092_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16615),hAPP(c_Nat_OSuc,U_16616)),U_16617) = hAPP(hAPP(c_List_Odrop(U_16615),U_16616),hAPP(c_List_Otl(U_16615),U_16617)),
    inference(clausify,[status(thm)],[f_4092_2]) ).

fof(f_4093_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_4093_2,plain,
    ! [U_16620,U_16619,U_16618] : hAPP(c_List_Orotate(U_16618,hAPP(c_Nat_OSuc,U_16619)),U_16620) = hAPP(c_List_Orotate1(U_16618),hAPP(c_List_Orotate(U_16618,U_16619),U_16620)),
    inference(variable_rename,[status(thm)],[f_4093_1]) ).

cnf(f_4093_3,plain,
    hAPP(c_List_Orotate(U_16618,hAPP(c_Nat_OSuc,U_16619)),U_16620) = hAPP(c_List_Orotate1(U_16618),hAPP(c_List_Orotate(U_16618,U_16619),U_16620)),
    inference(clausify,[status(thm)],[f_4093_2]) ).

fof(f_4094_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_4094_2,plain,
    ! [U_16623,U_16622,U_16621] : hAPP(c_List_Otl(U_16621),hAPP(hAPP(c_List_Oappend(U_16621),U_16622),U_16623)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16621),U_16621,hAPP(c_List_Otl(U_16621),U_16623),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_16621),tc_List_Olist(U_16621)),U_16621),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16621),tc_List_Olist(U_16621),tc_List_Olist(U_16621)),c_List_Oappend(U_16621)),U_16623))),U_16622),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

cnf(f_4094_3,plain,
    hAPP(c_List_Otl(U_16621),hAPP(hAPP(c_List_Oappend(U_16621),U_16622),U_16623)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16621),U_16621,hAPP(c_List_Otl(U_16621),U_16623),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_16621),tc_List_Olist(U_16621)),U_16621),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16621),tc_List_Olist(U_16621),tc_List_Olist(U_16621)),c_List_Oappend(U_16621)),U_16623))),U_16622),
    inference(clausify,[status(thm)],[f_4094_2]) ).

fof(f_4095_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_4095_2,plain,
    ! [U_16626,U_16625,U_16624] :
      ( hAPP(c_List_Orotate(U_16625,U_16624),U_16626) = U_16626
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16624,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16625)),U_16626)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

cnf(f_4095_3,plain,
    ( hAPP(c_List_Orotate(U_16625,U_16624),U_16626) = U_16626
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16624,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16625)),U_16626)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4095_2]) ).

fof(f_4096_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_4096_2,plain,
    ! [U_16629,U_16628,U_16627] :
      ( hAPP(c_List_Orotate(U_16627,U_16629),U_16628) = U_16628
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16628)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

cnf(f_4096_3,plain,
    ( hAPP(c_List_Orotate(U_16627,U_16629),U_16628) = U_16628
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16628)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4096_2]) ).

fof(f_4097_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_4097_2,plain,
    ! [U_16631,U_16630] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16630)),hAPP(c_List_Otl(U_16630),U_16631)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16630)),U_16631)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

cnf(f_4097_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16630)),hAPP(c_List_Otl(U_16630),U_16631)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16630)),U_16631)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4097_2]) ).

fof(f_4098_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_4098_2,plain,
    ! [U_16634,U_16633,U_16632] : hAPP(c_List_Otl(U_16632),hAPP(hAPP(c_List_Otake(U_16632),U_16633),U_16634)) = hAPP(hAPP(c_List_Otake(U_16632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16633),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_16632),U_16634)),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

cnf(f_4098_3,plain,
    hAPP(c_List_Otl(U_16632),hAPP(hAPP(c_List_Otake(U_16632),U_16633),U_16634)) = hAPP(hAPP(c_List_Otake(U_16632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16633),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_16632),U_16634)),
    inference(clausify,[status(thm)],[f_4098_2]) ).

fof(f_4099_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_4099_2,plain,
    ! [U_16637,U_16636,U_16635] :
      ( hAPP(hAPP(c_List_Otake(U_16636),hAPP(c_Nat_OSuc,U_16637)),U_16635) = hAPP(hAPP(c_List_Olist_OCons(U_16636),hAPP(c_List_Ohd(U_16636),U_16635)),hAPP(hAPP(c_List_Otake(U_16636),U_16637),hAPP(c_List_Otl(U_16636),U_16635)))
      | U_16635 = c_List_Olist_ONil(U_16636) ),
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

cnf(f_4099_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16636),hAPP(c_Nat_OSuc,U_16637)),U_16635) = hAPP(hAPP(c_List_Olist_OCons(U_16636),hAPP(c_List_Ohd(U_16636),U_16635)),hAPP(hAPP(c_List_Otake(U_16636),U_16637),hAPP(c_List_Otl(U_16636),U_16635)))
    | U_16635 = c_List_Olist_ONil(U_16636) ),
    inference(clausify,[status(thm)],[f_4099_2]) ).

fof(f_4100_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_4100_2,plain,
    ! [U_16640,U_16639,U_16638] : hAPP(c_List_Orotate(U_16638,U_16639),U_16640) = hAPP(hAPP(c_List_Oappend(U_16638),hAPP(hAPP(c_List_Odrop(U_16638),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16639,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16638)),U_16640))),U_16640)),hAPP(hAPP(c_List_Otake(U_16638),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16639,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16638)),U_16640))),U_16640)),
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

cnf(f_4100_3,plain,
    hAPP(c_List_Orotate(U_16638,U_16639),U_16640) = hAPP(hAPP(c_List_Oappend(U_16638),hAPP(hAPP(c_List_Odrop(U_16638),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16639,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16638)),U_16640))),U_16640)),hAPP(hAPP(c_List_Otake(U_16638),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16639,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16638)),U_16640))),U_16640)),
    inference(clausify,[status(thm)],[f_4100_2]) ).

fof(f_4101_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_4101_2,plain,
    ! [U_16642,U_16641] :
      ( hAPP(c_Finite__Set_Ofold1(U_16641,c_Groups_Otimes__class_Otimes(U_16641)),hAPP(c_List_Oset(U_16641),U_16642)) = hAPP(c_List_Ofoldl(U_16641,U_16641,c_Groups_Otimes__class_Otimes(U_16641),hAPP(c_List_Ohd(U_16641),U_16642)),hAPP(c_List_Otl(U_16641),U_16642))
      | U_16642 = c_List_Olist_ONil(U_16641)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_16641) ),
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

cnf(f_4101_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_16641,c_Groups_Otimes__class_Otimes(U_16641)),hAPP(c_List_Oset(U_16641),U_16642)) = hAPP(c_List_Ofoldl(U_16641,U_16641,c_Groups_Otimes__class_Otimes(U_16641),hAPP(c_List_Ohd(U_16641),U_16642)),hAPP(c_List_Otl(U_16641),U_16642))
    | U_16642 = c_List_Olist_ONil(U_16641)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_16641) ),
    inference(clausify,[status(thm)],[f_4101_2]) ).

fof(f_4102_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_4102_2,plain,
    ! [U_16645,U_16644,U_16643] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_16643,hAPP(hAPP(c_Set_Oinsert(U_16643),U_16645),U_16644)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16643,U_16643,c_COMBI(U_16643)),U_16645),c_List_Olinorder__class_Osorted__list__of__set(U_16643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16643,tc_HOL_Obool)),U_16644),hAPP(hAPP(c_Set_Oinsert(U_16643),U_16645),c_Orderings_Obot__class_Obot(tc_fun(U_16643,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),U_16644))
      | ~ class_Orderings_Olinorder(U_16643) ),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

cnf(f_4102_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_16643,hAPP(hAPP(c_Set_Oinsert(U_16643),U_16645),U_16644)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16643,U_16643,c_COMBI(U_16643)),U_16645),c_List_Olinorder__class_Osorted__list__of__set(U_16643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16643,tc_HOL_Obool)),U_16644),hAPP(hAPP(c_Set_Oinsert(U_16643),U_16645),c_Orderings_Obot__class_Obot(tc_fun(U_16643,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16643),U_16644))
    | ~ class_Orderings_Olinorder(U_16643) ),
    inference(clausify,[status(thm)],[f_4102_2]) ).

fof(f_4103_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_4103_2,plain,
    ! [U_16650,U_16649,U_16648,U_16647,U_16646] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16647,U_16646,U_16648),U_16649),U_16650) != c_List_Olist_ONil(U_16647)
      | ~ class_Orderings_Olinorder(U_16646) ),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

cnf(f_4103_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16647,U_16646,U_16648),U_16649),U_16650) != c_List_Olist_ONil(U_16647)
    | ~ class_Orderings_Olinorder(U_16646) ),
    inference(clausify,[status(thm)],[f_4103_2]) ).

fof(f_4104_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_4104_2,plain,
    ! [U_16654,U_16653,U_16652,U_16651] : hAPP(c_List_Ofoldl(U_16651,U_16652,U_16653,U_16654),c_List_Olist_ONil(U_16652)) = U_16654,
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

cnf(f_4104_3,plain,
    hAPP(c_List_Ofoldl(U_16651,U_16652,U_16653,U_16654),c_List_Olist_ONil(U_16652)) = U_16654,
    inference(clausify,[status(thm)],[f_4104_2]) ).

fof(f_4105_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_4105_2,plain,
    ! [U_16657,U_16656,U_16655] :
      ( c_List_Oremove1(U_16655,U_16656,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16655,U_16655,c_COMBI(U_16655)),U_16656),U_16657)) = U_16657
      | ~ class_Orderings_Olinorder(U_16655) ),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

cnf(f_4105_3,plain,
    ( c_List_Oremove1(U_16655,U_16656,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16655,U_16655,c_COMBI(U_16655)),U_16656),U_16657)) = U_16657
    | ~ class_Orderings_Olinorder(U_16655) ),
    inference(clausify,[status(thm)],[f_4105_2]) ).

fof(f_4106_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_4106_2,plain,
    ! [U_16660,U_16659,U_16658] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16658),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16659),U_16660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16658),U_16659)) ),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

cnf(f_4106_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16658),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16659),U_16660)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16658),U_16659)) ),
    inference(clausify,[status(thm)],[f_4106_2]) ).

fof(f_4107_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_4107_2,plain,
    ! [U_16663,U_16662,U_16661] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16661),U_16662),hAPP(c_List_Ofoldl(U_16661,U_16661,c_Groups_Oplus__class_Oplus(U_16661),c_Groups_Ozero__class_Ozero(U_16661)),U_16663)) = hAPP(c_List_Ofoldl(U_16661,U_16661,c_Groups_Oplus__class_Oplus(U_16661),U_16662),U_16663)
      | ~ class_Groups_Omonoid__add(U_16661) ),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

cnf(f_4107_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16661),U_16662),hAPP(c_List_Ofoldl(U_16661,U_16661,c_Groups_Oplus__class_Oplus(U_16661),c_Groups_Ozero__class_Ozero(U_16661)),U_16663)) = hAPP(c_List_Ofoldl(U_16661,U_16661,c_Groups_Oplus__class_Oplus(U_16661),U_16662),U_16663)
    | ~ class_Groups_Omonoid__add(U_16661) ),
    inference(clausify,[status(thm)],[f_4107_2]) ).

fof(f_4108_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_4108_2,plain,
    ! [U_16664] :
      ( c_Finite__Set_Ofun__left__comm(U_16664,tc_List_Olist(U_16664),c_List_Olinorder__class_Oinsort__key(U_16664,U_16664,c_COMBI(U_16664)))
      | ~ class_Orderings_Olinorder(U_16664) ),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

cnf(f_4108_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_16664,tc_List_Olist(U_16664),c_List_Olinorder__class_Oinsort__key(U_16664,U_16664,c_COMBI(U_16664)))
    | ~ class_Orderings_Olinorder(U_16664) ),
    inference(clausify,[status(thm)],[f_4108_2]) ).

fof(f_4109_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_4109_2,plain,
    ! [U_16668,U_16667,U_16666,U_16665] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16666),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16667),U_16668)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16667),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16666),U_16668))
      | ~ class_Orderings_Olinorder(U_16665) ),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

cnf(f_4109_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16666),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16667),U_16668)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16667),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16665,U_16665,c_COMBI(U_16665)),U_16666),U_16668))
    | ~ class_Orderings_Olinorder(U_16665) ),
    inference(clausify,[status(thm)],[f_4109_2]) ).

fof(f_4110_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_4110_2,plain,
    ! [U_16672,U_16671,U_16670,U_16669] :
      ( hAPP(c_List_Ofoldl(U_16669,U_16669,c_Groups_Oplus__class_Oplus(U_16669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16669),U_16670),U_16671)),U_16672) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16669),U_16670),hAPP(c_List_Ofoldl(U_16669,U_16669,c_Groups_Oplus__class_Oplus(U_16669),U_16671),U_16672))
      | ~ class_Groups_Osemigroup__add(U_16669) ),
    inference(variable_rename,[status(thm)],[f_4110_1]) ).

cnf(f_4110_3,plain,
    ( hAPP(c_List_Ofoldl(U_16669,U_16669,c_Groups_Oplus__class_Oplus(U_16669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16669),U_16670),U_16671)),U_16672) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16669),U_16670),hAPP(c_List_Ofoldl(U_16669,U_16669,c_Groups_Oplus__class_Oplus(U_16669),U_16671),U_16672))
    | ~ class_Groups_Osemigroup__add(U_16669) ),
    inference(clausify,[status(thm)],[f_4110_2]) ).

fof(f_4111_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_4111_2,plain,
    ! [U_16678,U_16677,U_16676,U_16675,U_16674,U_16673] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16676),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16675),U_16678)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16675),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16676),U_16678))
      | hAPP(U_16674,U_16675) = hAPP(U_16674,U_16676)
      | ~ class_Orderings_Olinorder(U_16673) ),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

cnf(f_4111_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16676),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16675),U_16678)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16675),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16677,U_16673,U_16674),U_16676),U_16678))
    | hAPP(U_16674,U_16675) = hAPP(U_16674,U_16676)
    | ~ class_Orderings_Olinorder(U_16673) ),
    inference(clausify,[status(thm)],[f_4111_2]) ).

fof(f_4112_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_4112_2,plain,
    ! [U_16683,U_16682,U_16681,U_16680,U_16679] :
      ( hAPP(c_List_Oset(U_16680),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16680,U_16679,U_16681),U_16682),U_16683)) = hAPP(hAPP(c_Set_Oinsert(U_16680),U_16682),hAPP(c_List_Oset(U_16680),U_16683))
      | ~ class_Orderings_Olinorder(U_16679) ),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

cnf(f_4112_3,plain,
    ( hAPP(c_List_Oset(U_16680),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16680,U_16679,U_16681),U_16682),U_16683)) = hAPP(hAPP(c_Set_Oinsert(U_16680),U_16682),hAPP(c_List_Oset(U_16680),U_16683))
    | ~ class_Orderings_Olinorder(U_16679) ),
    inference(clausify,[status(thm)],[f_4112_2]) ).

fof(f_4113_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_4113_2,plain,
    ! [U_16688,U_16687,U_16686,U_16685,U_16684] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16685)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16685,U_16684,U_16686),U_16687),U_16688)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16685)),U_16688))
      | ~ class_Orderings_Olinorder(U_16684) ),
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

cnf(f_4113_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16685)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16685,U_16684,U_16686),U_16687),U_16688)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16685)),U_16688))
    | ~ class_Orderings_Olinorder(U_16684) ),
    inference(clausify,[status(thm)],[f_4113_2]) ).

fof(f_4114_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_4114_2,plain,
    ! [U_16694,U_16693,U_16692,U_16691,U_16690,U_16689] : hAPP(c_List_Ofoldl(U_16689,U_16690,U_16691,U_16692),hAPP(hAPP(c_List_Olist_OCons(U_16690),U_16693),U_16694)) = hAPP(c_List_Ofoldl(U_16689,U_16690,U_16691,hAPP(hAPP(U_16691,U_16692),U_16693)),U_16694),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

cnf(f_4114_3,plain,
    hAPP(c_List_Ofoldl(U_16689,U_16690,U_16691,U_16692),hAPP(hAPP(c_List_Olist_OCons(U_16690),U_16693),U_16694)) = hAPP(c_List_Ofoldl(U_16689,U_16690,U_16691,hAPP(hAPP(U_16691,U_16692),U_16693)),U_16694),
    inference(clausify,[status(thm)],[f_4114_2]) ).

fof(f_4115_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_4115_2,plain,
    ! [U_16700,U_16699,U_16698,U_16697,U_16696,U_16695] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700)) = hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),U_16700))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16695),hAPP(U_16696,U_16697)),hAPP(U_16696,U_16698))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700)) = hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16695),hAPP(U_16696,U_16697)),hAPP(U_16696,U_16698))) ) )
      | ~ class_Orderings_Olinorder(U_16695) ),
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

cnf(f_4115_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700)) = hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16695),hAPP(U_16696,U_16697)),hAPP(U_16696,U_16698)))
    | ~ class_Orderings_Olinorder(U_16695) ),
    inference(clausify,[status(thm)],[f_4115_2]) ).

cnf(f_4115_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),U_16700)) = hAPP(hAPP(c_List_Olist_OCons(U_16699),U_16698),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16699,U_16695,U_16696),U_16697),U_16700))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16695),hAPP(U_16696,U_16697)),hAPP(U_16696,U_16698)))
    | ~ class_Orderings_Olinorder(U_16695) ),
    inference(clausify,[status(thm)],[f_4115_2]) ).

fof(f_4116_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_4116_2,plain,
    ! [U_16704,U_16703,U_16702,U_16701] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16702,U_16701,U_16703),U_16704),c_List_Olist_ONil(U_16702)) = hAPP(hAPP(c_List_Olist_OCons(U_16702),U_16704),c_List_Olist_ONil(U_16702))
      | ~ class_Orderings_Olinorder(U_16701) ),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

cnf(f_4116_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16702,U_16701,U_16703),U_16704),c_List_Olist_ONil(U_16702)) = hAPP(hAPP(c_List_Olist_OCons(U_16702),U_16704),c_List_Olist_ONil(U_16702))
    | ~ class_Orderings_Olinorder(U_16701) ),
    inference(clausify,[status(thm)],[f_4116_2]) ).

fof(f_4117_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_4117_2,plain,
    ! [U_16710,U_16709,U_16708,U_16707,U_16706,U_16705] : hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,U_16708),hAPP(hAPP(c_List_Oappend(U_16706),U_16709),U_16710)) = hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,U_16708),U_16709)),U_16710),
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

cnf(f_4117_3,plain,
    hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,U_16708),hAPP(hAPP(c_List_Oappend(U_16706),U_16709),U_16710)) = hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,hAPP(c_List_Ofoldl(U_16705,U_16706,U_16707,U_16708),U_16709)),U_16710),
    inference(clausify,[status(thm)],[f_4117_2]) ).

fof(f_4118_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_4118_2,plain,
    ! [U_16711] :
      ( c_List_Omonoid__add__class_Olistsum(U_16711) = c_List_Ofoldl(U_16711,U_16711,c_Groups_Oplus__class_Oplus(U_16711),c_Groups_Ozero__class_Ozero(U_16711))
      | ~ class_Groups_Omonoid__add(U_16711) ),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

cnf(f_4118_3,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_16711) = c_List_Ofoldl(U_16711,U_16711,c_Groups_Oplus__class_Oplus(U_16711),c_Groups_Ozero__class_Ozero(U_16711))
    | ~ class_Groups_Omonoid__add(U_16711) ),
    inference(clausify,[status(thm)],[f_4118_2]) ).

fof(f_4119_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_4119_2,plain,
    ! [U_16715,U_16714] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16714),U_16715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16713] :
            ( U_16713 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16713),hAPP(c_List_Oset(tc_Nat_Onat),U_16715))) )
        | U_16714 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_16712] :
              ( U_16712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16712),hAPP(c_List_Oset(tc_Nat_Onat),U_16715))) )
          & U_16714 = 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_16714),U_16715) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

fof(f_4119_3,plain,
    ( ! [U_16719,U_16717] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16717),U_16719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16713] :
            ( U_16713 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16713),hAPP(c_List_Oset(tc_Nat_Onat),U_16719))) )
        | U_16717 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16718,U_16716] :
        ( ( ! [U_16712] :
              ( U_16712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16712),hAPP(c_List_Oset(tc_Nat_Onat),U_16718))) )
          & U_16716 = 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_16716),U_16718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4119_2]) ).

fof(f_4119_4,plain,
    ( ! [U_16719,U_16717] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16717),U_16719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK422(U_16719,U_16717) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK422(U_16719,U_16717)),hAPP(c_List_Oset(tc_Nat_Onat),U_16719))) )
        | U_16717 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16718,U_16716] :
        ( ( ! [U_16712] :
              ( U_16712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16712),hAPP(c_List_Oset(tc_Nat_Onat),U_16718))) )
          & U_16716 = 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_16716),U_16718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_16713,sK422(U_16719,U_16717))],[f_4119_3]) ).

cnf(f_4119_5,plain,
    ( U_16716 = 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_16716),U_16718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

cnf(f_4119_6,plain,
    ( U_16712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16712),hAPP(c_List_Oset(tc_Nat_Onat),U_16718)))
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16716),U_16718) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

cnf(f_4119_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK422(U_16719,U_16717)),hAPP(c_List_Oset(tc_Nat_Onat),U_16719)))
    | U_16717 != 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_16717),U_16719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

cnf(f_4119_8,plain,
    ( sK422(U_16719,U_16717) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_16717 != 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_16717),U_16719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

fof(f_4120_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_4120_2,plain,
    ! [U_16724,U_16723,U_16722,U_16721,U_16720] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_16721),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16721,U_16720,U_16722),U_16723),U_16724)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_16721),U_16724))
          | hBOOL(hAPP(hAPP(c_member(U_16721),U_16723),hAPP(c_List_Oset(U_16721),U_16724))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_16721),U_16724))
            & ~ hBOOL(hAPP(hAPP(c_member(U_16721),U_16723),hAPP(c_List_Oset(U_16721),U_16724))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_16721),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16721,U_16720,U_16722),U_16723),U_16724))) ) )
      | ~ class_Orderings_Olinorder(U_16720) ),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

cnf(f_4120_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16721),U_16723),hAPP(c_List_Oset(U_16721),U_16724)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16721),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16721,U_16720,U_16722),U_16723),U_16724)))
    | ~ class_Orderings_Olinorder(U_16720) ),
    inference(clausify,[status(thm)],[f_4120_2]) ).

cnf(f_4120_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16721),U_16724))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16721),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16721,U_16720,U_16722),U_16723),U_16724)))
    | ~ class_Orderings_Olinorder(U_16720) ),
    inference(clausify,[status(thm)],[f_4120_2]) ).

cnf(f_4120_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16721),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16721,U_16720,U_16722),U_16723),U_16724)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16721),U_16724))
    | hBOOL(hAPP(hAPP(c_member(U_16721),U_16723),hAPP(c_List_Oset(U_16721),U_16724)))
    | ~ class_Orderings_Olinorder(U_16720) ),
    inference(clausify,[status(thm)],[f_4120_2]) ).

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_16729,U_16728,U_16727,U_16726,U_16725] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16725,U_16726,U_16727),U_16728),hAPP(c_List_Oset(U_16725),U_16729)) = hAPP(c_List_Ofoldl(U_16726,U_16725,hAPP(c_COMBC(U_16725,U_16726,U_16726),U_16727),U_16728),U_16729)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_16725,U_16726,U_16727) ),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

cnf(f_4121_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16725,U_16726,U_16727),U_16728),hAPP(c_List_Oset(U_16725),U_16729)) = hAPP(c_List_Ofoldl(U_16726,U_16725,hAPP(c_COMBC(U_16725,U_16726,U_16726),U_16727),U_16728),U_16729)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_16725,U_16726,U_16727) ),
    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_16731,U_16730] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16730,hAPP(c_List_Oset(U_16730),U_16731)) = hAPP(c_List_Ofoldl(U_16730,U_16730,c_Lattices_Osemilattice__sup__class_Osup(U_16730),c_Orderings_Obot__class_Obot(U_16730)),U_16731)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

cnf(f_4122_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16730,hAPP(c_List_Oset(U_16730),U_16731)) = hAPP(c_List_Ofoldl(U_16730,U_16730,c_Lattices_Osemilattice__sup__class_Osup(U_16730),c_Orderings_Obot__class_Obot(U_16730)),U_16731)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ),
    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_16733,U_16732] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16732,hAPP(c_List_Oset(U_16732),U_16733)) = hAPP(c_List_Ofoldl(U_16732,U_16732,c_Lattices_Osemilattice__inf__class_Oinf(U_16732),c_Orderings_Otop__class_Otop(U_16732)),U_16733)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16732) ),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

cnf(f_4123_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16732,hAPP(c_List_Oset(U_16732),U_16733)) = hAPP(c_List_Ofoldl(U_16732,U_16732,c_Lattices_Osemilattice__inf__class_Oinf(U_16732),c_Orderings_Otop__class_Otop(U_16732)),U_16733)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16732) ),
    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_16736,U_16735,U_16734] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16734,hAPP(c_List_Oset(U_16734),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16735),U_16736))) = hAPP(c_List_Ofoldl(U_16734,U_16734,c_Lattices_Osemilattice__sup__class_Osup(U_16734),U_16735),U_16736)
      | ~ class_Lattices_Olattice(U_16734) ),
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

cnf(f_4124_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_16734,hAPP(c_List_Oset(U_16734),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16735),U_16736))) = hAPP(c_List_Ofoldl(U_16734,U_16734,c_Lattices_Osemilattice__sup__class_Osup(U_16734),U_16735),U_16736)
    | ~ class_Lattices_Olattice(U_16734) ),
    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_16739,U_16738,U_16737] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16737,hAPP(c_List_Oset(U_16737),hAPP(hAPP(c_List_Olist_OCons(U_16737),U_16738),U_16739))) = hAPP(c_List_Ofoldl(U_16737,U_16737,c_Lattices_Osemilattice__inf__class_Oinf(U_16737),U_16738),U_16739)
      | ~ class_Lattices_Olattice(U_16737) ),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

cnf(f_4125_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_16737,hAPP(c_List_Oset(U_16737),hAPP(hAPP(c_List_Olist_OCons(U_16737),U_16738),U_16739))) = hAPP(c_List_Ofoldl(U_16737,U_16737,c_Lattices_Osemilattice__inf__class_Oinf(U_16737),U_16738),U_16739)
    | ~ class_Lattices_Olattice(U_16737) ),
    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_16742,U_16741,U_16740] :
      ( c_Big__Operators_Olinorder__class_OMin(U_16740,hAPP(c_List_Oset(U_16740),hAPP(hAPP(c_List_Olist_OCons(U_16740),U_16741),U_16742))) = hAPP(c_List_Ofoldl(U_16740,U_16740,c_Orderings_Oord__class_Omin(U_16740),U_16741),U_16742)
      | ~ class_Orderings_Olinorder(U_16740) ),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

cnf(f_4126_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_16740,hAPP(c_List_Oset(U_16740),hAPP(hAPP(c_List_Olist_OCons(U_16740),U_16741),U_16742))) = hAPP(c_List_Ofoldl(U_16740,U_16740,c_Orderings_Oord__class_Omin(U_16740),U_16741),U_16742)
    | ~ class_Orderings_Olinorder(U_16740) ),
    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_16745,U_16744,U_16743] :
      ( c_Big__Operators_Olinorder__class_OMax(U_16743,hAPP(c_List_Oset(U_16743),hAPP(hAPP(c_List_Olist_OCons(U_16743),U_16744),U_16745))) = hAPP(c_List_Ofoldl(U_16743,U_16743,c_Orderings_Oord__class_Omax(U_16743),U_16744),U_16745)
      | ~ class_Orderings_Olinorder(U_16743) ),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

cnf(f_4127_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_16743,hAPP(c_List_Oset(U_16743),hAPP(hAPP(c_List_Olist_OCons(U_16743),U_16744),U_16745))) = hAPP(c_List_Ofoldl(U_16743,U_16743,c_Orderings_Oord__class_Omax(U_16743),U_16744),U_16745)
    | ~ class_Orderings_Olinorder(U_16743) ),
    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_16748,U_16747,U_16746] :
      ( c_Big__Operators_Olattice_OInf__fin(U_16746,c_Orderings_Oord__class_Omin(U_16746),hAPP(c_List_Oset(U_16746),hAPP(hAPP(c_List_Olist_OCons(U_16746),U_16747),U_16748))) = hAPP(c_List_Ofoldl(U_16746,U_16746,c_Orderings_Oord__class_Omin(U_16746),U_16747),U_16748)
      | ~ class_Orderings_Olinorder(U_16746) ),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

cnf(f_4128_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_16746,c_Orderings_Oord__class_Omin(U_16746),hAPP(c_List_Oset(U_16746),hAPP(hAPP(c_List_Olist_OCons(U_16746),U_16747),U_16748))) = hAPP(c_List_Ofoldl(U_16746,U_16746,c_Orderings_Oord__class_Omin(U_16746),U_16747),U_16748)
    | ~ class_Orderings_Olinorder(U_16746) ),
    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_16751,U_16750,U_16749] :
      ( c_Big__Operators_Olattice_OSup__fin(U_16749,c_Orderings_Oord__class_Omax(U_16749),hAPP(c_List_Oset(U_16749),hAPP(hAPP(c_List_Olist_OCons(U_16749),U_16750),U_16751))) = hAPP(c_List_Ofoldl(U_16749,U_16749,c_Orderings_Oord__class_Omax(U_16749),U_16750),U_16751)
      | ~ class_Orderings_Olinorder(U_16749) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

cnf(f_4129_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_16749,c_Orderings_Oord__class_Omax(U_16749),hAPP(c_List_Oset(U_16749),hAPP(hAPP(c_List_Olist_OCons(U_16749),U_16750),U_16751))) = hAPP(c_List_Ofoldl(U_16749,U_16749,c_Orderings_Oord__class_Omax(U_16749),U_16750),U_16751)
    | ~ class_Orderings_Olinorder(U_16749) ),
    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_16755,U_16754,U_16753,U_16752] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16753,U_16752),hAPP(c_List_Oset(U_16753),U_16754)),U_16755) = hAPP(c_List_Ofoldl(U_16752,U_16753,hAPP(c_COMBC(U_16753,U_16752,U_16752),hAPP(hAPP(c_COMBB(U_16752,tc_fun(U_16752,U_16752),U_16753),c_Lattices_Osemilattice__sup__class_Osup(U_16752)),U_16755)),c_Orderings_Obot__class_Obot(U_16752)),U_16754)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16752) ),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

cnf(f_4130_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16753,U_16752),hAPP(c_List_Oset(U_16753),U_16754)),U_16755) = hAPP(c_List_Ofoldl(U_16752,U_16753,hAPP(c_COMBC(U_16753,U_16752,U_16752),hAPP(hAPP(c_COMBB(U_16752,tc_fun(U_16752,U_16752),U_16753),c_Lattices_Osemilattice__sup__class_Osup(U_16752)),U_16755)),c_Orderings_Obot__class_Obot(U_16752)),U_16754)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16752) ),
    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_16759,U_16758,U_16757,U_16756] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16757,U_16756),hAPP(c_List_Oset(U_16757),U_16758)),U_16759) = hAPP(c_List_Ofoldl(U_16756,U_16757,hAPP(c_COMBC(U_16757,U_16756,U_16756),hAPP(hAPP(c_COMBB(U_16756,tc_fun(U_16756,U_16756),U_16757),c_Lattices_Osemilattice__inf__class_Oinf(U_16756)),U_16759)),c_Orderings_Otop__class_Otop(U_16756)),U_16758)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16756) ),
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

cnf(f_4131_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16757,U_16756),hAPP(c_List_Oset(U_16757),U_16758)),U_16759) = hAPP(c_List_Ofoldl(U_16756,U_16757,hAPP(c_COMBC(U_16757,U_16756,U_16756),hAPP(hAPP(c_COMBB(U_16756,tc_fun(U_16756,U_16756),U_16757),c_Lattices_Osemilattice__inf__class_Oinf(U_16756)),U_16759)),c_Orderings_Otop__class_Otop(U_16756)),U_16758)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16756) ),
    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_16761,U_16760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16760),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_16761)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16760),hAPP(c_List_Oset(tc_Nat_Onat),U_16761))) ),
    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_16760),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_16761)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16760),hAPP(c_List_Oset(tc_Nat_Onat),U_16761))) ),
    inference(clausify,[status(thm)],[f_4132_2]) ).

fof(f_4133_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_4133_2,plain,
    ! [U_16766,U_16765,U_16764,U_16763,U_16762] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16765,U_16762,U_16763,U_16764,U_16766) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16765,U_16762,U_16763),U_16764),U_16766)
      | hBOOL(hAPP(hAPP(c_member(U_16762),hAPP(U_16763,U_16764)),hAPP(c_Set_Oimage(U_16765,U_16762,U_16763),hAPP(c_List_Oset(U_16765),U_16766))))
      | ~ class_Orderings_Olinorder(U_16762) ),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

cnf(f_4133_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16765,U_16762,U_16763,U_16764,U_16766) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16765,U_16762,U_16763),U_16764),U_16766)
    | hBOOL(hAPP(hAPP(c_member(U_16762),hAPP(U_16763,U_16764)),hAPP(c_Set_Oimage(U_16765,U_16762,U_16763),hAPP(c_List_Oset(U_16765),U_16766))))
    | ~ class_Orderings_Olinorder(U_16762) ),
    inference(clausify,[status(thm)],[f_4133_2]) ).

fof(f_4134_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_4134_2,plain,
    ! [U_16772,U_16771,U_16770,U_16769] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16770),tc_List_Olist(U_16770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16770),tc_List_Olist(U_16770)),U_16771),hAPP(hAPP(c_List_Oappend(U_16770),U_16771),U_16769))),c_List_Olexord(U_16770,U_16772)))
      | ! [U_16768,U_16767] : U_16769 != hAPP(hAPP(c_List_Olist_OCons(U_16770),U_16768),U_16767) ),
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

cnf(f_4134_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16770),tc_List_Olist(U_16770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16770),tc_List_Olist(U_16770)),U_16771),hAPP(hAPP(c_List_Oappend(U_16770),U_16771),U_16769))),c_List_Olexord(U_16770,U_16772)))
    | U_16769 != hAPP(hAPP(c_List_Olist_OCons(U_16770),U_16768),U_16767) ),
    inference(clausify,[status(thm)],[f_4134_2]) ).

fof(f_4135_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_4135_2,plain,
    ! [U_16777,U_16776,U_16775,U_16774,U_16773] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16774),c_List_Olinorder__class_Oinsort__insert__key(U_16774,U_16773,U_16776,U_16777,U_16775)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16774),U_16775))
      | ~ class_Orderings_Olinorder(U_16773) ),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

cnf(f_4135_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16774),c_List_Olinorder__class_Oinsort__insert__key(U_16774,U_16773,U_16776,U_16777,U_16775)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16774),U_16775))
    | ~ class_Orderings_Olinorder(U_16773) ),
    inference(clausify,[status(thm)],[f_4135_2]) ).

fof(f_4136_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_4136_2,plain,
    ! [U_16780,U_16779,U_16778] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16778,U_16778,c_COMBI(U_16778),U_16779,U_16780) = U_16780
      | ~ hBOOL(hAPP(hAPP(c_member(U_16778),U_16779),hAPP(c_List_Oset(U_16778),U_16780)))
      | ~ class_Orderings_Olinorder(U_16778) ),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

cnf(f_4136_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16778,U_16778,c_COMBI(U_16778),U_16779,U_16780) = U_16780
    | ~ hBOOL(hAPP(hAPP(c_member(U_16778),U_16779),hAPP(c_List_Oset(U_16778),U_16780)))
    | ~ class_Orderings_Olinorder(U_16778) ),
    inference(clausify,[status(thm)],[f_4136_2]) ).

fof(f_4137_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_4137_2,plain,
    ! [U_16783,U_16782,U_16781] :
      ( hAPP(c_List_Oset(U_16781),c_List_Olinorder__class_Oinsort__insert__key(U_16781,U_16781,c_COMBI(U_16781),U_16782,U_16783)) = hAPP(hAPP(c_Set_Oinsert(U_16781),U_16782),hAPP(c_List_Oset(U_16781),U_16783))
      | ~ class_Orderings_Olinorder(U_16781) ),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

cnf(f_4137_3,plain,
    ( hAPP(c_List_Oset(U_16781),c_List_Olinorder__class_Oinsort__insert__key(U_16781,U_16781,c_COMBI(U_16781),U_16782,U_16783)) = hAPP(hAPP(c_Set_Oinsert(U_16781),U_16782),hAPP(c_List_Oset(U_16781),U_16783))
    | ~ class_Orderings_Olinorder(U_16781) ),
    inference(clausify,[status(thm)],[f_4137_2]) ).

fof(f_4138_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_4138_2,plain,
    ! [U_16788,U_16787,U_16786,U_16785,U_16784] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16787,U_16784,U_16785,U_16786,U_16788) = U_16788
      | ~ hBOOL(hAPP(hAPP(c_member(U_16784),hAPP(U_16785,U_16786)),hAPP(c_Set_Oimage(U_16787,U_16784,U_16785),hAPP(c_List_Oset(U_16787),U_16788))))
      | ~ class_Orderings_Olinorder(U_16784) ),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

cnf(f_4138_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16787,U_16784,U_16785,U_16786,U_16788) = U_16788
    | ~ hBOOL(hAPP(hAPP(c_member(U_16784),hAPP(U_16785,U_16786)),hAPP(c_Set_Oimage(U_16787,U_16784,U_16785),hAPP(c_List_Oset(U_16787),U_16788))))
    | ~ class_Orderings_Olinorder(U_16784) ),
    inference(clausify,[status(thm)],[f_4138_2]) ).

fof(f_4139_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_4139_2,plain,
    ! [U_16791,U_16790,U_16789] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16789,U_16789,c_COMBI(U_16789),U_16790,U_16791) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16789,U_16789,c_COMBI(U_16789)),U_16790),U_16791)
      | hBOOL(hAPP(hAPP(c_member(U_16789),U_16790),hAPP(c_List_Oset(U_16789),U_16791)))
      | ~ class_Orderings_Olinorder(U_16789) ),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

cnf(f_4139_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16789,U_16789,c_COMBI(U_16789),U_16790,U_16791) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16789,U_16789,c_COMBI(U_16789)),U_16790),U_16791)
    | hBOOL(hAPP(hAPP(c_member(U_16789),U_16790),hAPP(c_List_Oset(U_16789),U_16791)))
    | ~ class_Orderings_Olinorder(U_16789) ),
    inference(clausify,[status(thm)],[f_4139_2]) ).

fof(f_4140_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_4140_2,plain,
    ! [U_16798,U_16797,U_16796] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16796),tc_List_Olist(U_16796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16796),tc_List_Olist(U_16796)),c_List_Olist_ONil(U_16796)),U_16797)),c_List_Olexord(U_16796,U_16798)))
        | ! [U_16795,U_16794] : U_16797 != hAPP(hAPP(c_List_Olist_OCons(U_16796),U_16795),U_16794) )
      & ( ? [U_16793,U_16792] : U_16797 = hAPP(hAPP(c_List_Olist_OCons(U_16796),U_16793),U_16792)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16796),tc_List_Olist(U_16796))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16796),tc_List_Olist(U_16796)),c_List_Olist_ONil(U_16796)),U_16797)),c_List_Olexord(U_16796,U_16798))) ) ),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

fof(f_4140_3,plain,
    ( ! [U_16804,U_16802,U_16800] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16800),tc_List_Olist(U_16800))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16800),tc_List_Olist(U_16800)),c_List_Olist_ONil(U_16800)),U_16802)),c_List_Olexord(U_16800,U_16804)))
        | ! [U_16795,U_16794] : U_16802 != hAPP(hAPP(c_List_Olist_OCons(U_16800),U_16795),U_16794) )
    & ! [U_16803,U_16801,U_16799] :
        ( ? [U_16793,U_16792] : U_16801 = hAPP(hAPP(c_List_Olist_OCons(U_16799),U_16793),U_16792)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16799),tc_List_Olist(U_16799))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16799),tc_List_Olist(U_16799)),c_List_Olist_ONil(U_16799)),U_16801)),c_List_Olexord(U_16799,U_16803))) ) ),
    inference(miniscope,[status(thm)],[f_4140_2]) ).

fof(f_4140_4,plain,
    ( ! [U_16804,U_16802,U_16800] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16800),tc_List_Olist(U_16800))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16800),tc_List_Olist(U_16800)),c_List_Olist_ONil(U_16800)),U_16802)),c_List_Olexord(U_16800,U_16804)))
        | ! [U_16795,U_16794] : U_16802 != hAPP(hAPP(c_List_Olist_OCons(U_16800),U_16795),U_16794) )
    & ! [U_16803,U_16801,U_16799] :
        ( ? [U_16792] : U_16801 = hAPP(hAPP(c_List_Olist_OCons(U_16799),sK423(U_16803,U_16801,U_16799)),U_16792)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16799),tc_List_Olist(U_16799))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16799),tc_List_Olist(U_16799)),c_List_Olist_ONil(U_16799)),U_16801)),c_List_Olexord(U_16799,U_16803))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_16793,sK423(U_16803,U_16801,U_16799))],[f_4140_3]) ).

fof(f_4140_5,plain,
    ( ! [U_16804,U_16802,U_16800] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16800),tc_List_Olist(U_16800))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16800),tc_List_Olist(U_16800)),c_List_Olist_ONil(U_16800)),U_16802)),c_List_Olexord(U_16800,U_16804)))
        | ! [U_16795,U_16794] : U_16802 != hAPP(hAPP(c_List_Olist_OCons(U_16800),U_16795),U_16794) )
    & ! [U_16803,U_16801,U_16799] :
        ( U_16801 = hAPP(hAPP(c_List_Olist_OCons(U_16799),sK423(U_16803,U_16801,U_16799)),sK424(U_16803,U_16801,U_16799))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16799),tc_List_Olist(U_16799))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16799),tc_List_Olist(U_16799)),c_List_Olist_ONil(U_16799)),U_16801)),c_List_Olexord(U_16799,U_16803))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_16792,sK424(U_16803,U_16801,U_16799))],[f_4140_4]) ).

cnf(f_4140_6,plain,
    ( U_16801 = hAPP(hAPP(c_List_Olist_OCons(U_16799),sK423(U_16803,U_16801,U_16799)),sK424(U_16803,U_16801,U_16799))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16799),tc_List_Olist(U_16799))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16799),tc_List_Olist(U_16799)),c_List_Olist_ONil(U_16799)),U_16801)),c_List_Olexord(U_16799,U_16803))) ),
    inference(clausify,[status(thm)],[f_4140_5]) ).

cnf(f_4140_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16800),tc_List_Olist(U_16800))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16800),tc_List_Olist(U_16800)),c_List_Olist_ONil(U_16800)),U_16802)),c_List_Olexord(U_16800,U_16804)))
    | U_16802 != hAPP(hAPP(c_List_Olist_OCons(U_16800),U_16795),U_16794) ),
    inference(clausify,[status(thm)],[f_4140_5]) ).

fof(f_4141_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_4141_2,plain,
    ! [U_16808,U_16807,U_16806,U_16805] :
      ( ( ( c_List_Olast(U_16806,hAPP(hAPP(c_List_Olist__update(U_16806,U_16805),U_16807),U_16808)) = c_List_Olast(U_16806,U_16805)
          | U_16807 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16806)),U_16805)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_16806,hAPP(hAPP(c_List_Olist__update(U_16806,U_16805),U_16807),U_16808)) = U_16808
          | U_16807 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16806)),U_16805)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_16805 = c_List_Olist_ONil(U_16806) ),
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

cnf(f_4141_3,plain,
    ( c_List_Olast(U_16806,hAPP(hAPP(c_List_Olist__update(U_16806,U_16805),U_16807),U_16808)) = U_16808
    | U_16807 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16806)),U_16805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_16805 = c_List_Olist_ONil(U_16806) ),
    inference(clausify,[status(thm)],[f_4141_2]) ).

cnf(f_4141_4,plain,
    ( c_List_Olast(U_16806,hAPP(hAPP(c_List_Olist__update(U_16806,U_16805),U_16807),U_16808)) = c_List_Olast(U_16806,U_16805)
    | U_16807 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16806)),U_16805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_16805 = c_List_Olist_ONil(U_16806) ),
    inference(clausify,[status(thm)],[f_4141_2]) ).

fof(f_4142_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_4142_2,plain,
    ! [U_16811,U_16810,U_16809] :
      ( ( c_List_Olast(U_16810,hAPP(hAPP(c_List_Olist_OCons(U_16810),U_16811),U_16809)) = c_List_Olast(U_16810,U_16809)
        | U_16809 = c_List_Olist_ONil(U_16810) )
      & ( c_List_Olast(U_16810,hAPP(hAPP(c_List_Olist_OCons(U_16810),U_16811),U_16809)) = U_16811
        | U_16809 != c_List_Olist_ONil(U_16810) ) ),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

fof(f_4142_3,plain,
    ( ! [U_16817,U_16815,U_16813] :
        ( c_List_Olast(U_16815,hAPP(hAPP(c_List_Olist_OCons(U_16815),U_16817),U_16813)) = c_List_Olast(U_16815,U_16813)
        | U_16813 = c_List_Olist_ONil(U_16815) )
    & ! [U_16816,U_16814,U_16812] :
        ( c_List_Olast(U_16814,hAPP(hAPP(c_List_Olist_OCons(U_16814),U_16816),U_16812)) = U_16816
        | U_16812 != c_List_Olist_ONil(U_16814) ) ),
    inference(miniscope,[status(thm)],[f_4142_2]) ).

cnf(f_4142_4,plain,
    ( c_List_Olast(U_16814,hAPP(hAPP(c_List_Olist_OCons(U_16814),U_16816),U_16812)) = U_16816
    | U_16812 != c_List_Olist_ONil(U_16814) ),
    inference(clausify,[status(thm)],[f_4142_3]) ).

cnf(f_4142_5,plain,
    ( c_List_Olast(U_16815,hAPP(hAPP(c_List_Olist_OCons(U_16815),U_16817),U_16813)) = c_List_Olast(U_16815,U_16813)
    | U_16813 = c_List_Olist_ONil(U_16815) ),
    inference(clausify,[status(thm)],[f_4142_3]) ).

fof(f_4143_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_4143_2,plain,
    ! [U_16820,U_16819,U_16818] :
      ( c_List_Olast(U_16819,hAPP(hAPP(c_List_Olist_OCons(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_4143_1]) ).

cnf(f_4143_3,plain,
    ( c_List_Olast(U_16819,hAPP(hAPP(c_List_Olist_OCons(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_4143_2]) ).

fof(f_4144_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_4144_2,plain,
    ! [U_16823,U_16822,U_16821] :
      ( c_List_Olast(U_16822,hAPP(hAPP(c_List_Olist_OCons(U_16822),U_16823),U_16821)) = U_16823
      | U_16821 != c_List_Olist_ONil(U_16822) ),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

cnf(f_4144_3,plain,
    ( c_List_Olast(U_16822,hAPP(hAPP(c_List_Olist_OCons(U_16822),U_16823),U_16821)) = U_16823
    | U_16821 != c_List_Olist_ONil(U_16822) ),
    inference(clausify,[status(thm)],[f_4144_2]) ).

fof(f_4145_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_4145_2,plain,
    ! [U_16826,U_16825,U_16824] :
      ( ( c_List_Olast(U_16825,hAPP(hAPP(c_List_Oappend(U_16825),U_16826),U_16824)) = c_List_Olast(U_16825,U_16824)
        | U_16824 = c_List_Olist_ONil(U_16825) )
      & ( c_List_Olast(U_16825,hAPP(hAPP(c_List_Oappend(U_16825),U_16826),U_16824)) = c_List_Olast(U_16825,U_16826)
        | U_16824 != c_List_Olist_ONil(U_16825) ) ),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

fof(f_4145_3,plain,
    ( ! [U_16832,U_16830,U_16828] :
        ( c_List_Olast(U_16830,hAPP(hAPP(c_List_Oappend(U_16830),U_16832),U_16828)) = c_List_Olast(U_16830,U_16828)
        | U_16828 = c_List_Olist_ONil(U_16830) )
    & ! [U_16831,U_16829,U_16827] :
        ( c_List_Olast(U_16829,hAPP(hAPP(c_List_Oappend(U_16829),U_16831),U_16827)) = c_List_Olast(U_16829,U_16831)
        | U_16827 != c_List_Olist_ONil(U_16829) ) ),
    inference(miniscope,[status(thm)],[f_4145_2]) ).

cnf(f_4145_4,plain,
    ( c_List_Olast(U_16829,hAPP(hAPP(c_List_Oappend(U_16829),U_16831),U_16827)) = c_List_Olast(U_16829,U_16831)
    | U_16827 != c_List_Olist_ONil(U_16829) ),
    inference(clausify,[status(thm)],[f_4145_3]) ).

cnf(f_4145_5,plain,
    ( c_List_Olast(U_16830,hAPP(hAPP(c_List_Oappend(U_16830),U_16832),U_16828)) = c_List_Olast(U_16830,U_16828)
    | U_16828 = c_List_Olist_ONil(U_16830) ),
    inference(clausify,[status(thm)],[f_4145_3]) ).

fof(f_4146_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_4146_2,plain,
    ! [U_16835,U_16834,U_16833] :
      ( c_List_Olast(U_16834,hAPP(hAPP(c_List_Oappend(U_16834),U_16835),U_16833)) = c_List_Olast(U_16834,U_16833)
      | U_16833 = c_List_Olist_ONil(U_16834) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

cnf(f_4146_3,plain,
    ( c_List_Olast(U_16834,hAPP(hAPP(c_List_Oappend(U_16834),U_16835),U_16833)) = c_List_Olast(U_16834,U_16833)
    | U_16833 = c_List_Olist_ONil(U_16834) ),
    inference(clausify,[status(thm)],[f_4146_2]) ).

fof(f_4147_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_4147_2,plain,
    ! [U_16838,U_16837,U_16836] :
      ( c_List_Olast(U_16837,hAPP(hAPP(c_List_Oappend(U_16837),U_16838),U_16836)) = c_List_Olast(U_16837,U_16838)
      | U_16836 != c_List_Olist_ONil(U_16837) ),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

cnf(f_4147_3,plain,
    ( c_List_Olast(U_16837,hAPP(hAPP(c_List_Oappend(U_16837),U_16838),U_16836)) = c_List_Olast(U_16837,U_16838)
    | U_16836 != c_List_Olist_ONil(U_16837) ),
    inference(clausify,[status(thm)],[f_4147_2]) ).

fof(f_4148_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_4148_2,plain,
    ! [U_16840,U_16839] :
      ( hBOOL(hAPP(hAPP(c_member(U_16840),c_List_Olast(U_16840,U_16839)),hAPP(c_List_Oset(U_16840),U_16839)))
      | U_16839 = c_List_Olist_ONil(U_16840) ),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

cnf(f_4148_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16840),c_List_Olast(U_16840,U_16839)),hAPP(c_List_Oset(U_16840),U_16839)))
    | U_16839 = c_List_Olist_ONil(U_16840) ),
    inference(clausify,[status(thm)],[f_4148_2]) ).

fof(f_4149_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_4149_2,plain,
    ! [U_16843,U_16842,U_16841] : c_List_Olast(U_16841,hAPP(hAPP(c_List_Oappend(U_16841),U_16842),hAPP(hAPP(c_List_Olist_OCons(U_16841),U_16843),c_List_Olist_ONil(U_16841)))) = U_16843,
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

cnf(f_4149_3,plain,
    c_List_Olast(U_16841,hAPP(hAPP(c_List_Oappend(U_16841),U_16842),hAPP(hAPP(c_List_Olist_OCons(U_16841),U_16843),c_List_Olist_ONil(U_16841)))) = U_16843,
    inference(clausify,[status(thm)],[f_4149_2]) ).

fof(f_4150_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_4150_2,plain,
    ! [U_16846,U_16845,U_16844] :
      ( c_List_Olast(U_16845,hAPP(hAPP(c_List_Odrop(U_16845),U_16844),U_16846)) = c_List_Olast(U_16845,U_16846)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16844),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16845)),U_16846))) ),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

cnf(f_4150_3,plain,
    ( c_List_Olast(U_16845,hAPP(hAPP(c_List_Odrop(U_16845),U_16844),U_16846)) = c_List_Olast(U_16845,U_16846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16844),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16845)),U_16846))) ),
    inference(clausify,[status(thm)],[f_4150_2]) ).

fof(f_4151_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_4151_2,plain,
    ! [U_16848,U_16847] :
      ( hAPP(hAPP(c_List_Oappend(U_16848),c_List_Obutlast(U_16848,U_16847)),hAPP(hAPP(c_List_Olist_OCons(U_16848),c_List_Olast(U_16848,U_16847)),c_List_Olist_ONil(U_16848))) = U_16847
      | U_16847 = c_List_Olist_ONil(U_16848) ),
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

cnf(f_4151_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16848),c_List_Obutlast(U_16848,U_16847)),hAPP(hAPP(c_List_Olist_OCons(U_16848),c_List_Olast(U_16848,U_16847)),c_List_Olist_ONil(U_16848))) = U_16847
    | U_16847 = c_List_Olist_ONil(U_16848) ),
    inference(clausify,[status(thm)],[f_4151_2]) ).

fof(f_4152_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_4152_2,plain,
    ! [U_16852,U_16851,U_16850,U_16849] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16849),U_16850),hAPP(hAPP(c_List_Olist_OCons(U_16849),U_16851),c_List_Olist_ONil(U_16849))) = U_16852
        | c_List_Olast(U_16849,U_16852) != U_16851
        | c_List_Obutlast(U_16849,U_16852) != U_16850
        | U_16852 = c_List_Olist_ONil(U_16849) )
      & ( ( c_List_Olast(U_16849,U_16852) = U_16851
          & c_List_Obutlast(U_16849,U_16852) = U_16850
          & U_16852 != c_List_Olist_ONil(U_16849) )
        | hAPP(hAPP(c_List_Oappend(U_16849),U_16850),hAPP(hAPP(c_List_Olist_OCons(U_16849),U_16851),c_List_Olist_ONil(U_16849))) != U_16852 ) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

fof(f_4152_3,plain,
    ( ! [U_16860,U_16858,U_16856,U_16854] :
        ( hAPP(hAPP(c_List_Oappend(U_16854),U_16856),hAPP(hAPP(c_List_Olist_OCons(U_16854),U_16858),c_List_Olist_ONil(U_16854))) = U_16860
        | c_List_Olast(U_16854,U_16860) != U_16858
        | c_List_Obutlast(U_16854,U_16860) != U_16856
        | U_16860 = c_List_Olist_ONil(U_16854) )
    & ! [U_16859,U_16857,U_16855,U_16853] :
        ( ( c_List_Olast(U_16853,U_16859) = U_16857
          & c_List_Obutlast(U_16853,U_16859) = U_16855
          & U_16859 != c_List_Olist_ONil(U_16853) )
        | hAPP(hAPP(c_List_Oappend(U_16853),U_16855),hAPP(hAPP(c_List_Olist_OCons(U_16853),U_16857),c_List_Olist_ONil(U_16853))) != U_16859 ) ),
    inference(miniscope,[status(thm)],[f_4152_2]) ).

cnf(f_4152_4,plain,
    ( U_16859 != c_List_Olist_ONil(U_16853)
    | hAPP(hAPP(c_List_Oappend(U_16853),U_16855),hAPP(hAPP(c_List_Olist_OCons(U_16853),U_16857),c_List_Olist_ONil(U_16853))) != U_16859 ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

cnf(f_4152_5,plain,
    ( c_List_Obutlast(U_16853,U_16859) = U_16855
    | hAPP(hAPP(c_List_Oappend(U_16853),U_16855),hAPP(hAPP(c_List_Olist_OCons(U_16853),U_16857),c_List_Olist_ONil(U_16853))) != U_16859 ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

cnf(f_4152_6,plain,
    ( c_List_Olast(U_16853,U_16859) = U_16857
    | hAPP(hAPP(c_List_Oappend(U_16853),U_16855),hAPP(hAPP(c_List_Olist_OCons(U_16853),U_16857),c_List_Olist_ONil(U_16853))) != U_16859 ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

cnf(f_4152_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16854),U_16856),hAPP(hAPP(c_List_Olist_OCons(U_16854),U_16858),c_List_Olist_ONil(U_16854))) = U_16860
    | c_List_Olast(U_16854,U_16860) != U_16858
    | c_List_Obutlast(U_16854,U_16860) != U_16856
    | U_16860 = c_List_Olist_ONil(U_16854) ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

fof(f_4153_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_4153_2,plain,
    ! [U_16862,U_16861] :
      ( c_List_Olast(U_16862,U_16861) = hAPP(hAPP(c_List_Onth(U_16862),U_16861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16862)),U_16861)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_16861 = c_List_Olist_ONil(U_16862) ),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

cnf(f_4153_3,plain,
    ( c_List_Olast(U_16862,U_16861) = hAPP(hAPP(c_List_Onth(U_16862),U_16861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16862)),U_16861)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_16861 = c_List_Olist_ONil(U_16862) ),
    inference(clausify,[status(thm)],[f_4153_2]) ).

fof(f_4154_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_4154_2,plain,
    ! [U_16869,U_16868,U_16867] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16867)),U_16868),c_List_Olists(U_16867,U_16869)))
        | ( ! [U_16866,U_16865] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16867)),U_16865),c_List_Olists(U_16867,U_16869)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16867),U_16866),U_16869))
              | U_16868 != hAPP(hAPP(c_List_Olist_OCons(U_16867),U_16866),U_16865) )
          & U_16868 != c_List_Olist_ONil(U_16867) ) )
      & ( ? [U_16864,U_16863] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16867)),U_16863),c_List_Olists(U_16867,U_16869)))
            & hBOOL(hAPP(hAPP(c_member(U_16867),U_16864),U_16869))
            & U_16868 = hAPP(hAPP(c_List_Olist_OCons(U_16867),U_16864),U_16863) )
        | U_16868 = c_List_Olist_ONil(U_16867)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16867)),U_16868),c_List_Olists(U_16867,U_16869))) ) ),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

fof(f_4154_3,plain,
    ( ! [U_16875,U_16873,U_16871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16873),c_List_Olists(U_16871,U_16875)))
        | ( ! [U_16866] :
              ( ! [U_16865] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16865),c_List_Olists(U_16871,U_16875)))
                  | U_16873 != hAPP(hAPP(c_List_Olist_OCons(U_16871),U_16866),U_16865) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16871),U_16866),U_16875)) )
          & U_16873 != c_List_Olist_ONil(U_16871) ) )
    & ! [U_16874,U_16872,U_16870] :
        ( ? [U_16864] :
            ( ? [U_16863] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16863),c_List_Olists(U_16870,U_16874)))
                & U_16872 = hAPP(hAPP(c_List_Olist_OCons(U_16870),U_16864),U_16863) )
            & hBOOL(hAPP(hAPP(c_member(U_16870),U_16864),U_16874)) )
        | U_16872 = c_List_Olist_ONil(U_16870)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ) ),
    inference(miniscope,[status(thm)],[f_4154_2]) ).

fof(f_4154_4,plain,
    ( ! [U_16875,U_16873,U_16871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16873),c_List_Olists(U_16871,U_16875)))
        | ( ! [U_16866] :
              ( ! [U_16865] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16865),c_List_Olists(U_16871,U_16875)))
                  | U_16873 != hAPP(hAPP(c_List_Olist_OCons(U_16871),U_16866),U_16865) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16871),U_16866),U_16875)) )
          & U_16873 != c_List_Olist_ONil(U_16871) ) )
    & ! [U_16874,U_16872,U_16870] :
        ( ( ? [U_16863] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16863),c_List_Olists(U_16870,U_16874)))
              & U_16872 = hAPP(hAPP(c_List_Olist_OCons(U_16870),sK425(U_16874,U_16872,U_16870)),U_16863) )
          & hBOOL(hAPP(hAPP(c_member(U_16870),sK425(U_16874,U_16872,U_16870)),U_16874)) )
        | U_16872 = c_List_Olist_ONil(U_16870)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_16864,sK425(U_16874,U_16872,U_16870))],[f_4154_3]) ).

fof(f_4154_5,plain,
    ( ! [U_16875,U_16873,U_16871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16873),c_List_Olists(U_16871,U_16875)))
        | ( ! [U_16866] :
              ( ! [U_16865] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16865),c_List_Olists(U_16871,U_16875)))
                  | U_16873 != hAPP(hAPP(c_List_Olist_OCons(U_16871),U_16866),U_16865) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16871),U_16866),U_16875)) )
          & U_16873 != c_List_Olist_ONil(U_16871) ) )
    & ! [U_16874,U_16872,U_16870] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),sK426(U_16874,U_16872,U_16870)),c_List_Olists(U_16870,U_16874)))
          & U_16872 = hAPP(hAPP(c_List_Olist_OCons(U_16870),sK425(U_16874,U_16872,U_16870)),sK426(U_16874,U_16872,U_16870))
          & hBOOL(hAPP(hAPP(c_member(U_16870),sK425(U_16874,U_16872,U_16870)),U_16874)) )
        | U_16872 = c_List_Olist_ONil(U_16870)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_16863,sK426(U_16874,U_16872,U_16870))],[f_4154_4]) ).

cnf(f_4154_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16870),sK425(U_16874,U_16872,U_16870)),U_16874))
    | U_16872 = c_List_Olist_ONil(U_16870)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ),
    inference(clausify,[status(thm)],[f_4154_5]) ).

cnf(f_4154_7,plain,
    ( U_16872 = hAPP(hAPP(c_List_Olist_OCons(U_16870),sK425(U_16874,U_16872,U_16870)),sK426(U_16874,U_16872,U_16870))
    | U_16872 = c_List_Olist_ONil(U_16870)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ),
    inference(clausify,[status(thm)],[f_4154_5]) ).

cnf(f_4154_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),sK426(U_16874,U_16872,U_16870)),c_List_Olists(U_16870,U_16874)))
    | U_16872 = c_List_Olist_ONil(U_16870)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16870)),U_16872),c_List_Olists(U_16870,U_16874))) ),
    inference(clausify,[status(thm)],[f_4154_5]) ).

cnf(f_4154_9,plain,
    ( U_16873 != c_List_Olist_ONil(U_16871)
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16873),c_List_Olists(U_16871,U_16875))) ),
    inference(clausify,[status(thm)],[f_4154_5]) ).

cnf(f_4154_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16865),c_List_Olists(U_16871,U_16875)))
    | U_16873 != hAPP(hAPP(c_List_Olist_OCons(U_16871),U_16866),U_16865)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16871),U_16866),U_16875))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16871)),U_16873),c_List_Olists(U_16871,U_16875))) ),
    inference(clausify,[status(thm)],[f_4154_5]) ).

fof(f_4155_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_4155_2,plain,
    ! [U_16877,U_16876] :
      ( c_Random_Oselect__weight(U_16877,hAPP(hAPP(c_List_Omap(U_16877,tc_prod(tc_Code__Numeral_Ocode__numeral,U_16877)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_16877),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_16876)) = c_Random_Oselect(U_16877,U_16876)
      | U_16876 = c_List_Olist_ONil(U_16877) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

cnf(f_4155_3,plain,
    ( c_Random_Oselect__weight(U_16877,hAPP(hAPP(c_List_Omap(U_16877,tc_prod(tc_Code__Numeral_Ocode__numeral,U_16877)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_16877),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_16876)) = c_Random_Oselect(U_16877,U_16876)
    | U_16876 = c_List_Olist_ONil(U_16877) ),
    inference(clausify,[status(thm)],[f_4155_2]) ).

fof(f_4156_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_4156_2,plain,
    ! [U_16880,U_16879,U_16878] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_16878),tc_List_Olist(U_16879),hAPP(c_List_Omap(U_16878,U_16879),U_16880),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_16878),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_16878,U_16879,U_16880,c_Orderings_Otop__class_Otop(tc_fun(U_16878,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

cnf(f_4156_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_16878),tc_List_Olist(U_16879),hAPP(c_List_Omap(U_16878,U_16879),U_16880),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_16878),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_16878,U_16879,U_16880,c_Orderings_Otop__class_Otop(tc_fun(U_16878,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4156_2]) ).

fof(f_4157_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_4157_2,plain,
    ! [U_16884,U_16883,U_16882,U_16881] :
      ( c_List_Olast(U_16883,hAPP(hAPP(c_List_Omap(U_16882,U_16883),U_16884),U_16881)) = hAPP(U_16884,c_List_Olast(U_16882,U_16881))
      | U_16881 = c_List_Olist_ONil(U_16882) ),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

cnf(f_4157_3,plain,
    ( c_List_Olast(U_16883,hAPP(hAPP(c_List_Omap(U_16882,U_16883),U_16884),U_16881)) = hAPP(U_16884,c_List_Olast(U_16882,U_16881))
    | U_16881 = c_List_Olist_ONil(U_16882) ),
    inference(clausify,[status(thm)],[f_4157_2]) ).

fof(f_4158_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_4158_2,plain,
    ! [U_16889,U_16888,U_16887,U_16886,U_16885] : c_List_Olist_Olist__size(U_16885,U_16886,hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),U_16889)) = c_List_Olist_Olist__size(U_16887,hAPP(c_Fun_Ocomp(U_16885,tc_Nat_Onat,U_16887,U_16886),U_16888),U_16889),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

cnf(f_4158_3,plain,
    c_List_Olist_Olist__size(U_16885,U_16886,hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),U_16889)) = c_List_Olist_Olist__size(U_16887,hAPP(c_Fun_Ocomp(U_16885,tc_Nat_Onat,U_16887,U_16886),U_16888),U_16889),
    inference(clausify,[status(thm)],[f_4158_2]) ).

fof(f_4159_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_4159_2,plain,
    ! [U_16894,U_16893,U_16892,U_16891,U_16890] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_16890),tc_List_Olist(U_16891),tc_List_Olist(U_16892),hAPP(c_List_Omap(U_16890,U_16891),U_16893)),hAPP(c_List_Omap(U_16892,U_16890),U_16894)) = hAPP(c_List_Omap(U_16892,U_16891),hAPP(c_Fun_Ocomp(U_16890,U_16891,U_16892,U_16893),U_16894)),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

cnf(f_4159_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_16890),tc_List_Olist(U_16891),tc_List_Olist(U_16892),hAPP(c_List_Omap(U_16890,U_16891),U_16893)),hAPP(c_List_Omap(U_16892,U_16890),U_16894)) = hAPP(c_List_Omap(U_16892,U_16891),hAPP(c_Fun_Ocomp(U_16890,U_16891,U_16892,U_16893),U_16894)),
    inference(clausify,[status(thm)],[f_4159_2]) ).

fof(f_4160_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_4160_2,plain,
    ! [U_16899,U_16898,U_16897,U_16896,U_16895] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_16895),tc_List_Olist(U_16896),tc_List_Olist(U_16897),hAPP(c_List_Omap(U_16895,U_16896),U_16898)),hAPP(c_List_Omap(U_16897,U_16895),U_16899)) = hAPP(c_List_Omap(U_16897,U_16896),hAPP(c_Fun_Ocomp(U_16895,U_16896,U_16897,U_16898),U_16899)),
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

cnf(f_4160_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_16895),tc_List_Olist(U_16896),tc_List_Olist(U_16897),hAPP(c_List_Omap(U_16895,U_16896),U_16898)),hAPP(c_List_Omap(U_16897,U_16895),U_16899)) = hAPP(c_List_Omap(U_16897,U_16896),hAPP(c_Fun_Ocomp(U_16895,U_16896,U_16897,U_16898),U_16899)),
    inference(clausify,[status(thm)],[f_4160_2]) ).

fof(f_4161_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_4161_2,plain,
    ! [U_16905,U_16904,U_16903,U_16902,U_16901,U_16900] : hAPP(hAPP(c_List_Omap(U_16900,U_16901),U_16902),hAPP(hAPP(c_List_Omap(U_16903,U_16900),U_16904),U_16905)) = hAPP(hAPP(c_List_Omap(U_16903,U_16901),hAPP(c_Fun_Ocomp(U_16900,U_16901,U_16903,U_16902),U_16904)),U_16905),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

cnf(f_4161_3,plain,
    hAPP(hAPP(c_List_Omap(U_16900,U_16901),U_16902),hAPP(hAPP(c_List_Omap(U_16903,U_16900),U_16904),U_16905)) = hAPP(hAPP(c_List_Omap(U_16903,U_16901),hAPP(c_Fun_Ocomp(U_16900,U_16901,U_16903,U_16902),U_16904)),U_16905),
    inference(clausify,[status(thm)],[f_4161_2]) ).

fof(f_4162_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_4162_2,plain,
    ! [U_16911,U_16910,U_16909,U_16908,U_16907,U_16906] : hAPP(hAPP(c_List_Omap(U_16906,U_16907),U_16908),hAPP(hAPP(c_List_Omap(U_16909,U_16906),U_16910),U_16911)) = hAPP(hAPP(c_List_Omap(U_16909,U_16907),hAPP(c_Fun_Ocomp(U_16906,U_16907,U_16909,U_16908),U_16910)),U_16911),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

cnf(f_4162_3,plain,
    hAPP(hAPP(c_List_Omap(U_16906,U_16907),U_16908),hAPP(hAPP(c_List_Omap(U_16909,U_16906),U_16910),U_16911)) = hAPP(hAPP(c_List_Omap(U_16909,U_16907),hAPP(c_Fun_Ocomp(U_16906,U_16907,U_16909,U_16908),U_16910)),U_16911),
    inference(clausify,[status(thm)],[f_4162_2]) ).

fof(f_4163_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_4163_2,plain,
    ! [U_16912] : hAPP(c_List_Omap(U_16912,U_16912),c_COMBI(U_16912)) = c_Fun_Oid(tc_List_Olist(U_16912)),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

cnf(f_4163_3,plain,
    hAPP(c_List_Omap(U_16912,U_16912),c_COMBI(U_16912)) = c_Fun_Oid(tc_List_Olist(U_16912)),
    inference(clausify,[status(thm)],[f_4163_2]) ).

fof(f_4164_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_4164_2,plain,
    ! [U_16913] : hAPP(c_List_Omap(U_16913,U_16913),c_Fun_Oid(U_16913)) = c_Fun_Oid(tc_List_Olist(U_16913)),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

cnf(f_4164_3,plain,
    hAPP(c_List_Omap(U_16913,U_16913),c_Fun_Oid(U_16913)) = c_Fun_Oid(tc_List_Olist(U_16913)),
    inference(clausify,[status(thm)],[f_4164_2]) ).

fof(f_4165_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_4165_2,plain,
    ! [U_16918,U_16917,U_16916,U_16915,U_16914] : hAPP(hAPP(c_List_Odrop(U_16914),U_16915),hAPP(hAPP(c_List_Omap(U_16916,U_16914),U_16917),U_16918)) = hAPP(hAPP(c_List_Omap(U_16916,U_16914),U_16917),hAPP(hAPP(c_List_Odrop(U_16916),U_16915),U_16918)),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

cnf(f_4165_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16914),U_16915),hAPP(hAPP(c_List_Omap(U_16916,U_16914),U_16917),U_16918)) = hAPP(hAPP(c_List_Omap(U_16916,U_16914),U_16917),hAPP(hAPP(c_List_Odrop(U_16916),U_16915),U_16918)),
    inference(clausify,[status(thm)],[f_4165_2]) ).

fof(f_4166_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_4166_2,plain,
    ! [U_16922,U_16921,U_16920,U_16919] :
      ( hAPP(c_List_Ohd(U_16921),hAPP(hAPP(c_List_Omap(U_16920,U_16921),U_16922),U_16919)) = hAPP(U_16922,hAPP(c_List_Ohd(U_16920),U_16919))
      | U_16919 = c_List_Olist_ONil(U_16920) ),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

cnf(f_4166_3,plain,
    ( hAPP(c_List_Ohd(U_16921),hAPP(hAPP(c_List_Omap(U_16920,U_16921),U_16922),U_16919)) = hAPP(U_16922,hAPP(c_List_Ohd(U_16920),U_16919))
    | U_16919 = c_List_Olist_ONil(U_16920) ),
    inference(clausify,[status(thm)],[f_4166_2]) ).

fof(f_4167_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_4167_2,plain,
    ! [U_16927,U_16926,U_16925,U_16924,U_16923] : hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),hAPP(hAPP(c_List_Oappend(U_16923),U_16926),U_16927)) = hAPP(hAPP(c_List_Oappend(U_16924),hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),U_16926)),hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),U_16927)),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

cnf(f_4167_3,plain,
    hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),hAPP(hAPP(c_List_Oappend(U_16923),U_16926),U_16927)) = hAPP(hAPP(c_List_Oappend(U_16924),hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),U_16926)),hAPP(hAPP(c_List_Omap(U_16923,U_16924),U_16925),U_16927)),
    inference(clausify,[status(thm)],[f_4167_2]) ).

fof(f_4168_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_4168_2,plain,
    ! [U_16932,U_16931,U_16930,U_16929,U_16928] : hAPP(hAPP(c_List_Omap(U_16928,U_16929),U_16930),hAPP(hAPP(c_List_Olist_OCons(U_16928),U_16931),U_16932)) = hAPP(hAPP(c_List_Olist_OCons(U_16929),hAPP(U_16930,U_16931)),hAPP(hAPP(c_List_Omap(U_16928,U_16929),U_16930),U_16932)),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

cnf(f_4168_3,plain,
    hAPP(hAPP(c_List_Omap(U_16928,U_16929),U_16930),hAPP(hAPP(c_List_Olist_OCons(U_16928),U_16931),U_16932)) = hAPP(hAPP(c_List_Olist_OCons(U_16929),hAPP(U_16930,U_16931)),hAPP(hAPP(c_List_Omap(U_16928,U_16929),U_16930),U_16932)),
    inference(clausify,[status(thm)],[f_4168_2]) ).

fof(f_4169_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_4169_2,plain,
    ! [U_16936,U_16935,U_16934,U_16933] : hAPP(c_List_Oset(U_16933),hAPP(hAPP(c_List_Omap(U_16934,U_16933),U_16935),U_16936)) = hAPP(c_Set_Oimage(U_16934,U_16933,U_16935),hAPP(c_List_Oset(U_16934),U_16936)),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

cnf(f_4169_3,plain,
    hAPP(c_List_Oset(U_16933),hAPP(hAPP(c_List_Omap(U_16934,U_16933),U_16935),U_16936)) = hAPP(c_Set_Oimage(U_16934,U_16933,U_16935),hAPP(c_List_Oset(U_16934),U_16936)),
    inference(clausify,[status(thm)],[f_4169_2]) ).

fof(f_4170_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_4170_2,plain,
    ! [U_16940,U_16939,U_16938,U_16937] : hAPP(hAPP(c_List_Omap(U_16937,U_16938),U_16939),c_List_Obutlast(U_16937,U_16940)) = c_List_Obutlast(U_16938,hAPP(hAPP(c_List_Omap(U_16937,U_16938),U_16939),U_16940)),
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

cnf(f_4170_3,plain,
    hAPP(hAPP(c_List_Omap(U_16937,U_16938),U_16939),c_List_Obutlast(U_16937,U_16940)) = c_List_Obutlast(U_16938,hAPP(hAPP(c_List_Omap(U_16937,U_16938),U_16939),U_16940)),
    inference(clausify,[status(thm)],[f_4170_2]) ).

fof(f_4171_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_4171_2,plain,
    ! [U_16945,U_16944,U_16943,U_16942,U_16941] : hAPP(hAPP(c_List_Otake(U_16941),U_16942),hAPP(hAPP(c_List_Omap(U_16943,U_16941),U_16944),U_16945)) = hAPP(hAPP(c_List_Omap(U_16943,U_16941),U_16944),hAPP(hAPP(c_List_Otake(U_16943),U_16942),U_16945)),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

cnf(f_4171_3,plain,
    hAPP(hAPP(c_List_Otake(U_16941),U_16942),hAPP(hAPP(c_List_Omap(U_16943,U_16941),U_16944),U_16945)) = hAPP(hAPP(c_List_Omap(U_16943,U_16941),U_16944),hAPP(hAPP(c_List_Otake(U_16943),U_16942),U_16945)),
    inference(clausify,[status(thm)],[f_4171_2]) ).

fof(f_4172_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_4172_2,plain,
    ! [U_16947,U_16946] : hAPP(hAPP(c_List_Omap(U_16946,U_16946),c_COMBI(U_16946)),U_16947) = U_16947,
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

cnf(f_4172_3,plain,
    hAPP(hAPP(c_List_Omap(U_16946,U_16946),c_COMBI(U_16946)),U_16947) = U_16947,
    inference(clausify,[status(thm)],[f_4172_2]) ).

fof(f_4173_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_4173_2,plain,
    ! [U_16952,U_16951,U_16950,U_16949,U_16948] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16951) = hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16952)
          | U_16951 != U_16952 )
        & ( U_16951 = U_16952
          | hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16951) != hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16952) ) )
      | ~ c_Fun_Oinj__on(U_16948,U_16949,U_16950,c_Orderings_Otop__class_Otop(tc_fun(U_16948,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

cnf(f_4173_3,plain,
    ( U_16951 = U_16952
    | hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16951) != hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16952)
    | ~ c_Fun_Oinj__on(U_16948,U_16949,U_16950,c_Orderings_Otop__class_Otop(tc_fun(U_16948,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4173_2]) ).

cnf(f_4173_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16951) = hAPP(hAPP(c_List_Omap(U_16948,U_16949),U_16950),U_16952)
    | U_16951 != U_16952
    | ~ c_Fun_Oinj__on(U_16948,U_16949,U_16950,c_Orderings_Otop__class_Otop(tc_fun(U_16948,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4173_2]) ).

fof(f_4174_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_4174_2,plain,
    ! [U_16957,U_16956,U_16955,U_16954,U_16953] :
      ( U_16956 = U_16957
      | ~ c_Fun_Oinj__on(U_16953,U_16954,U_16955,c_Orderings_Otop__class_Otop(tc_fun(U_16953,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_16953,U_16954),U_16955),U_16956) != hAPP(hAPP(c_List_Omap(U_16953,U_16954),U_16955),U_16957) ),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

cnf(f_4174_3,plain,
    ( U_16956 = U_16957
    | ~ c_Fun_Oinj__on(U_16953,U_16954,U_16955,c_Orderings_Otop__class_Otop(tc_fun(U_16953,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_16953,U_16954),U_16955),U_16956) != hAPP(hAPP(c_List_Omap(U_16953,U_16954),U_16955),U_16957) ),
    inference(clausify,[status(thm)],[f_4174_2]) ).

fof(f_4175_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_4175_2,plain,
    ! [U_16962,U_16961,U_16960,U_16959,U_16958] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),hAPP(hAPP(c_COMBS(U_16959,U_16958,U_16958),hAPP(hAPP(c_COMBB(U_16958,tc_fun(U_16958,U_16958),U_16959),c_Groups_Ominus__class_Ominus(U_16958)),U_16960)),U_16961)),U_16962)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_16958),hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),U_16960),U_16962))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),U_16961),U_16962)))
      | ~ class_Groups_Oab__group__add(U_16958) ),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

cnf(f_4175_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),hAPP(hAPP(c_COMBS(U_16959,U_16958,U_16958),hAPP(hAPP(c_COMBB(U_16958,tc_fun(U_16958,U_16958),U_16959),c_Groups_Ominus__class_Ominus(U_16958)),U_16960)),U_16961)),U_16962)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_16958),hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),U_16960),U_16962))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16958),hAPP(hAPP(c_List_Omap(U_16959,U_16958),U_16961),U_16962)))
    | ~ class_Groups_Oab__group__add(U_16958) ),
    inference(clausify,[status(thm)],[f_4175_2]) ).

fof(f_4176_1,plain,
    ! [V_xs_2,V_ca_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_ca_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_ca_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mult__const]) ).

fof(f_4176_2,plain,
    ! [U_16967,U_16966,U_16965,U_16964,U_16963] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16963),hAPP(hAPP(c_List_Omap(U_16964,U_16963),hAPP(hAPP(c_COMBC(U_16964,U_16963,U_16963),hAPP(hAPP(c_COMBB(U_16963,tc_fun(U_16963,U_16963),U_16964),c_Groups_Otimes__class_Otimes(U_16963)),U_16965)),U_16966)),U_16967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16963),hAPP(c_List_Omonoid__add__class_Olistsum(U_16963),hAPP(hAPP(c_List_Omap(U_16964,U_16963),U_16965),U_16967))),U_16966)
      | ~ class_Rings_Osemiring__0(U_16963) ),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

cnf(f_4176_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16963),hAPP(hAPP(c_List_Omap(U_16964,U_16963),hAPP(hAPP(c_COMBC(U_16964,U_16963,U_16963),hAPP(hAPP(c_COMBB(U_16963,tc_fun(U_16963,U_16963),U_16964),c_Groups_Otimes__class_Otimes(U_16963)),U_16965)),U_16966)),U_16967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16963),hAPP(c_List_Omonoid__add__class_Olistsum(U_16963),hAPP(hAPP(c_List_Omap(U_16964,U_16963),U_16965),U_16967))),U_16966)
    | ~ class_Rings_Osemiring__0(U_16963) ),
    inference(clausify,[status(thm)],[f_4176_2]) ).

fof(f_4177_1,plain,
    ! [V_xs_2,V_f_2,V_ca_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_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_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_4177_2,plain,
    ! [U_16972,U_16971,U_16970,U_16969,U_16968] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16968),hAPP(hAPP(c_List_Omap(U_16969,U_16968),hAPP(hAPP(c_COMBB(U_16968,U_16968,U_16969),hAPP(c_Groups_Otimes__class_Otimes(U_16968),U_16970)),U_16971)),U_16972)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16968),U_16970),hAPP(c_List_Omonoid__add__class_Olistsum(U_16968),hAPP(hAPP(c_List_Omap(U_16969,U_16968),U_16971),U_16972)))
      | ~ class_Rings_Osemiring__0(U_16968) ),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

cnf(f_4177_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16968),hAPP(hAPP(c_List_Omap(U_16969,U_16968),hAPP(hAPP(c_COMBB(U_16968,U_16968,U_16969),hAPP(c_Groups_Otimes__class_Otimes(U_16968),U_16970)),U_16971)),U_16972)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16968),U_16970),hAPP(c_List_Omonoid__add__class_Olistsum(U_16968),hAPP(hAPP(c_List_Omap(U_16969,U_16968),U_16971),U_16972)))
    | ~ class_Rings_Osemiring__0(U_16968) ),
    inference(clausify,[status(thm)],[f_4177_2]) ).

fof(f_4178_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_4178_2,plain,
    ! [U_16975,U_16974,U_16973] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16973),hAPP(hAPP(c_List_Omap(U_16974,U_16973),hAPP(c_COMBK(U_16973,U_16974),c_Groups_Ozero__class_Ozero(U_16973))),U_16975)) = c_Groups_Ozero__class_Ozero(U_16973)
      | ~ class_Groups_Omonoid__add(U_16973) ),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

cnf(f_4178_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16973),hAPP(hAPP(c_List_Omap(U_16974,U_16973),hAPP(c_COMBK(U_16973,U_16974),c_Groups_Ozero__class_Ozero(U_16973))),U_16975)) = c_Groups_Ozero__class_Ozero(U_16973)
    | ~ class_Groups_Omonoid__add(U_16973) ),
    inference(clausify,[status(thm)],[f_4178_2]) ).

fof(f_4179_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_4179_2,plain,
    ! [U_16980,U_16979,U_16978,U_16977,U_16976] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),hAPP(hAPP(c_COMBS(U_16977,U_16976,U_16976),hAPP(hAPP(c_COMBB(U_16976,tc_fun(U_16976,U_16976),U_16977),c_Groups_Oplus__class_Oplus(U_16976)),U_16978)),U_16979)),U_16980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16976),hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),U_16978),U_16980))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),U_16979),U_16980)))
      | ~ class_Groups_Ocomm__monoid__add(U_16976) ),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

cnf(f_4179_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),hAPP(hAPP(c_COMBS(U_16977,U_16976,U_16976),hAPP(hAPP(c_COMBB(U_16976,tc_fun(U_16976,U_16976),U_16977),c_Groups_Oplus__class_Oplus(U_16976)),U_16978)),U_16979)),U_16980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16976),hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),U_16978),U_16980))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16976),hAPP(hAPP(c_List_Omap(U_16977,U_16976),U_16979),U_16980)))
    | ~ class_Groups_Ocomm__monoid__add(U_16976) ),
    inference(clausify,[status(thm)],[f_4179_2]) ).

fof(f_4180_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_4180_2,plain,
    ! [U_16987,U_16986,U_16985,U_16984,U_16983,U_16982,U_16981] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16981)),U_16984) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),U_16987)
      | hAPP(hAPP(c_List_Omap(U_16981,U_16982),U_16983),U_16984) != hAPP(hAPP(c_List_Omap(U_16985,U_16982),U_16986),U_16987) ),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

cnf(f_4180_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16981)),U_16984) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),U_16987)
    | hAPP(hAPP(c_List_Omap(U_16981,U_16982),U_16983),U_16984) != hAPP(hAPP(c_List_Omap(U_16985,U_16982),U_16986),U_16987) ),
    inference(clausify,[status(thm)],[f_4180_2]) ).

fof(f_4181_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_4181_2,plain,
    ! [U_16991,U_16990,U_16989,U_16988] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16988)),hAPP(hAPP(c_List_Omap(U_16989,U_16988),U_16990),U_16991)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16989)),U_16991),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

cnf(f_4181_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16988)),hAPP(hAPP(c_List_Omap(U_16989,U_16988),U_16990),U_16991)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16989)),U_16991),
    inference(clausify,[status(thm)],[f_4181_2]) ).

fof(f_4182_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_4182_2,plain,
    ! [U_16998,U_16997,U_16996,U_16995,U_16994] :
      ( ( hAPP(hAPP(c_List_Omap(U_16994,U_16995),U_16996),U_16997) = hAPP(hAPP(c_List_Omap(U_16994,U_16995),U_16998),U_16997)
        | ? [U_16993] :
            ( hAPP(U_16996,U_16993) != hAPP(U_16998,U_16993)
            & hBOOL(hAPP(hAPP(c_member(U_16994),U_16993),hAPP(c_List_Oset(U_16994),U_16997))) ) )
      & ( ! [U_16992] :
            ( hAPP(U_16996,U_16992) = hAPP(U_16998,U_16992)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16994),U_16992),hAPP(c_List_Oset(U_16994),U_16997))) )
        | hAPP(hAPP(c_List_Omap(U_16994,U_16995),U_16996),U_16997) != hAPP(hAPP(c_List_Omap(U_16994,U_16995),U_16998),U_16997) ) ),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

fof(f_4182_3,plain,
    ( ! [U_17008,U_17006,U_17004,U_17002,U_17000] :
        ( hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17004),U_17006) = hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17008),U_17006)
        | ? [U_16993] :
            ( hAPP(U_17004,U_16993) != hAPP(U_17008,U_16993)
            & hBOOL(hAPP(hAPP(c_member(U_17000),U_16993),hAPP(c_List_Oset(U_17000),U_17006))) ) )
    & ! [U_17007,U_17005,U_17003,U_17001,U_16999] :
        ( ! [U_16992] :
            ( hAPP(U_17003,U_16992) = hAPP(U_17007,U_16992)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_16992),hAPP(c_List_Oset(U_16999),U_17005))) )
        | hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17003),U_17005) != hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17007),U_17005) ) ),
    inference(miniscope,[status(thm)],[f_4182_2]) ).

fof(f_4182_4,plain,
    ( ! [U_17008,U_17006,U_17004,U_17002,U_17000] :
        ( hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17004),U_17006) = hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17008),U_17006)
        | ( hAPP(U_17004,sK427(U_17008,U_17006,U_17004,U_17002,U_17000)) != hAPP(U_17008,sK427(U_17008,U_17006,U_17004,U_17002,U_17000))
          & hBOOL(hAPP(hAPP(c_member(U_17000),sK427(U_17008,U_17006,U_17004,U_17002,U_17000)),hAPP(c_List_Oset(U_17000),U_17006))) ) )
    & ! [U_17007,U_17005,U_17003,U_17001,U_16999] :
        ( ! [U_16992] :
            ( hAPP(U_17003,U_16992) = hAPP(U_17007,U_16992)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_16992),hAPP(c_List_Oset(U_16999),U_17005))) )
        | hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17003),U_17005) != hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17007),U_17005) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_16993,sK427(U_17008,U_17006,U_17004,U_17002,U_17000))],[f_4182_3]) ).

cnf(f_4182_5,plain,
    ( hAPP(U_17003,U_16992) = hAPP(U_17007,U_16992)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16999),U_16992),hAPP(c_List_Oset(U_16999),U_17005)))
    | hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17003),U_17005) != hAPP(hAPP(c_List_Omap(U_16999,U_17001),U_17007),U_17005) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

cnf(f_4182_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17000),sK427(U_17008,U_17006,U_17004,U_17002,U_17000)),hAPP(c_List_Oset(U_17000),U_17006)))
    | hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17004),U_17006) = hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17008),U_17006) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

cnf(f_4182_7,plain,
    ( hAPP(U_17004,sK427(U_17008,U_17006,U_17004,U_17002,U_17000)) != hAPP(U_17008,sK427(U_17008,U_17006,U_17004,U_17002,U_17000))
    | hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17004),U_17006) = hAPP(hAPP(c_List_Omap(U_17000,U_17002),U_17008),U_17006) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

fof(f_4183_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_4183_2,plain,
    ! [U_17014,U_17013,U_17012,U_17011,U_17010,U_17009] : hAPP(hAPP(c_List_Omap(U_17009,U_17010),U_17011),hAPP(hAPP(c_List_Olist__update(U_17009,U_17012),U_17013),U_17014)) = hAPP(hAPP(c_List_Olist__update(U_17010,hAPP(hAPP(c_List_Omap(U_17009,U_17010),U_17011),U_17012)),U_17013),hAPP(U_17011,U_17014)),
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

cnf(f_4183_3,plain,
    hAPP(hAPP(c_List_Omap(U_17009,U_17010),U_17011),hAPP(hAPP(c_List_Olist__update(U_17009,U_17012),U_17013),U_17014)) = hAPP(hAPP(c_List_Olist__update(U_17010,hAPP(hAPP(c_List_Omap(U_17009,U_17010),U_17011),U_17012)),U_17013),hAPP(U_17011,U_17014)),
    inference(clausify,[status(thm)],[f_4183_2]) ).

fof(f_4184_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_4184_2,plain,
    ! [U_17018,U_17017,U_17016,U_17015] :
      ( ( hAPP(hAPP(c_List_Omap(U_17015,U_17016),U_17017),U_17018) = c_List_Olist_ONil(U_17016)
        | U_17018 != c_List_Olist_ONil(U_17015) )
      & ( U_17018 = c_List_Olist_ONil(U_17015)
        | hAPP(hAPP(c_List_Omap(U_17015,U_17016),U_17017),U_17018) != c_List_Olist_ONil(U_17016) ) ),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

fof(f_4184_3,plain,
    ( ! [U_17026,U_17024,U_17022,U_17020] :
        ( hAPP(hAPP(c_List_Omap(U_17020,U_17022),U_17024),U_17026) = c_List_Olist_ONil(U_17022)
        | U_17026 != c_List_Olist_ONil(U_17020) )
    & ! [U_17025,U_17023,U_17021,U_17019] :
        ( U_17025 = c_List_Olist_ONil(U_17019)
        | hAPP(hAPP(c_List_Omap(U_17019,U_17021),U_17023),U_17025) != c_List_Olist_ONil(U_17021) ) ),
    inference(miniscope,[status(thm)],[f_4184_2]) ).

cnf(f_4184_4,plain,
    ( U_17025 = c_List_Olist_ONil(U_17019)
    | hAPP(hAPP(c_List_Omap(U_17019,U_17021),U_17023),U_17025) != c_List_Olist_ONil(U_17021) ),
    inference(clausify,[status(thm)],[f_4184_3]) ).

cnf(f_4184_5,plain,
    ( hAPP(hAPP(c_List_Omap(U_17020,U_17022),U_17024),U_17026) = c_List_Olist_ONil(U_17022)
    | U_17026 != c_List_Olist_ONil(U_17020) ),
    inference(clausify,[status(thm)],[f_4184_3]) ).

fof(f_4185_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_4185_2,plain,
    ! [U_17029,U_17028,U_17027] : hAPP(hAPP(c_List_Omap(U_17027,U_17028),U_17029),c_List_Olist_ONil(U_17027)) = c_List_Olist_ONil(U_17028),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

cnf(f_4185_3,plain,
    hAPP(hAPP(c_List_Omap(U_17027,U_17028),U_17029),c_List_Olist_ONil(U_17027)) = c_List_Olist_ONil(U_17028),
    inference(clausify,[status(thm)],[f_4185_2]) ).

fof(f_4186_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_4186_2,plain,
    ! [U_17033,U_17032,U_17031,U_17030] :
      ( ( c_List_Olist_ONil(U_17030) = hAPP(hAPP(c_List_Omap(U_17031,U_17030),U_17032),U_17033)
        | U_17033 != c_List_Olist_ONil(U_17031) )
      & ( U_17033 = c_List_Olist_ONil(U_17031)
        | c_List_Olist_ONil(U_17030) != hAPP(hAPP(c_List_Omap(U_17031,U_17030),U_17032),U_17033) ) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

fof(f_4186_3,plain,
    ( ! [U_17041,U_17039,U_17037] :
        ( ! [U_17035] : c_List_Olist_ONil(U_17035) = hAPP(hAPP(c_List_Omap(U_17037,U_17035),U_17039),U_17041)
        | U_17041 != c_List_Olist_ONil(U_17037) )
    & ! [U_17040,U_17038,U_17036] :
        ( ! [U_17034] : c_List_Olist_ONil(U_17034) != hAPP(hAPP(c_List_Omap(U_17036,U_17034),U_17038),U_17040)
        | U_17040 = c_List_Olist_ONil(U_17036) ) ),
    inference(miniscope,[status(thm)],[f_4186_2]) ).

cnf(f_4186_4,plain,
    ( c_List_Olist_ONil(U_17034) != hAPP(hAPP(c_List_Omap(U_17036,U_17034),U_17038),U_17040)
    | U_17040 = c_List_Olist_ONil(U_17036) ),
    inference(clausify,[status(thm)],[f_4186_3]) ).

cnf(f_4186_5,plain,
    ( c_List_Olist_ONil(U_17035) = hAPP(hAPP(c_List_Omap(U_17037,U_17035),U_17039),U_17041)
    | U_17041 != c_List_Olist_ONil(U_17037) ),
    inference(clausify,[status(thm)],[f_4186_3]) ).

fof(f_4187_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_4187_2,plain,
    ! [U_17047,U_17046,U_17045,U_17044,U_17043,U_17042] : hAPP(hAPP(c_List_Ozip(U_17042,U_17043),U_17044),hAPP(hAPP(c_List_Omap(U_17045,U_17043),U_17046),U_17047)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17042,U_17045),tc_prod(U_17042,U_17043)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17042,U_17045,tc_prod(U_17042,U_17043)),hAPP(hAPP(c_COMBC(U_17042,tc_fun(U_17045,U_17043),tc_fun(U_17045,tc_prod(U_17042,U_17043))),hAPP(hAPP(c_COMBB(tc_fun(U_17043,tc_prod(U_17042,U_17043)),tc_fun(tc_fun(U_17045,U_17043),tc_fun(U_17045,tc_prod(U_17042,U_17043))),U_17042),c_COMBB(U_17043,tc_prod(U_17042,U_17043),U_17045)),c_Product__Type_OPair(U_17042,U_17043))),U_17046))),hAPP(hAPP(c_List_Ozip(U_17042,U_17045),U_17044),U_17047)),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

cnf(f_4187_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17042,U_17043),U_17044),hAPP(hAPP(c_List_Omap(U_17045,U_17043),U_17046),U_17047)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17042,U_17045),tc_prod(U_17042,U_17043)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17042,U_17045,tc_prod(U_17042,U_17043)),hAPP(hAPP(c_COMBC(U_17042,tc_fun(U_17045,U_17043),tc_fun(U_17045,tc_prod(U_17042,U_17043))),hAPP(hAPP(c_COMBB(tc_fun(U_17043,tc_prod(U_17042,U_17043)),tc_fun(tc_fun(U_17045,U_17043),tc_fun(U_17045,tc_prod(U_17042,U_17043))),U_17042),c_COMBB(U_17043,tc_prod(U_17042,U_17043),U_17045)),c_Product__Type_OPair(U_17042,U_17043))),U_17046))),hAPP(hAPP(c_List_Ozip(U_17042,U_17045),U_17044),U_17047)),
    inference(clausify,[status(thm)],[f_4187_2]) ).

fof(f_4188_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_4188_2,plain,
    ! [U_17055,U_17054,U_17053,U_17052,U_17051,U_17050,U_17049,U_17048] : hAPP(hAPP(c_List_Omap(tc_prod(U_17048,U_17049),U_17050),U_17051),hAPP(hAPP(c_List_Ozip(U_17048,U_17049),U_17052),hAPP(hAPP(c_List_Omap(U_17053,U_17049),U_17054),U_17055))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17048,U_17053),U_17050),hAPP(c_Product__Type_Oprod_Oprod__case(U_17048,U_17053,U_17050),hAPP(hAPP(c_COMBB(tc_fun(U_17053,tc_prod(U_17048,U_17049)),tc_fun(U_17053,U_17050),U_17048),hAPP(c_COMBB(tc_prod(U_17048,U_17049),U_17050,U_17053),U_17051)),hAPP(hAPP(c_COMBC(U_17048,tc_fun(U_17053,U_17049),tc_fun(U_17053,tc_prod(U_17048,U_17049))),hAPP(hAPP(c_COMBB(tc_fun(U_17049,tc_prod(U_17048,U_17049)),tc_fun(tc_fun(U_17053,U_17049),tc_fun(U_17053,tc_prod(U_17048,U_17049))),U_17048),c_COMBB(U_17049,tc_prod(U_17048,U_17049),U_17053)),c_Product__Type_OPair(U_17048,U_17049))),U_17054)))),hAPP(hAPP(c_List_Ozip(U_17048,U_17053),U_17052),U_17055)),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

cnf(f_4188_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17048,U_17049),U_17050),U_17051),hAPP(hAPP(c_List_Ozip(U_17048,U_17049),U_17052),hAPP(hAPP(c_List_Omap(U_17053,U_17049),U_17054),U_17055))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17048,U_17053),U_17050),hAPP(c_Product__Type_Oprod_Oprod__case(U_17048,U_17053,U_17050),hAPP(hAPP(c_COMBB(tc_fun(U_17053,tc_prod(U_17048,U_17049)),tc_fun(U_17053,U_17050),U_17048),hAPP(c_COMBB(tc_prod(U_17048,U_17049),U_17050,U_17053),U_17051)),hAPP(hAPP(c_COMBC(U_17048,tc_fun(U_17053,U_17049),tc_fun(U_17053,tc_prod(U_17048,U_17049))),hAPP(hAPP(c_COMBB(tc_fun(U_17049,tc_prod(U_17048,U_17049)),tc_fun(tc_fun(U_17053,U_17049),tc_fun(U_17053,tc_prod(U_17048,U_17049))),U_17048),c_COMBB(U_17049,tc_prod(U_17048,U_17049),U_17053)),c_Product__Type_OPair(U_17048,U_17049))),U_17054)))),hAPP(hAPP(c_List_Ozip(U_17048,U_17053),U_17052),U_17055)),
    inference(clausify,[status(thm)],[f_4188_2]) ).

fof(f_4189_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_4189_2,plain,
    ! [U_17063,U_17062,U_17061,U_17060,U_17059,U_17058,U_17057,U_17056] : hAPP(hAPP(c_List_Omap(tc_prod(U_17056,U_17057),U_17058),U_17059),hAPP(hAPP(c_List_Ozip(U_17056,U_17057),hAPP(hAPP(c_List_Omap(U_17060,U_17056),U_17061),U_17062)),U_17063)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17060,U_17057),U_17058),hAPP(c_Product__Type_Oprod_Oprod__case(U_17060,U_17057,U_17058),hAPP(hAPP(c_COMBB(tc_fun(U_17057,tc_prod(U_17056,U_17057)),tc_fun(U_17057,U_17058),U_17060),hAPP(c_COMBB(tc_prod(U_17056,U_17057),U_17058,U_17057),U_17059)),hAPP(hAPP(c_COMBB(U_17056,tc_fun(U_17057,tc_prod(U_17056,U_17057)),U_17060),c_Product__Type_OPair(U_17056,U_17057)),U_17061)))),hAPP(hAPP(c_List_Ozip(U_17060,U_17057),U_17062),U_17063)),
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

cnf(f_4189_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17056,U_17057),U_17058),U_17059),hAPP(hAPP(c_List_Ozip(U_17056,U_17057),hAPP(hAPP(c_List_Omap(U_17060,U_17056),U_17061),U_17062)),U_17063)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17060,U_17057),U_17058),hAPP(c_Product__Type_Oprod_Oprod__case(U_17060,U_17057,U_17058),hAPP(hAPP(c_COMBB(tc_fun(U_17057,tc_prod(U_17056,U_17057)),tc_fun(U_17057,U_17058),U_17060),hAPP(c_COMBB(tc_prod(U_17056,U_17057),U_17058,U_17057),U_17059)),hAPP(hAPP(c_COMBB(U_17056,tc_fun(U_17057,tc_prod(U_17056,U_17057)),U_17060),c_Product__Type_OPair(U_17056,U_17057)),U_17061)))),hAPP(hAPP(c_List_Ozip(U_17060,U_17057),U_17062),U_17063)),
    inference(clausify,[status(thm)],[f_4189_2]) ).

fof(f_4190_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_4190_2,plain,
    ! [U_17069,U_17068,U_17067,U_17066,U_17065,U_17064] : hAPP(hAPP(c_List_Ozip(U_17064,U_17065),hAPP(hAPP(c_List_Omap(U_17066,U_17064),U_17067),U_17068)),U_17069) = hAPP(hAPP(c_List_Omap(tc_prod(U_17066,U_17065),tc_prod(U_17064,U_17065)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17066,U_17065,tc_prod(U_17064,U_17065)),hAPP(hAPP(c_COMBB(U_17064,tc_fun(U_17065,tc_prod(U_17064,U_17065)),U_17066),c_Product__Type_OPair(U_17064,U_17065)),U_17067))),hAPP(hAPP(c_List_Ozip(U_17066,U_17065),U_17068),U_17069)),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

cnf(f_4190_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17064,U_17065),hAPP(hAPP(c_List_Omap(U_17066,U_17064),U_17067),U_17068)),U_17069) = hAPP(hAPP(c_List_Omap(tc_prod(U_17066,U_17065),tc_prod(U_17064,U_17065)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17066,U_17065,tc_prod(U_17064,U_17065)),hAPP(hAPP(c_COMBB(U_17064,tc_fun(U_17065,tc_prod(U_17064,U_17065)),U_17066),c_Product__Type_OPair(U_17064,U_17065)),U_17067))),hAPP(hAPP(c_List_Ozip(U_17066,U_17065),U_17068),U_17069)),
    inference(clausify,[status(thm)],[f_4190_2]) ).

fof(f_4191_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_4191_2,plain,
    ! [U_17077,U_17076,U_17075,U_17074,U_17073,U_17072,U_17071,U_17070] : hAPP(hAPP(c_List_Ozip(U_17070,U_17071),hAPP(hAPP(c_List_Omap(U_17072,U_17070),U_17073),U_17074)),hAPP(hAPP(c_List_Omap(U_17075,U_17071),U_17076),U_17077)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17072,U_17075),tc_prod(U_17070,U_17071)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17072,U_17075,tc_prod(U_17070,U_17071)),hAPP(hAPP(c_COMBC(U_17072,tc_fun(U_17075,U_17071),tc_fun(U_17075,tc_prod(U_17070,U_17071))),hAPP(hAPP(c_COMBB(tc_fun(U_17071,tc_prod(U_17070,U_17071)),tc_fun(tc_fun(U_17075,U_17071),tc_fun(U_17075,tc_prod(U_17070,U_17071))),U_17072),c_COMBB(U_17071,tc_prod(U_17070,U_17071),U_17075)),hAPP(hAPP(c_COMBB(U_17070,tc_fun(U_17071,tc_prod(U_17070,U_17071)),U_17072),c_Product__Type_OPair(U_17070,U_17071)),U_17073))),U_17076))),hAPP(hAPP(c_List_Ozip(U_17072,U_17075),U_17074),U_17077)),
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

cnf(f_4191_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17070,U_17071),hAPP(hAPP(c_List_Omap(U_17072,U_17070),U_17073),U_17074)),hAPP(hAPP(c_List_Omap(U_17075,U_17071),U_17076),U_17077)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17072,U_17075),tc_prod(U_17070,U_17071)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17072,U_17075,tc_prod(U_17070,U_17071)),hAPP(hAPP(c_COMBC(U_17072,tc_fun(U_17075,U_17071),tc_fun(U_17075,tc_prod(U_17070,U_17071))),hAPP(hAPP(c_COMBB(tc_fun(U_17071,tc_prod(U_17070,U_17071)),tc_fun(tc_fun(U_17075,U_17071),tc_fun(U_17075,tc_prod(U_17070,U_17071))),U_17072),c_COMBB(U_17071,tc_prod(U_17070,U_17071),U_17075)),hAPP(hAPP(c_COMBB(U_17070,tc_fun(U_17071,tc_prod(U_17070,U_17071)),U_17072),c_Product__Type_OPair(U_17070,U_17071)),U_17073))),U_17076))),hAPP(hAPP(c_List_Ozip(U_17072,U_17075),U_17074),U_17077)),
    inference(clausify,[status(thm)],[f_4191_2]) ).

fof(f_4192_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_4192_2,plain,
    ! [U_17079,U_17078] : hAPP(hAPP(c_List_Ozip(U_17078,U_17078),U_17079),U_17079) = hAPP(hAPP(c_List_Omap(U_17078,tc_prod(U_17078,U_17078)),hAPP(hAPP(c_COMBS(U_17078,U_17078,tc_prod(U_17078,U_17078)),c_Product__Type_OPair(U_17078,U_17078)),c_COMBI(U_17078))),U_17079),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

cnf(f_4192_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17078,U_17078),U_17079),U_17079) = hAPP(hAPP(c_List_Omap(U_17078,tc_prod(U_17078,U_17078)),hAPP(hAPP(c_COMBS(U_17078,U_17078,tc_prod(U_17078,U_17078)),c_Product__Type_OPair(U_17078,U_17078)),c_COMBI(U_17078))),U_17079),
    inference(clausify,[status(thm)],[f_4192_2]) ).

fof(f_4193_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_4193_2,plain,
    ! [U_17084,U_17083,U_17082,U_17081,U_17080] : hAPP(c_List_Orotate(U_17080,U_17081),hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),U_17084)) = hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),hAPP(c_List_Orotate(U_17082,U_17081),U_17084)),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

cnf(f_4193_3,plain,
    hAPP(c_List_Orotate(U_17080,U_17081),hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),U_17084)) = hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),hAPP(c_List_Orotate(U_17082,U_17081),U_17084)),
    inference(clausify,[status(thm)],[f_4193_2]) ).

fof(f_4194_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_4194_2,plain,
    ! [U_17088,U_17087,U_17086,U_17085] : hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),hAPP(c_List_Otl(U_17085),U_17088)) = hAPP(c_List_Otl(U_17086),hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17088)),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

cnf(f_4194_3,plain,
    hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),hAPP(c_List_Otl(U_17085),U_17088)) = hAPP(c_List_Otl(U_17086),hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17088)),
    inference(clausify,[status(thm)],[f_4194_2]) ).

fof(f_4195_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_4195_2,plain,
    ! [U_17095,U_17094,U_17093,U_17092,U_17091,U_17090,U_17089] : hAPP(c_List_Ofoldl(U_17089,U_17090,U_17091,U_17092),hAPP(hAPP(c_List_Omap(U_17093,U_17090),U_17094),U_17095)) = hAPP(c_List_Ofoldl(U_17089,U_17093,hAPP(hAPP(c_COMBC(U_17089,tc_fun(U_17093,U_17090),tc_fun(U_17093,U_17089)),hAPP(hAPP(c_COMBB(tc_fun(U_17090,U_17089),tc_fun(tc_fun(U_17093,U_17090),tc_fun(U_17093,U_17089)),U_17089),c_COMBB(U_17090,U_17089,U_17093)),U_17091)),U_17094),U_17092),U_17095),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

cnf(f_4195_3,plain,
    hAPP(c_List_Ofoldl(U_17089,U_17090,U_17091,U_17092),hAPP(hAPP(c_List_Omap(U_17093,U_17090),U_17094),U_17095)) = hAPP(c_List_Ofoldl(U_17089,U_17093,hAPP(hAPP(c_COMBC(U_17089,tc_fun(U_17093,U_17090),tc_fun(U_17093,U_17089)),hAPP(hAPP(c_COMBB(tc_fun(U_17090,U_17089),tc_fun(tc_fun(U_17093,U_17090),tc_fun(U_17093,U_17089)),U_17089),c_COMBB(U_17090,U_17089,U_17093)),U_17091)),U_17094),U_17092),U_17095),
    inference(clausify,[status(thm)],[f_4195_2]) ).

fof(f_4196_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_4196_2,plain,
    ! [U_17100,U_17099,U_17098,U_17097,U_17096] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17099) = hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17100)
          | U_17099 != U_17100 )
        & ( U_17099 = U_17100
          | hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17099) != hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17100) ) )
      | ~ c_Fun_Oinj__on(U_17096,U_17097,U_17098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17096,tc_HOL_Obool)),hAPP(c_List_Oset(U_17096),U_17099)),hAPP(c_List_Oset(U_17096),U_17100))) ),
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

cnf(f_4196_3,plain,
    ( U_17099 = U_17100
    | hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17099) != hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17100)
    | ~ c_Fun_Oinj__on(U_17096,U_17097,U_17098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17096,tc_HOL_Obool)),hAPP(c_List_Oset(U_17096),U_17099)),hAPP(c_List_Oset(U_17096),U_17100))) ),
    inference(clausify,[status(thm)],[f_4196_2]) ).

cnf(f_4196_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17099) = hAPP(hAPP(c_List_Omap(U_17096,U_17097),U_17098),U_17100)
    | U_17099 != U_17100
    | ~ c_Fun_Oinj__on(U_17096,U_17097,U_17098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17096,tc_HOL_Obool)),hAPP(c_List_Oset(U_17096),U_17099)),hAPP(c_List_Oset(U_17096),U_17100))) ),
    inference(clausify,[status(thm)],[f_4196_2]) ).

fof(f_4197_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_4197_2,plain,
    ! [U_17105,U_17104,U_17103,U_17102,U_17101] :
      ( U_17104 = U_17105
      | ~ c_Fun_Oinj__on(U_17101,U_17102,U_17103,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17101,tc_HOL_Obool)),hAPP(c_List_Oset(U_17101),U_17104)),hAPP(c_List_Oset(U_17101),U_17105)))
      | hAPP(hAPP(c_List_Omap(U_17101,U_17102),U_17103),U_17104) != hAPP(hAPP(c_List_Omap(U_17101,U_17102),U_17103),U_17105) ),
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

cnf(f_4197_3,plain,
    ( U_17104 = U_17105
    | ~ c_Fun_Oinj__on(U_17101,U_17102,U_17103,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17101,tc_HOL_Obool)),hAPP(c_List_Oset(U_17101),U_17104)),hAPP(c_List_Oset(U_17101),U_17105)))
    | hAPP(hAPP(c_List_Omap(U_17101,U_17102),U_17103),U_17104) != hAPP(hAPP(c_List_Omap(U_17101,U_17102),U_17103),U_17105) ),
    inference(clausify,[status(thm)],[f_4197_2]) ).

fof(f_4198_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_4198_2,plain,
    ! [U_17110,U_17109,U_17108,U_17107,U_17106] :
      ( hAPP(hAPP(c_List_Onth(U_17109),hAPP(hAPP(c_List_Omap(U_17107,U_17109),U_17110),U_17108)),U_17106) = hAPP(U_17110,hAPP(hAPP(c_List_Onth(U_17107),U_17108),U_17106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17107)),U_17108))) ),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

cnf(f_4198_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_17109),hAPP(hAPP(c_List_Omap(U_17107,U_17109),U_17110),U_17108)),U_17106) = hAPP(U_17110,hAPP(hAPP(c_List_Onth(U_17107),U_17108),U_17106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17106),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17107)),U_17108))) ),
    inference(clausify,[status(thm)],[f_4198_2]) ).

fof(f_4199_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_4199_2,plain,
    ! [U_17116,U_17115,U_17114,U_17113,U_17112,U_17111] :
      ( hAPP(hAPP(c_List_Omap(U_17111,U_17114),c_Fun_Ofun__upd(U_17111,U_17114,U_17115,U_17112,U_17116)),U_17113) = hAPP(hAPP(c_List_Omap(U_17111,U_17114),U_17115),U_17113)
      | hBOOL(hAPP(hAPP(c_member(U_17111),U_17112),hAPP(c_List_Oset(U_17111),U_17113))) ),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

cnf(f_4199_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17111,U_17114),c_Fun_Ofun__upd(U_17111,U_17114,U_17115,U_17112,U_17116)),U_17113) = hAPP(hAPP(c_List_Omap(U_17111,U_17114),U_17115),U_17113)
    | hBOOL(hAPP(hAPP(c_member(U_17111),U_17112),hAPP(c_List_Oset(U_17111),U_17113))) ),
    inference(clausify,[status(thm)],[f_4199_2]) ).

fof(f_4200_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_4200_2,plain,
    ! [U_17120,U_17119,U_17118,U_17117] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17117),hAPP(hAPP(c_List_Omap(U_17118,U_17117),U_17119),U_17120)))
        | ~ c_Fun_Oinj__on(U_17118,U_17117,U_17119,hAPP(c_List_Oset(U_17118),U_17120))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17118),U_17120)) )
      & ( ( c_Fun_Oinj__on(U_17118,U_17117,U_17119,hAPP(c_List_Oset(U_17118),U_17120))
          & hBOOL(hAPP(c_List_Odistinct(U_17118),U_17120)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17117),hAPP(hAPP(c_List_Omap(U_17118,U_17117),U_17119),U_17120))) ) ),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

fof(f_4200_3,plain,
    ( ! [U_17128,U_17126,U_17124,U_17122] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17122),hAPP(hAPP(c_List_Omap(U_17124,U_17122),U_17126),U_17128)))
        | ~ c_Fun_Oinj__on(U_17124,U_17122,U_17126,hAPP(c_List_Oset(U_17124),U_17128))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17124),U_17128)) )
    & ! [U_17127,U_17125,U_17123,U_17121] :
        ( ( c_Fun_Oinj__on(U_17123,U_17121,U_17125,hAPP(c_List_Oset(U_17123),U_17127))
          & hBOOL(hAPP(c_List_Odistinct(U_17123),U_17127)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17121),hAPP(hAPP(c_List_Omap(U_17123,U_17121),U_17125),U_17127))) ) ),
    inference(miniscope,[status(thm)],[f_4200_2]) ).

cnf(f_4200_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17123),U_17127))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17121),hAPP(hAPP(c_List_Omap(U_17123,U_17121),U_17125),U_17127))) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_5,plain,
    ( c_Fun_Oinj__on(U_17123,U_17121,U_17125,hAPP(c_List_Oset(U_17123),U_17127))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17121),hAPP(hAPP(c_List_Omap(U_17123,U_17121),U_17125),U_17127))) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

cnf(f_4200_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17122),hAPP(hAPP(c_List_Omap(U_17124,U_17122),U_17126),U_17128)))
    | ~ c_Fun_Oinj__on(U_17124,U_17122,U_17126,hAPP(c_List_Oset(U_17124),U_17128))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17124),U_17128)) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

fof(f_4201_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_4201_2,plain,
    ! [U_17130,U_17129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17129),hAPP(c_Groups_Oabs__class_Oabs(U_17129),hAPP(c_List_Omonoid__add__class_Olistsum(U_17129),U_17130))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17129),hAPP(hAPP(c_List_Omap(U_17129,U_17129),c_Groups_Oabs__class_Oabs(U_17129)),U_17130))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_17129) ),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

cnf(f_4201_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17129),hAPP(c_Groups_Oabs__class_Oabs(U_17129),hAPP(c_List_Omonoid__add__class_Olistsum(U_17129),U_17130))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17129),hAPP(hAPP(c_List_Omap(U_17129,U_17129),c_Groups_Oabs__class_Oabs(U_17129)),U_17130))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_17129) ),
    inference(clausify,[status(thm)],[f_4201_2]) ).

fof(f_4202_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_4202_2,plain,
    ! [U_17134,U_17133,U_17132,U_17131] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_17131),hAPP(c_List_Omonoid__add__class_Olistsum(U_17131),hAPP(hAPP(c_List_Omap(U_17132,U_17131),U_17133),U_17134))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17131),hAPP(hAPP(c_List_Omap(U_17132,U_17131),hAPP(c_Fun_Ocomp(U_17131,U_17131,U_17132,c_Groups_Ouminus__class_Ouminus(U_17131)),U_17133)),U_17134))
      | ~ class_Groups_Oab__group__add(U_17131) ),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

cnf(f_4202_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_17131),hAPP(c_List_Omonoid__add__class_Olistsum(U_17131),hAPP(hAPP(c_List_Omap(U_17132,U_17131),U_17133),U_17134))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17131),hAPP(hAPP(c_List_Omap(U_17132,U_17131),hAPP(c_Fun_Ocomp(U_17131,U_17131,U_17132,c_Groups_Ouminus__class_Ouminus(U_17131)),U_17133)),U_17134))
    | ~ class_Groups_Oab__group__add(U_17131) ),
    inference(clausify,[status(thm)],[f_4202_2]) ).

fof(f_4203_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_4203_2,plain,
    ! [U_17138,U_17137,U_17136,U_17135] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17135),tc_List_Olist(U_17136),hAPP(c_List_Omap(U_17135,U_17136),U_17137),U_17138)
      | ~ c_Fun_Oinj__on(U_17135,U_17136,U_17137,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17135,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17135),tc_fun(U_17135,tc_HOL_Obool),c_List_Oset(U_17135)),U_17138))) ),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

cnf(f_4203_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17135),tc_List_Olist(U_17136),hAPP(c_List_Omap(U_17135,U_17136),U_17137),U_17138)
    | ~ c_Fun_Oinj__on(U_17135,U_17136,U_17137,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17135,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17135),tc_fun(U_17135,tc_HOL_Obool),c_List_Oset(U_17135)),U_17138))) ),
    inference(clausify,[status(thm)],[f_4203_2]) ).

fof(f_4204_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_4204_2,plain,
    ! [U_17141,U_17140,U_17139] :
      ( c_Fun_Oinj__on(U_17139,U_17140,U_17141,c_Orderings_Otop__class_Otop(tc_fun(U_17139,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17139),tc_List_Olist(U_17140),hAPP(c_List_Omap(U_17139,U_17140),U_17141),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17139),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

cnf(f_4204_3,plain,
    ( c_Fun_Oinj__on(U_17139,U_17140,U_17141,c_Orderings_Otop__class_Otop(tc_fun(U_17139,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17139),tc_List_Olist(U_17140),hAPP(c_List_Omap(U_17139,U_17140),U_17141),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17139),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4204_2]) ).

fof(f_4205_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_4205_2,plain,
    ! [U_17144,U_17143,U_17142] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_17142),tc_List_Olist(U_17143),hAPP(c_List_Omap(U_17142,U_17143),U_17144),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17142),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17142,U_17143,U_17144,c_Orderings_Otop__class_Otop(tc_fun(U_17142,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_17142,U_17143,U_17144,c_Orderings_Otop__class_Otop(tc_fun(U_17142,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17142),tc_List_Olist(U_17143),hAPP(c_List_Omap(U_17142,U_17143),U_17144),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17142),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

fof(f_4205_3,plain,
    ( ! [U_17150,U_17148,U_17146] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17146),tc_List_Olist(U_17148),hAPP(c_List_Omap(U_17146,U_17148),U_17150),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17146),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17146,U_17148,U_17150,c_Orderings_Otop__class_Otop(tc_fun(U_17146,tc_HOL_Obool))) )
    & ! [U_17149,U_17147,U_17145] :
        ( c_Fun_Oinj__on(U_17145,U_17147,U_17149,c_Orderings_Otop__class_Otop(tc_fun(U_17145,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17145),tc_List_Olist(U_17147),hAPP(c_List_Omap(U_17145,U_17147),U_17149),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17145),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4205_2]) ).

cnf(f_4205_4,plain,
    ( c_Fun_Oinj__on(U_17145,U_17147,U_17149,c_Orderings_Otop__class_Otop(tc_fun(U_17145,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17145),tc_List_Olist(U_17147),hAPP(c_List_Omap(U_17145,U_17147),U_17149),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17145),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4205_3]) ).

cnf(f_4205_5,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17146),tc_List_Olist(U_17148),hAPP(c_List_Omap(U_17146,U_17148),U_17150),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17146),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17146,U_17148,U_17150,c_Orderings_Otop__class_Otop(tc_fun(U_17146,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4205_3]) ).

fof(f_4206_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_4206_2,plain,
    ! [U_17154,U_17153,U_17152,U_17151] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17151),hAPP(hAPP(c_List_Omap(U_17152,U_17151),U_17154),U_17153)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_17152,U_17151),U_17154),hAPP(c_List_Oset(U_17152),U_17153))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17152),U_17153))
      | ~ class_Groups_Ocomm__monoid__add(U_17151) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

cnf(f_4206_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17151),hAPP(hAPP(c_List_Omap(U_17152,U_17151),U_17154),U_17153)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_17152,U_17151),U_17154),hAPP(c_List_Oset(U_17152),U_17153))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17152),U_17153))
    | ~ class_Groups_Ocomm__monoid__add(U_17151) ),
    inference(clausify,[status(thm)],[f_4206_2]) ).

fof(f_4207_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_4207_2,plain,
    ! [U_17158,U_17157,U_17156,U_17155] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17155),hAPP(hAPP(c_List_Omap(U_17156,U_17155),hAPP(c_COMBK(U_17155,U_17156),U_17157)),U_17158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17155),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_17155),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17156)),U_17158))),U_17157)
      | ~ class_Rings_Osemiring__1(U_17155) ),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

cnf(f_4207_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17155),hAPP(hAPP(c_List_Omap(U_17156,U_17155),hAPP(c_COMBK(U_17155,U_17156),U_17157)),U_17158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17155),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_17155),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17156)),U_17158))),U_17157)
    | ~ class_Rings_Osemiring__1(U_17155) ),
    inference(clausify,[status(thm)],[f_4207_2]) ).

fof(f_4208_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_4208_2,plain,
    ! [U_17163,U_17162,U_17161,U_17160,U_17159] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17159),hAPP(hAPP(c_List_Omap(U_17160,U_17159),U_17163),U_17162)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17159),hAPP(U_17163,U_17161)),hAPP(c_List_Omonoid__add__class_Olistsum(U_17159),hAPP(hAPP(c_List_Omap(U_17160,U_17159),U_17163),c_List_Oremove1(U_17160,U_17161,U_17162))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17160),U_17161),hAPP(c_List_Oset(U_17160),U_17162)))
      | ~ class_Groups_Ocomm__monoid__add(U_17159) ),
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

cnf(f_4208_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17159),hAPP(hAPP(c_List_Omap(U_17160,U_17159),U_17163),U_17162)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17159),hAPP(U_17163,U_17161)),hAPP(c_List_Omonoid__add__class_Olistsum(U_17159),hAPP(hAPP(c_List_Omap(U_17160,U_17159),U_17163),c_List_Oremove1(U_17160,U_17161,U_17162))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17160),U_17161),hAPP(c_List_Oset(U_17160),U_17162)))
    | ~ class_Groups_Ocomm__monoid__add(U_17159) ),
    inference(clausify,[status(thm)],[f_4208_2]) ).

fof(f_4209_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_4209_2,plain,
    ! [U_17167,U_17166,U_17165,U_17164] :
      ( ( ( c_Nitpick_Osetsum_H(U_17165,U_17164,U_17167,U_17166) = c_Groups_Ozero__class_Ozero(U_17164)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17165),U_17166)) )
        & ( c_Nitpick_Osetsum_H(U_17165,U_17164,U_17167,U_17166) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17164),hAPP(hAPP(c_List_Omap(U_17165,U_17164),U_17167),c_Hilbert__Choice_OEps(tc_List_Olist(U_17165),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17165),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_17165)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17165),tc_fun(U_17165,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17165,tc_HOL_Obool),tc_fun(tc_fun(U_17165,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17165)),c_fequal),c_List_Oset(U_17165))),U_17166))),c_List_Odistinct(U_17165)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17165),U_17166)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_17164) ),
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

cnf(f_4209_3,plain,
    ( c_Nitpick_Osetsum_H(U_17165,U_17164,U_17167,U_17166) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17164),hAPP(hAPP(c_List_Omap(U_17165,U_17164),U_17167),c_Hilbert__Choice_OEps(tc_List_Olist(U_17165),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17165),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_17165)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17165),tc_fun(U_17165,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17165,tc_HOL_Obool),tc_fun(tc_fun(U_17165,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17165)),c_fequal),c_List_Oset(U_17165))),U_17166))),c_List_Odistinct(U_17165)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17165),U_17166))
    | ~ class_Groups_Ocomm__monoid__add(U_17164) ),
    inference(clausify,[status(thm)],[f_4209_2]) ).

cnf(f_4209_4,plain,
    ( c_Nitpick_Osetsum_H(U_17165,U_17164,U_17167,U_17166) = c_Groups_Ozero__class_Ozero(U_17164)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17165),U_17166))
    | ~ class_Groups_Ocomm__monoid__add(U_17164) ),
    inference(clausify,[status(thm)],[f_4209_2]) ).

fof(f_4210_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_4210_2,plain,
    ! [U_17170,U_17169,U_17168] :
      ( hAPP(c_Random_Opick(U_17169,hAPP(hAPP(c_List_Omap(U_17169,tc_prod(tc_Code__Numeral_Ocode__numeral,U_17169)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17169),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_17170)),hAPP(c_Code__Numeral_Oof__nat,U_17168)) = hAPP(hAPP(c_List_Onth(U_17169),U_17170),U_17168)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17169)),U_17170))) ),
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

cnf(f_4210_3,plain,
    ( hAPP(c_Random_Opick(U_17169,hAPP(hAPP(c_List_Omap(U_17169,tc_prod(tc_Code__Numeral_Ocode__numeral,U_17169)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17169),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_17170)),hAPP(c_Code__Numeral_Oof__nat,U_17168)) = hAPP(hAPP(c_List_Onth(U_17169),U_17170),U_17168)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17169)),U_17170))) ),
    inference(clausify,[status(thm)],[f_4210_2]) ).

fof(f_4211_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_4211_2,plain,
    ! [U_17172,U_17171] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17171)),hAPP(c_Code__Numeral_Oof__nat,U_17172)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17171),U_17172)),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

cnf(f_4211_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17171)),hAPP(c_Code__Numeral_Oof__nat,U_17172)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17171),U_17172)),
    inference(clausify,[status(thm)],[f_4211_2]) ).

fof(f_4212_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_4212_2,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_4212_1]) ).

fof(f_4213_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_4213_2,plain,
    ! [U_17174,U_17173] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_17173) = hAPP(c_Code__Numeral_Oof__nat,U_17174)
        | U_17173 != U_17174 )
      & ( U_17173 = U_17174
        | hAPP(c_Code__Numeral_Oof__nat,U_17173) != hAPP(c_Code__Numeral_Oof__nat,U_17174) ) ),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

fof(f_4213_3,plain,
    ( ! [U_17178,U_17176] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_17176) = hAPP(c_Code__Numeral_Oof__nat,U_17178)
        | U_17176 != U_17178 )
    & ! [U_17177,U_17175] :
        ( U_17175 = U_17177
        | hAPP(c_Code__Numeral_Oof__nat,U_17175) != hAPP(c_Code__Numeral_Oof__nat,U_17177) ) ),
    inference(miniscope,[status(thm)],[f_4213_2]) ).

cnf(f_4213_4,plain,
    ( U_17175 = U_17177
    | hAPP(c_Code__Numeral_Oof__nat,U_17175) != hAPP(c_Code__Numeral_Oof__nat,U_17177) ),
    inference(clausify,[status(thm)],[f_4213_3]) ).

cnf(f_4213_5,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_17176) = hAPP(c_Code__Numeral_Oof__nat,U_17178)
    | U_17176 != U_17178 ),
    inference(clausify,[status(thm)],[f_4213_3]) ).

fof(f_4214_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_4214_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_4214_1]) ).

fof(f_4215_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_4215_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_4215_1]) ).

fof(f_4216_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_4216_2,plain,
    ! [U_17180,U_17179] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17179)),hAPP(c_Code__Numeral_Oof__nat,U_17180)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17179),U_17180)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17179),U_17180))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17179)),hAPP(c_Code__Numeral_Oof__nat,U_17180))) ) ),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

fof(f_4216_3,plain,
    ( ! [U_17184,U_17182] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17182)),hAPP(c_Code__Numeral_Oof__nat,U_17184)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17182),U_17184)) )
    & ! [U_17183,U_17181] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17181),U_17183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17181)),hAPP(c_Code__Numeral_Oof__nat,U_17183))) ) ),
    inference(miniscope,[status(thm)],[f_4216_2]) ).

cnf(f_4216_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17181),U_17183))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17181)),hAPP(c_Code__Numeral_Oof__nat,U_17183))) ),
    inference(clausify,[status(thm)],[f_4216_3]) ).

cnf(f_4216_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17182)),hAPP(c_Code__Numeral_Oof__nat,U_17184)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17182),U_17184)) ),
    inference(clausify,[status(thm)],[f_4216_3]) ).

fof(f_4217_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_4217_2,plain,
    ! [U_17186,U_17185] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_17185) = hAPP(c_Code__Numeral_Oof__nat,U_17186)
          | U_17185 != U_17186 )
        & ( U_17185 = U_17186
          | hAPP(c_Code__Numeral_Oof__nat,U_17185) != hAPP(c_Code__Numeral_Oof__nat,U_17186) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

cnf(f_4217_3,plain,
    ( U_17185 = U_17186
    | hAPP(c_Code__Numeral_Oof__nat,U_17185) != hAPP(c_Code__Numeral_Oof__nat,U_17186)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4217_2]) ).

cnf(f_4217_4,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_17185) = hAPP(c_Code__Numeral_Oof__nat,U_17186)
    | U_17185 != U_17186
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17186),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17185),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4217_2]) ).

fof(f_4218_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_4218_2,plain,
    ! [U_17190,U_17189,U_17188,U_17187] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17187,U_17189),U_17187),c_Product__Type_Ofst(U_17187,U_17189)),hAPP(hAPP(c_List_Ozip(U_17187,U_17189),U_17188),U_17190)) = U_17188
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17187)),U_17188) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17189)),U_17190) ),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

cnf(f_4218_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17187,U_17189),U_17187),c_Product__Type_Ofst(U_17187,U_17189)),hAPP(hAPP(c_List_Ozip(U_17187,U_17189),U_17188),U_17190)) = U_17188
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17187)),U_17188) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17189)),U_17190) ),
    inference(clausify,[status(thm)],[f_4218_2]) ).

fof(f_4219_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_4219_2,plain,
    ! [U_17194,U_17193,U_17192,U_17191] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17191,U_17193),U_17193),c_Product__Type_Osnd(U_17191,U_17193)),hAPP(hAPP(c_List_Ozip(U_17191,U_17193),U_17192),U_17194)) = U_17194
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17191)),U_17192) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17193)),U_17194) ),
    inference(variable_rename,[status(thm)],[f_4219_1]) ).

cnf(f_4219_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17191,U_17193),U_17193),c_Product__Type_Osnd(U_17191,U_17193)),hAPP(hAPP(c_List_Ozip(U_17191,U_17193),U_17192),U_17194)) = U_17194
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17191)),U_17192) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17193)),U_17194) ),
    inference(clausify,[status(thm)],[f_4219_2]) ).

fof(f_4220_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_4220_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_4220_1]) ).

fof(f_4221_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_4221_2,plain,
    ! [U_17197,U_17196,U_17195] : hAPP(hAPP(c_List_Ozip(U_17195,U_17196),hAPP(hAPP(c_List_Omap(tc_prod(U_17195,U_17196),U_17195),c_Product__Type_Ofst(U_17195,U_17196)),U_17197)),hAPP(hAPP(c_List_Omap(tc_prod(U_17195,U_17196),U_17196),c_Product__Type_Osnd(U_17195,U_17196)),U_17197)) = U_17197,
    inference(variable_rename,[status(thm)],[f_4221_1]) ).

cnf(f_4221_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17195,U_17196),hAPP(hAPP(c_List_Omap(tc_prod(U_17195,U_17196),U_17195),c_Product__Type_Ofst(U_17195,U_17196)),U_17197)),hAPP(hAPP(c_List_Omap(tc_prod(U_17195,U_17196),U_17196),c_Product__Type_Osnd(U_17195,U_17196)),U_17197)) = U_17197,
    inference(clausify,[status(thm)],[f_4221_2]) ).

fof(f_4222_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_4222_2,plain,
    ! [U_17199,U_17198] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17198)),hAPP(c_Code__Numeral_Oof__nat,U_17199)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17198),U_17199)),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

cnf(f_4222_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17198)),hAPP(c_Code__Numeral_Oof__nat,U_17199)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17198),U_17199)),
    inference(clausify,[status(thm)],[f_4222_2]) ).

fof(f_4223_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_4223_2,plain,
    ! [U_17201,U_17200] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17200)),hAPP(c_Code__Numeral_Oof__nat,U_17201)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17200),U_17201)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17200),U_17201))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17200)),hAPP(c_Code__Numeral_Oof__nat,U_17201))) ) ),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

fof(f_4223_3,plain,
    ( ! [U_17205,U_17203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17203)),hAPP(c_Code__Numeral_Oof__nat,U_17205)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17203),U_17205)) )
    & ! [U_17204,U_17202] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17202),U_17204))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17202)),hAPP(c_Code__Numeral_Oof__nat,U_17204))) ) ),
    inference(miniscope,[status(thm)],[f_4223_2]) ).

cnf(f_4223_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17202),U_17204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17202)),hAPP(c_Code__Numeral_Oof__nat,U_17204))) ),
    inference(clausify,[status(thm)],[f_4223_3]) ).

cnf(f_4223_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17203)),hAPP(c_Code__Numeral_Oof__nat,U_17205)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17203),U_17205)) ),
    inference(clausify,[status(thm)],[f_4223_3]) ).

fof(f_4224_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_4224_2,plain,
    ! [U_17207,U_17206] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_17206)),hAPP(c_Code__Numeral_Oof__nat,U_17207)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17206),U_17207)),
    inference(variable_rename,[status(thm)],[f_4224_1]) ).

cnf(f_4224_3,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_17206)),hAPP(c_Code__Numeral_Oof__nat,U_17207)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17206),U_17207)),
    inference(clausify,[status(thm)],[f_4224_2]) ).

fof(f_4225_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_4225_2,plain,
    ! [U_17210,U_17209,U_17208] :
      ( hBOOL(hAPP(hAPP(c_member(U_17209),hAPP(c_Random_Opick(U_17209,U_17210),U_17208)),hAPP(c_List_Oset(U_17209),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17209),U_17209),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17209)),U_17210))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17208),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_17209),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17209)),U_17210)))) ),
    inference(variable_rename,[status(thm)],[f_4225_1]) ).

cnf(f_4225_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17209),hAPP(c_Random_Opick(U_17209,U_17210),U_17208)),hAPP(c_List_Oset(U_17209),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17209),U_17209),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17209)),U_17210))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17208),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_17209),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17209)),U_17210)))) ),
    inference(clausify,[status(thm)],[f_4225_2]) ).

fof(f_4226_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_4226_2,plain,
    ! [U_17215,U_17214,U_17213,U_17212,U_17211] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_17211,U_17213),U_17212),U_17214) = U_17215
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17213),c_Product__Type_Osnd(U_17211,U_17213)),U_17215) != U_17214
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17211),c_Product__Type_Ofst(U_17211,U_17213)),U_17215) != U_17212 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17213),c_Product__Type_Osnd(U_17211,U_17213)),U_17215) = U_17214
            & hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17211),c_Product__Type_Ofst(U_17211,U_17213)),U_17215) = U_17212 )
          | hAPP(hAPP(c_List_Ozip(U_17211,U_17213),U_17212),U_17214) != U_17215 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17211)),U_17212) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17213)),U_17214) ),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

cnf(f_4226_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17211),c_Product__Type_Ofst(U_17211,U_17213)),U_17215) = U_17212
    | hAPP(hAPP(c_List_Ozip(U_17211,U_17213),U_17212),U_17214) != U_17215
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17211)),U_17212) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17213)),U_17214) ),
    inference(clausify,[status(thm)],[f_4226_2]) ).

cnf(f_4226_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17213),c_Product__Type_Osnd(U_17211,U_17213)),U_17215) = U_17214
    | hAPP(hAPP(c_List_Ozip(U_17211,U_17213),U_17212),U_17214) != U_17215
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17211)),U_17212) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17213)),U_17214) ),
    inference(clausify,[status(thm)],[f_4226_2]) ).

cnf(f_4226_5,plain,
    ( hAPP(hAPP(c_List_Ozip(U_17211,U_17213),U_17212),U_17214) = U_17215
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17213),c_Product__Type_Osnd(U_17211,U_17213)),U_17215) != U_17214
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17211,U_17213),U_17211),c_Product__Type_Ofst(U_17211,U_17213)),U_17215) != U_17212
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17211)),U_17212) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17213)),U_17214) ),
    inference(clausify,[status(thm)],[f_4226_2]) ).

fof(f_4227_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_4227_2,plain,
    ! [U_17218,U_17217,U_17216] : c_List_Olist_Olist__size(U_17216,U_17217,U_17218) = 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_17216,tc_Nat_Onat),U_17217),U_17218))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17216)),U_17218)),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

cnf(f_4227_3,plain,
    c_List_Olist_Olist__size(U_17216,U_17217,U_17218) = 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_17216,tc_Nat_Onat),U_17217),U_17218))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17216)),U_17218)),
    inference(clausify,[status(thm)],[f_4227_2]) ).

fof(f_4228_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_4228_2,plain,
    ! [U_17219] :
      ( ( U_17219 != 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_17219)) )
      & ( 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_17219))
        | U_17219 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

fof(f_4228_3,plain,
    ( ! [U_17221] :
        ( U_17221 != 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_17221)) )
    & ! [U_17220] :
        ( 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_17220))
        | U_17220 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4228_2]) ).

cnf(f_4228_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_17220))
    | U_17220 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4228_3]) ).

cnf(f_4228_5,plain,
    ( U_17221 != 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_17221)) ),
    inference(clausify,[status(thm)],[f_4228_3]) ).

fof(f_4229_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_4229_2,plain,
    ! [U_17225,U_17224,U_17223,U_17222] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17222),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17222),U_17223),c_List_Oupto(U_17224,U_17225))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17222),U_17223),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17224,U_17225)))
      | ~ class_Groups_Ocomm__monoid__add(U_17222) ),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

cnf(f_4229_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17222),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17222),U_17223),c_List_Oupto(U_17224,U_17225))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17222),U_17223),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17224,U_17225)))
    | ~ class_Groups_Ocomm__monoid__add(U_17222) ),
    inference(clausify,[status(thm)],[f_4229_2]) ).

fof(f_4230_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_4230_2,plain,
    ! [U_17229,U_17228,U_17227,U_17226] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17226),U_17227),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17228,U_17229))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17226),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17226),U_17227),c_List_Oupto(U_17228,U_17229)))
      | ~ class_Groups_Ocomm__monoid__add(U_17226) ),
    inference(variable_rename,[status(thm)],[f_4230_1]) ).

cnf(f_4230_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17226),U_17227),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17228,U_17229))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17226),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17226),U_17227),c_List_Oupto(U_17228,U_17229)))
    | ~ class_Groups_Ocomm__monoid__add(U_17226) ),
    inference(clausify,[status(thm)],[f_4230_2]) ).

fof(f_4231_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_4231_2,plain,
    ! [U_17232,U_17231,U_17230] :
      ( hBOOL(hAPP(hAPP(c_member(U_17230),hAPP(c_Product__Type_Ofst(U_17230,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_17230,U_17231),U_17232))),hAPP(c_List_Oset(U_17230),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17230),U_17230),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17230)),U_17231))))
      | ~ 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_17230),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17230)),U_17231)))) ),
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

cnf(f_4231_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17230),hAPP(c_Product__Type_Ofst(U_17230,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_17230,U_17231),U_17232))),hAPP(c_List_Oset(U_17230),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17230),U_17230),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17230)),U_17231))))
    | ~ 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_17230),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17230)),U_17231)))) ),
    inference(clausify,[status(thm)],[f_4231_2]) ).

fof(f_4232_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_4232_2,plain,
    ! [U_17234,U_17233] : c_Random_Oselect__weight(U_17233,U_17234) = 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_17233,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_17233),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17233)),U_17234)))),hAPP(hAPP(c_COMBB(U_17233,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17233,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17233,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_17233,U_17234))),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

cnf(f_4232_3,plain,
    c_Random_Oselect__weight(U_17233,U_17234) = 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_17233,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_17233),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17233)),U_17234)))),hAPP(hAPP(c_COMBB(U_17233,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17233,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17233,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_17233,U_17234))),
    inference(clausify,[status(thm)],[f_4232_2]) ).

fof(f_4233_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_4233_2,plain,
    ! [U_17236,U_17235] : c_Random_Oselect(U_17235,U_17236) = 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_17235,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_17235)),U_17236)))),hAPP(hAPP(c_COMBB(U_17235,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17235,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17235,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_17235,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_17235),U_17236)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4233_1]) ).

cnf(f_4233_3,plain,
    c_Random_Oselect(U_17235,U_17236) = 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_17235,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_17235)),U_17236)))),hAPP(hAPP(c_COMBB(U_17235,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17235,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17235,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_17235,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_17235),U_17236)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4233_2]) ).

fof(f_4234_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_4234_2,plain,
    ! [U_17242,U_17241,U_17240,U_17239,U_17238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17241),U_17240))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17242),U_17240))))
      | ? [U_17237] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(U_17241,U_17237)),hAPP(U_17242,U_17237)))
          & hBOOL(hAPP(hAPP(c_member(U_17239),U_17237),hAPP(c_List_Oset(U_17239),U_17240))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_17238)
      | ~ class_Groups_Omonoid__add(U_17238) ),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

fof(f_4234_3,plain,
    ! [U_17242,U_17241,U_17240,U_17239,U_17238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17241),U_17240))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17242),U_17240))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(U_17241,sK428(U_17242,U_17241,U_17240,U_17239,U_17238))),hAPP(U_17242,sK428(U_17242,U_17241,U_17240,U_17239,U_17238))))
        & hBOOL(hAPP(hAPP(c_member(U_17239),sK428(U_17242,U_17241,U_17240,U_17239,U_17238)),hAPP(c_List_Oset(U_17239),U_17240))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_17238)
      | ~ class_Groups_Omonoid__add(U_17238) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_17237,sK428(U_17242,U_17241,U_17240,U_17239,U_17238))],[f_4234_2]) ).

cnf(f_4234_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17239),sK428(U_17242,U_17241,U_17240,U_17239,U_17238)),hAPP(c_List_Oset(U_17239),U_17240)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17241),U_17240))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17242),U_17240))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_17238)
    | ~ class_Groups_Omonoid__add(U_17238) ),
    inference(clausify,[status(thm)],[f_4234_3]) ).

cnf(f_4234_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(U_17241,sK428(U_17242,U_17241,U_17240,U_17239,U_17238))),hAPP(U_17242,sK428(U_17242,U_17241,U_17240,U_17239,U_17238))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17238),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17241),U_17240))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17238),hAPP(hAPP(c_List_Omap(U_17239,U_17238),U_17242),U_17240))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_17238)
    | ~ class_Groups_Omonoid__add(U_17238) ),
    inference(clausify,[status(thm)],[f_4234_3]) ).

fof(f_4235_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_4235_2,plain,
    ! [U_17244,U_17243] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_17243),U_17244) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17243)),hAPP(c_Code__Numeral_Onat__of,U_17244))),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

cnf(f_4235_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_17243),U_17244) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17243)),hAPP(c_Code__Numeral_Onat__of,U_17244))),
    inference(clausify,[status(thm)],[f_4235_2]) ).

fof(f_4236_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_4236_2,plain,
    ! [U_17245] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17245)) = U_17245,
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

cnf(f_4236_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17245)) = U_17245,
    inference(clausify,[status(thm)],[f_4236_2]) ).

fof(f_4237_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_4237_2,plain,
    ! [U_17246] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17246)) = U_17246,
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

cnf(f_4237_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17246)) = U_17246,
    inference(clausify,[status(thm)],[f_4237_2]) ).

fof(f_4238_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_4238_2,plain,
    ! [U_17247] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17247)) = U_17247,
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

cnf(f_4238_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17247)) = U_17247,
    inference(clausify,[status(thm)],[f_4238_2]) ).

fof(f_4239_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_4239_2,plain,
    ! [U_17249,U_17248] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_17248) = hAPP(c_Code__Numeral_Onat__of,U_17249)
        | U_17248 != U_17249 )
      & ( U_17248 = U_17249
        | hAPP(c_Code__Numeral_Onat__of,U_17248) != hAPP(c_Code__Numeral_Onat__of,U_17249) ) ),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

fof(f_4239_3,plain,
    ( ! [U_17253,U_17251] :
        ( hAPP(c_Code__Numeral_Onat__of,U_17251) = hAPP(c_Code__Numeral_Onat__of,U_17253)
        | U_17251 != U_17253 )
    & ! [U_17252,U_17250] :
        ( U_17250 = U_17252
        | hAPP(c_Code__Numeral_Onat__of,U_17250) != hAPP(c_Code__Numeral_Onat__of,U_17252) ) ),
    inference(miniscope,[status(thm)],[f_4239_2]) ).

cnf(f_4239_4,plain,
    ( U_17250 = U_17252
    | hAPP(c_Code__Numeral_Onat__of,U_17250) != hAPP(c_Code__Numeral_Onat__of,U_17252) ),
    inference(clausify,[status(thm)],[f_4239_3]) ).

cnf(f_4239_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_17251) = hAPP(c_Code__Numeral_Onat__of,U_17253)
    | U_17251 != U_17253 ),
    inference(clausify,[status(thm)],[f_4239_3]) ).

fof(f_4240_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_4240_2,plain,
    ! [U_17255,U_17254] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_17254) = hAPP(c_Code__Numeral_Onat__of,U_17255)
        | U_17254 != U_17255 )
      & ( U_17254 = U_17255
        | hAPP(c_Code__Numeral_Onat__of,U_17254) != hAPP(c_Code__Numeral_Onat__of,U_17255) ) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

fof(f_4240_3,plain,
    ( ! [U_17259,U_17257] :
        ( hAPP(c_Code__Numeral_Onat__of,U_17257) = hAPP(c_Code__Numeral_Onat__of,U_17259)
        | U_17257 != U_17259 )
    & ! [U_17258,U_17256] :
        ( U_17256 = U_17258
        | hAPP(c_Code__Numeral_Onat__of,U_17256) != hAPP(c_Code__Numeral_Onat__of,U_17258) ) ),
    inference(miniscope,[status(thm)],[f_4240_2]) ).

cnf(f_4240_4,plain,
    ( U_17256 = U_17258
    | hAPP(c_Code__Numeral_Onat__of,U_17256) != hAPP(c_Code__Numeral_Onat__of,U_17258) ),
    inference(clausify,[status(thm)],[f_4240_3]) ).

cnf(f_4240_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_17257) = hAPP(c_Code__Numeral_Onat__of,U_17259)
    | U_17257 != U_17259 ),
    inference(clausify,[status(thm)],[f_4240_3]) ).

fof(f_4241_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_4241_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_4241_1]) ).

fof(f_4242_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_4242_2,plain,
    ! [U_17261,U_17260] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17260),U_17261))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17260)),hAPP(c_Code__Numeral_Onat__of,U_17261))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17260)),hAPP(c_Code__Numeral_Onat__of,U_17261)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17260),U_17261)) ) ),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

fof(f_4242_3,plain,
    ( ! [U_17265,U_17263] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17263),U_17265))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17263)),hAPP(c_Code__Numeral_Onat__of,U_17265))) )
    & ! [U_17264,U_17262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17262)),hAPP(c_Code__Numeral_Onat__of,U_17264)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17262),U_17264)) ) ),
    inference(miniscope,[status(thm)],[f_4242_2]) ).

cnf(f_4242_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17262)),hAPP(c_Code__Numeral_Onat__of,U_17264)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17262),U_17264)) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

cnf(f_4242_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17263),U_17265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17263)),hAPP(c_Code__Numeral_Onat__of,U_17265))) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

fof(f_4243_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_4243_2,plain,
    ! [U_17266] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17266)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

cnf(f_4243_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17266)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4243_2]) ).

fof(f_4244_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_4244_2,plain,
    ! [U_17267] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_17267)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17267),
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

cnf(f_4244_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_17267)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17267),
    inference(clausify,[status(thm)],[f_4244_2]) ).

fof(f_4245_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_4245_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_4245_1]) ).

fof(f_4246_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_4246_2,plain,
    ! [U_17269,U_17268] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17268),U_17269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17268)),hAPP(c_Code__Numeral_Onat__of,U_17269))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17268)),hAPP(c_Code__Numeral_Onat__of,U_17269)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17268),U_17269)) ) ),
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

fof(f_4246_3,plain,
    ( ! [U_17273,U_17271] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17271),U_17273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17271)),hAPP(c_Code__Numeral_Onat__of,U_17273))) )
    & ! [U_17272,U_17270] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17270)),hAPP(c_Code__Numeral_Onat__of,U_17272)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17270),U_17272)) ) ),
    inference(miniscope,[status(thm)],[f_4246_2]) ).

cnf(f_4246_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17270)),hAPP(c_Code__Numeral_Onat__of,U_17272)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17270),U_17272)) ),
    inference(clausify,[status(thm)],[f_4246_3]) ).

cnf(f_4246_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17271),U_17273))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17271)),hAPP(c_Code__Numeral_Onat__of,U_17273))) ),
    inference(clausify,[status(thm)],[f_4246_3]) ).

fof(f_4247_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_4247_2,plain,
    ! [U_17274] : hAPP(c_Code__Numeral_Onat__of,U_17274) = c_Code__Numeral_Onat__of__aux(U_17274,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

cnf(f_4247_3,plain,
    hAPP(c_Code__Numeral_Onat__of,U_17274) = c_Code__Numeral_Onat__of__aux(U_17274,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4247_2]) ).

fof(f_4248_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_4248_2,plain,
    ! [U_17276,U_17275] : c_Code__Numeral_Onat__of__aux(U_17275,U_17276) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17275)),U_17276),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

cnf(f_4248_3,plain,
    c_Code__Numeral_Onat__of__aux(U_17275,U_17276) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17275)),U_17276),
    inference(clausify,[status(thm)],[f_4248_2]) ).

fof(f_4249_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_4249_2,plain,
    ! [U_17277] : c_Code__Numeral_OSuc__code__numeral(U_17277) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_17277))),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

cnf(f_4249_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_17277) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_17277))),
    inference(clausify,[status(thm)],[f_4249_2]) ).

fof(f_4250_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_4250_2,plain,
    ! [U_17279,U_17278] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17278),U_17279) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17278)),hAPP(c_Code__Numeral_Onat__of,U_17279))),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

cnf(f_4250_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17278),U_17279) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17278)),hAPP(c_Code__Numeral_Onat__of,U_17279))),
    inference(clausify,[status(thm)],[f_4250_2]) ).

fof(f_4251_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_4251_2,plain,
    ! [U_17280] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17280)) = U_17280
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17280),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4251_1]) ).

cnf(f_4251_3,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17280)) = U_17280
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17280),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4251_2]) ).

fof(f_4252_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_4252_2,plain,
    ! [U_17282,U_17281] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_17281),U_17282) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17281)),hAPP(c_Code__Numeral_Onat__of,U_17282))),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

cnf(f_4252_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_17281),U_17282) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17281)),hAPP(c_Code__Numeral_Onat__of,U_17282))),
    inference(clausify,[status(thm)],[f_4252_2]) ).

fof(f_4253_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_4253_2,plain,
    ! [U_17284,U_17283] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_17283),U_17284) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17283)),hAPP(c_Code__Numeral_Onat__of,U_17284))),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

cnf(f_4253_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_17283),U_17284) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17283)),hAPP(c_Code__Numeral_Onat__of,U_17284))),
    inference(clausify,[status(thm)],[f_4253_2]) ).

fof(f_4254_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_4254_2,plain,
    ! [U_17286,U_17285] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_17285,U_17286) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_17285),hAPP(c_Code__Numeral_Onat__of,U_17286))),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

cnf(f_4254_3,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_17285,U_17286) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_17285),hAPP(c_Code__Numeral_Onat__of,U_17286))),
    inference(clausify,[status(thm)],[f_4254_2]) ).

fof(f_4255_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_4255_2,plain,
    ! [U_17287] :
      ( 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_17287)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_17287)))
      | U_17287 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_4255_1]) ).

cnf(f_4255_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_17287)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_17287)))
    | U_17287 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4255_2]) ).

fof(f_4256_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_4256_2,plain,
    ! [U_17289,U_17288] : hAPP(c_New__DSequence_Opos__not__seq(U_17288),U_17289) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_17288,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_17289))),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

cnf(f_4256_3,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_17288),U_17289) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_17288,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_17289))),
    inference(clausify,[status(thm)],[f_4256_2]) ).

fof(f_4257_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_Pa_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_Pa_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_4257_2,plain,
    ! [U_17294,U_17293,U_17292,U_17291,U_17290] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17290,tc_HOL_Obool)),hAPP(c_List_Oset(U_17290),U_17293)),hAPP(c_List_Oset(U_17290),U_17294)) = hAPP(c_List_Oset(U_17290),U_17292)
      | c_List_Opartition(U_17290,U_17291,U_17292) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17290),tc_List_Olist(U_17290)),U_17293),U_17294) ),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

cnf(f_4257_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17290,tc_HOL_Obool)),hAPP(c_List_Oset(U_17290),U_17293)),hAPP(c_List_Oset(U_17290),U_17294)) = hAPP(c_List_Oset(U_17290),U_17292)
    | c_List_Opartition(U_17290,U_17291,U_17292) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17290),tc_List_Olist(U_17290)),U_17293),U_17294) ),
    inference(clausify,[status(thm)],[f_4257_2]) ).

fof(f_4258_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
      ( ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_4258_2,plain,
    ! [U_17301,U_17300,U_17299,U_17298,U_17297] :
      ( ( ! [U_17296] :
            ( ~ hBOOL(hAPP(U_17298,U_17296))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17297),U_17296),hAPP(c_List_Oset(U_17297),U_17301))) )
        & ! [U_17295] :
            ( hBOOL(hAPP(U_17298,U_17295))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17297),U_17295),hAPP(c_List_Oset(U_17297),U_17300))) ) )
      | c_List_Opartition(U_17297,U_17298,U_17299) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17297),tc_List_Olist(U_17297)),U_17300),U_17301) ),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

cnf(f_4258_3,plain,
    ( hBOOL(hAPP(U_17298,U_17295))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17297),U_17295),hAPP(c_List_Oset(U_17297),U_17300)))
    | c_List_Opartition(U_17297,U_17298,U_17299) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17297),tc_List_Olist(U_17297)),U_17300),U_17301) ),
    inference(clausify,[status(thm)],[f_4258_2]) ).

cnf(f_4258_4,plain,
    ( ~ hBOOL(hAPP(U_17298,U_17296))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17297),U_17296),hAPP(c_List_Oset(U_17297),U_17301)))
    | c_List_Opartition(U_17297,U_17298,U_17299) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17297),tc_List_Olist(U_17297)),U_17300),U_17301) ),
    inference(clausify,[status(thm)],[f_4258_2]) ).

fof(f_4259_1,plain,
    ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_4259_2,plain,
    ! [U_17303,U_17302] : c_List_Opartition(U_17302,U_17303,c_List_Olist_ONil(U_17302)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17302),tc_List_Olist(U_17302)),c_List_Olist_ONil(U_17302)),c_List_Olist_ONil(U_17302)),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

cnf(f_4259_3,plain,
    c_List_Opartition(U_17302,U_17303,c_List_Olist_ONil(U_17302)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17302),tc_List_Olist(U_17302)),c_List_Olist_ONil(U_17302)),c_List_Olist_ONil(U_17302)),
    inference(clausify,[status(thm)],[f_4259_2]) ).

fof(f_4260_1,plain,
    ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(f_4260_2,plain,
    ! [U_17307,U_17306,U_17305,U_17304] : c_List_Opartition(U_17304,U_17305,hAPP(hAPP(c_List_Olist_OCons(U_17304),U_17306),U_17307)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17304),tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_fun(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),c_COMBS(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_List_Olist(U_17304)),hAPP(c_If(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(U_17305,U_17306)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_List_Olist(U_17304)),c_Product__Type_OPair(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(c_List_Olist_OCons(U_17304),U_17306))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_fun(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),c_COMBB(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_List_Olist(U_17304))),c_Product__Type_OPair(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(c_List_Olist_OCons(U_17304),U_17306)))),c_List_Opartition(U_17304,U_17305,U_17307)),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

cnf(f_4260_3,plain,
    c_List_Opartition(U_17304,U_17305,hAPP(hAPP(c_List_Olist_OCons(U_17304),U_17306),U_17307)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17304),tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_fun(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),c_COMBS(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_List_Olist(U_17304),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_List_Olist(U_17304)),hAPP(c_If(tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(U_17305,U_17306)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_List_Olist(U_17304)),c_Product__Type_OPair(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),hAPP(c_List_Olist_OCons(U_17304),U_17306))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17304),tc_fun(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304))),tc_fun(tc_fun(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_fun(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),tc_List_Olist(U_17304)),c_COMBB(tc_List_Olist(U_17304),tc_prod(tc_List_Olist(U_17304),tc_List_Olist(U_17304)),tc_List_Olist(U_17304))),c_Product__Type_OPair(tc_List_Olist(U_17304),tc_List_Olist(U_17304)))),hAPP(c_List_Olist_OCons(U_17304),U_17306)))),c_List_Opartition(U_17304,U_17305,U_17307)),
    inference(clausify,[status(thm)],[f_4260_2]) ).

fof(f_4261_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_4261_2,plain,
    ! [U_17310,U_17309,U_17308] : c_List_Olistsp(U_17308,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17308,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17308,tc_fun(U_17308,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17308)),U_17309)),hAPP(hAPP(c_COMBC(U_17308,tc_fun(U_17308,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17308)),U_17310))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17308),tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17308))),c_List_Olists(U_17308,U_17309))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17308),tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17308))),c_List_Olists(U_17308,U_17310))),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

cnf(f_4261_3,plain,
    c_List_Olistsp(U_17308,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17308,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17308,tc_fun(U_17308,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17308)),U_17309)),hAPP(hAPP(c_COMBC(U_17308,tc_fun(U_17308,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17308)),U_17310))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17308),tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17308))),c_List_Olists(U_17308,U_17309))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17308),tc_fun(tc_List_Olist(U_17308),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17308))),c_List_Olists(U_17308,U_17310))),
    inference(clausify,[status(thm)],[f_4261_2]) ).

fof(f_4262_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_4262_2,plain,
    ! [U_17314,U_17313,U_17312,U_17311] :
      ( hBOOL(hAPP(c_List_Olistsp(U_17311,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17311,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17311,tc_fun(U_17311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17311)),U_17313)),hAPP(hAPP(c_COMBC(U_17311,tc_fun(U_17311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17311)),U_17314))),U_17312))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17311)),U_17312),c_List_Olists(U_17311,U_17314)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17311)),U_17312),c_List_Olists(U_17311,U_17313))) ),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

cnf(f_4262_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17311,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17311,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17311,tc_fun(U_17311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17311)),U_17313)),hAPP(hAPP(c_COMBC(U_17311,tc_fun(U_17311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17311)),U_17314))),U_17312))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17311)),U_17312),c_List_Olists(U_17311,U_17314)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17311)),U_17312),c_List_Olists(U_17311,U_17313))) ),
    inference(clausify,[status(thm)],[f_4262_2]) ).

fof(f_4263_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_4263_2,plain,
    ! [U_17316,U_17315] : hBOOL(hAPP(c_List_Olistsp(U_17315,U_17316),c_List_Olist_ONil(U_17315))),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

cnf(f_4263_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_17315,U_17316),c_List_Olist_ONil(U_17315))),
    inference(clausify,[status(thm)],[f_4263_2]) ).

fof(f_4264_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_4264_2,plain,
    ! [U_17320,U_17319,U_17318,U_17317] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),hAPP(hAPP(c_List_Oappend(U_17317),U_17319),U_17320)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),U_17320))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),U_17319)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),U_17320))
          & hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),U_17319)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17317,U_17318),hAPP(hAPP(c_List_Oappend(U_17317),U_17319),U_17320))) ) ),
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

fof(f_4264_3,plain,
    ( ! [U_17328,U_17326,U_17324,U_17322] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),hAPP(hAPP(c_List_Oappend(U_17322),U_17326),U_17328)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),U_17328))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),U_17326)) )
    & ! [U_17327,U_17325,U_17323,U_17321] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),U_17327))
          & hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),U_17325)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),hAPP(hAPP(c_List_Oappend(U_17321),U_17325),U_17327))) ) ),
    inference(miniscope,[status(thm)],[f_4264_2]) ).

cnf(f_4264_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),U_17325))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),hAPP(hAPP(c_List_Oappend(U_17321),U_17325),U_17327))) ),
    inference(clausify,[status(thm)],[f_4264_3]) ).

cnf(f_4264_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),U_17327))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17321,U_17323),hAPP(hAPP(c_List_Oappend(U_17321),U_17325),U_17327))) ),
    inference(clausify,[status(thm)],[f_4264_3]) ).

cnf(f_4264_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),hAPP(hAPP(c_List_Oappend(U_17322),U_17326),U_17328)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),U_17328))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17322,U_17324),U_17326)) ),
    inference(clausify,[status(thm)],[f_4264_3]) ).

fof(f_4265_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_4265_2,plain,
    ! [U_17332,U_17331,U_17330,U_17329] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17329,U_17330),hAPP(hAPP(c_List_Olist_OCons(U_17329),U_17331),U_17332)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17329,U_17330),U_17332))
        | ~ hBOOL(hAPP(U_17330,U_17331)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17329,U_17330),U_17332))
          & hBOOL(hAPP(U_17330,U_17331)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17329,U_17330),hAPP(hAPP(c_List_Olist_OCons(U_17329),U_17331),U_17332))) ) ),
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

fof(f_4265_3,plain,
    ( ! [U_17340,U_17338,U_17336,U_17334] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17334,U_17336),hAPP(hAPP(c_List_Olist_OCons(U_17334),U_17338),U_17340)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17334,U_17336),U_17340))
        | ~ hBOOL(hAPP(U_17336,U_17338)) )
    & ! [U_17339,U_17337,U_17335,U_17333] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17333,U_17335),U_17339))
          & hBOOL(hAPP(U_17335,U_17337)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17333,U_17335),hAPP(hAPP(c_List_Olist_OCons(U_17333),U_17337),U_17339))) ) ),
    inference(miniscope,[status(thm)],[f_4265_2]) ).

cnf(f_4265_4,plain,
    ( hBOOL(hAPP(U_17335,U_17337))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17333,U_17335),hAPP(hAPP(c_List_Olist_OCons(U_17333),U_17337),U_17339))) ),
    inference(clausify,[status(thm)],[f_4265_3]) ).

cnf(f_4265_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17333,U_17335),U_17339))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17333,U_17335),hAPP(hAPP(c_List_Olist_OCons(U_17333),U_17337),U_17339))) ),
    inference(clausify,[status(thm)],[f_4265_3]) ).

cnf(f_4265_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17334,U_17336),hAPP(hAPP(c_List_Olist_OCons(U_17334),U_17338),U_17340)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17334,U_17336),U_17340))
    | ~ hBOOL(hAPP(U_17336,U_17338)) ),
    inference(clausify,[status(thm)],[f_4265_3]) ).

fof(f_4266_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_4266_2,plain,
    ! [U_17344,U_17343,U_17342,U_17341] :
      ( hBOOL(hAPP(c_List_Olistsp(U_17341,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17341,tc_HOL_Obool)),U_17342),U_17344)),U_17343))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_17341,U_17344),U_17343))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_17341,U_17342),U_17343)) ),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

cnf(f_4266_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17341,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17341,tc_HOL_Obool)),U_17342),U_17344)),U_17343))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17341,U_17344),U_17343))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17341,U_17342),U_17343)) ),
    inference(clausify,[status(thm)],[f_4266_2]) ).

fof(f_4267_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_4267_2,plain,
    ! [U_17347,U_17346,U_17345] : c_List_Olistsp(U_17345,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17345,tc_HOL_Obool)),U_17346),U_17347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17345),tc_HOL_Obool)),c_List_Olistsp(U_17345,U_17346)),c_List_Olistsp(U_17345,U_17347)),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

cnf(f_4267_3,plain,
    c_List_Olistsp(U_17345,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17345,tc_HOL_Obool)),U_17346),U_17347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17345),tc_HOL_Obool)),c_List_Olistsp(U_17345,U_17346)),c_List_Olistsp(U_17345,U_17347)),
    inference(clausify,[status(thm)],[f_4267_2]) ).

fof(f_4268_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_4268_2,plain,
    ! [U_17351,U_17350,U_17349,U_17348] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17348,hAPP(hAPP(c_COMBS(U_17348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17348),c_fconj),U_17349)),U_17350)),U_17351))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17348,U_17350),U_17351))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17348,U_17349),U_17351)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17348,U_17350),U_17351))
          & hBOOL(hAPP(c_List_Olistsp(U_17348,U_17349),U_17351)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17348,hAPP(hAPP(c_COMBS(U_17348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17348),c_fconj),U_17349)),U_17350)),U_17351)) ) ),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

fof(f_4268_3,plain,
    ( ! [U_17359,U_17357,U_17355,U_17353] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17353,hAPP(hAPP(c_COMBS(U_17353,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17353),c_fconj),U_17355)),U_17357)),U_17359))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17353,U_17357),U_17359))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17353,U_17355),U_17359)) )
    & ! [U_17358,U_17356,U_17354,U_17352] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17352,U_17356),U_17358))
          & hBOOL(hAPP(c_List_Olistsp(U_17352,U_17354),U_17358)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17352,hAPP(hAPP(c_COMBS(U_17352,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17352),c_fconj),U_17354)),U_17356)),U_17358)) ) ),
    inference(miniscope,[status(thm)],[f_4268_2]) ).

cnf(f_4268_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17352,U_17354),U_17358))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17352,hAPP(hAPP(c_COMBS(U_17352,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17352),c_fconj),U_17354)),U_17356)),U_17358)) ),
    inference(clausify,[status(thm)],[f_4268_3]) ).

cnf(f_4268_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17352,U_17356),U_17358))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17352,hAPP(hAPP(c_COMBS(U_17352,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17352),c_fconj),U_17354)),U_17356)),U_17358)) ),
    inference(clausify,[status(thm)],[f_4268_3]) ).

cnf(f_4268_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17353,hAPP(hAPP(c_COMBS(U_17353,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17353),c_fconj),U_17355)),U_17357)),U_17359))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17353,U_17357),U_17359))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17353,U_17355),U_17359)) ),
    inference(clausify,[status(thm)],[f_4268_3]) ).

fof(f_4269_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_4269_2,plain,
    ! [U_17364,U_17363,U_17362] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17362,U_17363),U_17364))
        | ? [U_17361] :
            ( ~ hBOOL(hAPP(U_17363,U_17361))
            & hBOOL(hAPP(hAPP(c_member(U_17362),U_17361),hAPP(c_List_Oset(U_17362),U_17364))) ) )
      & ( ! [U_17360] :
            ( hBOOL(hAPP(U_17363,U_17360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17362),U_17360),hAPP(c_List_Oset(U_17362),U_17364))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17362,U_17363),U_17364)) ) ),
    inference(variable_rename,[status(thm)],[f_4269_1]) ).

fof(f_4269_3,plain,
    ( ! [U_17370,U_17368,U_17366] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17366,U_17368),U_17370))
        | ? [U_17361] :
            ( ~ hBOOL(hAPP(U_17368,U_17361))
            & hBOOL(hAPP(hAPP(c_member(U_17366),U_17361),hAPP(c_List_Oset(U_17366),U_17370))) ) )
    & ! [U_17369,U_17367,U_17365] :
        ( ! [U_17360] :
            ( hBOOL(hAPP(U_17367,U_17360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17365),U_17360),hAPP(c_List_Oset(U_17365),U_17369))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17365,U_17367),U_17369)) ) ),
    inference(miniscope,[status(thm)],[f_4269_2]) ).

fof(f_4269_4,plain,
    ( ! [U_17370,U_17368,U_17366] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17366,U_17368),U_17370))
        | ( ~ hBOOL(hAPP(U_17368,sK429(U_17370,U_17368,U_17366)))
          & hBOOL(hAPP(hAPP(c_member(U_17366),sK429(U_17370,U_17368,U_17366)),hAPP(c_List_Oset(U_17366),U_17370))) ) )
    & ! [U_17369,U_17367,U_17365] :
        ( ! [U_17360] :
            ( hBOOL(hAPP(U_17367,U_17360))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17365),U_17360),hAPP(c_List_Oset(U_17365),U_17369))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17365,U_17367),U_17369)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_17361,sK429(U_17370,U_17368,U_17366))],[f_4269_3]) ).

cnf(f_4269_5,plain,
    ( hBOOL(hAPP(U_17367,U_17360))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17365),U_17360),hAPP(c_List_Oset(U_17365),U_17369)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17365,U_17367),U_17369)) ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

cnf(f_4269_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17366),sK429(U_17370,U_17368,U_17366)),hAPP(c_List_Oset(U_17366),U_17370)))
    | hBOOL(hAPP(c_List_Olistsp(U_17366,U_17368),U_17370)) ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

cnf(f_4269_7,plain,
    ( ~ hBOOL(hAPP(U_17368,sK429(U_17370,U_17368,U_17366)))
    | hBOOL(hAPP(c_List_Olistsp(U_17366,U_17368),U_17370)) ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

fof(f_4270_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_4270_2,plain,
    ! [U_17372,U_17371] : hBOOL(hAPP(c_List_Olistsp(U_17371,U_17372),c_List_Olist_ONil(U_17371))),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

cnf(f_4270_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_17371,U_17372),c_List_Olist_ONil(U_17371))),
    inference(clausify,[status(thm)],[f_4270_2]) ).

fof(f_4271_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_4271_2,plain,
    ! [U_17375,U_17374,U_17373] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_17373),tc_HOL_Obool)),c_List_Olistsp(U_17373,U_17374)),c_List_Olistsp(U_17373,U_17375)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17373,tc_HOL_Obool)),U_17374),U_17375)) ),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

cnf(f_4271_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_17373),tc_HOL_Obool)),c_List_Olistsp(U_17373,U_17374)),c_List_Olistsp(U_17373,U_17375)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17373,tc_HOL_Obool)),U_17374),U_17375)) ),
    inference(clausify,[status(thm)],[f_4271_2]) ).

fof(f_4272_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_4272_2,plain,
    ! [U_17378,U_17377,U_17376] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17376,hAPP(hAPP(c_COMBC(U_17376,tc_fun(U_17376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17376)),U_17377)),U_17378))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17376)),U_17378),c_List_Olists(U_17376,U_17377))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17376)),U_17378),c_List_Olists(U_17376,U_17377)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17376,hAPP(hAPP(c_COMBC(U_17376,tc_fun(U_17376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17376)),U_17377)),U_17378)) ) ),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

fof(f_4272_3,plain,
    ( ! [U_17384,U_17382,U_17380] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17380,hAPP(hAPP(c_COMBC(U_17380,tc_fun(U_17380,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17380)),U_17382)),U_17384))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17380)),U_17384),c_List_Olists(U_17380,U_17382))) )
    & ! [U_17383,U_17381,U_17379] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17379)),U_17383),c_List_Olists(U_17379,U_17381)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17379,hAPP(hAPP(c_COMBC(U_17379,tc_fun(U_17379,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17379)),U_17381)),U_17383)) ) ),
    inference(miniscope,[status(thm)],[f_4272_2]) ).

cnf(f_4272_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17379)),U_17383),c_List_Olists(U_17379,U_17381)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17379,hAPP(hAPP(c_COMBC(U_17379,tc_fun(U_17379,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17379)),U_17381)),U_17383)) ),
    inference(clausify,[status(thm)],[f_4272_3]) ).

cnf(f_4272_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17380,hAPP(hAPP(c_COMBC(U_17380,tc_fun(U_17380,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17380)),U_17382)),U_17384))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17380)),U_17384),c_List_Olists(U_17380,U_17382))) ),
    inference(clausify,[status(thm)],[f_4272_3]) ).

fof(f_4273_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_4273_2,plain,
    ! [U_17389,U_17388,U_17387,U_17386,U_17385] : c_Enum_Oproduct(U_17385,U_17386,hAPP(hAPP(c_List_Olist_OCons(U_17385),U_17387),U_17388),U_17389) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17385,U_17386)),hAPP(hAPP(c_List_Omap(U_17386,tc_prod(U_17385,U_17386)),hAPP(c_Product__Type_OPair(U_17385,U_17386),U_17387)),U_17389)),c_Enum_Oproduct(U_17385,U_17386,U_17388,U_17389)),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

cnf(f_4273_3,plain,
    c_Enum_Oproduct(U_17385,U_17386,hAPP(hAPP(c_List_Olist_OCons(U_17385),U_17387),U_17388),U_17389) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17385,U_17386)),hAPP(hAPP(c_List_Omap(U_17386,tc_prod(U_17385,U_17386)),hAPP(c_Product__Type_OPair(U_17385,U_17386),U_17387)),U_17389)),c_Enum_Oproduct(U_17385,U_17386,U_17388,U_17389)),
    inference(clausify,[status(thm)],[f_4273_2]) ).

fof(f_4274_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_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_Pa_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__def]) ).

fof(f_4274_2,plain,
    ! [U_17396,U_17395,U_17394,U_17393,U_17392] :
      ( ( c_List_Olist__all2(U_17392,U_17393,U_17394,U_17395,U_17396)
        | ? [U_17391] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17392,U_17393,tc_HOL_Obool),U_17394),U_17391))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17392,U_17393)),U_17391),hAPP(c_List_Oset(tc_prod(U_17392,U_17393)),hAPP(hAPP(c_List_Ozip(U_17392,U_17393),U_17395),U_17396)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17392)),U_17395) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17393)),U_17396) )
      & ( ( ! [U_17390] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17392,U_17393,tc_HOL_Obool),U_17394),U_17390))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17392,U_17393)),U_17390),hAPP(c_List_Oset(tc_prod(U_17392,U_17393)),hAPP(hAPP(c_List_Ozip(U_17392,U_17393),U_17395),U_17396)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17392)),U_17395) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17393)),U_17396) )
        | ~ c_List_Olist__all2(U_17392,U_17393,U_17394,U_17395,U_17396) ) ),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

fof(f_4274_3,plain,
    ( ! [U_17406,U_17404,U_17402,U_17400,U_17398] :
        ( c_List_Olist__all2(U_17398,U_17400,U_17402,U_17404,U_17406)
        | ? [U_17391] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17398,U_17400,tc_HOL_Obool),U_17402),U_17391))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17398,U_17400)),U_17391),hAPP(c_List_Oset(tc_prod(U_17398,U_17400)),hAPP(hAPP(c_List_Ozip(U_17398,U_17400),U_17404),U_17406)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17404) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17400)),U_17406) )
    & ! [U_17405,U_17403,U_17401,U_17399,U_17397] :
        ( ( ! [U_17390] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17397,U_17399,tc_HOL_Obool),U_17401),U_17390))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17397,U_17399)),U_17390),hAPP(c_List_Oset(tc_prod(U_17397,U_17399)),hAPP(hAPP(c_List_Ozip(U_17397,U_17399),U_17403),U_17405)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17397)),U_17403) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17399)),U_17405) )
        | ~ c_List_Olist__all2(U_17397,U_17399,U_17401,U_17403,U_17405) ) ),
    inference(miniscope,[status(thm)],[f_4274_2]) ).

fof(f_4274_4,plain,
    ( ! [U_17406,U_17404,U_17402,U_17400,U_17398] :
        ( c_List_Olist__all2(U_17398,U_17400,U_17402,U_17404,U_17406)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17398,U_17400,tc_HOL_Obool),U_17402),sK430(U_17406,U_17404,U_17402,U_17400,U_17398)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17398,U_17400)),sK430(U_17406,U_17404,U_17402,U_17400,U_17398)),hAPP(c_List_Oset(tc_prod(U_17398,U_17400)),hAPP(hAPP(c_List_Ozip(U_17398,U_17400),U_17404),U_17406)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17404) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17400)),U_17406) )
    & ! [U_17405,U_17403,U_17401,U_17399,U_17397] :
        ( ( ! [U_17390] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17397,U_17399,tc_HOL_Obool),U_17401),U_17390))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17397,U_17399)),U_17390),hAPP(c_List_Oset(tc_prod(U_17397,U_17399)),hAPP(hAPP(c_List_Ozip(U_17397,U_17399),U_17403),U_17405)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17397)),U_17403) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17399)),U_17405) )
        | ~ c_List_Olist__all2(U_17397,U_17399,U_17401,U_17403,U_17405) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_17391,sK430(U_17406,U_17404,U_17402,U_17400,U_17398))],[f_4274_3]) ).

cnf(f_4274_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17397)),U_17403) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17399)),U_17405)
    | ~ c_List_Olist__all2(U_17397,U_17399,U_17401,U_17403,U_17405) ),
    inference(clausify,[status(thm)],[f_4274_4]) ).

cnf(f_4274_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17397,U_17399,tc_HOL_Obool),U_17401),U_17390))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17397,U_17399)),U_17390),hAPP(c_List_Oset(tc_prod(U_17397,U_17399)),hAPP(hAPP(c_List_Ozip(U_17397,U_17399),U_17403),U_17405))))
    | ~ c_List_Olist__all2(U_17397,U_17399,U_17401,U_17403,U_17405) ),
    inference(clausify,[status(thm)],[f_4274_4]) ).

cnf(f_4274_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17398,U_17400)),sK430(U_17406,U_17404,U_17402,U_17400,U_17398)),hAPP(c_List_Oset(tc_prod(U_17398,U_17400)),hAPP(hAPP(c_List_Ozip(U_17398,U_17400),U_17404),U_17406))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17404) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17400)),U_17406)
    | c_List_Olist__all2(U_17398,U_17400,U_17402,U_17404,U_17406) ),
    inference(clausify,[status(thm)],[f_4274_4]) ).

cnf(f_4274_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17398,U_17400,tc_HOL_Obool),U_17402),sK430(U_17406,U_17404,U_17402,U_17400,U_17398)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17398)),U_17404) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17400)),U_17406)
    | c_List_Olist__all2(U_17398,U_17400,U_17402,U_17404,U_17406) ),
    inference(clausify,[status(thm)],[f_4274_4]) ).

fof(f_4275_1,plain,
    ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_2)),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4275_2,plain,
    ! [U_17413,U_17412,U_17411,U_17410,U_17409,U_17408,U_17407] :
      ( ( c_List_Olist__all2(U_17407,U_17408,U_17409,U_17410,hAPP(hAPP(c_List_Omap(U_17411,U_17408),U_17412),U_17413))
        | ~ c_List_Olist__all2(U_17407,U_17411,hAPP(hAPP(c_COMBC(U_17407,tc_fun(U_17411,U_17408),tc_fun(U_17411,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17408,tc_HOL_Obool),tc_fun(tc_fun(U_17411,U_17408),tc_fun(U_17411,tc_HOL_Obool)),U_17407),c_COMBB(U_17408,tc_HOL_Obool,U_17411)),U_17409)),U_17412),U_17410,U_17413) )
      & ( c_List_Olist__all2(U_17407,U_17411,hAPP(hAPP(c_COMBC(U_17407,tc_fun(U_17411,U_17408),tc_fun(U_17411,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17408,tc_HOL_Obool),tc_fun(tc_fun(U_17411,U_17408),tc_fun(U_17411,tc_HOL_Obool)),U_17407),c_COMBB(U_17408,tc_HOL_Obool,U_17411)),U_17409)),U_17412),U_17410,U_17413)
        | ~ c_List_Olist__all2(U_17407,U_17408,U_17409,U_17410,hAPP(hAPP(c_List_Omap(U_17411,U_17408),U_17412),U_17413)) ) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

fof(f_4275_3,plain,
    ( ! [U_17427,U_17425,U_17423,U_17421,U_17419,U_17417,U_17415] :
        ( c_List_Olist__all2(U_17415,U_17417,U_17419,U_17421,hAPP(hAPP(c_List_Omap(U_17423,U_17417),U_17425),U_17427))
        | ~ c_List_Olist__all2(U_17415,U_17423,hAPP(hAPP(c_COMBC(U_17415,tc_fun(U_17423,U_17417),tc_fun(U_17423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17417,tc_HOL_Obool),tc_fun(tc_fun(U_17423,U_17417),tc_fun(U_17423,tc_HOL_Obool)),U_17415),c_COMBB(U_17417,tc_HOL_Obool,U_17423)),U_17419)),U_17425),U_17421,U_17427) )
    & ! [U_17426,U_17424,U_17422,U_17420,U_17418,U_17416,U_17414] :
        ( c_List_Olist__all2(U_17414,U_17422,hAPP(hAPP(c_COMBC(U_17414,tc_fun(U_17422,U_17416),tc_fun(U_17422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17416,tc_HOL_Obool),tc_fun(tc_fun(U_17422,U_17416),tc_fun(U_17422,tc_HOL_Obool)),U_17414),c_COMBB(U_17416,tc_HOL_Obool,U_17422)),U_17418)),U_17424),U_17420,U_17426)
        | ~ c_List_Olist__all2(U_17414,U_17416,U_17418,U_17420,hAPP(hAPP(c_List_Omap(U_17422,U_17416),U_17424),U_17426)) ) ),
    inference(miniscope,[status(thm)],[f_4275_2]) ).

cnf(f_4275_4,plain,
    ( c_List_Olist__all2(U_17414,U_17422,hAPP(hAPP(c_COMBC(U_17414,tc_fun(U_17422,U_17416),tc_fun(U_17422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17416,tc_HOL_Obool),tc_fun(tc_fun(U_17422,U_17416),tc_fun(U_17422,tc_HOL_Obool)),U_17414),c_COMBB(U_17416,tc_HOL_Obool,U_17422)),U_17418)),U_17424),U_17420,U_17426)
    | ~ c_List_Olist__all2(U_17414,U_17416,U_17418,U_17420,hAPP(hAPP(c_List_Omap(U_17422,U_17416),U_17424),U_17426)) ),
    inference(clausify,[status(thm)],[f_4275_3]) ).

cnf(f_4275_5,plain,
    ( c_List_Olist__all2(U_17415,U_17417,U_17419,U_17421,hAPP(hAPP(c_List_Omap(U_17423,U_17417),U_17425),U_17427))
    | ~ c_List_Olist__all2(U_17415,U_17423,hAPP(hAPP(c_COMBC(U_17415,tc_fun(U_17423,U_17417),tc_fun(U_17423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17417,tc_HOL_Obool),tc_fun(tc_fun(U_17423,U_17417),tc_fun(U_17423,tc_HOL_Obool)),U_17415),c_COMBB(U_17417,tc_HOL_Obool,U_17423)),U_17419)),U_17425),U_17421,U_17427) ),
    inference(clausify,[status(thm)],[f_4275_3]) ).

fof(f_4276_1,plain,
    ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_Pa_2),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4276_2,plain,
    ! [U_17434,U_17433,U_17432,U_17431,U_17430,U_17429,U_17428] :
      ( ( c_List_Olist__all2(U_17428,U_17429,U_17430,hAPP(hAPP(c_List_Omap(U_17431,U_17428),U_17432),U_17433),U_17434)
        | ~ c_List_Olist__all2(U_17431,U_17429,hAPP(hAPP(c_COMBB(U_17428,tc_fun(U_17429,tc_HOL_Obool),U_17431),U_17430),U_17432),U_17433,U_17434) )
      & ( c_List_Olist__all2(U_17431,U_17429,hAPP(hAPP(c_COMBB(U_17428,tc_fun(U_17429,tc_HOL_Obool),U_17431),U_17430),U_17432),U_17433,U_17434)
        | ~ c_List_Olist__all2(U_17428,U_17429,U_17430,hAPP(hAPP(c_List_Omap(U_17431,U_17428),U_17432),U_17433),U_17434) ) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

fof(f_4276_3,plain,
    ( ! [U_17448,U_17446,U_17444,U_17442,U_17440,U_17438,U_17436] :
        ( c_List_Olist__all2(U_17436,U_17438,U_17440,hAPP(hAPP(c_List_Omap(U_17442,U_17436),U_17444),U_17446),U_17448)
        | ~ c_List_Olist__all2(U_17442,U_17438,hAPP(hAPP(c_COMBB(U_17436,tc_fun(U_17438,tc_HOL_Obool),U_17442),U_17440),U_17444),U_17446,U_17448) )
    & ! [U_17447,U_17445,U_17443,U_17441,U_17439,U_17437,U_17435] :
        ( c_List_Olist__all2(U_17441,U_17437,hAPP(hAPP(c_COMBB(U_17435,tc_fun(U_17437,tc_HOL_Obool),U_17441),U_17439),U_17443),U_17445,U_17447)
        | ~ c_List_Olist__all2(U_17435,U_17437,U_17439,hAPP(hAPP(c_List_Omap(U_17441,U_17435),U_17443),U_17445),U_17447) ) ),
    inference(miniscope,[status(thm)],[f_4276_2]) ).

cnf(f_4276_4,plain,
    ( c_List_Olist__all2(U_17441,U_17437,hAPP(hAPP(c_COMBB(U_17435,tc_fun(U_17437,tc_HOL_Obool),U_17441),U_17439),U_17443),U_17445,U_17447)
    | ~ c_List_Olist__all2(U_17435,U_17437,U_17439,hAPP(hAPP(c_List_Omap(U_17441,U_17435),U_17443),U_17445),U_17447) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

cnf(f_4276_5,plain,
    ( c_List_Olist__all2(U_17436,U_17438,U_17440,hAPP(hAPP(c_List_Omap(U_17442,U_17436),U_17444),U_17446),U_17448)
    | ~ c_List_Olist__all2(U_17442,U_17438,hAPP(hAPP(c_COMBB(U_17436,tc_fun(U_17438,tc_HOL_Obool),U_17442),U_17440),U_17444),U_17446,U_17448) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

fof(f_4277_1,plain,
    ! [V_ys_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil]) ).

fof(f_4277_2,plain,
    ! [U_17452,U_17451,U_17450,U_17449] :
      ( ( c_List_Olist__all2(U_17449,U_17450,U_17451,c_List_Olist_ONil(U_17449),U_17452)
        | U_17452 != c_List_Olist_ONil(U_17450) )
      & ( U_17452 = c_List_Olist_ONil(U_17450)
        | ~ c_List_Olist__all2(U_17449,U_17450,U_17451,c_List_Olist_ONil(U_17449),U_17452) ) ),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

fof(f_4277_3,plain,
    ( ! [U_17460,U_17458,U_17456] :
        ( ! [U_17454] : c_List_Olist__all2(U_17454,U_17456,U_17458,c_List_Olist_ONil(U_17454),U_17460)
        | U_17460 != c_List_Olist_ONil(U_17456) )
    & ! [U_17459,U_17457,U_17455] :
        ( ! [U_17453] : ~ c_List_Olist__all2(U_17453,U_17455,U_17457,c_List_Olist_ONil(U_17453),U_17459)
        | U_17459 = c_List_Olist_ONil(U_17455) ) ),
    inference(miniscope,[status(thm)],[f_4277_2]) ).

cnf(f_4277_4,plain,
    ( ~ c_List_Olist__all2(U_17453,U_17455,U_17457,c_List_Olist_ONil(U_17453),U_17459)
    | U_17459 = c_List_Olist_ONil(U_17455) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

cnf(f_4277_5,plain,
    ( c_List_Olist__all2(U_17454,U_17456,U_17458,c_List_Olist_ONil(U_17454),U_17460)
    | U_17460 != c_List_Olist_ONil(U_17456) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

fof(f_4278_1,plain,
    ! [V_xs_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2]) ).

fof(f_4278_2,plain,
    ! [U_17464,U_17463,U_17462,U_17461] :
      ( ( c_List_Olist__all2(U_17461,U_17462,U_17463,U_17464,c_List_Olist_ONil(U_17462))
        | U_17464 != c_List_Olist_ONil(U_17461) )
      & ( U_17464 = c_List_Olist_ONil(U_17461)
        | ~ c_List_Olist__all2(U_17461,U_17462,U_17463,U_17464,c_List_Olist_ONil(U_17462)) ) ),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

fof(f_4278_3,plain,
    ( ! [U_17472,U_17470,U_17468,U_17466] :
        ( c_List_Olist__all2(U_17466,U_17468,U_17470,U_17472,c_List_Olist_ONil(U_17468))
        | U_17472 != c_List_Olist_ONil(U_17466) )
    & ! [U_17471,U_17469,U_17467,U_17465] :
        ( U_17471 = c_List_Olist_ONil(U_17465)
        | ~ c_List_Olist__all2(U_17465,U_17467,U_17469,U_17471,c_List_Olist_ONil(U_17467)) ) ),
    inference(miniscope,[status(thm)],[f_4278_2]) ).

cnf(f_4278_4,plain,
    ( U_17471 = c_List_Olist_ONil(U_17465)
    | ~ c_List_Olist__all2(U_17465,U_17467,U_17469,U_17471,c_List_Olist_ONil(U_17467)) ),
    inference(clausify,[status(thm)],[f_4278_3]) ).

cnf(f_4278_5,plain,
    ( c_List_Olist__all2(U_17466,U_17468,U_17470,U_17472,c_List_Olist_ONil(U_17468))
    | U_17472 != c_List_Olist_ONil(U_17466) ),
    inference(clausify,[status(thm)],[f_4278_3]) ).

fof(f_4279_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_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_Pa_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD]) ).

fof(f_4279_2,plain,
    ! [U_17477,U_17476,U_17475,U_17474,U_17473] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17473)),U_17476) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17474)),U_17477)
      | ~ c_List_Olist__all2(U_17473,U_17474,U_17475,U_17476,U_17477) ),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

cnf(f_4279_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17473)),U_17476) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17474)),U_17477)
    | ~ c_List_Olist__all2(U_17473,U_17474,U_17475,U_17476,U_17477) ),
    inference(clausify,[status(thm)],[f_4279_2]) ).

fof(f_4280_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_4280_2,plain,
    ! [U_17480,U_17479,U_17478] :
      ( ( U_17478 = U_17479
        | ~ c_List_Olist__all2(U_17480,U_17480,c_fequal,U_17478,U_17479) )
      & ( c_List_Olist__all2(U_17480,U_17480,c_fequal,U_17478,U_17479)
        | U_17478 != U_17479 ) ),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

fof(f_4280_3,plain,
    ( ! [U_17486,U_17484,U_17482] :
        ( U_17482 = U_17484
        | ~ c_List_Olist__all2(U_17486,U_17486,c_fequal,U_17482,U_17484) )
    & ! [U_17485,U_17483,U_17481] :
        ( c_List_Olist__all2(U_17485,U_17485,c_fequal,U_17481,U_17483)
        | U_17481 != U_17483 ) ),
    inference(miniscope,[status(thm)],[f_4280_2]) ).

cnf(f_4280_4,plain,
    ( c_List_Olist__all2(U_17485,U_17485,c_fequal,U_17481,U_17483)
    | U_17481 != U_17483 ),
    inference(clausify,[status(thm)],[f_4280_3]) ).

cnf(f_4280_5,plain,
    ( U_17482 = U_17484
    | ~ c_List_Olist__all2(U_17486,U_17486,c_fequal,U_17482,U_17484) ),
    inference(clausify,[status(thm)],[f_4280_3]) ).

fof(f_4281_1,plain,
    ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__takeI]) ).

fof(f_4281_2,plain,
    ! [U_17492,U_17491,U_17490,U_17489,U_17488,U_17487] :
      ( c_List_Olist__all2(U_17487,U_17488,U_17489,hAPP(hAPP(c_List_Otake(U_17487),U_17492),U_17490),hAPP(hAPP(c_List_Otake(U_17488),U_17492),U_17491))
      | ~ c_List_Olist__all2(U_17487,U_17488,U_17489,U_17490,U_17491) ),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

cnf(f_4281_3,plain,
    ( c_List_Olist__all2(U_17487,U_17488,U_17489,hAPP(hAPP(c_List_Otake(U_17487),U_17492),U_17490),hAPP(hAPP(c_List_Otake(U_17488),U_17492),U_17491))
    | ~ c_List_Olist__all2(U_17487,U_17488,U_17489,U_17490,U_17491) ),
    inference(clausify,[status(thm)],[f_4281_2]) ).

fof(f_4282_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,V_ys_2)
        | ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) )
      & ( ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
          & hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) )
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4282_2,plain,
    ! [U_17499,U_17498,U_17497,U_17496,U_17495,U_17494,U_17493] :
      ( ( c_List_Olist__all2(U_17493,U_17494,U_17495,hAPP(hAPP(c_List_Olist_OCons(U_17493),U_17496),U_17497),hAPP(hAPP(c_List_Olist_OCons(U_17494),U_17498),U_17499))
        | ~ c_List_Olist__all2(U_17493,U_17494,U_17495,U_17497,U_17499)
        | ~ hBOOL(hAPP(hAPP(U_17495,U_17496),U_17498)) )
      & ( ( c_List_Olist__all2(U_17493,U_17494,U_17495,U_17497,U_17499)
          & hBOOL(hAPP(hAPP(U_17495,U_17496),U_17498)) )
        | ~ c_List_Olist__all2(U_17493,U_17494,U_17495,hAPP(hAPP(c_List_Olist_OCons(U_17493),U_17496),U_17497),hAPP(hAPP(c_List_Olist_OCons(U_17494),U_17498),U_17499)) ) ),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

fof(f_4282_3,plain,
    ( ! [U_17513,U_17511,U_17509,U_17507,U_17505,U_17503,U_17501] :
        ( c_List_Olist__all2(U_17501,U_17503,U_17505,hAPP(hAPP(c_List_Olist_OCons(U_17501),U_17507),U_17509),hAPP(hAPP(c_List_Olist_OCons(U_17503),U_17511),U_17513))
        | ~ c_List_Olist__all2(U_17501,U_17503,U_17505,U_17509,U_17513)
        | ~ hBOOL(hAPP(hAPP(U_17505,U_17507),U_17511)) )
    & ! [U_17512,U_17510,U_17508,U_17506,U_17504,U_17502,U_17500] :
        ( ( c_List_Olist__all2(U_17500,U_17502,U_17504,U_17508,U_17512)
          & hBOOL(hAPP(hAPP(U_17504,U_17506),U_17510)) )
        | ~ c_List_Olist__all2(U_17500,U_17502,U_17504,hAPP(hAPP(c_List_Olist_OCons(U_17500),U_17506),U_17508),hAPP(hAPP(c_List_Olist_OCons(U_17502),U_17510),U_17512)) ) ),
    inference(miniscope,[status(thm)],[f_4282_2]) ).

cnf(f_4282_4,plain,
    ( hBOOL(hAPP(hAPP(U_17504,U_17506),U_17510))
    | ~ c_List_Olist__all2(U_17500,U_17502,U_17504,hAPP(hAPP(c_List_Olist_OCons(U_17500),U_17506),U_17508),hAPP(hAPP(c_List_Olist_OCons(U_17502),U_17510),U_17512)) ),
    inference(clausify,[status(thm)],[f_4282_3]) ).

cnf(f_4282_5,plain,
    ( c_List_Olist__all2(U_17500,U_17502,U_17504,U_17508,U_17512)
    | ~ c_List_Olist__all2(U_17500,U_17502,U_17504,hAPP(hAPP(c_List_Olist_OCons(U_17500),U_17506),U_17508),hAPP(hAPP(c_List_Olist_OCons(U_17502),U_17510),U_17512)) ),
    inference(clausify,[status(thm)],[f_4282_3]) ).

cnf(f_4282_6,plain,
    ( c_List_Olist__all2(U_17501,U_17503,U_17505,hAPP(hAPP(c_List_Olist_OCons(U_17501),U_17507),U_17509),hAPP(hAPP(c_List_Olist_OCons(U_17503),U_17511),U_17513))
    | ~ c_List_Olist__all2(U_17501,U_17503,U_17505,U_17509,U_17513)
    | ~ hBOOL(hAPP(hAPP(U_17505,U_17507),U_17511)) ),
    inference(clausify,[status(thm)],[f_4282_3]) ).

fof(f_4283_1,plain,
    ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_us_2,V_vs_2)
          | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) )
        & ( ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2)
            & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) )
          | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4283_2,plain,
    ! [U_17520,U_17519,U_17518,U_17517,U_17516,U_17515,U_17514] :
      ( ( ( c_List_Olist__all2(U_17514,U_17516,U_17518,hAPP(hAPP(c_List_Oappend(U_17514),U_17515),U_17519),hAPP(hAPP(c_List_Oappend(U_17516),U_17517),U_17520))
          | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,U_17519,U_17520)
          | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,U_17515,U_17517) )
        & ( ( c_List_Olist__all2(U_17514,U_17516,U_17518,U_17519,U_17520)
            & c_List_Olist__all2(U_17514,U_17516,U_17518,U_17515,U_17517) )
          | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,hAPP(hAPP(c_List_Oappend(U_17514),U_17515),U_17519),hAPP(hAPP(c_List_Oappend(U_17516),U_17517),U_17520)) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17514)),U_17515) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17516)),U_17517) ),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

cnf(f_4283_3,plain,
    ( c_List_Olist__all2(U_17514,U_17516,U_17518,U_17515,U_17517)
    | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,hAPP(hAPP(c_List_Oappend(U_17514),U_17515),U_17519),hAPP(hAPP(c_List_Oappend(U_17516),U_17517),U_17520))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17514)),U_17515) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17516)),U_17517) ),
    inference(clausify,[status(thm)],[f_4283_2]) ).

cnf(f_4283_4,plain,
    ( c_List_Olist__all2(U_17514,U_17516,U_17518,U_17519,U_17520)
    | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,hAPP(hAPP(c_List_Oappend(U_17514),U_17515),U_17519),hAPP(hAPP(c_List_Oappend(U_17516),U_17517),U_17520))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17514)),U_17515) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17516)),U_17517) ),
    inference(clausify,[status(thm)],[f_4283_2]) ).

cnf(f_4283_5,plain,
    ( c_List_Olist__all2(U_17514,U_17516,U_17518,hAPP(hAPP(c_List_Oappend(U_17514),U_17515),U_17519),hAPP(hAPP(c_List_Oappend(U_17516),U_17517),U_17520))
    | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,U_17519,U_17520)
    | ~ c_List_Olist__all2(U_17514,U_17516,U_17518,U_17515,U_17517)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17514)),U_17515) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17516)),U_17517) ),
    inference(clausify,[status(thm)],[f_4283_2]) ).

fof(f_4284_1,plain,
    ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
      | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__appendI]) ).

fof(f_4284_2,plain,
    ! [U_17527,U_17526,U_17525,U_17524,U_17523,U_17522,U_17521] :
      ( c_List_Olist__all2(U_17521,U_17522,U_17523,hAPP(hAPP(c_List_Oappend(U_17521),U_17524),U_17526),hAPP(hAPP(c_List_Oappend(U_17522),U_17525),U_17527))
      | ~ c_List_Olist__all2(U_17521,U_17522,U_17523,U_17526,U_17527)
      | ~ c_List_Olist__all2(U_17521,U_17522,U_17523,U_17524,U_17525) ),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

cnf(f_4284_3,plain,
    ( c_List_Olist__all2(U_17521,U_17522,U_17523,hAPP(hAPP(c_List_Oappend(U_17521),U_17524),U_17526),hAPP(hAPP(c_List_Oappend(U_17522),U_17525),U_17527))
    | ~ c_List_Olist__all2(U_17521,U_17522,U_17523,U_17526,U_17527)
    | ~ c_List_Olist__all2(U_17521,U_17522,U_17523,U_17524,U_17525) ),
    inference(clausify,[status(thm)],[f_4284_2]) ).

fof(f_4285_1,plain,
    ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_as_2,V_bs_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__dropI]) ).

fof(f_4285_2,plain,
    ! [U_17533,U_17532,U_17531,U_17530,U_17529,U_17528] :
      ( c_List_Olist__all2(U_17528,U_17529,U_17530,hAPP(hAPP(c_List_Odrop(U_17528),U_17533),U_17531),hAPP(hAPP(c_List_Odrop(U_17529),U_17533),U_17532))
      | ~ c_List_Olist__all2(U_17528,U_17529,U_17530,U_17531,U_17532) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

cnf(f_4285_3,plain,
    ( c_List_Olist__all2(U_17528,U_17529,U_17530,hAPP(hAPP(c_List_Odrop(U_17528),U_17533),U_17531),hAPP(hAPP(c_List_Odrop(U_17529),U_17533),U_17532))
    | ~ c_List_Olist__all2(U_17528,U_17529,U_17530,U_17531,U_17532) ),
    inference(clausify,[status(thm)],[f_4285_2]) ).

fof(f_4286_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_4286_2,plain,
    ! [U_17536,U_17535,U_17534] : c_Enum_Oproduct(U_17534,U_17535,c_List_Olist_ONil(U_17534),U_17536) = c_List_Olist_ONil(tc_prod(U_17534,U_17535)),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

cnf(f_4286_3,plain,
    c_Enum_Oproduct(U_17534,U_17535,c_List_Olist_ONil(U_17534),U_17536) = c_List_Olist_ONil(tc_prod(U_17534,U_17535)),
    inference(clausify,[status(thm)],[f_4286_2]) ).

fof(f_4287_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
        | ? [B_i] :
            ( ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__conv__all__nth]) ).

fof(f_4287_2,plain,
    ! [U_17543,U_17542,U_17541,U_17540,U_17539] :
      ( ( c_List_Olist__all2(U_17539,U_17540,U_17541,U_17542,U_17543)
        | ? [U_17538] :
            ( ~ hBOOL(hAPP(hAPP(U_17541,hAPP(hAPP(c_List_Onth(U_17539),U_17542),U_17538)),hAPP(hAPP(c_List_Onth(U_17540),U_17543),U_17538)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17538),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17539)),U_17542))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17539)),U_17542) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17540)),U_17543) )
      & ( ( ! [U_17537] :
              ( hBOOL(hAPP(hAPP(U_17541,hAPP(hAPP(c_List_Onth(U_17539),U_17542),U_17537)),hAPP(hAPP(c_List_Onth(U_17540),U_17543),U_17537)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17537),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17539)),U_17542))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17539)),U_17542) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17540)),U_17543) )
        | ~ c_List_Olist__all2(U_17539,U_17540,U_17541,U_17542,U_17543) ) ),
    inference(variable_rename,[status(thm)],[f_4287_1]) ).

fof(f_4287_3,plain,
    ( ! [U_17553,U_17551,U_17549,U_17547,U_17545] :
        ( c_List_Olist__all2(U_17545,U_17547,U_17549,U_17551,U_17553)
        | ? [U_17538] :
            ( ~ hBOOL(hAPP(hAPP(U_17549,hAPP(hAPP(c_List_Onth(U_17545),U_17551),U_17538)),hAPP(hAPP(c_List_Onth(U_17547),U_17553),U_17538)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17538),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17547)),U_17553) )
    & ! [U_17552,U_17550,U_17548,U_17546,U_17544] :
        ( ( ! [U_17537] :
              ( hBOOL(hAPP(hAPP(U_17548,hAPP(hAPP(c_List_Onth(U_17544),U_17550),U_17537)),hAPP(hAPP(c_List_Onth(U_17546),U_17552),U_17537)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17537),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17546)),U_17552) )
        | ~ c_List_Olist__all2(U_17544,U_17546,U_17548,U_17550,U_17552) ) ),
    inference(miniscope,[status(thm)],[f_4287_2]) ).

fof(f_4287_4,plain,
    ( ! [U_17553,U_17551,U_17549,U_17547,U_17545] :
        ( c_List_Olist__all2(U_17545,U_17547,U_17549,U_17551,U_17553)
        | ( ~ hBOOL(hAPP(hAPP(U_17549,hAPP(hAPP(c_List_Onth(U_17545),U_17551),sK431(U_17553,U_17551,U_17549,U_17547,U_17545))),hAPP(hAPP(c_List_Onth(U_17547),U_17553),sK431(U_17553,U_17551,U_17549,U_17547,U_17545))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK431(U_17553,U_17551,U_17549,U_17547,U_17545)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17547)),U_17553) )
    & ! [U_17552,U_17550,U_17548,U_17546,U_17544] :
        ( ( ! [U_17537] :
              ( hBOOL(hAPP(hAPP(U_17548,hAPP(hAPP(c_List_Onth(U_17544),U_17550),U_17537)),hAPP(hAPP(c_List_Onth(U_17546),U_17552),U_17537)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17537),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17546)),U_17552) )
        | ~ c_List_Olist__all2(U_17544,U_17546,U_17548,U_17550,U_17552) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_17538,sK431(U_17553,U_17551,U_17549,U_17547,U_17545))],[f_4287_3]) ).

cnf(f_4287_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17546)),U_17552)
    | ~ c_List_Olist__all2(U_17544,U_17546,U_17548,U_17550,U_17552) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_6,plain,
    ( hBOOL(hAPP(hAPP(U_17548,hAPP(hAPP(c_List_Onth(U_17544),U_17550),U_17537)),hAPP(hAPP(c_List_Onth(U_17546),U_17552),U_17537)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17537),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17544)),U_17550)))
    | ~ c_List_Olist__all2(U_17544,U_17546,U_17548,U_17550,U_17552) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK431(U_17553,U_17551,U_17549,U_17547,U_17545)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17547)),U_17553)
    | c_List_Olist__all2(U_17545,U_17547,U_17549,U_17551,U_17553) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

cnf(f_4287_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_17549,hAPP(hAPP(c_List_Onth(U_17545),U_17551),sK431(U_17553,U_17551,U_17549,U_17547,U_17545))),hAPP(hAPP(c_List_Onth(U_17547),U_17553),sK431(U_17553,U_17551,U_17549,U_17547,U_17545))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17545)),U_17551) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17547)),U_17553)
    | c_List_Olist__all2(U_17545,U_17547,U_17549,U_17551,U_17553) ),
    inference(clausify,[status(thm)],[f_4287_4]) ).

fof(f_4288_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD]) ).

fof(f_4288_2,plain,
    ! [U_17559,U_17558,U_17557,U_17556,U_17555,U_17554] :
      ( hBOOL(hAPP(hAPP(U_17556,hAPP(hAPP(c_List_Onth(U_17554),U_17557),U_17559)),hAPP(hAPP(c_List_Onth(U_17555),U_17558),U_17559)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17559),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17554)),U_17557)))
      | ~ c_List_Olist__all2(U_17554,U_17555,U_17556,U_17557,U_17558) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

cnf(f_4288_3,plain,
    ( hBOOL(hAPP(hAPP(U_17556,hAPP(hAPP(c_List_Onth(U_17554),U_17557),U_17559)),hAPP(hAPP(c_List_Onth(U_17555),U_17558),U_17559)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17559),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17554)),U_17557)))
    | ~ c_List_Olist__all2(U_17554,U_17555,U_17556,U_17557,U_17558) ),
    inference(clausify,[status(thm)],[f_4288_2]) ).

fof(f_4289_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2]) ).

fof(f_4289_2,plain,
    ! [U_17565,U_17564,U_17563,U_17562,U_17561,U_17560] :
      ( hBOOL(hAPP(hAPP(U_17562,hAPP(hAPP(c_List_Onth(U_17560),U_17563),U_17565)),hAPP(hAPP(c_List_Onth(U_17561),U_17564),U_17565)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17565),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17561)),U_17564)))
      | ~ c_List_Olist__all2(U_17560,U_17561,U_17562,U_17563,U_17564) ),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

cnf(f_4289_3,plain,
    ( hBOOL(hAPP(hAPP(U_17562,hAPP(hAPP(c_List_Onth(U_17560),U_17563),U_17565)),hAPP(hAPP(c_List_Onth(U_17561),U_17564),U_17565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17565),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17561)),U_17564)))
    | ~ c_List_Olist__all2(U_17560,U_17561,U_17562,U_17563,U_17564) ),
    inference(clausify,[status(thm)],[f_4289_2]) ).

fof(f_4290_1,plain,
    ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4290_2,plain,
    ! [U_17573,U_17572,U_17571,U_17570,U_17569,U_17568,U_17567,U_17566] :
      ( c_List_Olist__all2(U_17567,U_17569,U_17570,hAPP(hAPP(c_List_Olist__update(U_17567,U_17568),U_17566),U_17572),hAPP(hAPP(c_List_Olist__update(U_17569,U_17571),U_17566),U_17573))
      | ~ hBOOL(hAPP(hAPP(U_17570,U_17572),U_17573))
      | ~ c_List_Olist__all2(U_17567,U_17569,U_17570,U_17568,U_17571)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17567)),U_17568))) ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

cnf(f_4290_3,plain,
    ( c_List_Olist__all2(U_17567,U_17569,U_17570,hAPP(hAPP(c_List_Olist__update(U_17567,U_17568),U_17566),U_17572),hAPP(hAPP(c_List_Olist__update(U_17569,U_17571),U_17566),U_17573))
    | ~ hBOOL(hAPP(hAPP(U_17570,U_17572),U_17573))
    | ~ c_List_Olist__all2(U_17567,U_17569,U_17570,U_17568,U_17571)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17567)),U_17568))) ),
    inference(clausify,[status(thm)],[f_4290_2]) ).

fof(f_4291_1,plain,
    ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2]) ).

fof(f_4291_2,plain,
    ! [U_17581,U_17580,U_17579,U_17578,U_17577,U_17576,U_17575,U_17574] :
      ( c_List_Olist__all2(U_17574,U_17575,U_17576,hAPP(hAPP(c_List_Olist__update(U_17574,U_17577),U_17581),U_17579),hAPP(hAPP(c_List_Olist__update(U_17575,U_17578),U_17581),U_17580))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17575)),U_17578)))
      | ~ hBOOL(hAPP(hAPP(U_17576,U_17579),U_17580))
      | ~ c_List_Olist__all2(U_17574,U_17575,U_17576,U_17577,U_17578) ),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

cnf(f_4291_3,plain,
    ( c_List_Olist__all2(U_17574,U_17575,U_17576,hAPP(hAPP(c_List_Olist__update(U_17574,U_17577),U_17581),U_17579),hAPP(hAPP(c_List_Olist__update(U_17575,U_17578),U_17581),U_17580))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17575)),U_17578)))
    | ~ hBOOL(hAPP(hAPP(U_17576,U_17579),U_17580))
    | ~ c_List_Olist__all2(U_17574,U_17575,U_17576,U_17577,U_17578) ),
    inference(clausify,[status(thm)],[f_4291_2]) ).

fof(f_4292_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_4292_2,plain,
    ! [U_17585,U_17584,U_17583,U_17582] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17582,U_17584)),c_Enum_Oproduct(U_17582,U_17584,U_17583,U_17585)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17584),U_17585))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17582),U_17583)) ),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

cnf(f_4292_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17582,U_17584)),c_Enum_Oproduct(U_17582,U_17584,U_17583,U_17585)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17584),U_17585))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17582),U_17583)) ),
    inference(clausify,[status(thm)],[f_4292_2]) ).

fof(f_4293_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_4293_2,plain,
    ! [U_17589,U_17588,U_17587,U_17586] : hAPP(c_List_Oset(tc_prod(U_17586,U_17587)),c_Enum_Oproduct(U_17586,U_17587,U_17588,U_17589)) = hAPP(hAPP(c_Product__Type_OSigma(U_17586,U_17587),hAPP(c_List_Oset(U_17586),U_17588)),hAPP(c_COMBK(tc_fun(U_17587,tc_HOL_Obool),U_17586),hAPP(c_List_Oset(U_17587),U_17589))),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

cnf(f_4293_3,plain,
    hAPP(c_List_Oset(tc_prod(U_17586,U_17587)),c_Enum_Oproduct(U_17586,U_17587,U_17588,U_17589)) = hAPP(hAPP(c_Product__Type_OSigma(U_17586,U_17587),hAPP(c_List_Oset(U_17586),U_17588)),hAPP(c_COMBK(tc_fun(U_17587,tc_HOL_Obool),U_17586),hAPP(c_List_Oset(U_17587),U_17589))),
    inference(clausify,[status(thm)],[f_4293_2]) ).

fof(f_4294_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_4294_2,plain,
    ! [U_17591,U_17590] : hAPP(c_Set_Oimage(tc_List_Olist(U_17590),tc_fun(U_17590,tc_HOL_Obool),c_List_Oset(U_17590)),hAPP(c_List_Oset(tc_List_Olist(U_17590)),c_Enum_Osublists(U_17590,U_17591))) = hAPP(c_Set_OPow(U_17590),hAPP(c_List_Oset(U_17590),U_17591)),
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

cnf(f_4294_3,plain,
    hAPP(c_Set_Oimage(tc_List_Olist(U_17590),tc_fun(U_17590,tc_HOL_Obool),c_List_Oset(U_17590)),hAPP(c_List_Oset(tc_List_Olist(U_17590)),c_Enum_Osublists(U_17590,U_17591))) = hAPP(c_Set_OPow(U_17590),hAPP(c_List_Oset(U_17590),U_17591)),
    inference(clausify,[status(thm)],[f_4294_2]) ).

fof(f_4295_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_4295_2,plain,
    ! [U_17593,U_17592] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17592))),c_Enum_Osublists(U_17592,U_17593)) = 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_17592)),U_17593)),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

cnf(f_4295_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17592))),c_Enum_Osublists(U_17592,U_17593)) = 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_17592)),U_17593)),
    inference(clausify,[status(thm)],[f_4295_2]) ).

fof(f_4296_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_4296_2,plain,
    ! [U_17594] : c_Enum_Osublists(U_17594,c_List_Olist_ONil(U_17594)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17594)),c_List_Olist_ONil(U_17594)),c_List_Olist_ONil(tc_List_Olist(U_17594))),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

cnf(f_4296_3,plain,
    c_Enum_Osublists(U_17594,c_List_Olist_ONil(U_17594)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17594)),c_List_Olist_ONil(U_17594)),c_List_Olist_ONil(tc_List_Olist(U_17594))),
    inference(clausify,[status(thm)],[f_4296_2]) ).

fof(f_4297_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_4297_2,plain,
    ! [U_17597,U_17596,U_17595] : c_Enum_Osublists(U_17595,hAPP(hAPP(c_List_Olist_OCons(U_17595),U_17596),U_17597)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),c_Enum_Osublists(U_17595,U_17597)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_17595)),tc_fun(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),tc_List_Olist(tc_List_Olist(U_17595))),c_List_Oappend(tc_List_Olist(U_17595))),hAPP(c_List_Omap(tc_List_Olist(U_17595),tc_List_Olist(U_17595)),hAPP(c_List_Olist_OCons(U_17595),U_17596)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_17595))))),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

cnf(f_4297_3,plain,
    c_Enum_Osublists(U_17595,hAPP(hAPP(c_List_Olist_OCons(U_17595),U_17596),U_17597)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),c_Enum_Osublists(U_17595,U_17597)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_17595)),tc_fun(tc_List_Olist(tc_List_Olist(U_17595)),tc_List_Olist(tc_List_Olist(U_17595))),tc_List_Olist(tc_List_Olist(U_17595))),c_List_Oappend(tc_List_Olist(U_17595))),hAPP(c_List_Omap(tc_List_Olist(U_17595),tc_List_Olist(U_17595)),hAPP(c_List_Olist_OCons(U_17595),U_17596)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_17595))))),
    inference(clausify,[status(thm)],[f_4297_2]) ).

fof(f_4298_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_4298_2,plain,
    ! [U_17599,U_17598] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_17598,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17598),tc_fun(U_17598,tc_HOL_Obool)),c_List_Oset(U_17598)),c_Enum_Osublists(U_17598,U_17599))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17598),U_17599)) ),
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

cnf(f_4298_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_17598,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17598),tc_fun(U_17598,tc_HOL_Obool)),c_List_Oset(U_17598)),c_Enum_Osublists(U_17598,U_17599))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17598),U_17599)) ),
    inference(clausify,[status(thm)],[f_4298_2]) ).

fof(f_4299_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_4299_2,plain,
    ! [U_17602,U_17601,U_17600] : hAPP(c_List_Oset(tc_List_Olist(U_17600)),c_Enum_On__lists(U_17600,U_17601,U_17602)) = hAPP(c_Set_OCollect(tc_List_Olist(U_17600)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17600),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_17600)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17600),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_17600)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17600)))),U_17601))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17600),tc_fun(U_17600,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17600,tc_HOL_Obool),tc_fun(tc_fun(U_17600,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17600)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17600,tc_HOL_Obool))),c_List_Oset(U_17600))),hAPP(c_List_Oset(U_17600),U_17602)))),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

cnf(f_4299_3,plain,
    hAPP(c_List_Oset(tc_List_Olist(U_17600)),c_Enum_On__lists(U_17600,U_17601,U_17602)) = hAPP(c_Set_OCollect(tc_List_Olist(U_17600)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17600),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_17600)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17600),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_17600)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17600)))),U_17601))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17600),tc_fun(U_17600,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17600,tc_HOL_Obool),tc_fun(tc_fun(U_17600,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17600)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17600,tc_HOL_Obool))),c_List_Oset(U_17600))),hAPP(c_List_Oset(U_17600),U_17602)))),
    inference(clausify,[status(thm)],[f_4299_2]) ).

fof(f_4300_1,plain,
    ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2),
    inference(fof_nnf,[status(thm)],[fact_enum__the__def]) ).

fof(f_4300_2,plain,
    ! [U_17604,U_17603] : c_Enum_Oenum__the(U_17603,U_17604) = c_HOL_OThe(U_17603,U_17604),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

cnf(f_4300_3,plain,
    c_Enum_Oenum__the(U_17603,U_17604) = c_HOL_OThe(U_17603,U_17604),
    inference(clausify,[status(thm)],[f_4300_2]) ).

fof(f_4301_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_4301_2,plain,
    ! [U_17607,U_17606,U_17605] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_17605)),c_Enum_On__lists(U_17605,U_17607,U_17606)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17605),U_17606)) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

cnf(f_4301_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_17605)),c_Enum_On__lists(U_17605,U_17607,U_17606)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17605),U_17606)) ),
    inference(clausify,[status(thm)],[f_4301_2]) ).

fof(f_4302_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_4302_2,plain,
    ! [U_17609,U_17608] :
      ( ( c_Enum_On__lists(U_17609,U_17608,c_List_Olist_ONil(U_17609)) = c_List_Olist_ONil(tc_List_Olist(U_17609))
        | U_17608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Enum_On__lists(U_17609,U_17608,c_List_Olist_ONil(U_17609)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17609)),c_List_Olist_ONil(U_17609)),c_List_Olist_ONil(tc_List_Olist(U_17609)))
        | U_17608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4302_1]) ).

fof(f_4302_3,plain,
    ( ! [U_17613,U_17611] :
        ( c_Enum_On__lists(U_17613,U_17611,c_List_Olist_ONil(U_17613)) = c_List_Olist_ONil(tc_List_Olist(U_17613))
        | U_17611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17612,U_17610] :
        ( c_Enum_On__lists(U_17612,U_17610,c_List_Olist_ONil(U_17612)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17612)),c_List_Olist_ONil(U_17612)),c_List_Olist_ONil(tc_List_Olist(U_17612)))
        | U_17610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4302_2]) ).

cnf(f_4302_4,plain,
    ( c_Enum_On__lists(U_17612,U_17610,c_List_Olist_ONil(U_17612)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17612)),c_List_Olist_ONil(U_17612)),c_List_Olist_ONil(tc_List_Olist(U_17612)))
    | U_17610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4302_3]) ).

cnf(f_4302_5,plain,
    ( c_Enum_On__lists(U_17613,U_17611,c_List_Olist_ONil(U_17613)) = c_List_Olist_ONil(tc_List_Olist(U_17613))
    | U_17611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4302_3]) ).

fof(f_4303_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_4303_2,plain,
    ! [U_17615,U_17614] : c_Enum_On__lists(U_17614,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_17615) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17614)),c_List_Olist_ONil(U_17614)),c_List_Olist_ONil(tc_List_Olist(U_17614))),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

cnf(f_4303_3,plain,
    c_Enum_On__lists(U_17614,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_17615) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17614)),c_List_Olist_ONil(U_17614)),c_List_Olist_ONil(tc_List_Olist(U_17614))),
    inference(clausify,[status(thm)],[f_4303_2]) ).

fof(f_4304_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_4304_2,plain,
    ! [U_17618,U_17617,U_17616] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17616))),c_Enum_On__lists(U_17616,U_17617,U_17618)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17616)),U_17618)),U_17617),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

cnf(f_4304_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17616))),c_Enum_On__lists(U_17616,U_17617,U_17618)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17616)),U_17618)),U_17617),
    inference(clausify,[status(thm)],[f_4304_2]) ).

fof(f_4305_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_4305_2,plain,
    ! [U_17622,U_17621,U_17620,U_17619] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17619)),U_17620) = U_17621
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17619)),U_17620),hAPP(c_List_Oset(tc_List_Olist(U_17619)),c_Enum_On__lists(U_17619,U_17621,U_17622)))) ),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

cnf(f_4305_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17619)),U_17620) = U_17621
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17619)),U_17620),hAPP(c_List_Oset(tc_List_Olist(U_17619)),c_Enum_On__lists(U_17619,U_17621,U_17622)))) ),
    inference(clausify,[status(thm)],[f_4305_2]) ).

fof(f_4306_1,plain,
    ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_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_4306_2,plain,
    ! [U_17628,U_17627,U_17626,U_17625,U_17624] :
      ( c_List_Olist__all2(U_17624,U_17625,U_17628,U_17626,U_17627)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17624)),U_17626) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17625)),U_17627)
      | ? [U_17623] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17624,U_17625,tc_HOL_Obool),U_17628),U_17623))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17624,U_17625)),U_17623),hAPP(c_List_Oset(tc_prod(U_17624,U_17625)),hAPP(hAPP(c_List_Ozip(U_17624,U_17625),U_17626),U_17627)))) ) ),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

fof(f_4306_3,plain,
    ! [U_17628,U_17627,U_17626,U_17625,U_17624] :
      ( c_List_Olist__all2(U_17624,U_17625,U_17628,U_17626,U_17627)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17624)),U_17626) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17625)),U_17627)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17624,U_17625,tc_HOL_Obool),U_17628),sK432(U_17628,U_17627,U_17626,U_17625,U_17624)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17624,U_17625)),sK432(U_17628,U_17627,U_17626,U_17625,U_17624)),hAPP(c_List_Oset(tc_prod(U_17624,U_17625)),hAPP(hAPP(c_List_Ozip(U_17624,U_17625),U_17626),U_17627)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_17623,sK432(U_17628,U_17627,U_17626,U_17625,U_17624))],[f_4306_2]) ).

cnf(f_4306_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17624,U_17625)),sK432(U_17628,U_17627,U_17626,U_17625,U_17624)),hAPP(c_List_Oset(tc_prod(U_17624,U_17625)),hAPP(hAPP(c_List_Ozip(U_17624,U_17625),U_17626),U_17627))))
    | c_List_Olist__all2(U_17624,U_17625,U_17628,U_17626,U_17627)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17624)),U_17626) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17625)),U_17627) ),
    inference(clausify,[status(thm)],[f_4306_3]) ).

cnf(f_4306_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17624,U_17625,tc_HOL_Obool),U_17628),sK432(U_17628,U_17627,U_17626,U_17625,U_17624)))
    | c_List_Olist__all2(U_17624,U_17625,U_17628,U_17626,U_17627)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17624)),U_17626) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17625)),U_17627) ),
    inference(clausify,[status(thm)],[f_4306_3]) ).

fof(f_4307_1,plain,
    ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_4307_2,plain,
    ! [U_17633,U_17632,U_17631,U_17630] :
      ( hBOOL(hAPP(U_17632,U_17633))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17630),U_17633),hAPP(c_List_Oset(U_17630),U_17631)))
      | ? [U_17629] :
          ( ~ hBOOL(hAPP(U_17632,hAPP(hAPP(c_List_Onth(U_17630),U_17631),U_17629)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17629),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17630)),U_17631))) ) ),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

fof(f_4307_3,plain,
    ! [U_17633,U_17632,U_17631,U_17630] :
      ( hBOOL(hAPP(U_17632,U_17633))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17630),U_17633),hAPP(c_List_Oset(U_17630),U_17631)))
      | ( ~ hBOOL(hAPP(U_17632,hAPP(hAPP(c_List_Onth(U_17630),U_17631),sK433(U_17633,U_17632,U_17631,U_17630))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK433(U_17633,U_17632,U_17631,U_17630)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17630)),U_17631))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_17629,sK433(U_17633,U_17632,U_17631,U_17630))],[f_4307_2]) ).

cnf(f_4307_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK433(U_17633,U_17632,U_17631,U_17630)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17630)),U_17631)))
    | hBOOL(hAPP(U_17632,U_17633))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17630),U_17633),hAPP(c_List_Oset(U_17630),U_17631))) ),
    inference(clausify,[status(thm)],[f_4307_3]) ).

cnf(f_4307_5,plain,
    ( ~ hBOOL(hAPP(U_17632,hAPP(hAPP(c_List_Onth(U_17630),U_17631),sK433(U_17633,U_17632,U_17631,U_17630))))
    | hBOOL(hAPP(U_17632,U_17633))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17630),U_17633),hAPP(c_List_Oset(U_17630),U_17631))) ),
    inference(clausify,[status(thm)],[f_4307_3]) ).

fof(f_4308_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_4308_2,plain,
    ! [U_17638,U_17637,U_17636,U_17635,U_17634] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_17634,U_17635,U_17636),U_17637),hAPP(c_List_Oset(U_17634),U_17638)) = hAPP(c_List_Ofoldl(U_17635,U_17634,hAPP(c_COMBC(U_17634,U_17635,U_17635),U_17636),U_17637),c_List_Oremdups(U_17634,U_17638))
      | ~ c_Finite__Set_Ofun__left__comm(U_17634,U_17635,U_17636) ),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

cnf(f_4308_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_17634,U_17635,U_17636),U_17637),hAPP(c_List_Oset(U_17634),U_17638)) = hAPP(c_List_Ofoldl(U_17635,U_17634,hAPP(c_COMBC(U_17634,U_17635,U_17635),U_17636),U_17637),c_List_Oremdups(U_17634,U_17638))
    | ~ c_Finite__Set_Ofun__left__comm(U_17634,U_17635,U_17636) ),
    inference(clausify,[status(thm)],[f_4308_2]) ).

fof(f_4309_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_4309_2,plain,
    ! [U_17643,U_17642,U_17641,U_17640,U_17639] :
      ( hAPP(hAPP(c_List_Omap(U_17639,U_17640),U_17641),hAPP(c_List_OremoveAll(U_17639,U_17642),U_17643)) = hAPP(c_List_OremoveAll(U_17640,hAPP(U_17641,U_17642)),hAPP(hAPP(c_List_Omap(U_17639,U_17640),U_17641),U_17643))
      | ~ c_Fun_Oinj__on(U_17639,U_17640,U_17641,hAPP(hAPP(c_Set_Oinsert(U_17639),U_17642),hAPP(c_List_Oset(U_17639),U_17643))) ),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

cnf(f_4309_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17639,U_17640),U_17641),hAPP(c_List_OremoveAll(U_17639,U_17642),U_17643)) = hAPP(c_List_OremoveAll(U_17640,hAPP(U_17641,U_17642)),hAPP(hAPP(c_List_Omap(U_17639,U_17640),U_17641),U_17643))
    | ~ c_Fun_Oinj__on(U_17639,U_17640,U_17641,hAPP(hAPP(c_Set_Oinsert(U_17639),U_17642),hAPP(c_List_Oset(U_17639),U_17643))) ),
    inference(clausify,[status(thm)],[f_4309_2]) ).

fof(f_4310_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_4310_2,plain,
    ! [U_17645,U_17644] : hBOOL(hAPP(c_List_Odistinct(U_17644),c_List_Oremdups(U_17644,U_17645))),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

cnf(f_4310_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_17644),c_List_Oremdups(U_17644,U_17645))),
    inference(clausify,[status(thm)],[f_4310_2]) ).

fof(f_4311_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_4311_2,plain,
    ! [U_17647,U_17646] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17646)),c_List_Oremdups(U_17646,U_17647))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17646)),U_17647))),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

cnf(f_4311_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17646)),c_List_Oremdups(U_17646,U_17647))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17646)),U_17647))),
    inference(clausify,[status(thm)],[f_4311_2]) ).

fof(f_4312_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_4312_2,plain,
    ! [U_17649,U_17648] :
      ( c_List_Oremdups(U_17648,U_17649) = U_17649
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17648),U_17649)) ),
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

cnf(f_4312_3,plain,
    ( c_List_Oremdups(U_17648,U_17649) = U_17649
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17648),U_17649)) ),
    inference(clausify,[status(thm)],[f_4312_2]) ).

fof(f_4313_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_4313_2,plain,
    ! [U_17652,U_17651,U_17650] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17650),hAPP(c_List_OremoveAll(U_17650,U_17652),U_17651)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17650),U_17651)) ),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

cnf(f_4313_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17650),hAPP(c_List_OremoveAll(U_17650,U_17652),U_17651)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17650),U_17651)) ),
    inference(clausify,[status(thm)],[f_4313_2]) ).

fof(f_4314_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_4314_2,plain,
    ! [U_17654,U_17653] :
      ( ( c_List_Oremdups(U_17653,U_17654) = U_17654
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17653),U_17654)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_17653),U_17654))
        | c_List_Oremdups(U_17653,U_17654) != U_17654 ) ),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

fof(f_4314_3,plain,
    ( ! [U_17658,U_17656] :
        ( c_List_Oremdups(U_17656,U_17658) = U_17658
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17656),U_17658)) )
    & ! [U_17657,U_17655] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17655),U_17657))
        | c_List_Oremdups(U_17655,U_17657) != U_17657 ) ),
    inference(miniscope,[status(thm)],[f_4314_2]) ).

cnf(f_4314_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17655),U_17657))
    | c_List_Oremdups(U_17655,U_17657) != U_17657 ),
    inference(clausify,[status(thm)],[f_4314_3]) ).

cnf(f_4314_5,plain,
    ( c_List_Oremdups(U_17656,U_17658) = U_17658
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17656),U_17658)) ),
    inference(clausify,[status(thm)],[f_4314_3]) ).

fof(f_4315_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_4315_2,plain,
    ! [U_17660,U_17659] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17659)),c_List_Oremdups(U_17659,U_17660)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17659)),U_17660)
        | c_List_Oremdups(U_17659,U_17660) != U_17660 )
      & ( c_List_Oremdups(U_17659,U_17660) = U_17660
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17659)),c_List_Oremdups(U_17659,U_17660)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17659)),U_17660) ) ),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

fof(f_4315_3,plain,
    ( ! [U_17664,U_17662] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),c_List_Oremdups(U_17662,U_17664)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17664)
        | c_List_Oremdups(U_17662,U_17664) != U_17664 )
    & ! [U_17663,U_17661] :
        ( c_List_Oremdups(U_17661,U_17663) = U_17663
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17661)),c_List_Oremdups(U_17661,U_17663)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17661)),U_17663) ) ),
    inference(miniscope,[status(thm)],[f_4315_2]) ).

cnf(f_4315_4,plain,
    ( c_List_Oremdups(U_17661,U_17663) = U_17663
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17661)),c_List_Oremdups(U_17661,U_17663)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17661)),U_17663) ),
    inference(clausify,[status(thm)],[f_4315_3]) ).

cnf(f_4315_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),c_List_Oremdups(U_17662,U_17664)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17664)
    | c_List_Oremdups(U_17662,U_17664) != U_17664 ),
    inference(clausify,[status(thm)],[f_4315_3]) ).

fof(f_4316_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_4316_2,plain,
    ! [U_17666,U_17665] : hAPP(c_List_Oset(U_17665),c_List_Oremdups(U_17665,U_17666)) = hAPP(c_List_Oset(U_17665),U_17666),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

cnf(f_4316_3,plain,
    hAPP(c_List_Oset(U_17665),c_List_Oremdups(U_17665,U_17666)) = hAPP(c_List_Oset(U_17665),U_17666),
    inference(clausify,[status(thm)],[f_4316_2]) ).

fof(f_4317_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_4317_2,plain,
    ! [U_17668,U_17667] : c_List_Oremdups(U_17667,c_List_Oremdups(U_17667,U_17668)) = c_List_Oremdups(U_17667,U_17668),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

cnf(f_4317_3,plain,
    c_List_Oremdups(U_17667,c_List_Oremdups(U_17667,U_17668)) = c_List_Oremdups(U_17667,U_17668),
    inference(clausify,[status(thm)],[f_4317_2]) ).

fof(f_4318_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_4318_2,plain,
    ! [U_17672,U_17671,U_17670,U_17669] : hAPP(c_List_OremoveAll(U_17669,U_17670),hAPP(hAPP(c_List_Oappend(U_17669),U_17671),U_17672)) = hAPP(hAPP(c_List_Oappend(U_17669),hAPP(c_List_OremoveAll(U_17669,U_17670),U_17671)),hAPP(c_List_OremoveAll(U_17669,U_17670),U_17672)),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

cnf(f_4318_3,plain,
    hAPP(c_List_OremoveAll(U_17669,U_17670),hAPP(hAPP(c_List_Oappend(U_17669),U_17671),U_17672)) = hAPP(hAPP(c_List_Oappend(U_17669),hAPP(c_List_OremoveAll(U_17669,U_17670),U_17671)),hAPP(c_List_OremoveAll(U_17669,U_17670),U_17672)),
    inference(clausify,[status(thm)],[f_4318_2]) ).

fof(f_4319_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_4319_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_4319_1]) ).

fof(f_4319_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_4319_2]) ).

cnf(f_4319_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_4319_3]) ).

cnf(f_4319_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_4319_3]) ).

fof(f_4320_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_4320_2,plain,
    ! [U_17686,U_17685] :
      ( ( c_List_Oremdups(U_17685,U_17686) = c_List_Olist_ONil(U_17685)
        | U_17686 != c_List_Olist_ONil(U_17685) )
      & ( U_17686 = c_List_Olist_ONil(U_17685)
        | c_List_Oremdups(U_17685,U_17686) != c_List_Olist_ONil(U_17685) ) ),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

fof(f_4320_3,plain,
    ( ! [U_17690,U_17688] :
        ( c_List_Oremdups(U_17688,U_17690) = c_List_Olist_ONil(U_17688)
        | U_17690 != c_List_Olist_ONil(U_17688) )
    & ! [U_17689,U_17687] :
        ( U_17689 = c_List_Olist_ONil(U_17687)
        | c_List_Oremdups(U_17687,U_17689) != c_List_Olist_ONil(U_17687) ) ),
    inference(miniscope,[status(thm)],[f_4320_2]) ).

cnf(f_4320_4,plain,
    ( U_17689 = c_List_Olist_ONil(U_17687)
    | c_List_Oremdups(U_17687,U_17689) != c_List_Olist_ONil(U_17687) ),
    inference(clausify,[status(thm)],[f_4320_3]) ).

cnf(f_4320_5,plain,
    ( c_List_Oremdups(U_17688,U_17690) = c_List_Olist_ONil(U_17688)
    | U_17690 != c_List_Olist_ONil(U_17688) ),
    inference(clausify,[status(thm)],[f_4320_3]) ).

fof(f_4321_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_4321_2,plain,
    ! [U_17692,U_17691] : hAPP(c_List_OremoveAll(U_17691,U_17692),c_List_Olist_ONil(U_17691)) = c_List_Olist_ONil(U_17691),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

cnf(f_4321_3,plain,
    hAPP(c_List_OremoveAll(U_17691,U_17692),c_List_Olist_ONil(U_17691)) = c_List_Olist_ONil(U_17691),
    inference(clausify,[status(thm)],[f_4321_2]) ).

fof(f_4322_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_4322_2,plain,
    ! [U_17694,U_17693] :
      ( ( c_List_Olist_ONil(U_17693) = c_List_Oremdups(U_17693,U_17694)
        | U_17694 != c_List_Olist_ONil(U_17693) )
      & ( U_17694 = c_List_Olist_ONil(U_17693)
        | c_List_Olist_ONil(U_17693) != c_List_Oremdups(U_17693,U_17694) ) ),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

fof(f_4322_3,plain,
    ( ! [U_17698,U_17696] :
        ( c_List_Olist_ONil(U_17696) = c_List_Oremdups(U_17696,U_17698)
        | U_17698 != c_List_Olist_ONil(U_17696) )
    & ! [U_17697,U_17695] :
        ( U_17697 = c_List_Olist_ONil(U_17695)
        | c_List_Olist_ONil(U_17695) != c_List_Oremdups(U_17695,U_17697) ) ),
    inference(miniscope,[status(thm)],[f_4322_2]) ).

cnf(f_4322_4,plain,
    ( U_17697 = c_List_Olist_ONil(U_17695)
    | c_List_Olist_ONil(U_17695) != c_List_Oremdups(U_17695,U_17697) ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

cnf(f_4322_5,plain,
    ( c_List_Olist_ONil(U_17696) = c_List_Oremdups(U_17696,U_17698)
    | U_17698 != c_List_Olist_ONil(U_17696) ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

fof(f_4323_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_4323_2,plain,
    ! [U_17699] : c_List_Oremdups(U_17699,c_List_Olist_ONil(U_17699)) = c_List_Olist_ONil(U_17699),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

cnf(f_4323_3,plain,
    c_List_Oremdups(U_17699,c_List_Olist_ONil(U_17699)) = c_List_Olist_ONil(U_17699),
    inference(clausify,[status(thm)],[f_4323_2]) ).

fof(f_4324_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_4324_2,plain,
    ! [U_17703,U_17702,U_17701,U_17700] : c_List_Oremdups(U_17700,hAPP(hAPP(c_List_Omap(U_17701,U_17700),U_17702),c_List_Oremdups(U_17701,U_17703))) = c_List_Oremdups(U_17700,hAPP(hAPP(c_List_Omap(U_17701,U_17700),U_17702),U_17703)),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

cnf(f_4324_3,plain,
    c_List_Oremdups(U_17700,hAPP(hAPP(c_List_Omap(U_17701,U_17700),U_17702),c_List_Oremdups(U_17701,U_17703))) = c_List_Oremdups(U_17700,hAPP(hAPP(c_List_Omap(U_17701,U_17700),U_17702),U_17703)),
    inference(clausify,[status(thm)],[f_4324_2]) ).

fof(f_4325_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_4325_2,plain,
    ! [U_17706,U_17705,U_17704] :
      ( c_List_Oremove1(U_17704,U_17706,c_List_Oremdups(U_17704,U_17705)) = c_List_Oremdups(U_17704,c_List_Oremove1(U_17704,U_17706,U_17705))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17704),U_17705)) ),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

cnf(f_4325_3,plain,
    ( c_List_Oremove1(U_17704,U_17706,c_List_Oremdups(U_17704,U_17705)) = c_List_Oremdups(U_17704,c_List_Oremove1(U_17704,U_17706,U_17705))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17704),U_17705)) ),
    inference(clausify,[status(thm)],[f_4325_2]) ).

fof(f_4326_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_4326_2,plain,
    ! [U_17709,U_17708,U_17707] :
      ( hAPP(c_List_OremoveAll(U_17707,U_17708),U_17709) = U_17709
      | hBOOL(hAPP(hAPP(c_member(U_17707),U_17708),hAPP(c_List_Oset(U_17707),U_17709))) ),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

cnf(f_4326_3,plain,
    ( hAPP(c_List_OremoveAll(U_17707,U_17708),U_17709) = U_17709
    | hBOOL(hAPP(hAPP(c_member(U_17707),U_17708),hAPP(c_List_Oset(U_17707),U_17709))) ),
    inference(clausify,[status(thm)],[f_4326_2]) ).

fof(f_4327_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_4327_2,plain,
    ! [U_17712,U_17711,U_17710] :
      ( c_List_Oremove1(U_17710,U_17712,U_17711) = hAPP(c_List_OremoveAll(U_17710,U_17712),U_17711)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17710),U_17711)) ),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

cnf(f_4327_3,plain,
    ( c_List_Oremove1(U_17710,U_17712,U_17711) = hAPP(c_List_OremoveAll(U_17710,U_17712),U_17711)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17710),U_17711)) ),
    inference(clausify,[status(thm)],[f_4327_2]) ).

fof(f_4328_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_4328_2,plain,
    ! [U_17715,U_17714,U_17713] :
      ( ( c_List_Oremdups(U_17713,hAPP(hAPP(c_List_Olist_OCons(U_17713),U_17714),U_17715)) = hAPP(hAPP(c_List_Olist_OCons(U_17713),U_17714),c_List_Oremdups(U_17713,U_17715))
        | hBOOL(hAPP(hAPP(c_member(U_17713),U_17714),hAPP(c_List_Oset(U_17713),U_17715))) )
      & ( c_List_Oremdups(U_17713,hAPP(hAPP(c_List_Olist_OCons(U_17713),U_17714),U_17715)) = c_List_Oremdups(U_17713,U_17715)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17713),U_17714),hAPP(c_List_Oset(U_17713),U_17715))) ) ),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

fof(f_4328_3,plain,
    ( ! [U_17721,U_17719,U_17717] :
        ( c_List_Oremdups(U_17717,hAPP(hAPP(c_List_Olist_OCons(U_17717),U_17719),U_17721)) = hAPP(hAPP(c_List_Olist_OCons(U_17717),U_17719),c_List_Oremdups(U_17717,U_17721))
        | hBOOL(hAPP(hAPP(c_member(U_17717),U_17719),hAPP(c_List_Oset(U_17717),U_17721))) )
    & ! [U_17720,U_17718,U_17716] :
        ( c_List_Oremdups(U_17716,hAPP(hAPP(c_List_Olist_OCons(U_17716),U_17718),U_17720)) = c_List_Oremdups(U_17716,U_17720)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17716),U_17718),hAPP(c_List_Oset(U_17716),U_17720))) ) ),
    inference(miniscope,[status(thm)],[f_4328_2]) ).

cnf(f_4328_4,plain,
    ( c_List_Oremdups(U_17716,hAPP(hAPP(c_List_Olist_OCons(U_17716),U_17718),U_17720)) = c_List_Oremdups(U_17716,U_17720)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17716),U_17718),hAPP(c_List_Oset(U_17716),U_17720))) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

cnf(f_4328_5,plain,
    ( c_List_Oremdups(U_17717,hAPP(hAPP(c_List_Olist_OCons(U_17717),U_17719),U_17721)) = hAPP(hAPP(c_List_Olist_OCons(U_17717),U_17719),c_List_Oremdups(U_17717,U_17721))
    | hBOOL(hAPP(hAPP(c_member(U_17717),U_17719),hAPP(c_List_Oset(U_17717),U_17721))) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

fof(f_4329_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_4329_2,plain,
    ! [U_17723,U_17722] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),c_List_Oremdups(U_17722,U_17723)) = hAPP(c_Finite__Set_Ocard(U_17722),hAPP(c_List_Oset(U_17722),U_17723)),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

cnf(f_4329_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17722)),c_List_Oremdups(U_17722,U_17723)) = hAPP(c_Finite__Set_Ocard(U_17722),hAPP(c_List_Oset(U_17722),U_17723)),
    inference(clausify,[status(thm)],[f_4329_2]) ).

fof(f_4330_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_4330_2,plain,
    ! [U_17728,U_17727,U_17726,U_17725,U_17724] :
      ( hAPP(hAPP(c_List_Omap(U_17724,U_17725),U_17726),hAPP(c_List_OremoveAll(U_17724,U_17727),U_17728)) = hAPP(c_List_OremoveAll(U_17725,hAPP(U_17726,U_17727)),hAPP(hAPP(c_List_Omap(U_17724,U_17725),U_17726),U_17728))
      | ~ c_Fun_Oinj__on(U_17724,U_17725,U_17726,c_Orderings_Otop__class_Otop(tc_fun(U_17724,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

cnf(f_4330_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17724,U_17725),U_17726),hAPP(c_List_OremoveAll(U_17724,U_17727),U_17728)) = hAPP(c_List_OremoveAll(U_17725,hAPP(U_17726,U_17727)),hAPP(hAPP(c_List_Omap(U_17724,U_17725),U_17726),U_17728))
    | ~ c_Fun_Oinj__on(U_17724,U_17725,U_17726,c_Orderings_Otop__class_Otop(tc_fun(U_17724,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4330_2]) ).

fof(f_4331_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_4331_2,plain,
    ! [U_17731,U_17730,U_17729] : hAPP(c_List_Oset(U_17729),hAPP(c_List_OremoveAll(U_17729,U_17730),U_17731)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17729,tc_HOL_Obool)),hAPP(c_List_Oset(U_17729),U_17731)),hAPP(hAPP(c_Set_Oinsert(U_17729),U_17730),c_Orderings_Obot__class_Obot(tc_fun(U_17729,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

cnf(f_4331_3,plain,
    hAPP(c_List_Oset(U_17729),hAPP(c_List_OremoveAll(U_17729,U_17730),U_17731)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17729,tc_HOL_Obool)),hAPP(c_List_Oset(U_17729),U_17731)),hAPP(hAPP(c_Set_Oinsert(U_17729),U_17730),c_Orderings_Obot__class_Obot(tc_fun(U_17729,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4331_2]) ).

fof(f_4332_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_4332_2,plain,
    ! [U_17733,U_17732] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17732)),c_List_Oremdups(U_17732,c_List_Oconcat(U_17732,U_17733))) = hAPP(c_Finite__Set_Ocard(U_17732),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17732),tc_fun(U_17732,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17732)),U_17733)),c_List_Oset(U_17732))),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

cnf(f_4332_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17732)),c_List_Oremdups(U_17732,c_List_Oconcat(U_17732,U_17733))) = hAPP(c_Finite__Set_Ocard(U_17732),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17732),tc_fun(U_17732,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17732)),U_17733)),c_List_Oset(U_17732))),
    inference(clausify,[status(thm)],[f_4332_2]) ).

fof(f_4333_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_4333_2,plain,
    ! [U_17735,U_17734] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17734,hAPP(c_List_Oset(U_17734),U_17735)) = c_List_Olinorder__class_Osort__key(U_17734,U_17734,c_COMBI(U_17734),c_List_Oremdups(U_17734,U_17735))
      | ~ class_Orderings_Olinorder(U_17734) ),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

cnf(f_4333_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17734,hAPP(c_List_Oset(U_17734),U_17735)) = c_List_Olinorder__class_Osort__key(U_17734,U_17734,c_COMBI(U_17734),c_List_Oremdups(U_17734,U_17735))
    | ~ class_Orderings_Olinorder(U_17734) ),
    inference(clausify,[status(thm)],[f_4333_2]) ).

fof(f_4334_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_4334_2,plain,
    ! [U_17737,U_17736] : c_List_Oconcat(U_17736,U_17737) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17736),tc_List_Olist(U_17736),c_List_Oappend(U_17736),c_List_Olist_ONil(U_17736)),U_17737),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

cnf(f_4334_3,plain,
    c_List_Oconcat(U_17736,U_17737) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17736),tc_List_Olist(U_17736),c_List_Oappend(U_17736),c_List_Olist_ONil(U_17736)),U_17737),
    inference(clausify,[status(thm)],[f_4334_2]) ).

fof(f_4335_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_4335_2,plain,
    ! [U_17740,U_17739,U_17738] : hAPP(c_List_Ofoldl(tc_List_Olist(U_17738),tc_List_Olist(U_17738),c_List_Oappend(U_17738),U_17739),U_17740) = hAPP(hAPP(c_List_Oappend(U_17738),U_17739),c_List_Oconcat(U_17738,U_17740)),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

cnf(f_4335_3,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_17738),tc_List_Olist(U_17738),c_List_Oappend(U_17738),U_17739),U_17740) = hAPP(hAPP(c_List_Oappend(U_17738),U_17739),c_List_Oconcat(U_17738,U_17740)),
    inference(clausify,[status(thm)],[f_4335_2]) ).

fof(f_4336_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_4336_2,plain,
    ! [U_17743,U_17742,U_17741] :
      ( c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,c_List_Olist_ONil(U_17742)) = c_List_Olist_ONil(U_17742)
      | ~ class_Orderings_Olinorder(U_17741) ),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

cnf(f_4336_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,c_List_Olist_ONil(U_17742)) = c_List_Olist_ONil(U_17742)
    | ~ class_Orderings_Olinorder(U_17741) ),
    inference(clausify,[status(thm)],[f_4336_2]) ).

fof(f_4337_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_4337_2,plain,
    ! [U_17747,U_17746,U_17745,U_17744] :
      ( hAPP(c_List_Oset(U_17745),c_List_Olinorder__class_Osort__key(U_17745,U_17744,U_17746,U_17747)) = hAPP(c_List_Oset(U_17745),U_17747)
      | ~ class_Orderings_Olinorder(U_17744) ),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

cnf(f_4337_3,plain,
    ( hAPP(c_List_Oset(U_17745),c_List_Olinorder__class_Osort__key(U_17745,U_17744,U_17746,U_17747)) = hAPP(c_List_Oset(U_17745),U_17747)
    | ~ class_Orderings_Olinorder(U_17744) ),
    inference(clausify,[status(thm)],[f_4337_2]) ).

fof(f_4338_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_4338_2,plain,
    ! [U_17751,U_17750,U_17749,U_17748] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),c_List_Olinorder__class_Osort__key(U_17749,U_17748,U_17750,U_17751)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),U_17751)
      | ~ class_Orderings_Olinorder(U_17748) ),
    inference(variable_rename,[status(thm)],[f_4338_1]) ).

cnf(f_4338_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),c_List_Olinorder__class_Osort__key(U_17749,U_17748,U_17750,U_17751)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17749)),U_17751)
    | ~ class_Orderings_Olinorder(U_17748) ),
    inference(clausify,[status(thm)],[f_4338_2]) ).

fof(f_4339_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_4339_2,plain,
    ! [U_17755,U_17754,U_17753,U_17752] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_17753),c_List_Olinorder__class_Osort__key(U_17753,U_17752,U_17754,U_17755)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17753),U_17755)) )
        & ( hBOOL(hAPP(c_List_Odistinct(U_17753),U_17755))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17753),c_List_Olinorder__class_Osort__key(U_17753,U_17752,U_17754,U_17755))) ) )
      | ~ class_Orderings_Olinorder(U_17752) ),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

cnf(f_4339_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17753),U_17755))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17753),c_List_Olinorder__class_Osort__key(U_17753,U_17752,U_17754,U_17755)))
    | ~ class_Orderings_Olinorder(U_17752) ),
    inference(clausify,[status(thm)],[f_4339_2]) ).

cnf(f_4339_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17753),c_List_Olinorder__class_Osort__key(U_17753,U_17752,U_17754,U_17755)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17753),U_17755))
    | ~ class_Orderings_Olinorder(U_17752) ),
    inference(clausify,[status(thm)],[f_4339_2]) ).

fof(f_4340_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_4340_2,plain,
    ! [U_17756] : c_List_Oconcat(U_17756,c_List_Olist_ONil(tc_List_Olist(U_17756))) = c_List_Olist_ONil(U_17756),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

cnf(f_4340_3,plain,
    c_List_Oconcat(U_17756,c_List_Olist_ONil(tc_List_Olist(U_17756))) = c_List_Olist_ONil(U_17756),
    inference(clausify,[status(thm)],[f_4340_2]) ).

fof(f_4341_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_4341_2,plain,
    ! [U_17759,U_17758,U_17757] : c_List_Oconcat(U_17757,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17757)),U_17758),U_17759)) = hAPP(hAPP(c_List_Oappend(U_17757),U_17758),c_List_Oconcat(U_17757,U_17759)),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

cnf(f_4341_3,plain,
    c_List_Oconcat(U_17757,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17757)),U_17758),U_17759)) = hAPP(hAPP(c_List_Oappend(U_17757),U_17758),c_List_Oconcat(U_17757,U_17759)),
    inference(clausify,[status(thm)],[f_4341_2]) ).

fof(f_4342_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_4342_2,plain,
    ! [U_17763,U_17762] :
      ( ( c_List_Oconcat(U_17762,U_17763) = c_List_Olist_ONil(U_17762)
        | ? [U_17761] :
            ( U_17761 != c_List_Olist_ONil(U_17762)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17762)),U_17761),hAPP(c_List_Oset(tc_List_Olist(U_17762)),U_17763))) ) )
      & ( ! [U_17760] :
            ( U_17760 = c_List_Olist_ONil(U_17762)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17762)),U_17760),hAPP(c_List_Oset(tc_List_Olist(U_17762)),U_17763))) )
        | c_List_Oconcat(U_17762,U_17763) != c_List_Olist_ONil(U_17762) ) ),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

fof(f_4342_3,plain,
    ( ! [U_17767,U_17765] :
        ( c_List_Oconcat(U_17765,U_17767) = c_List_Olist_ONil(U_17765)
        | ? [U_17761] :
            ( U_17761 != c_List_Olist_ONil(U_17765)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17765)),U_17761),hAPP(c_List_Oset(tc_List_Olist(U_17765)),U_17767))) ) )
    & ! [U_17766,U_17764] :
        ( ! [U_17760] :
            ( U_17760 = c_List_Olist_ONil(U_17764)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17764)),U_17760),hAPP(c_List_Oset(tc_List_Olist(U_17764)),U_17766))) )
        | c_List_Oconcat(U_17764,U_17766) != c_List_Olist_ONil(U_17764) ) ),
    inference(miniscope,[status(thm)],[f_4342_2]) ).

fof(f_4342_4,plain,
    ( ! [U_17767,U_17765] :
        ( c_List_Oconcat(U_17765,U_17767) = c_List_Olist_ONil(U_17765)
        | ( sK434(U_17767,U_17765) != c_List_Olist_ONil(U_17765)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17765)),sK434(U_17767,U_17765)),hAPP(c_List_Oset(tc_List_Olist(U_17765)),U_17767))) ) )
    & ! [U_17766,U_17764] :
        ( ! [U_17760] :
            ( U_17760 = c_List_Olist_ONil(U_17764)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17764)),U_17760),hAPP(c_List_Oset(tc_List_Olist(U_17764)),U_17766))) )
        | c_List_Oconcat(U_17764,U_17766) != c_List_Olist_ONil(U_17764) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_17761,sK434(U_17767,U_17765))],[f_4342_3]) ).

cnf(f_4342_5,plain,
    ( U_17760 = c_List_Olist_ONil(U_17764)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17764)),U_17760),hAPP(c_List_Oset(tc_List_Olist(U_17764)),U_17766)))
    | c_List_Oconcat(U_17764,U_17766) != c_List_Olist_ONil(U_17764) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

cnf(f_4342_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17765)),sK434(U_17767,U_17765)),hAPP(c_List_Oset(tc_List_Olist(U_17765)),U_17767)))
    | c_List_Oconcat(U_17765,U_17767) = c_List_Olist_ONil(U_17765) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

cnf(f_4342_7,plain,
    ( sK434(U_17767,U_17765) != c_List_Olist_ONil(U_17765)
    | c_List_Oconcat(U_17765,U_17767) = c_List_Olist_ONil(U_17765) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

fof(f_4343_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_4343_2,plain,
    ! [U_17771,U_17770] :
      ( ( c_List_Olist_ONil(U_17770) = c_List_Oconcat(U_17770,U_17771)
        | ? [U_17769] :
            ( U_17769 != c_List_Olist_ONil(U_17770)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17770)),U_17769),hAPP(c_List_Oset(tc_List_Olist(U_17770)),U_17771))) ) )
      & ( ! [U_17768] :
            ( U_17768 = c_List_Olist_ONil(U_17770)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17770)),U_17768),hAPP(c_List_Oset(tc_List_Olist(U_17770)),U_17771))) )
        | c_List_Olist_ONil(U_17770) != c_List_Oconcat(U_17770,U_17771) ) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

fof(f_4343_3,plain,
    ( ! [U_17775,U_17773] :
        ( c_List_Olist_ONil(U_17773) = c_List_Oconcat(U_17773,U_17775)
        | ? [U_17769] :
            ( U_17769 != c_List_Olist_ONil(U_17773)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17773)),U_17769),hAPP(c_List_Oset(tc_List_Olist(U_17773)),U_17775))) ) )
    & ! [U_17774,U_17772] :
        ( ! [U_17768] :
            ( U_17768 = c_List_Olist_ONil(U_17772)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17772)),U_17768),hAPP(c_List_Oset(tc_List_Olist(U_17772)),U_17774))) )
        | c_List_Olist_ONil(U_17772) != c_List_Oconcat(U_17772,U_17774) ) ),
    inference(miniscope,[status(thm)],[f_4343_2]) ).

fof(f_4343_4,plain,
    ( ! [U_17775,U_17773] :
        ( c_List_Olist_ONil(U_17773) = c_List_Oconcat(U_17773,U_17775)
        | ( sK435(U_17775,U_17773) != c_List_Olist_ONil(U_17773)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17773)),sK435(U_17775,U_17773)),hAPP(c_List_Oset(tc_List_Olist(U_17773)),U_17775))) ) )
    & ! [U_17774,U_17772] :
        ( ! [U_17768] :
            ( U_17768 = c_List_Olist_ONil(U_17772)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17772)),U_17768),hAPP(c_List_Oset(tc_List_Olist(U_17772)),U_17774))) )
        | c_List_Olist_ONil(U_17772) != c_List_Oconcat(U_17772,U_17774) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_17769,sK435(U_17775,U_17773))],[f_4343_3]) ).

cnf(f_4343_5,plain,
    ( U_17768 = c_List_Olist_ONil(U_17772)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17772)),U_17768),hAPP(c_List_Oset(tc_List_Olist(U_17772)),U_17774)))
    | c_List_Olist_ONil(U_17772) != c_List_Oconcat(U_17772,U_17774) ),
    inference(clausify,[status(thm)],[f_4343_4]) ).

cnf(f_4343_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17773)),sK435(U_17775,U_17773)),hAPP(c_List_Oset(tc_List_Olist(U_17773)),U_17775)))
    | c_List_Olist_ONil(U_17773) = c_List_Oconcat(U_17773,U_17775) ),
    inference(clausify,[status(thm)],[f_4343_4]) ).

cnf(f_4343_7,plain,
    ( sK435(U_17775,U_17773) != c_List_Olist_ONil(U_17773)
    | c_List_Olist_ONil(U_17773) = c_List_Oconcat(U_17773,U_17775) ),
    inference(clausify,[status(thm)],[f_4343_4]) ).

fof(f_4344_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_4344_2,plain,
    ! [U_17779,U_17778,U_17777,U_17776] : hAPP(hAPP(c_List_Omap(U_17776,U_17777),U_17778),c_List_Oconcat(U_17776,U_17779)) = c_List_Oconcat(U_17777,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17776),tc_List_Olist(U_17777)),hAPP(c_List_Omap(U_17776,U_17777),U_17778)),U_17779)),
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

cnf(f_4344_3,plain,
    hAPP(hAPP(c_List_Omap(U_17776,U_17777),U_17778),c_List_Oconcat(U_17776,U_17779)) = c_List_Oconcat(U_17777,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17776),tc_List_Olist(U_17777)),hAPP(c_List_Omap(U_17776,U_17777),U_17778)),U_17779)),
    inference(clausify,[status(thm)],[f_4344_2]) ).

fof(f_4345_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_4345_2,plain,
    ! [U_17781,U_17780] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17780)),c_List_Oconcat(U_17780,U_17781)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17780),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_17780))),U_17781)),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

cnf(f_4345_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17780)),c_List_Oconcat(U_17780,U_17781)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17780),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_17780))),U_17781)),
    inference(clausify,[status(thm)],[f_4345_2]) ).

fof(f_4346_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_4346_2,plain,
    ! [U_17783,U_17782] : hAPP(c_List_Oset(U_17782),c_List_Oconcat(U_17782,U_17783)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17782),tc_fun(U_17782,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17782)),U_17783)),c_List_Oset(U_17782)),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

cnf(f_4346_3,plain,
    hAPP(c_List_Oset(U_17782),c_List_Oconcat(U_17782,U_17783)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17782),tc_fun(U_17782,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17782)),U_17783)),c_List_Oset(U_17782)),
    inference(clausify,[status(thm)],[f_4346_2]) ).

fof(f_4347_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_4347_2,plain,
    ! [U_17788,U_17787,U_17786,U_17785,U_17784] :
      ( c_List_Olinorder__class_Osort__key(U_17785,U_17784,U_17786,hAPP(hAPP(c_List_Olist_OCons(U_17785),U_17787),U_17788)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17785,U_17784,U_17786),U_17787),c_List_Olinorder__class_Osort__key(U_17785,U_17784,U_17786,U_17788))
      | ~ class_Orderings_Olinorder(U_17784) ),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

cnf(f_4347_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17785,U_17784,U_17786,hAPP(hAPP(c_List_Olist_OCons(U_17785),U_17787),U_17788)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17785,U_17784,U_17786),U_17787),c_List_Olinorder__class_Osort__key(U_17785,U_17784,U_17786,U_17788))
    | ~ class_Orderings_Olinorder(U_17784) ),
    inference(clausify,[status(thm)],[f_4347_2]) ).

fof(f_4348_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_4348_2,plain,
    ! [U_17791,U_17790,U_17789] : c_List_Oconcat(U_17789,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_17789)),U_17790),U_17791)) = hAPP(hAPP(c_List_Oappend(U_17789),c_List_Oconcat(U_17789,U_17790)),c_List_Oconcat(U_17789,U_17791)),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

cnf(f_4348_3,plain,
    c_List_Oconcat(U_17789,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_17789)),U_17790),U_17791)) = hAPP(hAPP(c_List_Oappend(U_17789),c_List_Oconcat(U_17789,U_17790)),c_List_Oconcat(U_17789,U_17791)),
    inference(clausify,[status(thm)],[f_4348_2]) ).

fof(f_4349_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_4349_2,plain,
    ! [U_17793,U_17792] :
      ( c_List_Olinorder__class_Osort__key(U_17792,U_17792,c_COMBI(U_17792),U_17793) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17792),U_17792,hAPP(c_COMBC(U_17792,tc_List_Olist(U_17792),tc_List_Olist(U_17792)),c_List_Olinorder__class_Oinsort__key(U_17792,U_17792,c_COMBI(U_17792))),c_List_Olist_ONil(U_17792)),U_17793)
      | ~ class_Orderings_Olinorder(U_17792) ),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

cnf(f_4349_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17792,U_17792,c_COMBI(U_17792),U_17793) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17792),U_17792,hAPP(c_COMBC(U_17792,tc_List_Olist(U_17792),tc_List_Olist(U_17792)),c_List_Olinorder__class_Oinsort__key(U_17792,U_17792,c_COMBI(U_17792))),c_List_Olist_ONil(U_17792)),U_17793)
    | ~ class_Orderings_Olinorder(U_17792) ),
    inference(clausify,[status(thm)],[f_4349_2]) ).

fof(f_4350_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_4350_2,plain,
    ! [U_17797,U_17796,U_17795] :
      ( ( ( c_List_Oconcat(U_17795,U_17796) = c_List_Oconcat(U_17795,U_17797)
          | U_17796 != U_17797 )
        & ( U_17796 = U_17797
          | c_List_Oconcat(U_17795,U_17796) != c_List_Oconcat(U_17795,U_17797) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
      | ? [U_17794] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),tc_List_Olist(U_17795)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17795)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)))),U_17794))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),U_17794),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17795),tc_List_Olist(U_17795)),U_17796),U_17797)))) ) ),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

fof(f_4350_3,plain,
    ! [U_17797,U_17796,U_17795] :
      ( ( ( c_List_Oconcat(U_17795,U_17796) = c_List_Oconcat(U_17795,U_17797)
          | U_17796 != U_17797 )
        & ( U_17796 = U_17797
          | c_List_Oconcat(U_17795,U_17796) != c_List_Oconcat(U_17795,U_17797) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),tc_List_Olist(U_17795)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17795)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)))),sK436(U_17797,U_17796,U_17795)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),sK436(U_17797,U_17796,U_17795)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17795),tc_List_Olist(U_17795)),U_17796),U_17797)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_17794,sK436(U_17797,U_17796,U_17795))],[f_4350_2]) ).

cnf(f_4350_4,plain,
    ( U_17796 = U_17797
    | c_List_Oconcat(U_17795,U_17796) != c_List_Oconcat(U_17795,U_17797)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),sK436(U_17797,U_17796,U_17795)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17795),tc_List_Olist(U_17795)),U_17796),U_17797)))) ),
    inference(clausify,[status(thm)],[f_4350_3]) ).

cnf(f_4350_5,plain,
    ( c_List_Oconcat(U_17795,U_17796) = c_List_Oconcat(U_17795,U_17797)
    | U_17796 != U_17797
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),sK436(U_17797,U_17796,U_17795)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17795),tc_List_Olist(U_17795))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17795),tc_List_Olist(U_17795)),U_17796),U_17797)))) ),
    inference(clausify,[status(thm)],[f_4350_3]) ).

cnf(f_4350_6,plain,
    ( U_17796 = U_17797
    | c_List_Oconcat(U_17795,U_17796) != c_List_Oconcat(U_17795,U_17797)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),tc_List_Olist(U_17795)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17795)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)))),sK436(U_17797,U_17796,U_17795))) ),
    inference(clausify,[status(thm)],[f_4350_3]) ).

cnf(f_4350_7,plain,
    ( c_List_Oconcat(U_17795,U_17796) = c_List_Oconcat(U_17795,U_17797)
    | U_17796 != U_17797
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17796) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17795))),U_17797)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17795),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17795),tc_HOL_Obool)),tc_List_Olist(U_17795)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17795)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17795)))),sK436(U_17797,U_17796,U_17795))) ),
    inference(clausify,[status(thm)],[f_4350_3]) ).

fof(f_4351_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_4351_2,plain,
    ! [U_17801,U_17800,U_17799] :
      ( U_17800 = U_17801
      | ? [U_17798] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17799),tc_List_Olist(U_17799),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17799),tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),tc_List_Olist(U_17799)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17799))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17799)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799)))),U_17798))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),U_17798),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17799),tc_List_Olist(U_17799)),U_17800),U_17801)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17800) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17801)
      | c_List_Oconcat(U_17799,U_17800) != c_List_Oconcat(U_17799,U_17801) ),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

fof(f_4351_3,plain,
    ! [U_17801,U_17800,U_17799] :
      ( U_17800 = U_17801
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17799),tc_List_Olist(U_17799),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17799),tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),tc_List_Olist(U_17799)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17799))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17799)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799)))),sK437(U_17801,U_17800,U_17799)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),sK437(U_17801,U_17800,U_17799)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17799),tc_List_Olist(U_17799)),U_17800),U_17801)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17800) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17801)
      | c_List_Oconcat(U_17799,U_17800) != c_List_Oconcat(U_17799,U_17801) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_17798,sK437(U_17801,U_17800,U_17799))],[f_4351_2]) ).

cnf(f_4351_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),sK437(U_17801,U_17800,U_17799)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17799),tc_List_Olist(U_17799))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17799),tc_List_Olist(U_17799)),U_17800),U_17801))))
    | U_17800 = U_17801
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17800) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17801)
    | c_List_Oconcat(U_17799,U_17800) != c_List_Oconcat(U_17799,U_17801) ),
    inference(clausify,[status(thm)],[f_4351_3]) ).

cnf(f_4351_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17799),tc_List_Olist(U_17799),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17799),tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17799),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17799),tc_HOL_Obool)),tc_List_Olist(U_17799)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17799))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17799)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17799)))),sK437(U_17801,U_17800,U_17799)))
    | U_17800 = U_17801
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17800) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17799))),U_17801)
    | c_List_Oconcat(U_17799,U_17800) != c_List_Oconcat(U_17799,U_17801) ),
    inference(clausify,[status(thm)],[f_4351_3]) ).

fof(f_4352_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_4352_2,plain,
    ! [U_17805,U_17804,U_17803,U_17802] : c_List_Oconcat(U_17802,hAPP(hAPP(c_List_Omap(U_17803,tc_List_Olist(U_17802)),hAPP(hAPP(c_COMBC(U_17803,tc_List_Olist(U_17802),tc_List_Olist(U_17802)),hAPP(hAPP(c_COMBB(U_17802,tc_fun(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),U_17803),c_List_Olist_OCons(U_17802)),U_17804)),c_List_Olist_ONil(U_17802))),U_17805)) = hAPP(hAPP(c_List_Omap(U_17803,U_17802),U_17804),U_17805),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

cnf(f_4352_3,plain,
    c_List_Oconcat(U_17802,hAPP(hAPP(c_List_Omap(U_17803,tc_List_Olist(U_17802)),hAPP(hAPP(c_COMBC(U_17803,tc_List_Olist(U_17802),tc_List_Olist(U_17802)),hAPP(hAPP(c_COMBB(U_17802,tc_fun(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),U_17803),c_List_Olist_OCons(U_17802)),U_17804)),c_List_Olist_ONil(U_17802))),U_17805)) = hAPP(hAPP(c_List_Omap(U_17803,U_17802),U_17804),U_17805),
    inference(clausify,[status(thm)],[f_4352_2]) ).

fof(f_4353_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_4353_2,plain,
    ! [U_17808,U_17807,U_17806] : c_Enum_On__lists(U_17806,hAPP(c_Nat_OSuc,U_17807),U_17808) = c_List_Oconcat(tc_List_Olist(U_17806),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17806),tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),hAPP(hAPP(c_COMBB(tc_fun(U_17806,tc_List_Olist(U_17806)),tc_fun(tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),tc_List_Olist(U_17806)),c_List_Omap(U_17806,tc_List_Olist(U_17806))),hAPP(c_COMBC(U_17806,tc_List_Olist(U_17806),tc_List_Olist(U_17806)),c_List_Olist_OCons(U_17806)))),U_17808)),c_Enum_On__lists(U_17806,U_17807,U_17808))),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

cnf(f_4353_3,plain,
    c_Enum_On__lists(U_17806,hAPP(c_Nat_OSuc,U_17807),U_17808) = c_List_Oconcat(tc_List_Olist(U_17806),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17806),tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),hAPP(hAPP(c_COMBB(tc_fun(U_17806,tc_List_Olist(U_17806)),tc_fun(tc_List_Olist(U_17806),tc_List_Olist(tc_List_Olist(U_17806))),tc_List_Olist(U_17806)),c_List_Omap(U_17806,tc_List_Olist(U_17806))),hAPP(c_COMBC(U_17806,tc_List_Olist(U_17806),tc_List_Olist(U_17806)),c_List_Olist_OCons(U_17806)))),U_17808)),c_Enum_On__lists(U_17806,U_17807,U_17808))),
    inference(clausify,[status(thm)],[f_4353_2]) ).

fof(f_4354_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_4354_2,plain,
    ! [U_17812,U_17811,U_17810,U_17809] : c_List_Otranspose(U_17809,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),U_17811)),U_17812)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),c_List_Oconcat(U_17809,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17809),tc_List_Olist(U_17809)),c_List_Olist_Olist__case(tc_List_Olist(U_17809),U_17809,c_List_Olist_ONil(U_17809),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17809),tc_fun(tc_List_Olist(U_17809),tc_List_Olist(U_17809)),U_17809),c_COMBK(tc_List_Olist(U_17809),tc_List_Olist(U_17809))),hAPP(hAPP(c_COMBC(U_17809,tc_List_Olist(U_17809),tc_List_Olist(U_17809)),c_List_Olist_OCons(U_17809)),c_List_Olist_ONil(U_17809))))),U_17812)))),c_List_Otranspose(U_17809,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),U_17811),c_List_Oconcat(tc_List_Olist(U_17809),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17809)),U_17809,c_List_Olist_ONil(tc_List_Olist(U_17809)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809))),U_17809),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809)),tc_List_Olist(tc_List_Olist(U_17809))),c_List_Olist_OCons(tc_List_Olist(U_17809))),c_List_Olist_ONil(tc_List_Olist(U_17809)))))),U_17812))))),
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

cnf(f_4354_3,plain,
    c_List_Otranspose(U_17809,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),U_17811)),U_17812)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),c_List_Oconcat(U_17809,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17809),tc_List_Olist(U_17809)),c_List_Olist_Olist__case(tc_List_Olist(U_17809),U_17809,c_List_Olist_ONil(U_17809),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17809),tc_fun(tc_List_Olist(U_17809),tc_List_Olist(U_17809)),U_17809),c_COMBK(tc_List_Olist(U_17809),tc_List_Olist(U_17809))),hAPP(hAPP(c_COMBC(U_17809,tc_List_Olist(U_17809),tc_List_Olist(U_17809)),c_List_Olist_OCons(U_17809)),c_List_Olist_ONil(U_17809))))),U_17812)))),c_List_Otranspose(U_17809,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17809)),U_17811),c_List_Oconcat(tc_List_Olist(U_17809),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17809)),U_17809,c_List_Olist_ONil(tc_List_Olist(U_17809)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809))),U_17809),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17809),tc_List_Olist(tc_List_Olist(U_17809)),tc_List_Olist(tc_List_Olist(U_17809))),c_List_Olist_OCons(tc_List_Olist(U_17809))),c_List_Olist_ONil(tc_List_Olist(U_17809)))))),U_17812))))),
    inference(clausify,[status(thm)],[f_4354_2]) ).

fof(f_4355_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_4355_2,plain,
    ! [U_17814,U_17813] : c_List_Oconcat(U_17813,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17813),tc_List_Olist(U_17813)),c_List_Olist_Olist__case(tc_List_Olist(U_17813),U_17813,c_List_Olist_ONil(U_17813),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17813),tc_fun(tc_List_Olist(U_17813),tc_List_Olist(U_17813)),U_17813),c_COMBK(tc_List_Olist(U_17813),tc_List_Olist(U_17813))),hAPP(hAPP(c_COMBC(U_17813,tc_List_Olist(U_17813),tc_List_Olist(U_17813)),c_List_Olist_OCons(U_17813)),c_List_Olist_ONil(U_17813))))),U_17814)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17813),U_17813),c_List_Ohd(U_17813)),hAPP(c_List_Ofilter(tc_List_Olist(U_17813),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17813)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17813),tc_List_Olist(U_17813),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17813)))),U_17814)),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

cnf(f_4355_3,plain,
    c_List_Oconcat(U_17813,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17813),tc_List_Olist(U_17813)),c_List_Olist_Olist__case(tc_List_Olist(U_17813),U_17813,c_List_Olist_ONil(U_17813),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17813),tc_fun(tc_List_Olist(U_17813),tc_List_Olist(U_17813)),U_17813),c_COMBK(tc_List_Olist(U_17813),tc_List_Olist(U_17813))),hAPP(hAPP(c_COMBC(U_17813,tc_List_Olist(U_17813),tc_List_Olist(U_17813)),c_List_Olist_OCons(U_17813)),c_List_Olist_ONil(U_17813))))),U_17814)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17813),U_17813),c_List_Ohd(U_17813)),hAPP(c_List_Ofilter(tc_List_Olist(U_17813),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17813)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17813),tc_List_Olist(U_17813),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17813)))),U_17814)),
    inference(clausify,[status(thm)],[f_4355_2]) ).

fof(f_4356_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_4356_2,plain,
    ! [U_17817,U_17816,U_17815] : hAPP(c_List_Ofilter(U_17815,U_17816),c_List_Oconcat(U_17815,U_17817)) = c_List_Oconcat(U_17815,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17815),tc_List_Olist(U_17815)),c_List_Ofilter(U_17815,U_17816)),U_17817)),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

cnf(f_4356_3,plain,
    hAPP(c_List_Ofilter(U_17815,U_17816),c_List_Oconcat(U_17815,U_17817)) = c_List_Oconcat(U_17815,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17815),tc_List_Olist(U_17815)),c_List_Ofilter(U_17815,U_17816)),U_17817)),
    inference(clausify,[status(thm)],[f_4356_2]) ).

fof(f_4357_1,plain,
    ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__sort]) ).

fof(f_4357_2,plain,
    ! [U_17822,U_17821,U_17820,U_17819,U_17818] :
      ( hAPP(c_List_Ofilter(U_17819,U_17820),c_List_Olinorder__class_Osort__key(U_17819,U_17818,U_17821,U_17822)) = c_List_Olinorder__class_Osort__key(U_17819,U_17818,U_17821,hAPP(c_List_Ofilter(U_17819,U_17820),U_17822))
      | ~ class_Orderings_Olinorder(U_17818) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

cnf(f_4357_3,plain,
    ( hAPP(c_List_Ofilter(U_17819,U_17820),c_List_Olinorder__class_Osort__key(U_17819,U_17818,U_17821,U_17822)) = c_List_Olinorder__class_Osort__key(U_17819,U_17818,U_17821,hAPP(c_List_Ofilter(U_17819,U_17820),U_17822))
    | ~ class_Orderings_Olinorder(U_17818) ),
    inference(clausify,[status(thm)],[f_4357_2]) ).

fof(f_4358_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__filter]) ).

fof(f_4358_2,plain,
    ! [U_17825,U_17824,U_17823] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17823),hAPP(c_List_Ofilter(U_17823,U_17825),U_17824)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17823),U_17824)) ),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

cnf(f_4358_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17823),hAPP(c_List_Ofilter(U_17823,U_17825),U_17824)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17823),U_17824)) ),
    inference(clausify,[status(thm)],[f_4358_2]) ).

fof(f_4359_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_4359_2,plain,
    ! [U_17828,U_17827,U_17826] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),hAPP(c_List_Ofilter(U_17826,U_17827),U_17828))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828))),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

cnf(f_4359_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),hAPP(c_List_Ofilter(U_17826,U_17827),U_17828))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17826)),U_17828))),
    inference(clausify,[status(thm)],[f_4359_2]) ).

fof(f_4360_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_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_4360_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_4360_1]) ).

cnf(f_4360_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_4360_2]) ).

fof(f_4361_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2),V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__id__conv]) ).

fof(f_4361_2,plain,
    ! [U_17836,U_17835,U_17834] :
      ( ( hAPP(c_List_Ofilter(U_17834,U_17835),U_17836) = U_17836
        | ? [U_17833] :
            ( ~ hBOOL(hAPP(U_17835,U_17833))
            & hBOOL(hAPP(hAPP(c_member(U_17834),U_17833),hAPP(c_List_Oset(U_17834),U_17836))) ) )
      & ( ! [U_17832] :
            ( hBOOL(hAPP(U_17835,U_17832))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17834),U_17832),hAPP(c_List_Oset(U_17834),U_17836))) )
        | hAPP(c_List_Ofilter(U_17834,U_17835),U_17836) != U_17836 ) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

fof(f_4361_3,plain,
    ( ! [U_17842,U_17840,U_17838] :
        ( hAPP(c_List_Ofilter(U_17838,U_17840),U_17842) = U_17842
        | ? [U_17833] :
            ( ~ hBOOL(hAPP(U_17840,U_17833))
            & hBOOL(hAPP(hAPP(c_member(U_17838),U_17833),hAPP(c_List_Oset(U_17838),U_17842))) ) )
    & ! [U_17841,U_17839,U_17837] :
        ( ! [U_17832] :
            ( hBOOL(hAPP(U_17839,U_17832))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17837),U_17832),hAPP(c_List_Oset(U_17837),U_17841))) )
        | hAPP(c_List_Ofilter(U_17837,U_17839),U_17841) != U_17841 ) ),
    inference(miniscope,[status(thm)],[f_4361_2]) ).

fof(f_4361_4,plain,
    ( ! [U_17842,U_17840,U_17838] :
        ( hAPP(c_List_Ofilter(U_17838,U_17840),U_17842) = U_17842
        | ( ~ hBOOL(hAPP(U_17840,sK438(U_17842,U_17840,U_17838)))
          & hBOOL(hAPP(hAPP(c_member(U_17838),sK438(U_17842,U_17840,U_17838)),hAPP(c_List_Oset(U_17838),U_17842))) ) )
    & ! [U_17841,U_17839,U_17837] :
        ( ! [U_17832] :
            ( hBOOL(hAPP(U_17839,U_17832))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17837),U_17832),hAPP(c_List_Oset(U_17837),U_17841))) )
        | hAPP(c_List_Ofilter(U_17837,U_17839),U_17841) != U_17841 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_17833,sK438(U_17842,U_17840,U_17838))],[f_4361_3]) ).

cnf(f_4361_5,plain,
    ( hBOOL(hAPP(U_17839,U_17832))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17837),U_17832),hAPP(c_List_Oset(U_17837),U_17841)))
    | hAPP(c_List_Ofilter(U_17837,U_17839),U_17841) != U_17841 ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

cnf(f_4361_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17838),sK438(U_17842,U_17840,U_17838)),hAPP(c_List_Oset(U_17838),U_17842)))
    | hAPP(c_List_Ofilter(U_17838,U_17840),U_17842) = U_17842 ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

cnf(f_4361_7,plain,
    ( ~ hBOOL(hAPP(U_17840,sK438(U_17842,U_17840,U_17838)))
    | hAPP(c_List_Ofilter(U_17838,U_17840),U_17842) = U_17842 ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

fof(f_4362_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_filter__is__subset]) ).

fof(f_4362_2,plain,
    ! [U_17845,U_17844,U_17843] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17843,tc_HOL_Obool)),hAPP(c_List_Oset(U_17843),hAPP(c_List_Ofilter(U_17843,U_17844),U_17845))),hAPP(c_List_Oset(U_17843),U_17845))),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

cnf(f_4362_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17843,tc_HOL_Obool)),hAPP(c_List_Oset(U_17843),hAPP(c_List_Ofilter(U_17843,U_17844),U_17845))),hAPP(c_List_Oset(U_17843),U_17845))),
    inference(clausify,[status(thm)],[f_4362_2]) ).

fof(f_4363_1,plain,
    ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__remove1]) ).

fof(f_4363_2,plain,
    ! [U_17849,U_17848,U_17847,U_17846] : hAPP(c_List_Ofilter(U_17846,U_17847),c_List_Oremove1(U_17846,U_17848,U_17849)) = c_List_Oremove1(U_17846,U_17848,hAPP(c_List_Ofilter(U_17846,U_17847),U_17849)),
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

cnf(f_4363_3,plain,
    hAPP(c_List_Ofilter(U_17846,U_17847),c_List_Oremove1(U_17846,U_17848,U_17849)) = c_List_Oremove1(U_17846,U_17848,hAPP(c_List_Ofilter(U_17846,U_17847),U_17849)),
    inference(clausify,[status(thm)],[f_4363_2]) ).

fof(f_4364_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__filter__not]) ).

fof(f_4364_2,plain,
    ! [U_17853,U_17852,U_17851,U_17850] :
      ( c_List_Oremove1(U_17852,U_17851,hAPP(c_List_Ofilter(U_17852,U_17850),U_17853)) = hAPP(c_List_Ofilter(U_17852,U_17850),U_17853)
      | hBOOL(hAPP(U_17850,U_17851)) ),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

cnf(f_4364_3,plain,
    ( c_List_Oremove1(U_17852,U_17851,hAPP(c_List_Ofilter(U_17852,U_17850),U_17853)) = hAPP(c_List_Ofilter(U_17852,U_17850),U_17853)
    | hBOOL(hAPP(U_17850,U_17851)) ),
    inference(clausify,[status(thm)],[f_4364_2]) ).

fof(f_4365_1,plain,
    ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2)),V_Pa_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_filter__filter]) ).

fof(f_4365_2,plain,
    ! [U_17857,U_17856,U_17855,U_17854] : hAPP(c_List_Ofilter(U_17854,U_17855),hAPP(c_List_Ofilter(U_17854,U_17856),U_17857)) = hAPP(c_List_Ofilter(U_17854,hAPP(hAPP(c_COMBS(U_17854,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17854),c_fconj),U_17856)),U_17855)),U_17857),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

cnf(f_4365_3,plain,
    hAPP(c_List_Ofilter(U_17854,U_17855),hAPP(c_List_Ofilter(U_17854,U_17856),U_17857)) = hAPP(c_List_Ofilter(U_17854,hAPP(hAPP(c_COMBS(U_17854,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17854),c_fconj),U_17856)),U_17855)),U_17857),
    inference(clausify,[status(thm)],[f_4365_2]) ).

fof(f_4366_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort__triv]) ).

fof(f_4366_2,plain,
    ! [U_17863,U_17862,U_17861,U_17860,U_17859,U_17858] :
      ( hAPP(c_List_Ofilter(U_17861,U_17859),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17861,U_17858,U_17862),U_17860),U_17863)) = hAPP(c_List_Ofilter(U_17861,U_17859),U_17863)
      | hBOOL(hAPP(U_17859,U_17860))
      | ~ class_Orderings_Olinorder(U_17858) ),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

cnf(f_4366_3,plain,
    ( hAPP(c_List_Ofilter(U_17861,U_17859),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17861,U_17858,U_17862),U_17860),U_17863)) = hAPP(c_List_Ofilter(U_17861,U_17859),U_17863)
    | hBOOL(hAPP(U_17859,U_17860))
    | ~ class_Orderings_Olinorder(U_17858) ),
    inference(clausify,[status(thm)],[f_4366_2]) ).

fof(f_4367_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter1]) ).

fof(f_4367_2,plain,
    ! [U_17866,U_17865,U_17864] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_17864),tc_List_Olist(U_17864)),c_List_Opartition(U_17864,U_17865,U_17866)) = hAPP(c_List_Ofilter(U_17864,U_17865),U_17866),
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

cnf(f_4367_3,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_17864),tc_List_Olist(U_17864)),c_List_Opartition(U_17864,U_17865,U_17866)) = hAPP(c_List_Ofilter(U_17864,U_17865),U_17866),
    inference(clausify,[status(thm)],[f_4367_2]) ).

fof(f_4368_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__map]) ).

fof(f_4368_2,plain,
    ! [U_17871,U_17870,U_17869,U_17868,U_17867] : hAPP(c_List_Ofilter(U_17867,U_17868),hAPP(hAPP(c_List_Omap(U_17869,U_17867),U_17870),U_17871)) = hAPP(hAPP(c_List_Omap(U_17869,U_17867),U_17870),hAPP(c_List_Ofilter(U_17869,hAPP(c_Fun_Ocomp(U_17867,tc_HOL_Obool,U_17869,U_17868),U_17870)),U_17871)),
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

cnf(f_4368_3,plain,
    hAPP(c_List_Ofilter(U_17867,U_17868),hAPP(hAPP(c_List_Omap(U_17869,U_17867),U_17870),U_17871)) = hAPP(hAPP(c_List_Omap(U_17869,U_17867),U_17870),hAPP(c_List_Ofilter(U_17869,hAPP(c_Fun_Ocomp(U_17867,tc_HOL_Obool,U_17869,U_17868),U_17870)),U_17871)),
    inference(clausify,[status(thm)],[f_4368_2]) ).

fof(f_4369_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__append]) ).

fof(f_4369_2,plain,
    ! [U_17875,U_17874,U_17873,U_17872] : hAPP(c_List_Ofilter(U_17872,U_17873),hAPP(hAPP(c_List_Oappend(U_17872),U_17874),U_17875)) = hAPP(hAPP(c_List_Oappend(U_17872),hAPP(c_List_Ofilter(U_17872,U_17873),U_17874)),hAPP(c_List_Ofilter(U_17872,U_17873),U_17875)),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

cnf(f_4369_3,plain,
    hAPP(c_List_Ofilter(U_17872,U_17873),hAPP(hAPP(c_List_Oappend(U_17872),U_17874),U_17875)) = hAPP(hAPP(c_List_Oappend(U_17872),hAPP(c_List_Ofilter(U_17872,U_17873),U_17874)),hAPP(c_List_Ofilter(U_17872,U_17873),U_17875)),
    inference(clausify,[status(thm)],[f_4369_2]) ).

fof(f_4370_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(f_4370_2,plain,
    ! [U_17879,U_17878,U_17877,U_17876] :
      ( ( hAPP(c_List_Ofilter(U_17878,U_17876),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17877),U_17879)) = hAPP(c_List_Ofilter(U_17878,U_17876),U_17879)
        | hBOOL(hAPP(U_17876,U_17877)) )
      & ( hAPP(c_List_Ofilter(U_17878,U_17876),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17877),U_17879)) = hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17877),hAPP(c_List_Ofilter(U_17878,U_17876),U_17879))
        | ~ hBOOL(hAPP(U_17876,U_17877)) ) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

fof(f_4370_3,plain,
    ( ! [U_17887,U_17885,U_17883,U_17881] :
        ( hAPP(c_List_Ofilter(U_17885,U_17881),hAPP(hAPP(c_List_Olist_OCons(U_17885),U_17883),U_17887)) = hAPP(c_List_Ofilter(U_17885,U_17881),U_17887)
        | hBOOL(hAPP(U_17881,U_17883)) )
    & ! [U_17886,U_17884,U_17882,U_17880] :
        ( hAPP(c_List_Ofilter(U_17884,U_17880),hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17882),U_17886)) = hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17882),hAPP(c_List_Ofilter(U_17884,U_17880),U_17886))
        | ~ hBOOL(hAPP(U_17880,U_17882)) ) ),
    inference(miniscope,[status(thm)],[f_4370_2]) ).

cnf(f_4370_4,plain,
    ( hAPP(c_List_Ofilter(U_17884,U_17880),hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17882),U_17886)) = hAPP(hAPP(c_List_Olist_OCons(U_17884),U_17882),hAPP(c_List_Ofilter(U_17884,U_17880),U_17886))
    | ~ hBOOL(hAPP(U_17880,U_17882)) ),
    inference(clausify,[status(thm)],[f_4370_3]) ).

cnf(f_4370_5,plain,
    ( hAPP(c_List_Ofilter(U_17885,U_17881),hAPP(hAPP(c_List_Olist_OCons(U_17885),U_17883),U_17887)) = hAPP(c_List_Ofilter(U_17885,U_17881),U_17887)
    | hBOOL(hAPP(U_17881,U_17883)) ),
    inference(clausify,[status(thm)],[f_4370_3]) ).

fof(f_4371_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_4371_2,plain,
    ! [U_17889,U_17888] : hAPP(c_List_Ofilter(U_17888,U_17889),c_List_Olist_ONil(U_17888)) = c_List_Olist_ONil(U_17888),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

cnf(f_4371_3,plain,
    hAPP(c_List_Ofilter(U_17888,U_17889),c_List_Olist_ONil(U_17888)) = c_List_Olist_ONil(U_17888),
    inference(clausify,[status(thm)],[f_4371_2]) ).

fof(f_4372_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_4372_2,plain,
    ! [U_17890] : c_List_Otranspose(U_17890,c_List_Olist_ONil(tc_List_Olist(U_17890))) = c_List_Olist_ONil(tc_List_Olist(U_17890)),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

cnf(f_4372_3,plain,
    c_List_Otranspose(U_17890,c_List_Olist_ONil(tc_List_Olist(U_17890))) = c_List_Olist_ONil(tc_List_Olist(U_17890)),
    inference(clausify,[status(thm)],[f_4372_2]) ).

fof(f_4373_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__empty__conv]) ).

fof(f_4373_2,plain,
    ! [U_17895,U_17894,U_17893] :
      ( ( hAPP(c_List_Ofilter(U_17893,U_17894),U_17895) = c_List_Olist_ONil(U_17893)
        | ? [U_17892] :
            ( hBOOL(hAPP(U_17894,U_17892))
            & hBOOL(hAPP(hAPP(c_member(U_17893),U_17892),hAPP(c_List_Oset(U_17893),U_17895))) ) )
      & ( ! [U_17891] :
            ( ~ hBOOL(hAPP(U_17894,U_17891))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17893),U_17891),hAPP(c_List_Oset(U_17893),U_17895))) )
        | hAPP(c_List_Ofilter(U_17893,U_17894),U_17895) != c_List_Olist_ONil(U_17893) ) ),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

fof(f_4373_3,plain,
    ( ! [U_17901,U_17899,U_17897] :
        ( hAPP(c_List_Ofilter(U_17897,U_17899),U_17901) = c_List_Olist_ONil(U_17897)
        | ? [U_17892] :
            ( hBOOL(hAPP(U_17899,U_17892))
            & hBOOL(hAPP(hAPP(c_member(U_17897),U_17892),hAPP(c_List_Oset(U_17897),U_17901))) ) )
    & ! [U_17900,U_17898,U_17896] :
        ( ! [U_17891] :
            ( ~ hBOOL(hAPP(U_17898,U_17891))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17896),U_17891),hAPP(c_List_Oset(U_17896),U_17900))) )
        | hAPP(c_List_Ofilter(U_17896,U_17898),U_17900) != c_List_Olist_ONil(U_17896) ) ),
    inference(miniscope,[status(thm)],[f_4373_2]) ).

fof(f_4373_4,plain,
    ( ! [U_17901,U_17899,U_17897] :
        ( hAPP(c_List_Ofilter(U_17897,U_17899),U_17901) = c_List_Olist_ONil(U_17897)
        | ( hBOOL(hAPP(U_17899,sK439(U_17901,U_17899,U_17897)))
          & hBOOL(hAPP(hAPP(c_member(U_17897),sK439(U_17901,U_17899,U_17897)),hAPP(c_List_Oset(U_17897),U_17901))) ) )
    & ! [U_17900,U_17898,U_17896] :
        ( ! [U_17891] :
            ( ~ hBOOL(hAPP(U_17898,U_17891))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17896),U_17891),hAPP(c_List_Oset(U_17896),U_17900))) )
        | hAPP(c_List_Ofilter(U_17896,U_17898),U_17900) != c_List_Olist_ONil(U_17896) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_17892,sK439(U_17901,U_17899,U_17897))],[f_4373_3]) ).

cnf(f_4373_5,plain,
    ( ~ hBOOL(hAPP(U_17898,U_17891))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17896),U_17891),hAPP(c_List_Oset(U_17896),U_17900)))
    | hAPP(c_List_Ofilter(U_17896,U_17898),U_17900) != c_List_Olist_ONil(U_17896) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17897),sK439(U_17901,U_17899,U_17897)),hAPP(c_List_Oset(U_17897),U_17901)))
    | hAPP(c_List_Ofilter(U_17897,U_17899),U_17901) = c_List_Olist_ONil(U_17897) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_7,plain,
    ( hBOOL(hAPP(U_17899,sK439(U_17901,U_17899,U_17897)))
    | hAPP(c_List_Ofilter(U_17897,U_17899),U_17901) = c_List_Olist_ONil(U_17897) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

fof(f_4374_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__filter]) ).

fof(f_4374_2,plain,
    ! [U_17904,U_17903,U_17902] : c_List_Oremdups(U_17902,hAPP(c_List_Ofilter(U_17902,U_17903),U_17904)) = hAPP(c_List_Ofilter(U_17902,U_17903),c_List_Oremdups(U_17902,U_17904)),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

cnf(f_4374_3,plain,
    c_List_Oremdups(U_17902,hAPP(c_List_Ofilter(U_17902,U_17903),U_17904)) = hAPP(c_List_Ofilter(U_17902,U_17903),c_List_Oremdups(U_17902,U_17904)),
    inference(clausify,[status(thm)],[f_4374_2]) ).

fof(f_4375_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll__filter__not]) ).

fof(f_4375_2,plain,
    ! [U_17908,U_17907,U_17906,U_17905] :
      ( hAPP(c_List_OremoveAll(U_17907,U_17906),hAPP(c_List_Ofilter(U_17907,U_17905),U_17908)) = hAPP(c_List_Ofilter(U_17907,U_17905),U_17908)
      | hBOOL(hAPP(U_17905,U_17906)) ),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

cnf(f_4375_3,plain,
    ( hAPP(c_List_OremoveAll(U_17907,U_17906),hAPP(c_List_Ofilter(U_17907,U_17905),U_17908)) = hAPP(c_List_Ofilter(U_17907,U_17905),U_17908)
    | hBOOL(hAPP(U_17905,U_17906)) ),
    inference(clausify,[status(thm)],[f_4375_2]) ).

fof(f_4376_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_4376_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_4376_1]) ).

cnf(f_4376_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_4376_2]) ).

fof(f_4377_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_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_Pa_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter2]) ).

fof(f_4377_2,plain,
    ! [U_17913,U_17912,U_17911] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_17911),tc_List_Olist(U_17911)),c_List_Opartition(U_17911,U_17912,U_17913)) = hAPP(c_List_Ofilter(U_17911,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17911,c_fNot),U_17912)),U_17913),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

cnf(f_4377_3,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_17911),tc_List_Olist(U_17911)),c_List_Opartition(U_17911,U_17912,U_17913)) = hAPP(c_List_Ofilter(U_17911,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17911,c_fNot),U_17912)),U_17913),
    inference(clausify,[status(thm)],[f_4377_2]) ).

fof(f_4378_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_4378_2,plain,
    ! [U_17915,U_17914] : c_List_Otranspose(U_17914,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17914)),c_List_Olist_ONil(U_17914)),U_17915)) = c_List_Otranspose(U_17914,U_17915),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

cnf(f_4378_3,plain,
    c_List_Otranspose(U_17914,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17914)),c_List_Olist_ONil(U_17914)),U_17915)) = c_List_Otranspose(U_17914,U_17915),
    inference(clausify,[status(thm)],[f_4378_2]) ).

fof(f_4379_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_4379_2,plain,
    ! [U_17918,U_17917,U_17916] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_17917)),c_List_Otranspose(U_17917,U_17918)),U_17916) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),U_17917),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17917),tc_Nat_Onat,U_17917),c_List_Onth(U_17917)),U_17916)),hAPP(c_List_Ofilter(tc_List_Olist(U_17917),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17917)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17916)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17917)))),U_17918))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17916),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17917))),c_List_Otranspose(U_17917,U_17918)))) ),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

cnf(f_4379_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_17917)),c_List_Otranspose(U_17917,U_17918)),U_17916) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),U_17917),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17917),tc_Nat_Onat,U_17917),c_List_Onth(U_17917)),U_17916)),hAPP(c_List_Ofilter(tc_List_Olist(U_17917),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17917)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17916)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17917)))),U_17918))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17916),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17917))),c_List_Otranspose(U_17917,U_17918)))) ),
    inference(clausify,[status(thm)],[f_4379_2]) ).

fof(f_4380_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_4380_2,plain,
    ! [U_17922,U_17921,U_17920,U_17919] : c_List_Otranspose(U_17919,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17920),tc_List_Olist(U_17919)),hAPP(c_List_Omap(U_17920,U_17919),U_17921)),U_17922)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17920),tc_List_Olist(U_17919)),hAPP(c_List_Omap(U_17920,U_17919),U_17921)),c_List_Otranspose(U_17920,U_17922)),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

cnf(f_4380_3,plain,
    c_List_Otranspose(U_17919,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17920),tc_List_Olist(U_17919)),hAPP(c_List_Omap(U_17920,U_17919),U_17921)),U_17922)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17920),tc_List_Olist(U_17919)),hAPP(c_List_Omap(U_17920,U_17919),U_17921)),c_List_Otranspose(U_17920,U_17922)),
    inference(clausify,[status(thm)],[f_4380_2]) ).

fof(f_4381_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_set__filter]) ).

fof(f_4381_2,plain,
    ! [U_17925,U_17924,U_17923] : hAPP(c_List_Oset(U_17923),hAPP(c_List_Ofilter(U_17923,U_17924),U_17925)) = hAPP(c_Set_OCollect(U_17923),hAPP(hAPP(c_COMBS(U_17923,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17923),c_fconj),hAPP(hAPP(c_COMBC(U_17923,tc_fun(U_17923,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17923)),hAPP(c_List_Oset(U_17923),U_17925)))),U_17924)),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

cnf(f_4381_3,plain,
    hAPP(c_List_Oset(U_17923),hAPP(c_List_Ofilter(U_17923,U_17924),U_17925)) = hAPP(c_Set_OCollect(U_17923),hAPP(hAPP(c_COMBS(U_17923,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17923),c_fconj),hAPP(hAPP(c_COMBC(U_17923,tc_fun(U_17923,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17923)),hAPP(c_List_Oset(U_17923),U_17925)))),U_17924)),
    inference(clausify,[status(thm)],[f_4381_2]) ).

fof(f_4382_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__filter__map]) ).

fof(f_4382_2,plain,
    ! [U_17930,U_17929,U_17928,U_17927,U_17926] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17926)),hAPP(c_List_Ofilter(U_17926,U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17926),U_17929),U_17930))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17928)),hAPP(c_List_Ofilter(U_17928,hAPP(c_Fun_Ocomp(U_17926,tc_HOL_Obool,U_17928,U_17927),U_17929)),U_17930)),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

cnf(f_4382_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17926)),hAPP(c_List_Ofilter(U_17926,U_17927),hAPP(hAPP(c_List_Omap(U_17928,U_17926),U_17929),U_17930))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17928)),hAPP(c_List_Ofilter(U_17928,hAPP(c_Fun_Ocomp(U_17926,tc_HOL_Obool,U_17928,U_17927),U_17929)),U_17930)),
    inference(clausify,[status(thm)],[f_4382_2]) ).

fof(f_4383_1,plain,
    ! [V_Pa_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_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | hBOOL(hAPP(V_Pa_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_4383_2,plain,
    ! [U_17934,U_17933,U_17932,U_17931] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17931)),hAPP(c_List_Ofilter(U_17931,U_17934),U_17933))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17931)),U_17933)))
      | hBOOL(hAPP(U_17934,U_17932))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17931),U_17932),hAPP(c_List_Oset(U_17931),U_17933))) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

cnf(f_4383_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17931)),hAPP(c_List_Ofilter(U_17931,U_17934),U_17933))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17931)),U_17933)))
    | hBOOL(hAPP(U_17934,U_17932))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17931),U_17932),hAPP(c_List_Oset(U_17931),U_17933))) ),
    inference(clausify,[status(thm)],[f_4383_2]) ).

fof(f_4384_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_4384_2,plain,
    ! [U_17937,U_17936,U_17935] : c_List_Opartition(U_17935,U_17936,U_17937) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17935),tc_List_Olist(U_17935)),hAPP(c_List_Ofilter(U_17935,U_17936),U_17937)),hAPP(c_List_Ofilter(U_17935,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17935,c_fNot),U_17936)),U_17937)),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

cnf(f_4384_3,plain,
    c_List_Opartition(U_17935,U_17936,U_17937) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17935),tc_List_Olist(U_17935)),hAPP(c_List_Ofilter(U_17935,U_17936),U_17937)),hAPP(c_List_Ofilter(U_17935,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17935,c_fNot),U_17936)),U_17937)),
    inference(clausify,[status(thm)],[f_4384_2]) ).

fof(f_4385_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_4385_2,plain,
    ! [U_17940,U_17939,U_17938] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17938,tc_HOL_Obool)),hAPP(c_List_Oset(U_17938),U_17939)),hAPP(hAPP(c_Set_Oinsert(U_17938),U_17940),c_Orderings_Obot__class_Obot(tc_fun(U_17938,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_17938),hAPP(c_List_Ofilter(U_17938,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17938),c_fNot),hAPP(hAPP(c_COMBC(U_17938,U_17938,tc_HOL_Obool),c_fequal),U_17940))),U_17939)),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

cnf(f_4385_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17938,tc_HOL_Obool)),hAPP(c_List_Oset(U_17938),U_17939)),hAPP(hAPP(c_Set_Oinsert(U_17938),U_17940),c_Orderings_Obot__class_Obot(tc_fun(U_17938,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_17938),hAPP(c_List_Ofilter(U_17938,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17938),c_fNot),hAPP(hAPP(c_COMBC(U_17938,U_17938,tc_HOL_Obool),c_fequal),U_17940))),U_17939)),
    inference(clausify,[status(thm)],[f_4385_2]) ).

fof(f_4386_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_4386_2,plain,
    ! [U_17943,U_17942,U_17941] :
      ( hAPP(c_List_Ofilter(U_17941,hAPP(hAPP(c_COMBC(U_17941,tc_fun(U_17941,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17941)),hAPP(c_List_Oset(U_17941),c_List_Osublist(U_17941,U_17942,U_17943)))),U_17942) = c_List_Osublist(U_17941,U_17942,U_17943)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17941),U_17942)) ),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

cnf(f_4386_3,plain,
    ( hAPP(c_List_Ofilter(U_17941,hAPP(hAPP(c_COMBC(U_17941,tc_fun(U_17941,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17941)),hAPP(c_List_Oset(U_17941),c_List_Osublist(U_17941,U_17942,U_17943)))),U_17942) = c_List_Osublist(U_17941,U_17942,U_17943)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17941),U_17942)) ),
    inference(clausify,[status(thm)],[f_4386_2]) ).

fof(f_4387_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_4387_2,plain,
    ! [U_17947,U_17946] :
      ( ( c_List_Otranspose(U_17946,U_17947) = c_List_Olist_ONil(tc_List_Olist(U_17946))
        | ? [U_17945] :
            ( U_17945 != c_List_Olist_ONil(U_17946)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17946)),U_17945),hAPP(c_List_Oset(tc_List_Olist(U_17946)),U_17947))) ) )
      & ( ! [U_17944] :
            ( U_17944 = c_List_Olist_ONil(U_17946)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17946)),U_17944),hAPP(c_List_Oset(tc_List_Olist(U_17946)),U_17947))) )
        | c_List_Otranspose(U_17946,U_17947) != c_List_Olist_ONil(tc_List_Olist(U_17946)) ) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

fof(f_4387_3,plain,
    ( ! [U_17951,U_17949] :
        ( c_List_Otranspose(U_17949,U_17951) = c_List_Olist_ONil(tc_List_Olist(U_17949))
        | ? [U_17945] :
            ( U_17945 != c_List_Olist_ONil(U_17949)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17949)),U_17945),hAPP(c_List_Oset(tc_List_Olist(U_17949)),U_17951))) ) )
    & ! [U_17950,U_17948] :
        ( ! [U_17944] :
            ( U_17944 = c_List_Olist_ONil(U_17948)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17948)),U_17944),hAPP(c_List_Oset(tc_List_Olist(U_17948)),U_17950))) )
        | c_List_Otranspose(U_17948,U_17950) != c_List_Olist_ONil(tc_List_Olist(U_17948)) ) ),
    inference(miniscope,[status(thm)],[f_4387_2]) ).

fof(f_4387_4,plain,
    ( ! [U_17951,U_17949] :
        ( c_List_Otranspose(U_17949,U_17951) = c_List_Olist_ONil(tc_List_Olist(U_17949))
        | ( sK440(U_17951,U_17949) != c_List_Olist_ONil(U_17949)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17949)),sK440(U_17951,U_17949)),hAPP(c_List_Oset(tc_List_Olist(U_17949)),U_17951))) ) )
    & ! [U_17950,U_17948] :
        ( ! [U_17944] :
            ( U_17944 = c_List_Olist_ONil(U_17948)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17948)),U_17944),hAPP(c_List_Oset(tc_List_Olist(U_17948)),U_17950))) )
        | c_List_Otranspose(U_17948,U_17950) != c_List_Olist_ONil(tc_List_Olist(U_17948)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_17945,sK440(U_17951,U_17949))],[f_4387_3]) ).

cnf(f_4387_5,plain,
    ( U_17944 = c_List_Olist_ONil(U_17948)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17948)),U_17944),hAPP(c_List_Oset(tc_List_Olist(U_17948)),U_17950)))
    | c_List_Otranspose(U_17948,U_17950) != c_List_Olist_ONil(tc_List_Olist(U_17948)) ),
    inference(clausify,[status(thm)],[f_4387_4]) ).

cnf(f_4387_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17949)),sK440(U_17951,U_17949)),hAPP(c_List_Oset(tc_List_Olist(U_17949)),U_17951)))
    | c_List_Otranspose(U_17949,U_17951) = c_List_Olist_ONil(tc_List_Olist(U_17949)) ),
    inference(clausify,[status(thm)],[f_4387_4]) ).

cnf(f_4387_7,plain,
    ( sK440(U_17951,U_17949) != c_List_Olist_ONil(U_17949)
    | c_List_Otranspose(U_17949,U_17951) = c_List_Olist_ONil(tc_List_Olist(U_17949)) ),
    inference(clausify,[status(thm)],[f_4387_4]) ).

fof(f_4388_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_4388_2,plain,
    ! [U_17954,U_17953,U_17952] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17952)),hAPP(c_List_Ofilter(U_17952,U_17953),U_17954)) = 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_17952)),U_17954)))),hAPP(hAPP(c_COMBB(U_17952,tc_HOL_Obool,tc_Nat_Onat),U_17953),hAPP(c_List_Onth(U_17952),U_17954))))),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

cnf(f_4388_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17952)),hAPP(c_List_Ofilter(U_17952,U_17953),U_17954)) = 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_17952)),U_17954)))),hAPP(hAPP(c_COMBB(U_17952,tc_HOL_Obool,tc_Nat_Onat),U_17953),hAPP(c_List_Onth(U_17952),U_17954))))),
    inference(clausify,[status(thm)],[f_4388_2]) ).

fof(f_4389_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_4389_2,plain,
    ! [U_17956,U_17955] : c_List_Oconcat(tc_List_Olist(U_17955),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17955)),U_17955,c_List_Olist_ONil(tc_List_Olist(U_17955)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955))),U_17955),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955)),tc_List_Olist(tc_List_Olist(U_17955))),c_List_Olist_OCons(tc_List_Olist(U_17955))),c_List_Olist_ONil(tc_List_Olist(U_17955)))))),U_17956)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17955),tc_List_Olist(U_17955)),c_List_Otl(U_17955)),hAPP(c_List_Ofilter(tc_List_Olist(U_17955),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17955)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17955),tc_List_Olist(U_17955),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17955)))),U_17956)),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

cnf(f_4389_3,plain,
    c_List_Oconcat(tc_List_Olist(U_17955),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17955)),U_17955,c_List_Olist_ONil(tc_List_Olist(U_17955)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955))),U_17955),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17955),tc_List_Olist(tc_List_Olist(U_17955)),tc_List_Olist(tc_List_Olist(U_17955))),c_List_Olist_OCons(tc_List_Olist(U_17955))),c_List_Olist_ONil(tc_List_Olist(U_17955)))))),U_17956)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17955),tc_List_Olist(U_17955)),c_List_Otl(U_17955)),hAPP(c_List_Ofilter(tc_List_Olist(U_17955),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17955)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17955),tc_List_Olist(U_17955),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17955)))),U_17956)),
    inference(clausify,[status(thm)],[f_4389_2]) ).

fof(f_4390_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_4390_2,plain,
    ! [U_17960,U_17959,U_17958,U_17957] :
      ( c_List_Otranspose(U_17957,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),U_17959)),U_17960)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),c_List_Oconcat(U_17957,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17957),tc_List_Olist(U_17957)),c_List_Olist_Olist__case(tc_List_Olist(U_17957),U_17957,c_List_Olist_ONil(U_17957),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17957),tc_fun(tc_List_Olist(U_17957),tc_List_Olist(U_17957)),U_17957),c_COMBK(tc_List_Olist(U_17957),tc_List_Olist(U_17957))),hAPP(hAPP(c_COMBC(U_17957,tc_List_Olist(U_17957),tc_List_Olist(U_17957)),c_List_Olist_OCons(U_17957)),c_List_Olist_ONil(U_17957))))),U_17960)))),c_List_Otranspose(U_17957,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),U_17959),c_List_Oconcat(tc_List_Olist(U_17957),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17957)),U_17957,c_List_Olist_ONil(tc_List_Olist(U_17957)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957))),U_17957),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957)),tc_List_Olist(tc_List_Olist(U_17957))),c_List_Olist_OCons(tc_List_Olist(U_17957))),c_List_Olist_ONil(tc_List_Olist(U_17957)))))),U_17960)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17957)),c_List_Otranspose__rel(U_17957)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),U_17959)),U_17960))) ),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

cnf(f_4390_3,plain,
    ( c_List_Otranspose(U_17957,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),U_17959)),U_17960)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),c_List_Oconcat(U_17957,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17957),tc_List_Olist(U_17957)),c_List_Olist_Olist__case(tc_List_Olist(U_17957),U_17957,c_List_Olist_ONil(U_17957),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17957),tc_fun(tc_List_Olist(U_17957),tc_List_Olist(U_17957)),U_17957),c_COMBK(tc_List_Olist(U_17957),tc_List_Olist(U_17957))),hAPP(hAPP(c_COMBC(U_17957,tc_List_Olist(U_17957),tc_List_Olist(U_17957)),c_List_Olist_OCons(U_17957)),c_List_Olist_ONil(U_17957))))),U_17960)))),c_List_Otranspose(U_17957,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),U_17959),c_List_Oconcat(tc_List_Olist(U_17957),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17957)),U_17957,c_List_Olist_ONil(tc_List_Olist(U_17957)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957))),U_17957),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17957),tc_List_Olist(tc_List_Olist(U_17957)),tc_List_Olist(tc_List_Olist(U_17957))),c_List_Olist_OCons(tc_List_Olist(U_17957))),c_List_Olist_ONil(tc_List_Olist(U_17957)))))),U_17960)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17957)),c_List_Otranspose__rel(U_17957)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17957)),hAPP(hAPP(c_List_Olist_OCons(U_17957),U_17958),U_17959)),U_17960))) ),
    inference(clausify,[status(thm)],[f_4390_2]) ).

fof(f_4391_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_4391_2,plain,
    ! [U_17962,U_17961] :
      ( c_List_Otranspose(U_17961,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17961)),c_List_Olist_ONil(U_17961)),U_17962)) = c_List_Otranspose(U_17961,U_17962)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17961)),c_List_Otranspose__rel(U_17961)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17961)),c_List_Olist_ONil(U_17961)),U_17962))) ),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

cnf(f_4391_3,plain,
    ( c_List_Otranspose(U_17961,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17961)),c_List_Olist_ONil(U_17961)),U_17962)) = c_List_Otranspose(U_17961,U_17962)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17961)),c_List_Otranspose__rel(U_17961)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17961)),c_List_Olist_ONil(U_17961)),U_17962))) ),
    inference(clausify,[status(thm)],[f_4391_2]) ).

fof(f_4392_1,plain,
    ! [V_is_2,V_xs_2,V_Pa_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_Pa_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_Pa_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_4392_2,plain,
    ! [U_17966,U_17965,U_17964,U_17963] : hAPP(hAPP(c_List_Omap(tc_prod(U_17963,tc_Nat_Onat),U_17963),c_Product__Type_Ofst(U_17963,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17963,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17963,tc_Nat_Onat)),U_17964),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_17963,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_17963,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_17963,tc_Nat_Onat),U_17965),U_17966))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17963,tc_Nat_Onat),U_17963),c_Product__Type_Ofst(U_17963,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17963,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17963,tc_Nat_Onat)),U_17964),c_Product__Type_Osnd(U_17963,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_17963,tc_Nat_Onat),U_17965),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_17966)))),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

cnf(f_4392_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17963,tc_Nat_Onat),U_17963),c_Product__Type_Ofst(U_17963,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17963,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17963,tc_Nat_Onat)),U_17964),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_17963,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_17963,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_17963,tc_Nat_Onat),U_17965),U_17966))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17963,tc_Nat_Onat),U_17963),c_Product__Type_Ofst(U_17963,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17963,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17963,tc_Nat_Onat)),U_17964),c_Product__Type_Osnd(U_17963,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_17963,tc_Nat_Onat),U_17965),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_17966)))),
    inference(clausify,[status(thm)],[f_4392_2]) ).

fof(f_4393_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_4393_2,plain,
    ! [U_17968,U_17967] : c_Random_Opick(U_17967,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17967),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17967,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17967,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17967)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17968)) = c_Random_Opick(U_17967,U_17968),
    inference(variable_rename,[status(thm)],[f_4393_1]) ).

cnf(f_4393_3,plain,
    c_Random_Opick(U_17967,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17967),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17967,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17967,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17967)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17968)) = c_Random_Opick(U_17967,U_17968),
    inference(clausify,[status(thm)],[f_4393_2]) ).

fof(f_4394_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_4394_2,plain,
    ! [U_17970,U_17969] : c_Random_Oselect__weight(U_17969,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17969),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17969,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17969,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17969)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17970)) = c_Random_Oselect__weight(U_17969,U_17970),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

cnf(f_4394_3,plain,
    c_Random_Oselect__weight(U_17969,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17969),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17969,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17969,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17969)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17970)) = c_Random_Oselect__weight(U_17969,U_17970),
    inference(clausify,[status(thm)],[f_4394_2]) ).

fof(f_4395_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_4395_2,plain,
    ! [U_17971] :
      ( c_List_Otranspose(U_17971,c_List_Olist_ONil(tc_List_Olist(U_17971))) = c_List_Olist_ONil(tc_List_Olist(U_17971))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17971)),c_List_Otranspose__rel(U_17971)),c_List_Olist_ONil(tc_List_Olist(U_17971)))) ),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

cnf(f_4395_3,plain,
    ( c_List_Otranspose(U_17971,c_List_Olist_ONil(tc_List_Olist(U_17971))) = c_List_Olist_ONil(tc_List_Olist(U_17971))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17971)),c_List_Otranspose__rel(U_17971)),c_List_Olist_ONil(tc_List_Olist(U_17971)))) ),
    inference(clausify,[status(thm)],[f_4395_2]) ).

fof(f_4396_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_4396_2,plain,
    ! [U_17973,U_17972] : c_List_Ofoldr(tc_List_Olist(U_17972),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17972)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17972))),c_List_Otranspose(U_17972,U_17973),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17972))),hAPP(c_List_Ofilter(tc_List_Olist(U_17972),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17972)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17972),tc_List_Olist(U_17972),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17972)))),U_17973)),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

cnf(f_4396_3,plain,
    c_List_Ofoldr(tc_List_Olist(U_17972),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17972)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17972))),c_List_Otranspose(U_17972,U_17973),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17972))),hAPP(c_List_Ofilter(tc_List_Olist(U_17972),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17972)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17972),tc_List_Olist(U_17972),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17972)))),U_17973)),
    inference(clausify,[status(thm)],[f_4396_2]) ).

fof(f_4397_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_4397_2,plain,
    ! [U_17977,U_17976,U_17975,U_17974] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17974)),U_17975))),c_List_Ofoldr(tc_List_Olist(U_17976),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17976)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17976))),U_17977,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_17974)),U_17975)),c_List_Ofoldr(tc_List_Olist(U_17976),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17976)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17976),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_17976)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17976)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_17976),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17976)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17976),tc_List_Olist(U_17976),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17976)))),U_17977),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

cnf(f_4397_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_17974)),U_17975))),c_List_Ofoldr(tc_List_Olist(U_17976),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17976)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17976))),U_17977,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_17974)),U_17975)),c_List_Ofoldr(tc_List_Olist(U_17976),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17976)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17976),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_17976)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17976)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_17976),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17976)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17976),tc_List_Olist(U_17976),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17976)))),U_17977),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4397_2]) ).

fof(f_4398_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_4398_2,plain,
    ! [U_17983,U_17982,U_17981,U_17980,U_17979,U_17978] : c_List_Ofoldr(U_17978,U_17979,U_17980,hAPP(hAPP(c_List_Oappend(U_17978),U_17981),U_17982),U_17983) = c_List_Ofoldr(U_17978,U_17979,U_17980,U_17981,c_List_Ofoldr(U_17978,U_17979,U_17980,U_17982,U_17983)),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

cnf(f_4398_3,plain,
    c_List_Ofoldr(U_17978,U_17979,U_17980,hAPP(hAPP(c_List_Oappend(U_17978),U_17981),U_17982),U_17983) = c_List_Ofoldr(U_17978,U_17979,U_17980,U_17981,c_List_Ofoldr(U_17978,U_17979,U_17980,U_17982,U_17983)),
    inference(clausify,[status(thm)],[f_4398_2]) ).

fof(f_4399_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_4399_2,plain,
    ! [U_17989,U_17988,U_17987,U_17986,U_17985,U_17984] : c_List_Ofoldr(U_17984,U_17985,U_17986,hAPP(hAPP(c_List_Olist_OCons(U_17984),U_17987),U_17988),U_17989) = hAPP(hAPP(U_17986,U_17987),c_List_Ofoldr(U_17984,U_17985,U_17986,U_17988,U_17989)),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

cnf(f_4399_3,plain,
    c_List_Ofoldr(U_17984,U_17985,U_17986,hAPP(hAPP(c_List_Olist_OCons(U_17984),U_17987),U_17988),U_17989) = hAPP(hAPP(U_17986,U_17987),c_List_Ofoldr(U_17984,U_17985,U_17986,U_17988,U_17989)),
    inference(clausify,[status(thm)],[f_4399_2]) ).

fof(f_4400_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_4400_2,plain,
    ! [U_17993,U_17992,U_17991,U_17990] : c_List_Ofoldr(U_17990,U_17991,U_17992,c_List_Olist_ONil(U_17990),U_17993) = U_17993,
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

cnf(f_4400_3,plain,
    c_List_Ofoldr(U_17990,U_17991,U_17992,c_List_Olist_ONil(U_17990),U_17993) = U_17993,
    inference(clausify,[status(thm)],[f_4400_2]) ).

fof(f_4401_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_4401_2,plain,
    ! [U_17996,U_17995,U_17994] :
      ( c_List_Ofoldr(U_17994,U_17994,c_Groups_Oplus__class_Oplus(U_17994),U_17995,U_17996) = hAPP(c_List_Ofoldl(U_17994,U_17994,c_Groups_Oplus__class_Oplus(U_17994),U_17996),U_17995)
      | ~ class_Groups_Oab__semigroup__add(U_17994) ),
    inference(variable_rename,[status(thm)],[f_4401_1]) ).

cnf(f_4401_3,plain,
    ( c_List_Ofoldr(U_17994,U_17994,c_Groups_Oplus__class_Oplus(U_17994),U_17995,U_17996) = hAPP(c_List_Ofoldl(U_17994,U_17994,c_Groups_Oplus__class_Oplus(U_17994),U_17996),U_17995)
    | ~ class_Groups_Oab__semigroup__add(U_17994) ),
    inference(clausify,[status(thm)],[f_4401_2]) ).

fof(f_4402_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_4402_2,plain,
    ! [U_18003,U_18002,U_18001,U_18000,U_17999,U_17998,U_17997] : c_List_Ofoldr(U_17997,U_17998,U_17999,hAPP(hAPP(c_List_Omap(U_18000,U_17997),U_18001),U_18002),U_18003) = c_List_Ofoldr(U_18000,U_17998,hAPP(c_Fun_Ocomp(U_17997,tc_fun(U_17998,U_17998),U_18000,U_17999),U_18001),U_18002,U_18003),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

cnf(f_4402_3,plain,
    c_List_Ofoldr(U_17997,U_17998,U_17999,hAPP(hAPP(c_List_Omap(U_18000,U_17997),U_18001),U_18002),U_18003) = c_List_Ofoldr(U_18000,U_17998,hAPP(c_Fun_Ocomp(U_17997,tc_fun(U_17998,U_17998),U_18000,U_17999),U_18001),U_18002,U_18003),
    inference(clausify,[status(thm)],[f_4402_2]) ).

fof(f_4403_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_4403_2,plain,
    ! [U_18005,U_18004] :
      ( hAPP(c_List_Ofoldl(U_18004,U_18004,c_Groups_Oplus__class_Oplus(U_18004),c_Groups_Ozero__class_Ozero(U_18004)),U_18005) = c_List_Ofoldr(U_18004,U_18004,c_Groups_Oplus__class_Oplus(U_18004),U_18005,c_Groups_Ozero__class_Ozero(U_18004))
      | ~ class_Groups_Omonoid__add(U_18004) ),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

cnf(f_4403_3,plain,
    ( hAPP(c_List_Ofoldl(U_18004,U_18004,c_Groups_Oplus__class_Oplus(U_18004),c_Groups_Ozero__class_Ozero(U_18004)),U_18005) = c_List_Ofoldr(U_18004,U_18004,c_Groups_Oplus__class_Oplus(U_18004),U_18005,c_Groups_Ozero__class_Ozero(U_18004))
    | ~ class_Groups_Omonoid__add(U_18004) ),
    inference(clausify,[status(thm)],[f_4403_2]) ).

fof(f_4404_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_4404_2,plain,
    ! [U_18008,U_18007,U_18006] :
      ( hAPP(c_List_Ofoldl(U_18006,U_18006,c_Groups_Oplus__class_Oplus(U_18006),U_18007),U_18008) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18006),U_18007),c_List_Ofoldr(U_18006,U_18006,c_Groups_Oplus__class_Oplus(U_18006),U_18008,c_Groups_Ozero__class_Ozero(U_18006)))
      | ~ class_Groups_Omonoid__add(U_18006) ),
    inference(variable_rename,[status(thm)],[f_4404_1]) ).

cnf(f_4404_3,plain,
    ( hAPP(c_List_Ofoldl(U_18006,U_18006,c_Groups_Oplus__class_Oplus(U_18006),U_18007),U_18008) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18006),U_18007),c_List_Ofoldr(U_18006,U_18006,c_Groups_Oplus__class_Oplus(U_18006),U_18008,c_Groups_Ozero__class_Ozero(U_18006)))
    | ~ class_Groups_Omonoid__add(U_18006) ),
    inference(clausify,[status(thm)],[f_4404_2]) ).

fof(f_4405_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_4405_2,plain,
    ! [U_18010,U_18009] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18009))),c_List_Otranspose(U_18009,U_18010)) = c_List_Ofoldr(tc_List_Olist(U_18009),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_18009)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18009))),U_18010,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4405_1]) ).

cnf(f_4405_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18009))),c_List_Otranspose(U_18009,U_18010)) = c_List_Ofoldr(tc_List_Olist(U_18009),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_18009)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18009))),U_18010,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4405_2]) ).

fof(f_4406_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_4406_2,plain,
    ! [U_18013,U_18012,U_18011] : c_List_Osublist(U_18011,U_18012,U_18013) = hAPP(hAPP(c_List_Omap(tc_prod(U_18011,tc_Nat_Onat),U_18011),c_Product__Type_Ofst(U_18011,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18011,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18011,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_18011,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18011,tc_Nat_Onat))),U_18013)),hAPP(hAPP(c_List_Ozip(U_18011,tc_Nat_Onat),U_18012),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18011)),U_18012))))),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

cnf(f_4406_3,plain,
    c_List_Osublist(U_18011,U_18012,U_18013) = hAPP(hAPP(c_List_Omap(tc_prod(U_18011,tc_Nat_Onat),U_18011),c_Product__Type_Ofst(U_18011,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18011,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18011,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_18011,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18011,tc_Nat_Onat))),U_18013)),hAPP(hAPP(c_List_Ozip(U_18011,tc_Nat_Onat),U_18012),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18011)),U_18012))))),
    inference(clausify,[status(thm)],[f_4406_2]) ).

fof(f_4407_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_4407_2,plain,
    ! [U_18017,U_18016,U_18015,U_18014] : hAPP(hAPP(c_List_Omap(tc_prod(U_18014,tc_Nat_Onat),U_18014),c_Product__Type_Ofst(U_18014,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18014,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18014,tc_Nat_Onat))),U_18015)),hAPP(hAPP(c_List_Ozip(U_18014,tc_Nat_Onat),U_18016),c_List_Oupt(U_18017,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18017),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18014)),U_18016)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_18014,tc_Nat_Onat),U_18014),c_Product__Type_Ofst(U_18014,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18014,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_18014,tc_Nat_Onat))),U_18017))),U_18015)),hAPP(hAPP(c_List_Ozip(U_18014,tc_Nat_Onat),U_18016),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18014)),U_18016))))),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

cnf(f_4407_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_18014,tc_Nat_Onat),U_18014),c_Product__Type_Ofst(U_18014,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18014,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18014,tc_Nat_Onat))),U_18015)),hAPP(hAPP(c_List_Ozip(U_18014,tc_Nat_Onat),U_18016),c_List_Oupt(U_18017,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18017),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18014)),U_18016)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_18014,tc_Nat_Onat),U_18014),c_Product__Type_Ofst(U_18014,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18014,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18014,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_18014,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_18014,tc_Nat_Onat))),U_18017))),U_18015)),hAPP(hAPP(c_List_Ozip(U_18014,tc_Nat_Onat),U_18016),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18014)),U_18016))))),
    inference(clausify,[status(thm)],[f_4407_2]) ).

fof(f_4408_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_4408_2,plain,
    ! [U_18019,U_18018] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18018,U_18019)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18018),U_18019),
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

cnf(f_4408_3,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18018,U_18019)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18018),U_18019),
    inference(clausify,[status(thm)],[f_4408_2]) ).

fof(f_4409_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_4409_2,plain,
    ! [U_18021,U_18020] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18020),U_18021) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18020,U_18021)),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

cnf(f_4409_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18020),U_18021) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18020,U_18021)),
    inference(clausify,[status(thm)],[f_4409_2]) ).

fof(f_4410_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_4410_2,plain,
    ! [U_18022] : c_List_Oupt(U_18022,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

cnf(f_4410_3,plain,
    c_List_Oupt(U_18022,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4410_2]) ).

fof(f_4411_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_4411_2,plain,
    ! [U_18024,U_18023] :
      ( ( c_List_Oupt(U_18023,U_18024) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18024),U_18023))
          & U_18024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18024),U_18023))
        | U_18024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_18023,U_18024) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4411_1]) ).

fof(f_4411_3,plain,
    ( ! [U_18028,U_18026] :
        ( c_List_Oupt(U_18026,U_18028) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18028),U_18026))
          & U_18028 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_18027,U_18025] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18027),U_18025))
        | U_18027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_18025,U_18027) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4411_2]) ).

cnf(f_4411_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18027),U_18025))
    | U_18027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_18025,U_18027) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4411_3]) ).

cnf(f_4411_5,plain,
    ( U_18028 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_18026,U_18028) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4411_3]) ).

cnf(f_4411_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18028),U_18026))
    | c_List_Oupt(U_18026,U_18028) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4411_3]) ).

fof(f_4412_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_4412_2,plain,
    ! [U_18030,U_18029] :
      ( c_List_Oupt(U_18030,U_18029) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18029),U_18030)) ),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

cnf(f_4412_3,plain,
    ( c_List_Oupt(U_18030,U_18029) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18029),U_18030)) ),
    inference(clausify,[status(thm)],[f_4412_2]) ).

fof(f_4413_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_4413_2,plain,
    ! [U_18032,U_18031] :
      ( c_List_Oupt(U_18031,U_18032) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18031),c_List_Oupt(hAPP(c_Nat_OSuc,U_18031),U_18032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18031),U_18032)) ),
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

cnf(f_4413_3,plain,
    ( c_List_Oupt(U_18031,U_18032) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18031),c_List_Oupt(hAPP(c_Nat_OSuc,U_18031),U_18032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18031),U_18032)) ),
    inference(clausify,[status(thm)],[f_4413_2]) ).

fof(f_4414_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_4414_2,plain,
    ! [U_18034,U_18033] :
      ( ( c_List_Oupt(U_18033,U_18034) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18033),U_18034)) )
      & ( c_List_Oupt(U_18033,U_18034) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18033),c_List_Oupt(hAPP(c_Nat_OSuc,U_18033),U_18034))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18033),U_18034)) ) ),
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

fof(f_4414_3,plain,
    ( ! [U_18038,U_18036] :
        ( c_List_Oupt(U_18036,U_18038) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18036),U_18038)) )
    & ! [U_18037,U_18035] :
        ( c_List_Oupt(U_18035,U_18037) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18035),c_List_Oupt(hAPP(c_Nat_OSuc,U_18035),U_18037))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18035),U_18037)) ) ),
    inference(miniscope,[status(thm)],[f_4414_2]) ).

cnf(f_4414_4,plain,
    ( c_List_Oupt(U_18035,U_18037) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18035),c_List_Oupt(hAPP(c_Nat_OSuc,U_18035),U_18037))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18035),U_18037)) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

cnf(f_4414_5,plain,
    ( c_List_Oupt(U_18036,U_18038) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18036),U_18038)) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

fof(f_4415_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_4415_2,plain,
    ! [U_18041,U_18040,U_18039] :
      ( c_List_Oupt(U_18039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18040),U_18041)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18039,U_18040)),c_List_Oupt(U_18040,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18040),U_18041)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18039),U_18040)) ),
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

cnf(f_4415_3,plain,
    ( c_List_Oupt(U_18039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18040),U_18041)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18039,U_18040)),c_List_Oupt(U_18040,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18040),U_18041)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18039),U_18040)) ),
    inference(clausify,[status(thm)],[f_4415_2]) ).

fof(f_4416_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_4416_2,plain,
    ! [U_18043,U_18042] :
      ( c_List_Oupt(U_18042,hAPP(c_Nat_OSuc,U_18043)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18042,U_18043)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18043),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18042),U_18043)) ),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

cnf(f_4416_3,plain,
    ( c_List_Oupt(U_18042,hAPP(c_Nat_OSuc,U_18043)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18042,U_18043)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18043),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18042),U_18043)) ),
    inference(clausify,[status(thm)],[f_4416_2]) ).

fof(f_4417_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_4417_2,plain,
    ! [U_18045,U_18044] :
      ( ( c_List_Oupt(U_18044,hAPP(c_Nat_OSuc,U_18045)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18044),U_18045)) )
      & ( c_List_Oupt(U_18044,hAPP(c_Nat_OSuc,U_18045)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18044,U_18045)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18045),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18044),U_18045)) ) ),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

fof(f_4417_3,plain,
    ( ! [U_18049,U_18047] :
        ( c_List_Oupt(U_18047,hAPP(c_Nat_OSuc,U_18049)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18047),U_18049)) )
    & ! [U_18048,U_18046] :
        ( c_List_Oupt(U_18046,hAPP(c_Nat_OSuc,U_18048)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18046,U_18048)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18048),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18046),U_18048)) ) ),
    inference(miniscope,[status(thm)],[f_4417_2]) ).

cnf(f_4417_4,plain,
    ( c_List_Oupt(U_18046,hAPP(c_Nat_OSuc,U_18048)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18046,U_18048)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18048),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18046),U_18048)) ),
    inference(clausify,[status(thm)],[f_4417_3]) ).

cnf(f_4417_5,plain,
    ( c_List_Oupt(U_18047,hAPP(c_Nat_OSuc,U_18049)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18047),U_18049)) ),
    inference(clausify,[status(thm)],[f_4417_3]) ).

fof(f_4418_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_4418_2,plain,
    ! [U_18052,U_18051,U_18050] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_18050),c_List_Oupt(U_18051,U_18052)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18051),U_18050),U_18052),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

cnf(f_4418_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_18050),c_List_Oupt(U_18051,U_18052)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18051),U_18050),U_18052),
    inference(clausify,[status(thm)],[f_4418_2]) ).

fof(f_4419_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_4419_2,plain,
    ! [U_18054,U_18053] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_18053,U_18054)) = U_18053
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18053),U_18054)) ),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

cnf(f_4419_3,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_18053,U_18054)) = U_18053
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18053),U_18054)) ),
    inference(clausify,[status(thm)],[f_4419_2]) ).

fof(f_4420_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_4420_2,plain,
    ! [U_18056,U_18055] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18055),U_18056)) = c_List_Oupt(U_18055,U_18056),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

cnf(f_4420_3,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18055),U_18056)) = c_List_Oupt(U_18055,U_18056),
    inference(clausify,[status(thm)],[f_4420_2]) ).

fof(f_4421_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_4421_2,plain,
    ! [U_18059,U_18058,U_18057] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_18058),c_List_Oupt(U_18057,U_18059)) = c_List_Oupt(U_18057,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18057),U_18058))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18057),U_18058)),U_18059)) ),
    inference(variable_rename,[status(thm)],[f_4421_1]) ).

cnf(f_4421_3,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_18058),c_List_Oupt(U_18057,U_18059)) = c_List_Oupt(U_18057,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18057),U_18058))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18057),U_18058)),U_18059)) ),
    inference(clausify,[status(thm)],[f_4421_2]) ).

fof(f_4422_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_4422_2,plain,
    ! [U_18061,U_18060] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_18060,U_18061))),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

cnf(f_4422_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_18060,U_18061))),
    inference(clausify,[status(thm)],[f_4422_2]) ).

fof(f_4423_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_4423_2,plain,
    ! [U_18063,U_18062] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_18062,U_18063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18063),U_18062),
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

cnf(f_4423_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_18062,U_18063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18063),U_18062),
    inference(clausify,[status(thm)],[f_4423_2]) ).

fof(f_4424_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_4424_2,plain,
    ! [U_18065,U_18064] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18064),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18065)) = 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_18064)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18065))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18064),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18065)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18064)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18064)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18065)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18064)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18065))) ) ),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

fof(f_4424_3,plain,
    ( ! [U_18069,U_18067] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18069)) = 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_18067)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18069))) )
    & ! [U_18068,U_18066] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068))) ) ),
    inference(miniscope,[status(thm)],[f_4424_2]) ).

cnf(f_4424_4,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18066)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18068))) ),
    inference(clausify,[status(thm)],[f_4424_3]) ).

cnf(f_4424_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18067),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18069)) = 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_18067)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18069))) ),
    inference(clausify,[status(thm)],[f_4424_3]) ).

fof(f_4425_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_4425_2,plain,
    ! [U_18073,U_18072,U_18071,U_18070] :
      ( ( c_List_Oupt(U_18070,U_18071) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18072),U_18073)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18070),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18071) != U_18073
        | U_18070 != U_18072
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18070),U_18071)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18070),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18071) = U_18073
          & U_18070 = U_18072
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18070),U_18071)) )
        | c_List_Oupt(U_18070,U_18071) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18072),U_18073) ) ),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

fof(f_4425_3,plain,
    ( ! [U_18081,U_18079,U_18077,U_18075] :
        ( c_List_Oupt(U_18075,U_18077) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18079),U_18081)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18075),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18077) != U_18081
        | U_18075 != U_18079
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18075),U_18077)) )
    & ! [U_18080,U_18078,U_18076,U_18074] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18074),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18076) = U_18080
          & U_18074 = U_18078
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18074),U_18076)) )
        | c_List_Oupt(U_18074,U_18076) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18078),U_18080) ) ),
    inference(miniscope,[status(thm)],[f_4425_2]) ).

cnf(f_4425_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18074),U_18076))
    | c_List_Oupt(U_18074,U_18076) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18078),U_18080) ),
    inference(clausify,[status(thm)],[f_4425_3]) ).

cnf(f_4425_5,plain,
    ( U_18074 = U_18078
    | c_List_Oupt(U_18074,U_18076) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18078),U_18080) ),
    inference(clausify,[status(thm)],[f_4425_3]) ).

cnf(f_4425_6,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18074),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18076) = U_18080
    | c_List_Oupt(U_18074,U_18076) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18078),U_18080) ),
    inference(clausify,[status(thm)],[f_4425_3]) ).

cnf(f_4425_7,plain,
    ( c_List_Oupt(U_18075,U_18077) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18079),U_18081)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18075),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18077) != U_18081
    | U_18075 != U_18079
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18075),U_18077)) ),
    inference(clausify,[status(thm)],[f_4425_3]) ).

fof(f_4426_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_4426_2,plain,
    ! [U_18083,U_18082] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_18082,U_18083)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18083),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18082),U_18083)) ),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

cnf(f_4426_3,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_18082,U_18083)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18083),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18082),U_18083)) ),
    inference(clausify,[status(thm)],[f_4426_2]) ).

fof(f_4427_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_4427_2,plain,
    ! [U_18085,U_18084] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_18084,U_18085)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_18084),hAPP(c_Nat_OSuc,U_18085)),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

cnf(f_4427_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_18084,U_18085)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_18084),hAPP(c_Nat_OSuc,U_18085)),
    inference(clausify,[status(thm)],[f_4427_2]) ).

fof(f_4428_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_4428_2,plain,
    ! [U_18087,U_18086] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_18086,U_18087) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18086,hAPP(c_Nat_OSuc,U_18087))),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

cnf(f_4428_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_18086,U_18087) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18086,hAPP(c_Nat_OSuc,U_18087))),
    inference(clausify,[status(thm)],[f_4428_2]) ).

fof(f_4429_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_4429_2,plain,
    ! [U_18088] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18088) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18088)),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

cnf(f_4429_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18088) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18088)),
    inference(clausify,[status(thm)],[f_4429_2]) ).

fof(f_4430_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_4430_2,plain,
    ! [U_18091,U_18090,U_18089] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_18089,U_18091)),U_18090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18089),U_18090)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18089),U_18090)),U_18091)) ),
    inference(variable_rename,[status(thm)],[f_4430_1]) ).

cnf(f_4430_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_18089,U_18091)),U_18090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18089),U_18090)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18089),U_18090)),U_18091)) ),
    inference(clausify,[status(thm)],[f_4430_2]) ).

fof(f_4431_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_4431_2,plain,
    ! [U_18093,U_18092] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_18092,U_18093) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18092),hAPP(c_Nat_OSuc,U_18093))),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

cnf(f_4431_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_18092,U_18093) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18092),hAPP(c_Nat_OSuc,U_18093))),
    inference(clausify,[status(thm)],[f_4431_2]) ).

fof(f_4432_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_4432_2,plain,
    ! [U_18095,U_18094] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_18094,U_18095) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18094),U_18095)),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

cnf(f_4432_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_18094,U_18095) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18094),U_18095)),
    inference(clausify,[status(thm)],[f_4432_2]) ).

fof(f_4433_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_4433_2,plain,
    ! [U_18096] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_18096) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_18096))),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

cnf(f_4433_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_18096) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_18096))),
    inference(clausify,[status(thm)],[f_4433_2]) ).

fof(f_4434_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_4434_2,plain,
    ! [U_18098,U_18097] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18097),hAPP(c_List_Onth(U_18097),U_18098)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18097)),U_18098))) = U_18098,
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

cnf(f_4434_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18097),hAPP(c_List_Onth(U_18097),U_18098)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18097)),U_18098))) = U_18098,
    inference(clausify,[status(thm)],[f_4434_2]) ).

fof(f_4435_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_4435_2,plain,
    ! [U_18102,U_18101,U_18100,U_18099] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18099),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18099),U_18100),c_List_Oupt(U_18101,U_18102))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18099),U_18100),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18101,U_18102)))
      | ~ class_Groups_Ocomm__monoid__add(U_18099) ),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

cnf(f_4435_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18099),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18099),U_18100),c_List_Oupt(U_18101,U_18102))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18099),U_18100),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18101,U_18102)))
    | ~ class_Groups_Ocomm__monoid__add(U_18099) ),
    inference(clausify,[status(thm)],[f_4435_2]) ).

fof(f_4436_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_4436_2,plain,
    ! [U_18106,U_18105,U_18104,U_18103] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18103),U_18104),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18105,U_18106))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18103),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18103),U_18104),c_List_Oupt(U_18105,U_18106)))
      | ~ class_Groups_Ocomm__monoid__add(U_18103) ),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

cnf(f_4436_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18103),U_18104),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18105,U_18106))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18103),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18103),U_18104),c_List_Oupt(U_18105,U_18106)))
    | ~ class_Groups_Ocomm__monoid__add(U_18103) ),
    inference(clausify,[status(thm)],[f_4436_2]) ).

fof(f_4437_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_4437_2,plain,
    ! [U_18111,U_18110,U_18109,U_18108,U_18107] :
      ( hAPP(hAPP(c_List_Onth(U_18110),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18110),U_18111),c_List_Oupt(U_18109,U_18108))),U_18107) = hAPP(U_18111,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18109),U_18107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18108),U_18109))) ),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

cnf(f_4437_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18110),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18110),U_18111),c_List_Oupt(U_18109,U_18108))),U_18107) = hAPP(U_18111,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18109),U_18107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18108),U_18109))) ),
    inference(clausify,[status(thm)],[f_4437_2]) ).

fof(f_4438_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_4438_2,plain,
    ! [U_18115,U_18114,U_18113] :
      ( c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
      | ? [U_18112] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113),U_18112)) != U_18115
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18112),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113))) )
      | ( U_18115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_18113 = c_List_Olist_ONil(tc_List_Olist(U_18114)) ) ),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

fof(f_4438_3,plain,
    ! [U_18115,U_18114,U_18113] :
      ( c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113),sK441(U_18115,U_18114,U_18113))) != U_18115
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK441(U_18115,U_18114,U_18113)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113))) )
      | ( U_18115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_18113 = c_List_Olist_ONil(tc_List_Olist(U_18114)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_18112,sK441(U_18115,U_18114,U_18113))],[f_4438_2]) ).

cnf(f_4438_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK441(U_18115,U_18114,U_18113)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))
    | c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
    | U_18113 = c_List_Olist_ONil(tc_List_Olist(U_18114)) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

cnf(f_4438_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113),sK441(U_18115,U_18114,U_18113))) != U_18115
    | c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
    | U_18113 = c_List_Olist_ONil(tc_List_Olist(U_18114)) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

cnf(f_4438_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK441(U_18115,U_18114,U_18113)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))
    | c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
    | U_18115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

cnf(f_4438_7,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113),sK441(U_18115,U_18114,U_18113))) != U_18115
    | c_List_Otranspose(U_18114,U_18113) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18114),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18114)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18114)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18114),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18114),tc_fun(tc_Nat_Onat,U_18114),tc_Nat_Onat),c_List_Onth(U_18114)),hAPP(c_List_Onth(tc_List_Olist(U_18114)),U_18113))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18114))),U_18113)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18115))
    | U_18115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

fof(f_4439_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_4439_2,plain,
    ! [U_18120,U_18119,U_18118,U_18117,U_18116] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18117,U_18116,U_18120),U_18118),c_List_Oremove1(U_18117,U_18118,U_18119)) = U_18119
      | hAPP(c_List_Ohd(U_18117),hAPP(c_List_Ofilter(U_18117,hAPP(hAPP(c_COMBB(U_18116,tc_HOL_Obool,U_18117),hAPP(c_fequal,hAPP(U_18120,U_18118))),U_18120)),U_18119)) != U_18118
      | ~ c_List_Olinorder__class_Osorted(U_18116,hAPP(hAPP(c_List_Omap(U_18117,U_18116),U_18120),U_18119))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18117),U_18118),hAPP(c_List_Oset(U_18117),U_18119)))
      | ~ class_Orderings_Olinorder(U_18116) ),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

cnf(f_4439_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18117,U_18116,U_18120),U_18118),c_List_Oremove1(U_18117,U_18118,U_18119)) = U_18119
    | hAPP(c_List_Ohd(U_18117),hAPP(c_List_Ofilter(U_18117,hAPP(hAPP(c_COMBB(U_18116,tc_HOL_Obool,U_18117),hAPP(c_fequal,hAPP(U_18120,U_18118))),U_18120)),U_18119)) != U_18118
    | ~ c_List_Olinorder__class_Osorted(U_18116,hAPP(hAPP(c_List_Omap(U_18117,U_18116),U_18120),U_18119))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18117),U_18118),hAPP(c_List_Oset(U_18117),U_18119)))
    | ~ class_Orderings_Olinorder(U_18116) ),
    inference(clausify,[status(thm)],[f_4439_2]) ).

fof(f_4440_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_4440_2,plain,
    ! [U_18121] :
      ( c_List_Olinorder__class_Osorted(U_18121,c_List_Olist_ONil(U_18121))
      | ~ class_Orderings_Olinorder(U_18121) ),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

cnf(f_4440_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18121,c_List_Olist_ONil(U_18121))
    | ~ class_Orderings_Olinorder(U_18121) ),
    inference(clausify,[status(thm)],[f_4440_2]) ).

fof(f_4441_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_4441_2,plain,
    ! [U_18123,U_18122] :
      ( c_List_Olinorder__class_Osorted(U_18122,hAPP(hAPP(c_List_Olist_OCons(U_18122),U_18123),c_List_Olist_ONil(U_18122)))
      | ~ class_Orderings_Olinorder(U_18122) ),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

cnf(f_4441_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18122,hAPP(hAPP(c_List_Olist_OCons(U_18122),U_18123),c_List_Olist_ONil(U_18122)))
    | ~ class_Orderings_Olinorder(U_18122) ),
    inference(clausify,[status(thm)],[f_4441_2]) ).

fof(f_4442_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_4442_2,plain,
    ! [U_18125,U_18124] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_18124,U_18125)),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

cnf(f_4442_3,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_18124,U_18125)),
    inference(clausify,[status(thm)],[f_4442_2]) ).

fof(f_4443_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_4443_2,plain,
    ! [U_18127,U_18126] :
      ( c_List_Olinorder__class_Osorted(U_18126,c_List_Olinorder__class_Osort__key(U_18126,U_18126,c_COMBI(U_18126),U_18127))
      | ~ class_Orderings_Olinorder(U_18126) ),
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

cnf(f_4443_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18126,c_List_Olinorder__class_Osort__key(U_18126,U_18126,c_COMBI(U_18126),U_18127))
    | ~ class_Orderings_Olinorder(U_18126) ),
    inference(clausify,[status(thm)],[f_4443_2]) ).

fof(f_4444_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_4444_2,plain,
    ! [U_18130,U_18129,U_18128] :
      ( c_List_Olinorder__class_Osorted(U_18128,c_List_Olinorder__class_Oinsort__insert__key(U_18128,U_18128,c_COMBI(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_4444_1]) ).

cnf(f_4444_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18128,c_List_Olinorder__class_Oinsort__insert__key(U_18128,U_18128,c_COMBI(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_4444_2]) ).

fof(f_4445_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_4445_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_4445_1]) ).

cnf(f_4445_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_4445_2]) ).

fof(f_4446_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_4446_2,plain,
    ! [U_18135,U_18134,U_18133] :
      ( c_List_Olinorder__class_Osorted(U_18133,c_List_Oremove1(U_18133,U_18135,U_18134))
      | ~ c_List_Olinorder__class_Osorted(U_18133,U_18134)
      | ~ class_Orderings_Olinorder(U_18133) ),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

cnf(f_4446_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18133,c_List_Oremove1(U_18133,U_18135,U_18134))
    | ~ c_List_Olinorder__class_Osorted(U_18133,U_18134)
    | ~ class_Orderings_Olinorder(U_18133) ),
    inference(clausify,[status(thm)],[f_4446_2]) ).

fof(f_4447_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_4447_2,plain,
    ! [U_18138,U_18137,U_18136] :
      ( c_List_Olinorder__class_Osorted(U_18136,hAPP(hAPP(c_List_Otake(U_18136),U_18138),U_18137))
      | ~ c_List_Olinorder__class_Osorted(U_18136,U_18137)
      | ~ class_Orderings_Olinorder(U_18136) ),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

cnf(f_4447_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18136,hAPP(hAPP(c_List_Otake(U_18136),U_18138),U_18137))
    | ~ c_List_Olinorder__class_Osorted(U_18136,U_18137)
    | ~ class_Orderings_Olinorder(U_18136) ),
    inference(clausify,[status(thm)],[f_4447_2]) ).

fof(f_4448_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_4448_2,plain,
    ! [U_18140,U_18139] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_18139,U_18140)),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

cnf(f_4448_3,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_18139,U_18140)),
    inference(clausify,[status(thm)],[f_4448_2]) ).

fof(f_4449_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_4449_2,plain,
    ! [U_18143,U_18142,U_18141] :
      ( c_List_Olinorder__class_Osorted(U_18141,hAPP(hAPP(c_List_Odrop(U_18141),U_18143),U_18142))
      | ~ c_List_Olinorder__class_Osorted(U_18141,U_18142)
      | ~ class_Orderings_Olinorder(U_18141) ),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

cnf(f_4449_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18141,hAPP(hAPP(c_List_Odrop(U_18141),U_18143),U_18142))
    | ~ c_List_Olinorder__class_Osorted(U_18141,U_18142)
    | ~ class_Orderings_Olinorder(U_18141) ),
    inference(clausify,[status(thm)],[f_4449_2]) ).

fof(f_4450_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_4450_2,plain,
    ! [U_18146,U_18145,U_18144] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18144,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18144,U_18144,c_COMBI(U_18144)),U_18145),U_18146))
          | ~ c_List_Olinorder__class_Osorted(U_18144,U_18146) )
        & ( c_List_Olinorder__class_Osorted(U_18144,U_18146)
          | ~ c_List_Olinorder__class_Osorted(U_18144,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18144,U_18144,c_COMBI(U_18144)),U_18145),U_18146)) ) )
      | ~ class_Orderings_Olinorder(U_18144) ),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

cnf(f_4450_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18144,U_18146)
    | ~ c_List_Olinorder__class_Osorted(U_18144,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18144,U_18144,c_COMBI(U_18144)),U_18145),U_18146))
    | ~ class_Orderings_Olinorder(U_18144) ),
    inference(clausify,[status(thm)],[f_4450_2]) ).

cnf(f_4450_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18144,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18144,U_18144,c_COMBI(U_18144)),U_18145),U_18146))
    | ~ c_List_Olinorder__class_Osorted(U_18144,U_18146)
    | ~ class_Orderings_Olinorder(U_18144) ),
    inference(clausify,[status(thm)],[f_4450_2]) ).

fof(f_4451_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_4451_2,plain,
    ! [U_18150,U_18149,U_18148,U_18147] :
      ( c_List_Olinorder__class_Osorted(U_18147,hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18148),hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18149),U_18150)))
      | ~ c_List_Olinorder__class_Osorted(U_18147,hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18149),U_18150))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18147),U_18148),U_18149))
      | ~ class_Orderings_Olinorder(U_18147) ),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

cnf(f_4451_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18147,hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18148),hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18149),U_18150)))
    | ~ c_List_Olinorder__class_Osorted(U_18147,hAPP(hAPP(c_List_Olist_OCons(U_18147),U_18149),U_18150))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18147),U_18148),U_18149))
    | ~ class_Orderings_Olinorder(U_18147) ),
    inference(clausify,[status(thm)],[f_4451_2]) ).

fof(f_4452_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_4452_2,plain,
    ! [U_18154,U_18153,U_18152,U_18151] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18152),hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154)))
          | ~ c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18151),U_18152),U_18153)) )
        & ( ( c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18151),U_18152),U_18153)) )
          | ~ c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18152),hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154))) ) )
      | ~ class_Orderings_Olinorder(U_18151) ),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

cnf(f_4452_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18151),U_18152),U_18153))
    | ~ c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18152),hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154)))
    | ~ class_Orderings_Olinorder(U_18151) ),
    inference(clausify,[status(thm)],[f_4452_2]) ).

cnf(f_4452_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154))
    | ~ c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18152),hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154)))
    | ~ class_Orderings_Olinorder(U_18151) ),
    inference(clausify,[status(thm)],[f_4452_2]) ).

cnf(f_4452_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18152),hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154)))
    | ~ c_List_Olinorder__class_Osorted(U_18151,hAPP(hAPP(c_List_Olist_OCons(U_18151),U_18153),U_18154))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18151),U_18152),U_18153))
    | ~ class_Orderings_Olinorder(U_18151) ),
    inference(clausify,[status(thm)],[f_4452_2]) ).

fof(f_4453_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_4453_2,plain,
    ! [U_18155] :
      ( c_List_Olinorder__class_Osorted(U_18155,c_List_Olist_ONil(U_18155))
      | ~ class_Orderings_Olinorder(U_18155) ),
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

cnf(f_4453_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18155,c_List_Olist_ONil(U_18155))
    | ~ class_Orderings_Olinorder(U_18155) ),
    inference(clausify,[status(thm)],[f_4453_2]) ).

fof(f_4454_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_4454_2,plain,
    ! [U_18157,U_18156] :
      ( c_List_Olinorder__class_Osorted(U_18156,c_List_Obutlast(U_18156,U_18157))
      | ~ c_List_Olinorder__class_Osorted(U_18156,U_18157)
      | U_18157 = c_List_Olist_ONil(U_18156)
      | ~ class_Orderings_Olinorder(U_18156) ),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

cnf(f_4454_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18156,c_List_Obutlast(U_18156,U_18157))
    | ~ c_List_Olinorder__class_Osorted(U_18156,U_18157)
    | U_18157 = c_List_Olist_ONil(U_18156)
    | ~ class_Orderings_Olinorder(U_18156) ),
    inference(clausify,[status(thm)],[f_4454_2]) ).

fof(f_4455_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_4455_2,plain,
    ! [U_18159,U_18158] :
      ( c_List_Olinorder__class_Osorted(U_18158,c_List_Oremdups(U_18158,U_18159))
      | ~ c_List_Olinorder__class_Osorted(U_18158,U_18159)
      | ~ class_Orderings_Olinorder(U_18158) ),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

cnf(f_4455_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18158,c_List_Oremdups(U_18158,U_18159))
    | ~ c_List_Olinorder__class_Osorted(U_18158,U_18159)
    | ~ class_Orderings_Olinorder(U_18158) ),
    inference(clausify,[status(thm)],[f_4455_2]) ).

fof(f_4456_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_4456_2,plain,
    ! [U_18162,U_18161,U_18160] :
      ( U_18161 = U_18162
      | hAPP(c_List_Oset(U_18160),U_18161) != hAPP(c_List_Oset(U_18160),U_18162)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18160),U_18162))
      | ~ c_List_Olinorder__class_Osorted(U_18160,U_18162)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18160),U_18161))
      | ~ c_List_Olinorder__class_Osorted(U_18160,U_18161)
      | ~ class_Orderings_Olinorder(U_18160) ),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

cnf(f_4456_3,plain,
    ( U_18161 = U_18162
    | hAPP(c_List_Oset(U_18160),U_18161) != hAPP(c_List_Oset(U_18160),U_18162)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18160),U_18162))
    | ~ c_List_Olinorder__class_Osorted(U_18160,U_18162)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18160),U_18161))
    | ~ c_List_Olinorder__class_Osorted(U_18160,U_18161)
    | ~ class_Orderings_Olinorder(U_18160) ),
    inference(clausify,[status(thm)],[f_4456_2]) ).

fof(f_4457_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_4457_2,plain,
    ! [U_18166,U_18165,U_18164,U_18163] :
      ( c_List_Olinorder__class_Osorted(U_18163,hAPP(hAPP(c_List_Omap(U_18164,U_18163),U_18165),c_List_Olinorder__class_Osort__key(U_18164,U_18163,U_18165,U_18166)))
      | ~ class_Orderings_Olinorder(U_18163) ),
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

cnf(f_4457_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18163,hAPP(hAPP(c_List_Omap(U_18164,U_18163),U_18165),c_List_Olinorder__class_Osort__key(U_18164,U_18163,U_18165,U_18166)))
    | ~ class_Orderings_Olinorder(U_18163) ),
    inference(clausify,[status(thm)],[f_4457_2]) ).

fof(f_4458_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_4458_2,plain,
    ! [U_18171,U_18170,U_18169,U_18168,U_18167] :
      ( c_List_Olinorder__class_Osorted(U_18167,hAPP(hAPP(c_List_Omap(U_18168,U_18167),U_18169),c_List_Olinorder__class_Oinsort__insert__key(U_18168,U_18167,U_18169,U_18171,U_18170)))
      | ~ c_List_Olinorder__class_Osorted(U_18167,hAPP(hAPP(c_List_Omap(U_18168,U_18167),U_18169),U_18170))
      | ~ class_Orderings_Olinorder(U_18167) ),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

cnf(f_4458_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18167,hAPP(hAPP(c_List_Omap(U_18168,U_18167),U_18169),c_List_Olinorder__class_Oinsort__insert__key(U_18168,U_18167,U_18169,U_18171,U_18170)))
    | ~ c_List_Olinorder__class_Osorted(U_18167,hAPP(hAPP(c_List_Omap(U_18168,U_18167),U_18169),U_18170))
    | ~ class_Orderings_Olinorder(U_18167) ),
    inference(clausify,[status(thm)],[f_4458_2]) ).

fof(f_4459_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_4459_2,plain,
    ! [U_18176,U_18175,U_18174,U_18173,U_18172] :
      ( c_List_Olinorder__class_Osorted(U_18172,hAPP(hAPP(c_List_Omap(U_18173,U_18172),U_18174),c_List_Oremove1(U_18173,U_18176,U_18175)))
      | ~ c_List_Olinorder__class_Osorted(U_18172,hAPP(hAPP(c_List_Omap(U_18173,U_18172),U_18174),U_18175))
      | ~ class_Orderings_Olinorder(U_18172) ),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

cnf(f_4459_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18172,hAPP(hAPP(c_List_Omap(U_18173,U_18172),U_18174),c_List_Oremove1(U_18173,U_18176,U_18175)))
    | ~ c_List_Olinorder__class_Osorted(U_18172,hAPP(hAPP(c_List_Omap(U_18173,U_18172),U_18174),U_18175))
    | ~ class_Orderings_Olinorder(U_18172) ),
    inference(clausify,[status(thm)],[f_4459_2]) ).

fof(f_4460_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_4460_2,plain,
    ! [U_18181,U_18180,U_18179,U_18178,U_18177] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18178,U_18177,U_18179),U_18180),U_18181)))
          | ~ c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),U_18181)) )
        & ( c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),U_18181))
          | ~ c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18178,U_18177,U_18179),U_18180),U_18181))) ) )
      | ~ class_Orderings_Olinorder(U_18177) ),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

cnf(f_4460_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),U_18181))
    | ~ c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18178,U_18177,U_18179),U_18180),U_18181)))
    | ~ class_Orderings_Olinorder(U_18177) ),
    inference(clausify,[status(thm)],[f_4460_2]) ).

cnf(f_4460_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18178,U_18177,U_18179),U_18180),U_18181)))
    | ~ c_List_Olinorder__class_Osorted(U_18177,hAPP(hAPP(c_List_Omap(U_18178,U_18177),U_18179),U_18181))
    | ~ class_Orderings_Olinorder(U_18177) ),
    inference(clausify,[status(thm)],[f_4460_2]) ).

fof(f_4461_1,plain,
    ! [V_Pa_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_Pa_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_4461_2,plain,
    ! [U_18186,U_18185,U_18184,U_18183,U_18182] :
      ( c_List_Olinorder__class_Osorted(U_18182,hAPP(hAPP(c_List_Omap(U_18183,U_18182),U_18184),hAPP(c_List_Ofilter(U_18183,U_18186),U_18185)))
      | ~ c_List_Olinorder__class_Osorted(U_18182,hAPP(hAPP(c_List_Omap(U_18183,U_18182),U_18184),U_18185))
      | ~ class_Orderings_Olinorder(U_18182) ),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

cnf(f_4461_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18182,hAPP(hAPP(c_List_Omap(U_18183,U_18182),U_18184),hAPP(c_List_Ofilter(U_18183,U_18186),U_18185)))
    | ~ c_List_Olinorder__class_Osorted(U_18182,hAPP(hAPP(c_List_Omap(U_18183,U_18182),U_18184),U_18185))
    | ~ class_Orderings_Olinorder(U_18182) ),
    inference(clausify,[status(thm)],[f_4461_2]) ).

fof(f_4462_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_4462_2,plain,
    ! [U_18191,U_18190,U_18189,U_18188,U_18187] :
      ( c_List_Olinorder__class_Osorted(U_18187,hAPP(hAPP(c_List_Omap(U_18188,U_18187),U_18189),hAPP(c_List_Ofilter(U_18188,hAPP(hAPP(c_COMBC(U_18188,U_18187,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18187,tc_fun(U_18187,tc_HOL_Obool),U_18188),c_fequal),U_18189)),hAPP(U_18190,U_18191))),U_18191)))
      | ~ class_Orderings_Olinorder(U_18187) ),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

cnf(f_4462_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18187,hAPP(hAPP(c_List_Omap(U_18188,U_18187),U_18189),hAPP(c_List_Ofilter(U_18188,hAPP(hAPP(c_COMBC(U_18188,U_18187,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18187,tc_fun(U_18187,tc_HOL_Obool),U_18188),c_fequal),U_18189)),hAPP(U_18190,U_18191))),U_18191)))
    | ~ class_Orderings_Olinorder(U_18187) ),
    inference(clausify,[status(thm)],[f_4462_2]) ).

fof(f_4463_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_4463_2,plain,
    ! [U_18194,U_18193,U_18192] :
      ( c_List_Olinorder__class_Osorted(U_18192,hAPP(c_List_Ofilter(U_18192,hAPP(hAPP(c_COMBC(U_18192,U_18192,tc_HOL_Obool),c_fequal),hAPP(U_18193,U_18194))),U_18194))
      | ~ class_Orderings_Olinorder(U_18192) ),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

cnf(f_4463_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18192,hAPP(c_List_Ofilter(U_18192,hAPP(hAPP(c_COMBC(U_18192,U_18192,tc_HOL_Obool),c_fequal),hAPP(U_18193,U_18194))),U_18194))
    | ~ class_Orderings_Olinorder(U_18192) ),
    inference(clausify,[status(thm)],[f_4463_2]) ).

fof(f_4464_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_4464_2,plain,
    ! [U_18199,U_18198,U_18197] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
          | ? [U_18196] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),U_18196))
              & hBOOL(hAPP(hAPP(c_member(U_18197),U_18196),hAPP(c_List_Oset(U_18197),U_18199))) )
          | ~ c_List_Olinorder__class_Osorted(U_18197,U_18199) )
        & ( ( ! [U_18195] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),U_18195))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18197),U_18195),hAPP(c_List_Oset(U_18197),U_18199))) )
            & c_List_Olinorder__class_Osorted(U_18197,U_18199) )
          | ~ c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199)) ) )
      | ~ class_Orderings_Olinorder(U_18197) ),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

fof(f_4464_3,plain,
    ! [U_18199,U_18198,U_18197] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),sK442(U_18199,U_18198,U_18197)))
            & hBOOL(hAPP(hAPP(c_member(U_18197),sK442(U_18199,U_18198,U_18197)),hAPP(c_List_Oset(U_18197),U_18199))) )
          | ~ c_List_Olinorder__class_Osorted(U_18197,U_18199) )
        & ( ( ! [U_18195] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),U_18195))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18197),U_18195),hAPP(c_List_Oset(U_18197),U_18199))) )
            & c_List_Olinorder__class_Osorted(U_18197,U_18199) )
          | ~ c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199)) ) )
      | ~ class_Orderings_Olinorder(U_18197) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_18196,sK442(U_18199,U_18198,U_18197))],[f_4464_2]) ).

cnf(f_4464_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18197,U_18199)
    | ~ c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
    | ~ class_Orderings_Olinorder(U_18197) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

cnf(f_4464_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),U_18195))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18197),U_18195),hAPP(c_List_Oset(U_18197),U_18199)))
    | ~ c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
    | ~ class_Orderings_Olinorder(U_18197) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

cnf(f_4464_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18197),sK442(U_18199,U_18198,U_18197)),hAPP(c_List_Oset(U_18197),U_18199)))
    | ~ c_List_Olinorder__class_Osorted(U_18197,U_18199)
    | c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
    | ~ class_Orderings_Olinorder(U_18197) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

cnf(f_4464_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18197),U_18198),sK442(U_18199,U_18198,U_18197)))
    | ~ c_List_Olinorder__class_Osorted(U_18197,U_18199)
    | c_List_Olinorder__class_Osorted(U_18197,hAPP(hAPP(c_List_Olist_OCons(U_18197),U_18198),U_18199))
    | ~ class_Orderings_Olinorder(U_18197) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

fof(f_4465_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_4465_2,plain,
    ! [U_18206,U_18205,U_18204] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
          | ? [U_18203] :
              ( ? [U_18202] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18203),U_18202))
                  & hBOOL(hAPP(hAPP(c_member(U_18204),U_18202),hAPP(c_List_Oset(U_18204),U_18206))) )
              & hBOOL(hAPP(hAPP(c_member(U_18204),U_18203),hAPP(c_List_Oset(U_18204),U_18205))) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18205) )
        & ( ( ! [U_18201] :
                ( ! [U_18200] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18201),U_18200))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18200),hAPP(c_List_Oset(U_18204),U_18206))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18201),hAPP(c_List_Oset(U_18204),U_18205))) )
            & c_List_Olinorder__class_Osorted(U_18204,U_18206)
            & c_List_Olinorder__class_Osorted(U_18204,U_18205) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206)) ) )
      | ~ class_Orderings_Olinorder(U_18204) ),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

fof(f_4465_3,plain,
    ! [U_18206,U_18205,U_18204] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
          | ( ? [U_18202] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),sK443(U_18206,U_18205,U_18204)),U_18202))
                & hBOOL(hAPP(hAPP(c_member(U_18204),U_18202),hAPP(c_List_Oset(U_18204),U_18206))) )
            & hBOOL(hAPP(hAPP(c_member(U_18204),sK443(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18205))) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18205) )
        & ( ( ! [U_18201] :
                ( ! [U_18200] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18201),U_18200))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18200),hAPP(c_List_Oset(U_18204),U_18206))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18201),hAPP(c_List_Oset(U_18204),U_18205))) )
            & c_List_Olinorder__class_Osorted(U_18204,U_18206)
            & c_List_Olinorder__class_Osorted(U_18204,U_18205) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206)) ) )
      | ~ class_Orderings_Olinorder(U_18204) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_18203,sK443(U_18206,U_18205,U_18204))],[f_4465_2]) ).

fof(f_4465_4,plain,
    ! [U_18206,U_18205,U_18204] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),sK443(U_18206,U_18205,U_18204)),sK444(U_18206,U_18205,U_18204)))
            & hBOOL(hAPP(hAPP(c_member(U_18204),sK444(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18206)))
            & hBOOL(hAPP(hAPP(c_member(U_18204),sK443(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18205))) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18205) )
        & ( ( ! [U_18201] :
                ( ! [U_18200] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18201),U_18200))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18200),hAPP(c_List_Oset(U_18204),U_18206))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18201),hAPP(c_List_Oset(U_18204),U_18205))) )
            & c_List_Olinorder__class_Osorted(U_18204,U_18206)
            & c_List_Olinorder__class_Osorted(U_18204,U_18205) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206)) ) )
      | ~ class_Orderings_Olinorder(U_18204) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_18202,sK444(U_18206,U_18205,U_18204))],[f_4465_3]) ).

cnf(f_4465_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18204,U_18205)
    | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

cnf(f_4465_6,plain,
    ( c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

cnf(f_4465_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18201),U_18200))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18200),hAPP(c_List_Oset(U_18204),U_18206)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18201),hAPP(c_List_Oset(U_18204),U_18205)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

cnf(f_4465_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18204),sK443(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18205)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18205)
    | c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

cnf(f_4465_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18204),sK444(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,U_18205)
    | c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

cnf(f_4465_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),sK443(U_18206,U_18205,U_18204)),sK444(U_18206,U_18205,U_18204)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18205)
    | c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Oappend(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4465_4]) ).

fof(f_4466_1,plain,
    ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,V_Pa_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_Pa_2),V_xs_2))
      | ~ hBOOL(hAPP(V_Pa_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_4466_2,plain,
    ! [U_18212,U_18211,U_18210,U_18209,U_18208,U_18207] :
      ( hAPP(c_List_Ofilter(U_18208,U_18211),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18208,U_18207,U_18209),U_18212),U_18210)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18208,U_18207,U_18209),U_18212),hAPP(c_List_Ofilter(U_18208,U_18211),U_18210))
      | ~ hBOOL(hAPP(U_18211,U_18212))
      | ~ c_List_Olinorder__class_Osorted(U_18207,hAPP(hAPP(c_List_Omap(U_18208,U_18207),U_18209),U_18210))
      | ~ class_Orderings_Olinorder(U_18207) ),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

cnf(f_4466_3,plain,
    ( hAPP(c_List_Ofilter(U_18208,U_18211),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18208,U_18207,U_18209),U_18212),U_18210)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18208,U_18207,U_18209),U_18212),hAPP(c_List_Ofilter(U_18208,U_18211),U_18210))
    | ~ hBOOL(hAPP(U_18211,U_18212))
    | ~ c_List_Olinorder__class_Osorted(U_18207,hAPP(hAPP(c_List_Omap(U_18208,U_18207),U_18209),U_18210))
    | ~ class_Orderings_Olinorder(U_18207) ),
    inference(clausify,[status(thm)],[f_4466_2]) ).

fof(f_4467_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_4467_2,plain,
    ! [U_18217,U_18216,U_18215] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
          | ~ c_List_Olinorder__class_Osorted(U_18215,U_18217)
          | ? [U_18214] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),U_18214))
              & hBOOL(hAPP(hAPP(c_member(U_18215),U_18214),hAPP(c_List_Oset(U_18215),U_18217))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_18215,U_18217)
            & ! [U_18213] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),U_18213))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18215),U_18213),hAPP(c_List_Oset(U_18215),U_18217))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217)) ) )
      | ~ class_Orderings_Olinorder(U_18215) ),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

fof(f_4467_3,plain,
    ! [U_18217,U_18216,U_18215] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
          | ~ c_List_Olinorder__class_Osorted(U_18215,U_18217)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),sK445(U_18217,U_18216,U_18215)))
            & hBOOL(hAPP(hAPP(c_member(U_18215),sK445(U_18217,U_18216,U_18215)),hAPP(c_List_Oset(U_18215),U_18217))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_18215,U_18217)
            & ! [U_18213] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),U_18213))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18215),U_18213),hAPP(c_List_Oset(U_18215),U_18217))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217)) ) )
      | ~ class_Orderings_Olinorder(U_18215) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_18214,sK445(U_18217,U_18216,U_18215))],[f_4467_2]) ).

cnf(f_4467_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),U_18213))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18215),U_18213),hAPP(c_List_Oset(U_18215),U_18217)))
    | ~ c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
    | ~ class_Orderings_Olinorder(U_18215) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

cnf(f_4467_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18215,U_18217)
    | ~ c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
    | ~ class_Orderings_Olinorder(U_18215) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

cnf(f_4467_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18215),sK445(U_18217,U_18216,U_18215)),hAPP(c_List_Oset(U_18215),U_18217)))
    | ~ c_List_Olinorder__class_Osorted(U_18215,U_18217)
    | c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
    | ~ class_Orderings_Olinorder(U_18215) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

cnf(f_4467_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18215),U_18216),sK445(U_18217,U_18216,U_18215)))
    | ~ c_List_Olinorder__class_Osorted(U_18215,U_18217)
    | c_List_Olinorder__class_Osorted(U_18215,hAPP(hAPP(c_List_Olist_OCons(U_18215),U_18216),U_18217))
    | ~ class_Orderings_Olinorder(U_18215) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

fof(f_4468_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_4468_2,plain,
    ! [U_18219,U_18218] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18218),c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219)))
        & c_List_Olinorder__class_Osorted(U_18218,c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219))
        & hAPP(c_List_Oset(U_18218),c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219)) = U_18219 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18218),U_18219))
      | ~ class_Orderings_Olinorder(U_18218) ),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

cnf(f_4468_3,plain,
    ( hAPP(c_List_Oset(U_18218),c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219)) = U_18219
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18218),U_18219))
    | ~ class_Orderings_Olinorder(U_18218) ),
    inference(clausify,[status(thm)],[f_4468_2]) ).

cnf(f_4468_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18218,c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18218),U_18219))
    | ~ class_Orderings_Olinorder(U_18218) ),
    inference(clausify,[status(thm)],[f_4468_2]) ).

cnf(f_4468_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18218),c_List_Olinorder__class_Osorted__list__of__set(U_18218,U_18219)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18218),U_18219))
    | ~ class_Orderings_Olinorder(U_18218) ),
    inference(clausify,[status(thm)],[f_4468_2]) ).

fof(f_4469_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_4469_2,plain,
    ! [U_18222,U_18221,U_18220] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18220,U_18220,c_COMBI(U_18220)),U_18221),c_List_Oremove1(U_18220,U_18221,U_18222)) = U_18222
      | ~ c_List_Olinorder__class_Osorted(U_18220,U_18222)
      | ~ hBOOL(hAPP(hAPP(c_member(U_18220),U_18221),hAPP(c_List_Oset(U_18220),U_18222)))
      | ~ class_Orderings_Olinorder(U_18220) ),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

cnf(f_4469_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18220,U_18220,c_COMBI(U_18220)),U_18221),c_List_Oremove1(U_18220,U_18221,U_18222)) = U_18222
    | ~ c_List_Olinorder__class_Osorted(U_18220,U_18222)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18220),U_18221),hAPP(c_List_Oset(U_18220),U_18222)))
    | ~ class_Orderings_Olinorder(U_18220) ),
    inference(clausify,[status(thm)],[f_4469_2]) ).

fof(f_4470_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_4470_2,plain,
    ! [U_18228,U_18227] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18227,U_18228)
          | ? [U_18226] :
              ( ? [U_18225] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18225)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18226)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18225),U_18226)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) ) )
        & ( ! [U_18224] :
              ( ! [U_18223] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18223)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18224)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18223),U_18224)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) )
          | ~ c_List_Olinorder__class_Osorted(U_18227,U_18228) ) )
      | ~ class_Orderings_Olinorder(U_18227) ),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

fof(f_4470_3,plain,
    ! [U_18228,U_18227] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18227,U_18228)
          | ( ? [U_18225] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18225)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),sK446(U_18228,U_18227))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18225),sK446(U_18228,U_18227))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK446(U_18228,U_18227)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) ) )
        & ( ! [U_18224] :
              ( ! [U_18223] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18223)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18224)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18223),U_18224)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) )
          | ~ c_List_Olinorder__class_Osorted(U_18227,U_18228) ) )
      | ~ class_Orderings_Olinorder(U_18227) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_18226,sK446(U_18228,U_18227))],[f_4470_2]) ).

fof(f_4470_4,plain,
    ! [U_18228,U_18227] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18227,U_18228)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),sK447(U_18228,U_18227))),hAPP(hAPP(c_List_Onth(U_18227),U_18228),sK446(U_18228,U_18227))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK447(U_18228,U_18227)),sK446(U_18228,U_18227)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK446(U_18228,U_18227)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) ) )
        & ( ! [U_18224] :
              ( ! [U_18223] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18223)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18224)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18223),U_18224)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228))) )
          | ~ c_List_Olinorder__class_Osorted(U_18227,U_18228) ) )
      | ~ class_Orderings_Olinorder(U_18227) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_18225,sK447(U_18228,U_18227))],[f_4470_3]) ).

cnf(f_4470_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18223)),hAPP(hAPP(c_List_Onth(U_18227),U_18228),U_18224)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18223),U_18224))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228)))
    | ~ c_List_Olinorder__class_Osorted(U_18227,U_18228)
    | ~ class_Orderings_Olinorder(U_18227) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

cnf(f_4470_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK446(U_18228,U_18227)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)),U_18228)))
    | c_List_Olinorder__class_Osorted(U_18227,U_18228)
    | ~ class_Orderings_Olinorder(U_18227) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

cnf(f_4470_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK447(U_18228,U_18227)),sK446(U_18228,U_18227)))
    | c_List_Olinorder__class_Osorted(U_18227,U_18228)
    | ~ class_Orderings_Olinorder(U_18227) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

cnf(f_4470_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18227),hAPP(hAPP(c_List_Onth(U_18227),U_18228),sK447(U_18228,U_18227))),hAPP(hAPP(c_List_Onth(U_18227),U_18228),sK446(U_18228,U_18227))))
    | c_List_Olinorder__class_Osorted(U_18227,U_18228)
    | ~ class_Orderings_Olinorder(U_18227) ),
    inference(clausify,[status(thm)],[f_4470_4]) ).

fof(f_4471_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_4471_2,plain,
    ! [U_18232,U_18231,U_18230,U_18229] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18230),U_18231)),hAPP(hAPP(c_List_Onth(U_18229),U_18230),U_18232)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18230)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18231),U_18232))
      | ~ c_List_Olinorder__class_Osorted(U_18229,U_18230)
      | ~ class_Orderings_Olinorder(U_18229) ),
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

cnf(f_4471_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18230),U_18231)),hAPP(hAPP(c_List_Onth(U_18229),U_18230),U_18232)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18230)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18231),U_18232))
    | ~ c_List_Olinorder__class_Osorted(U_18229,U_18230)
    | ~ class_Orderings_Olinorder(U_18229) ),
    inference(clausify,[status(thm)],[f_4471_2]) ).

fof(f_4472_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_4472_2,plain,
    ! [U_18237,U_18236,U_18235,U_18234,U_18233] :
      ( U_18236 = U_18237
      | hAPP(c_List_Oset(U_18234),U_18236) != hAPP(c_List_Oset(U_18234),U_18237)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18233),hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18237)))
      | ~ c_List_Olinorder__class_Osorted(U_18233,hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18237))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18233),hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18236)))
      | ~ c_List_Olinorder__class_Osorted(U_18233,hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18236))
      | ~ c_Fun_Oinj__on(U_18234,U_18233,U_18235,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18234,tc_HOL_Obool)),hAPP(c_List_Oset(U_18234),U_18236)),hAPP(c_List_Oset(U_18234),U_18237)))
      | ~ class_Orderings_Olinorder(U_18233) ),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

cnf(f_4472_3,plain,
    ( U_18236 = U_18237
    | hAPP(c_List_Oset(U_18234),U_18236) != hAPP(c_List_Oset(U_18234),U_18237)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18233),hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18237)))
    | ~ c_List_Olinorder__class_Osorted(U_18233,hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18237))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18233),hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18236)))
    | ~ c_List_Olinorder__class_Osorted(U_18233,hAPP(hAPP(c_List_Omap(U_18234,U_18233),U_18235),U_18236))
    | ~ c_Fun_Oinj__on(U_18234,U_18233,U_18235,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18234,tc_HOL_Obool)),hAPP(c_List_Oset(U_18234),U_18236)),hAPP(c_List_Oset(U_18234),U_18237)))
    | ~ class_Orderings_Olinorder(U_18233) ),
    inference(clausify,[status(thm)],[f_4472_2]) ).

fof(f_4473_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_4473_2,plain,
    ! [U_18240,U_18239,U_18238] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18238),U_18238),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18238),tc_Nat_Onat,U_18238),c_List_Onth(U_18238)),U_18240)),hAPP(c_List_Ofilter(tc_List_Olist(U_18238),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18238)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18240)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)))),c_List_Otranspose(U_18238,U_18239))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18238)),U_18239),U_18240)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18240),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18238))),U_18239)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18238),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18238))),U_18239))) ),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

cnf(f_4473_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18238),U_18238),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18238),tc_Nat_Onat,U_18238),c_List_Onth(U_18238)),U_18240)),hAPP(c_List_Ofilter(tc_List_Olist(U_18238),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18238)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18240)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)))),c_List_Otranspose(U_18238,U_18239))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18238)),U_18239),U_18240)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18240),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18238))),U_18239)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18238),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18238))),U_18239))) ),
    inference(clausify,[status(thm)],[f_4473_2]) ).

fof(f_4474_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_4474_2,plain,
    ! [U_18244,U_18243,U_18242,U_18241] :
      ( hAPP(hAPP(c_List_Onth(U_18241),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18241)),c_List_Otranspose(U_18241,U_18242)),U_18243)),U_18244) = hAPP(hAPP(c_List_Onth(U_18241),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18241)),U_18242),U_18244)),U_18243)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18244),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18241))),hAPP(c_List_Ofilter(tc_List_Olist(U_18241),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18241)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)))),U_18242))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18241))),c_List_Otranspose(U_18241,U_18242))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18241),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18241))),U_18242))) ),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

cnf(f_4474_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18241),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18241)),c_List_Otranspose(U_18241,U_18242)),U_18243)),U_18244) = hAPP(hAPP(c_List_Onth(U_18241),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18241)),U_18242),U_18244)),U_18243)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18244),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18241))),hAPP(c_List_Ofilter(tc_List_Olist(U_18241),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18241)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18241)))),U_18242))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18241))),c_List_Otranspose(U_18241,U_18242))))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18241),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18241))),U_18242))) ),
    inference(clausify,[status(thm)],[f_4474_2]) ).

fof(f_4475_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_4475_2,plain,
    ! [U_18246,U_18245] : c_Fun_Oinj__on(tc_List_Olist(U_18245),tc_List_Olist(U_18245),c_List_Orev(U_18245),U_18246),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

cnf(f_4475_3,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_18245),tc_List_Olist(U_18245),c_List_Orev(U_18245),U_18246),
    inference(clausify,[status(thm)],[f_4475_2]) ).

fof(f_4476_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_4476_2,plain,
    ! [U_18248,U_18247] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18247),hAPP(c_List_Orev(U_18247),U_18248)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18247),U_18248)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_18247),U_18248))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18247),hAPP(c_List_Orev(U_18247),U_18248))) ) ),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

fof(f_4476_3,plain,
    ( ! [U_18252,U_18250] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18250),hAPP(c_List_Orev(U_18250),U_18252)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18250),U_18252)) )
    & ! [U_18251,U_18249] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18249),U_18251))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18249),hAPP(c_List_Orev(U_18249),U_18251))) ) ),
    inference(miniscope,[status(thm)],[f_4476_2]) ).

cnf(f_4476_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18249),U_18251))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18249),hAPP(c_List_Orev(U_18249),U_18251))) ),
    inference(clausify,[status(thm)],[f_4476_3]) ).

cnf(f_4476_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18250),hAPP(c_List_Orev(U_18250),U_18252)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18250),U_18252)) ),
    inference(clausify,[status(thm)],[f_4476_3]) ).

fof(f_4477_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_4477_2,plain,
    ! [U_18255,U_18254,U_18253] : hAPP(c_List_Orev(U_18253),hAPP(hAPP(c_List_Oappend(U_18253),U_18254),U_18255)) = hAPP(hAPP(c_List_Oappend(U_18253),hAPP(c_List_Orev(U_18253),U_18255)),hAPP(c_List_Orev(U_18253),U_18254)),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

cnf(f_4477_3,plain,
    hAPP(c_List_Orev(U_18253),hAPP(hAPP(c_List_Oappend(U_18253),U_18254),U_18255)) = hAPP(hAPP(c_List_Oappend(U_18253),hAPP(c_List_Orev(U_18253),U_18255)),hAPP(c_List_Orev(U_18253),U_18254)),
    inference(clausify,[status(thm)],[f_4477_2]) ).

fof(f_4478_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_4478_2,plain,
    ! [U_18258,U_18257,U_18256] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18256),U_18257),c_List_Olist_ONil(U_18256)) = hAPP(c_List_Orev(U_18256),U_18258)
        | U_18258 != hAPP(hAPP(c_List_Olist_OCons(U_18256),U_18257),c_List_Olist_ONil(U_18256)) )
      & ( U_18258 = hAPP(hAPP(c_List_Olist_OCons(U_18256),U_18257),c_List_Olist_ONil(U_18256))
        | hAPP(hAPP(c_List_Olist_OCons(U_18256),U_18257),c_List_Olist_ONil(U_18256)) != hAPP(c_List_Orev(U_18256),U_18258) ) ),
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

fof(f_4478_3,plain,
    ( ! [U_18264,U_18262,U_18260] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18260),U_18262),c_List_Olist_ONil(U_18260)) = hAPP(c_List_Orev(U_18260),U_18264)
        | U_18264 != hAPP(hAPP(c_List_Olist_OCons(U_18260),U_18262),c_List_Olist_ONil(U_18260)) )
    & ! [U_18263,U_18261,U_18259] :
        ( U_18263 = hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18261),c_List_Olist_ONil(U_18259))
        | hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18261),c_List_Olist_ONil(U_18259)) != hAPP(c_List_Orev(U_18259),U_18263) ) ),
    inference(miniscope,[status(thm)],[f_4478_2]) ).

cnf(f_4478_4,plain,
    ( U_18263 = hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18261),c_List_Olist_ONil(U_18259))
    | hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18261),c_List_Olist_ONil(U_18259)) != hAPP(c_List_Orev(U_18259),U_18263) ),
    inference(clausify,[status(thm)],[f_4478_3]) ).

cnf(f_4478_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18260),U_18262),c_List_Olist_ONil(U_18260)) = hAPP(c_List_Orev(U_18260),U_18264)
    | U_18264 != hAPP(hAPP(c_List_Olist_OCons(U_18260),U_18262),c_List_Olist_ONil(U_18260)) ),
    inference(clausify,[status(thm)],[f_4478_3]) ).

fof(f_4479_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_4479_2,plain,
    ! [U_18267,U_18266,U_18265] :
      ( ( hAPP(c_List_Orev(U_18265),U_18266) = hAPP(hAPP(c_List_Olist_OCons(U_18265),U_18267),c_List_Olist_ONil(U_18265))
        | U_18266 != hAPP(hAPP(c_List_Olist_OCons(U_18265),U_18267),c_List_Olist_ONil(U_18265)) )
      & ( U_18266 = hAPP(hAPP(c_List_Olist_OCons(U_18265),U_18267),c_List_Olist_ONil(U_18265))
        | hAPP(c_List_Orev(U_18265),U_18266) != hAPP(hAPP(c_List_Olist_OCons(U_18265),U_18267),c_List_Olist_ONil(U_18265)) ) ),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

fof(f_4479_3,plain,
    ( ! [U_18273,U_18271,U_18269] :
        ( hAPP(c_List_Orev(U_18269),U_18271) = hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18273),c_List_Olist_ONil(U_18269))
        | U_18271 != hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18273),c_List_Olist_ONil(U_18269)) )
    & ! [U_18272,U_18270,U_18268] :
        ( U_18270 = hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18272),c_List_Olist_ONil(U_18268))
        | hAPP(c_List_Orev(U_18268),U_18270) != hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18272),c_List_Olist_ONil(U_18268)) ) ),
    inference(miniscope,[status(thm)],[f_4479_2]) ).

cnf(f_4479_4,plain,
    ( U_18270 = hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18272),c_List_Olist_ONil(U_18268))
    | hAPP(c_List_Orev(U_18268),U_18270) != hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18272),c_List_Olist_ONil(U_18268)) ),
    inference(clausify,[status(thm)],[f_4479_3]) ).

cnf(f_4479_5,plain,
    ( hAPP(c_List_Orev(U_18269),U_18271) = hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18273),c_List_Olist_ONil(U_18269))
    | U_18271 != hAPP(hAPP(c_List_Olist_OCons(U_18269),U_18273),c_List_Olist_ONil(U_18269)) ),
    inference(clausify,[status(thm)],[f_4479_3]) ).

fof(f_4480_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_4480_2,plain,
    ! [U_18275,U_18274] :
      ( ( hAPP(c_List_Orev(U_18274),U_18275) = c_List_Olist_ONil(U_18274)
        | U_18275 != c_List_Olist_ONil(U_18274) )
      & ( U_18275 = c_List_Olist_ONil(U_18274)
        | hAPP(c_List_Orev(U_18274),U_18275) != c_List_Olist_ONil(U_18274) ) ),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ( ! [U_18279,U_18277] :
        ( hAPP(c_List_Orev(U_18277),U_18279) = c_List_Olist_ONil(U_18277)
        | U_18279 != c_List_Olist_ONil(U_18277) )
    & ! [U_18278,U_18276] :
        ( U_18278 = c_List_Olist_ONil(U_18276)
        | hAPP(c_List_Orev(U_18276),U_18278) != c_List_Olist_ONil(U_18276) ) ),
    inference(miniscope,[status(thm)],[f_4480_2]) ).

cnf(f_4480_4,plain,
    ( U_18278 = c_List_Olist_ONil(U_18276)
    | hAPP(c_List_Orev(U_18276),U_18278) != c_List_Olist_ONil(U_18276) ),
    inference(clausify,[status(thm)],[f_4480_3]) ).

cnf(f_4480_5,plain,
    ( hAPP(c_List_Orev(U_18277),U_18279) = c_List_Olist_ONil(U_18277)
    | U_18279 != c_List_Olist_ONil(U_18277) ),
    inference(clausify,[status(thm)],[f_4480_3]) ).

fof(f_4481_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_4481_2,plain,
    ! [U_18281,U_18280] :
      ( ( c_List_Olist_ONil(U_18280) = hAPP(c_List_Orev(U_18280),U_18281)
        | U_18281 != c_List_Olist_ONil(U_18280) )
      & ( U_18281 = c_List_Olist_ONil(U_18280)
        | c_List_Olist_ONil(U_18280) != hAPP(c_List_Orev(U_18280),U_18281) ) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

fof(f_4481_3,plain,
    ( ! [U_18285,U_18283] :
        ( c_List_Olist_ONil(U_18283) = hAPP(c_List_Orev(U_18283),U_18285)
        | U_18285 != c_List_Olist_ONil(U_18283) )
    & ! [U_18284,U_18282] :
        ( U_18284 = c_List_Olist_ONil(U_18282)
        | c_List_Olist_ONil(U_18282) != hAPP(c_List_Orev(U_18282),U_18284) ) ),
    inference(miniscope,[status(thm)],[f_4481_2]) ).

cnf(f_4481_4,plain,
    ( U_18284 = c_List_Olist_ONil(U_18282)
    | c_List_Olist_ONil(U_18282) != hAPP(c_List_Orev(U_18282),U_18284) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

cnf(f_4481_5,plain,
    ( c_List_Olist_ONil(U_18283) = hAPP(c_List_Orev(U_18283),U_18285)
    | U_18285 != c_List_Olist_ONil(U_18283) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

fof(f_4482_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_4482_2,plain,
    ! [U_18286] : hAPP(c_List_Orev(U_18286),c_List_Olist_ONil(U_18286)) = c_List_Olist_ONil(U_18286),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

cnf(f_4482_3,plain,
    hAPP(c_List_Orev(U_18286),c_List_Olist_ONil(U_18286)) = c_List_Olist_ONil(U_18286),
    inference(clausify,[status(thm)],[f_4482_2]) ).

fof(f_4483_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_4483_2,plain,
    ! [U_18288,U_18287] : hAPP(c_List_Orev(U_18287),c_List_Oconcat(U_18287,U_18288)) = c_List_Oconcat(U_18287,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18287),tc_List_Olist(U_18287)),c_List_Orev(U_18287)),hAPP(c_List_Orev(tc_List_Olist(U_18287)),U_18288))),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

cnf(f_4483_3,plain,
    hAPP(c_List_Orev(U_18287),c_List_Oconcat(U_18287,U_18288)) = c_List_Oconcat(U_18287,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18287),tc_List_Olist(U_18287)),c_List_Orev(U_18287)),hAPP(c_List_Orev(tc_List_Olist(U_18287)),U_18288))),
    inference(clausify,[status(thm)],[f_4483_2]) ).

fof(f_4484_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_4484_2,plain,
    ! [U_18292,U_18291,U_18290,U_18289] : hAPP(c_List_Orev(U_18289),hAPP(hAPP(c_List_Omap(U_18290,U_18289),U_18291),U_18292)) = hAPP(hAPP(c_List_Omap(U_18290,U_18289),U_18291),hAPP(c_List_Orev(U_18290),U_18292)),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

cnf(f_4484_3,plain,
    hAPP(c_List_Orev(U_18289),hAPP(hAPP(c_List_Omap(U_18290,U_18289),U_18291),U_18292)) = hAPP(hAPP(c_List_Omap(U_18290,U_18289),U_18291),hAPP(c_List_Orev(U_18290),U_18292)),
    inference(clausify,[status(thm)],[f_4484_2]) ).

fof(f_4485_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__filter]) ).

fof(f_4485_2,plain,
    ! [U_18295,U_18294,U_18293] : hAPP(c_List_Orev(U_18293),hAPP(c_List_Ofilter(U_18293,U_18294),U_18295)) = hAPP(c_List_Ofilter(U_18293,U_18294),hAPP(c_List_Orev(U_18293),U_18295)),
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

cnf(f_4485_3,plain,
    hAPP(c_List_Orev(U_18293),hAPP(c_List_Ofilter(U_18293,U_18294),U_18295)) = hAPP(c_List_Ofilter(U_18293,U_18294),hAPP(c_List_Orev(U_18293),U_18295)),
    inference(clausify,[status(thm)],[f_4485_2]) ).

fof(f_4486_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_4486_2,plain,
    ! [U_18299,U_18298,U_18297,U_18296] :
      ( hAPP(hAPP(c_List_Ozip(U_18296,U_18298),hAPP(c_List_Orev(U_18296),U_18297)),hAPP(c_List_Orev(U_18298),U_18299)) = hAPP(c_List_Orev(tc_prod(U_18296,U_18298)),hAPP(hAPP(c_List_Ozip(U_18296,U_18298),U_18297),U_18299))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18296)),U_18297) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18299) ),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

cnf(f_4486_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18296,U_18298),hAPP(c_List_Orev(U_18296),U_18297)),hAPP(c_List_Orev(U_18298),U_18299)) = hAPP(c_List_Orev(tc_prod(U_18296,U_18298)),hAPP(hAPP(c_List_Ozip(U_18296,U_18298),U_18297),U_18299))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18296)),U_18297) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18298)),U_18299) ),
    inference(clausify,[status(thm)],[f_4486_2]) ).

fof(f_4487_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_4487_2,plain,
    ! [U_18301,U_18300] : hAPP(c_List_Oset(U_18300),hAPP(c_List_Orev(U_18300),U_18301)) = hAPP(c_List_Oset(U_18300),U_18301),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

cnf(f_4487_3,plain,
    hAPP(c_List_Oset(U_18300),hAPP(c_List_Orev(U_18300),U_18301)) = hAPP(c_List_Oset(U_18300),U_18301),
    inference(clausify,[status(thm)],[f_4487_2]) ).

fof(f_4488_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_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_Pa_2,V_xs_2,V_ys_2) )
      & ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_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_4488_2,plain,
    ! [U_18306,U_18305,U_18304,U_18303,U_18302] :
      ( ( c_List_Olist__all2(U_18302,U_18303,U_18304,hAPP(c_List_Orev(U_18302),U_18305),hAPP(c_List_Orev(U_18303),U_18306))
        | ~ c_List_Olist__all2(U_18302,U_18303,U_18304,U_18305,U_18306) )
      & ( c_List_Olist__all2(U_18302,U_18303,U_18304,U_18305,U_18306)
        | ~ c_List_Olist__all2(U_18302,U_18303,U_18304,hAPP(c_List_Orev(U_18302),U_18305),hAPP(c_List_Orev(U_18303),U_18306)) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18316,U_18314,U_18312,U_18310,U_18308] :
        ( c_List_Olist__all2(U_18308,U_18310,U_18312,hAPP(c_List_Orev(U_18308),U_18314),hAPP(c_List_Orev(U_18310),U_18316))
        | ~ c_List_Olist__all2(U_18308,U_18310,U_18312,U_18314,U_18316) )
    & ! [U_18315,U_18313,U_18311,U_18309,U_18307] :
        ( c_List_Olist__all2(U_18307,U_18309,U_18311,U_18313,U_18315)
        | ~ c_List_Olist__all2(U_18307,U_18309,U_18311,hAPP(c_List_Orev(U_18307),U_18313),hAPP(c_List_Orev(U_18309),U_18315)) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

cnf(f_4488_4,plain,
    ( c_List_Olist__all2(U_18307,U_18309,U_18311,U_18313,U_18315)
    | ~ c_List_Olist__all2(U_18307,U_18309,U_18311,hAPP(c_List_Orev(U_18307),U_18313),hAPP(c_List_Orev(U_18309),U_18315)) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( c_List_Olist__all2(U_18308,U_18310,U_18312,hAPP(c_List_Orev(U_18308),U_18314),hAPP(c_List_Orev(U_18310),U_18316))
    | ~ c_List_Olist__all2(U_18308,U_18310,U_18312,U_18314,U_18316) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

fof(f_4489_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) )
      & ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2))
        | ~ c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__rev1]) ).

fof(f_4489_2,plain,
    ! [U_18321,U_18320,U_18319,U_18318,U_18317] :
      ( ( c_List_Olist__all2(U_18317,U_18318,U_18319,hAPP(c_List_Orev(U_18317),U_18320),U_18321)
        | ~ c_List_Olist__all2(U_18317,U_18318,U_18319,U_18320,hAPP(c_List_Orev(U_18318),U_18321)) )
      & ( c_List_Olist__all2(U_18317,U_18318,U_18319,U_18320,hAPP(c_List_Orev(U_18318),U_18321))
        | ~ c_List_Olist__all2(U_18317,U_18318,U_18319,hAPP(c_List_Orev(U_18317),U_18320),U_18321) ) ),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

fof(f_4489_3,plain,
    ( ! [U_18331,U_18329,U_18327,U_18325,U_18323] :
        ( c_List_Olist__all2(U_18323,U_18325,U_18327,hAPP(c_List_Orev(U_18323),U_18329),U_18331)
        | ~ c_List_Olist__all2(U_18323,U_18325,U_18327,U_18329,hAPP(c_List_Orev(U_18325),U_18331)) )
    & ! [U_18330,U_18328,U_18326,U_18324,U_18322] :
        ( c_List_Olist__all2(U_18322,U_18324,U_18326,U_18328,hAPP(c_List_Orev(U_18324),U_18330))
        | ~ c_List_Olist__all2(U_18322,U_18324,U_18326,hAPP(c_List_Orev(U_18322),U_18328),U_18330) ) ),
    inference(miniscope,[status(thm)],[f_4489_2]) ).

cnf(f_4489_4,plain,
    ( c_List_Olist__all2(U_18322,U_18324,U_18326,U_18328,hAPP(c_List_Orev(U_18324),U_18330))
    | ~ c_List_Olist__all2(U_18322,U_18324,U_18326,hAPP(c_List_Orev(U_18322),U_18328),U_18330) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

cnf(f_4489_5,plain,
    ( c_List_Olist__all2(U_18323,U_18325,U_18327,hAPP(c_List_Orev(U_18323),U_18329),U_18331)
    | ~ c_List_Olist__all2(U_18323,U_18325,U_18327,U_18329,hAPP(c_List_Orev(U_18325),U_18331)) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

fof(f_4490_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_4490_2,plain,
    ! [U_18333,U_18332] : hAPP(c_List_Orev(U_18332),hAPP(c_List_Orev(U_18332),U_18333)) = U_18333,
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

cnf(f_4490_3,plain,
    hAPP(c_List_Orev(U_18332),hAPP(c_List_Orev(U_18332),U_18333)) = U_18333,
    inference(clausify,[status(thm)],[f_4490_2]) ).

fof(f_4491_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_4491_2,plain,
    ! [U_18336,U_18335,U_18334] :
      ( ( hAPP(c_List_Orev(U_18334),U_18335) = U_18336
        | U_18335 != hAPP(c_List_Orev(U_18334),U_18336) )
      & ( U_18335 = hAPP(c_List_Orev(U_18334),U_18336)
        | hAPP(c_List_Orev(U_18334),U_18335) != U_18336 ) ),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

fof(f_4491_3,plain,
    ( ! [U_18342,U_18340,U_18338] :
        ( hAPP(c_List_Orev(U_18338),U_18340) = U_18342
        | U_18340 != hAPP(c_List_Orev(U_18338),U_18342) )
    & ! [U_18341,U_18339,U_18337] :
        ( U_18339 = hAPP(c_List_Orev(U_18337),U_18341)
        | hAPP(c_List_Orev(U_18337),U_18339) != U_18341 ) ),
    inference(miniscope,[status(thm)],[f_4491_2]) ).

cnf(f_4491_4,plain,
    ( U_18339 = hAPP(c_List_Orev(U_18337),U_18341)
    | hAPP(c_List_Orev(U_18337),U_18339) != U_18341 ),
    inference(clausify,[status(thm)],[f_4491_3]) ).

cnf(f_4491_5,plain,
    ( hAPP(c_List_Orev(U_18338),U_18340) = U_18342
    | U_18340 != hAPP(c_List_Orev(U_18338),U_18342) ),
    inference(clausify,[status(thm)],[f_4491_3]) ).

fof(f_4492_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_4492_2,plain,
    ! [U_18345,U_18344,U_18343] :
      ( ( hAPP(c_List_Orev(U_18343),U_18344) = hAPP(c_List_Orev(U_18343),U_18345)
        | U_18344 != U_18345 )
      & ( U_18344 = U_18345
        | hAPP(c_List_Orev(U_18343),U_18344) != hAPP(c_List_Orev(U_18343),U_18345) ) ),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

fof(f_4492_3,plain,
    ( ! [U_18351,U_18349] :
        ( ! [U_18347] : hAPP(c_List_Orev(U_18347),U_18349) = hAPP(c_List_Orev(U_18347),U_18351)
        | U_18349 != U_18351 )
    & ! [U_18350,U_18348] :
        ( ! [U_18346] : hAPP(c_List_Orev(U_18346),U_18348) != hAPP(c_List_Orev(U_18346),U_18350)
        | U_18348 = U_18350 ) ),
    inference(miniscope,[status(thm)],[f_4492_2]) ).

cnf(f_4492_4,plain,
    ( hAPP(c_List_Orev(U_18346),U_18348) != hAPP(c_List_Orev(U_18346),U_18350)
    | U_18348 = U_18350 ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

cnf(f_4492_5,plain,
    ( hAPP(c_List_Orev(U_18347),U_18349) = hAPP(c_List_Orev(U_18347),U_18351)
    | U_18349 != U_18351 ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

fof(f_4493_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_4493_2,plain,
    ! [U_18353,U_18352] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18352),hAPP(c_List_Orev(U_18352),U_18353)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18352),U_18353)
      | ~ class_Groups_Ocomm__monoid__add(U_18352) ),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

cnf(f_4493_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18352),hAPP(c_List_Orev(U_18352),U_18353)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18352),U_18353)
    | ~ class_Groups_Ocomm__monoid__add(U_18352) ),
    inference(clausify,[status(thm)],[f_4493_2]) ).

fof(f_4494_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_4494_2,plain,
    ! [U_18355,U_18354] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18354)),hAPP(c_List_Orev(U_18354),U_18355)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18354)),U_18355),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

cnf(f_4494_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18354)),hAPP(c_List_Orev(U_18354),U_18355)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18354)),U_18355),
    inference(clausify,[status(thm)],[f_4494_2]) ).

fof(f_4495_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_4495_2,plain,
    ! [U_18360,U_18359,U_18358,U_18357,U_18356] : hAPP(c_List_Ofoldl(U_18356,U_18357,U_18358,U_18359),U_18360) = c_List_Ofoldr(U_18357,U_18356,hAPP(c_COMBC(U_18356,U_18357,U_18356),U_18358),hAPP(c_List_Orev(U_18357),U_18360),U_18359),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

cnf(f_4495_3,plain,
    hAPP(c_List_Ofoldl(U_18356,U_18357,U_18358,U_18359),U_18360) = c_List_Ofoldr(U_18357,U_18356,hAPP(c_COMBC(U_18356,U_18357,U_18356),U_18358),hAPP(c_List_Orev(U_18357),U_18360),U_18359),
    inference(clausify,[status(thm)],[f_4495_2]) ).

fof(f_4496_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_4496_2,plain,
    ! [U_18365,U_18364,U_18363,U_18362,U_18361] : c_List_Ofoldr(U_18361,U_18362,U_18363,U_18364,U_18365) = hAPP(c_List_Ofoldl(U_18362,U_18361,hAPP(c_COMBC(U_18361,U_18362,U_18362),U_18363),U_18365),hAPP(c_List_Orev(U_18361),U_18364)),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

cnf(f_4496_3,plain,
    c_List_Ofoldr(U_18361,U_18362,U_18363,U_18364,U_18365) = hAPP(c_List_Ofoldl(U_18362,U_18361,hAPP(c_COMBC(U_18361,U_18362,U_18362),U_18363),U_18365),hAPP(c_List_Orev(U_18361),U_18364)),
    inference(clausify,[status(thm)],[f_4496_2]) ).

fof(f_4497_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_4497_2,plain,
    ! [U_18369,U_18368,U_18367,U_18366] :
      ( ( hAPP(c_List_Orev(U_18366),U_18367) = hAPP(hAPP(c_List_Olist_OCons(U_18366),U_18368),U_18369)
        | U_18367 != hAPP(hAPP(c_List_Oappend(U_18366),hAPP(c_List_Orev(U_18366),U_18369)),hAPP(hAPP(c_List_Olist_OCons(U_18366),U_18368),c_List_Olist_ONil(U_18366))) )
      & ( U_18367 = hAPP(hAPP(c_List_Oappend(U_18366),hAPP(c_List_Orev(U_18366),U_18369)),hAPP(hAPP(c_List_Olist_OCons(U_18366),U_18368),c_List_Olist_ONil(U_18366)))
        | hAPP(c_List_Orev(U_18366),U_18367) != hAPP(hAPP(c_List_Olist_OCons(U_18366),U_18368),U_18369) ) ),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

fof(f_4497_3,plain,
    ( ! [U_18377,U_18375,U_18373,U_18371] :
        ( hAPP(c_List_Orev(U_18371),U_18373) = hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18375),U_18377)
        | U_18373 != hAPP(hAPP(c_List_Oappend(U_18371),hAPP(c_List_Orev(U_18371),U_18377)),hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18375),c_List_Olist_ONil(U_18371))) )
    & ! [U_18376,U_18374,U_18372,U_18370] :
        ( U_18372 = hAPP(hAPP(c_List_Oappend(U_18370),hAPP(c_List_Orev(U_18370),U_18376)),hAPP(hAPP(c_List_Olist_OCons(U_18370),U_18374),c_List_Olist_ONil(U_18370)))
        | hAPP(c_List_Orev(U_18370),U_18372) != hAPP(hAPP(c_List_Olist_OCons(U_18370),U_18374),U_18376) ) ),
    inference(miniscope,[status(thm)],[f_4497_2]) ).

cnf(f_4497_4,plain,
    ( U_18372 = hAPP(hAPP(c_List_Oappend(U_18370),hAPP(c_List_Orev(U_18370),U_18376)),hAPP(hAPP(c_List_Olist_OCons(U_18370),U_18374),c_List_Olist_ONil(U_18370)))
    | hAPP(c_List_Orev(U_18370),U_18372) != hAPP(hAPP(c_List_Olist_OCons(U_18370),U_18374),U_18376) ),
    inference(clausify,[status(thm)],[f_4497_3]) ).

cnf(f_4497_5,plain,
    ( hAPP(c_List_Orev(U_18371),U_18373) = hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18375),U_18377)
    | U_18373 != hAPP(hAPP(c_List_Oappend(U_18371),hAPP(c_List_Orev(U_18371),U_18377)),hAPP(hAPP(c_List_Olist_OCons(U_18371),U_18375),c_List_Olist_ONil(U_18371))) ),
    inference(clausify,[status(thm)],[f_4497_3]) ).

fof(f_4498_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_4498_2,plain,
    ! [U_18380,U_18379,U_18378] : hAPP(c_List_Orev(U_18378),hAPP(hAPP(c_List_Olist_OCons(U_18378),U_18379),U_18380)) = hAPP(hAPP(c_List_Oappend(U_18378),hAPP(c_List_Orev(U_18378),U_18380)),hAPP(hAPP(c_List_Olist_OCons(U_18378),U_18379),c_List_Olist_ONil(U_18378))),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

cnf(f_4498_3,plain,
    hAPP(c_List_Orev(U_18378),hAPP(hAPP(c_List_Olist_OCons(U_18378),U_18379),U_18380)) = hAPP(hAPP(c_List_Oappend(U_18378),hAPP(c_List_Orev(U_18378),U_18380)),hAPP(hAPP(c_List_Olist_OCons(U_18378),U_18379),c_List_Olist_ONil(U_18378))),
    inference(clausify,[status(thm)],[f_4498_2]) ).

fof(f_4499_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_4499_2,plain,
    ! [U_18382,U_18381] :
      ( hAPP(c_List_Ohd(U_18382),hAPP(c_List_Orev(U_18382),U_18381)) = c_List_Olast(U_18382,U_18381)
      | U_18381 = c_List_Olist_ONil(U_18382) ),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

cnf(f_4499_3,plain,
    ( hAPP(c_List_Ohd(U_18382),hAPP(c_List_Orev(U_18382),U_18381)) = c_List_Olast(U_18382,U_18381)
    | U_18381 = c_List_Olist_ONil(U_18382) ),
    inference(clausify,[status(thm)],[f_4499_2]) ).

fof(f_4500_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_4500_2,plain,
    ! [U_18384,U_18383] :
      ( c_List_Olast(U_18384,hAPP(c_List_Orev(U_18384),U_18383)) = hAPP(c_List_Ohd(U_18384),U_18383)
      | U_18383 = c_List_Olist_ONil(U_18384) ),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

cnf(f_4500_3,plain,
    ( c_List_Olast(U_18384,hAPP(c_List_Orev(U_18384),U_18383)) = hAPP(c_List_Ohd(U_18384),U_18383)
    | U_18383 = c_List_Olist_ONil(U_18384) ),
    inference(clausify,[status(thm)],[f_4500_2]) ).

fof(f_4501_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_4501_2,plain,
    ! [U_18386,U_18385] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18385),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18385))),c_List_Otranspose(U_18385,U_18386)))),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

cnf(f_4501_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_18385),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18385))),c_List_Otranspose(U_18385,U_18386)))),
    inference(clausify,[status(thm)],[f_4501_2]) ).

fof(f_4502_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_4502_2,plain,
    ! [U_18388,U_18387] : hAPP(c_List_Orev(U_18387),U_18388) = hAPP(c_List_Ofoldl(tc_List_Olist(U_18387),U_18387,hAPP(c_COMBC(U_18387,tc_List_Olist(U_18387),tc_List_Olist(U_18387)),c_List_Olist_OCons(U_18387)),c_List_Olist_ONil(U_18387)),U_18388),
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

cnf(f_4502_3,plain,
    hAPP(c_List_Orev(U_18387),U_18388) = hAPP(c_List_Ofoldl(tc_List_Olist(U_18387),U_18387,hAPP(c_COMBC(U_18387,tc_List_Olist(U_18387),tc_List_Olist(U_18387)),c_List_Olist_OCons(U_18387)),c_List_Olist_ONil(U_18387)),U_18388),
    inference(clausify,[status(thm)],[f_4502_2]) ).

fof(f_4503_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_4503_2,plain,
    ! [U_18391,U_18390,U_18389] : hAPP(c_List_Orev(U_18389),hAPP(hAPP(c_List_Odrop(U_18389),U_18390),U_18391)) = hAPP(hAPP(c_List_Otake(U_18389),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18389)),U_18391)),U_18390)),hAPP(c_List_Orev(U_18389),U_18391)),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

cnf(f_4503_3,plain,
    hAPP(c_List_Orev(U_18389),hAPP(hAPP(c_List_Odrop(U_18389),U_18390),U_18391)) = hAPP(hAPP(c_List_Otake(U_18389),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18389)),U_18391)),U_18390)),hAPP(c_List_Orev(U_18389),U_18391)),
    inference(clausify,[status(thm)],[f_4503_2]) ).

fof(f_4504_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_4504_2,plain,
    ! [U_18394,U_18393,U_18392] : hAPP(c_List_Orev(U_18392),hAPP(hAPP(c_List_Otake(U_18392),U_18393),U_18394)) = hAPP(hAPP(c_List_Odrop(U_18392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18392)),U_18394)),U_18393)),hAPP(c_List_Orev(U_18392),U_18394)),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

cnf(f_4504_3,plain,
    hAPP(c_List_Orev(U_18392),hAPP(hAPP(c_List_Otake(U_18392),U_18393),U_18394)) = hAPP(hAPP(c_List_Odrop(U_18392),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18392)),U_18394)),U_18393)),hAPP(c_List_Orev(U_18392),U_18394)),
    inference(clausify,[status(thm)],[f_4504_2]) ).

fof(f_4505_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_4505_2,plain,
    ! [U_18397,U_18396,U_18395] : hAPP(c_List_Orotate(U_18395,U_18396),hAPP(c_List_Orev(U_18395),U_18397)) = hAPP(c_List_Orev(U_18395),hAPP(c_List_Orotate(U_18395,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18395)),U_18397)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_18396,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18395)),U_18397)))),U_18397)),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

cnf(f_4505_3,plain,
    hAPP(c_List_Orotate(U_18395,U_18396),hAPP(c_List_Orev(U_18395),U_18397)) = hAPP(c_List_Orev(U_18395),hAPP(c_List_Orotate(U_18395,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18395)),U_18397)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_18396,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18395)),U_18397)))),U_18397)),
    inference(clausify,[status(thm)],[f_4505_2]) ).

fof(f_4506_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_4506_2,plain,
    ! [U_18400,U_18399,U_18398] :
      ( hAPP(hAPP(c_List_Onth(U_18399),hAPP(c_List_Orev(U_18399),U_18400)),U_18398) = hAPP(hAPP(c_List_Onth(U_18399),U_18400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18399)),U_18400)),hAPP(c_Nat_OSuc,U_18398)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18399)),U_18400))) ),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

cnf(f_4506_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18399),hAPP(c_List_Orev(U_18399),U_18400)),U_18398) = hAPP(hAPP(c_List_Onth(U_18399),U_18400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18399)),U_18400)),hAPP(c_Nat_OSuc,U_18398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18398),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18399)),U_18400))) ),
    inference(clausify,[status(thm)],[f_4506_2]) ).

fof(f_4507_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_4507_2,plain,
    ! [U_18404,U_18403,U_18402,U_18401] :
      ( hAPP(c_List_Orev(U_18402),hAPP(hAPP(c_List_Olist__update(U_18402,U_18403),U_18401),U_18404)) = hAPP(hAPP(c_List_Olist__update(U_18402,hAPP(c_List_Orev(U_18402),U_18403)),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_18402)),U_18403)),U_18401)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18404)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18401),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18402)),U_18403))) ),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

cnf(f_4507_3,plain,
    ( hAPP(c_List_Orev(U_18402),hAPP(hAPP(c_List_Olist__update(U_18402,U_18403),U_18401),U_18404)) = hAPP(hAPP(c_List_Olist__update(U_18402,hAPP(c_List_Orev(U_18402),U_18403)),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_18402)),U_18403)),U_18401)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18404)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18401),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18402)),U_18403))) ),
    inference(clausify,[status(thm)],[f_4507_2]) ).

fof(f_4508_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_4508_2,plain,
    ! [U_18408,U_18407,U_18406,U_18405] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18405),hAPP(hAPP(c_List_Onth(U_18405),U_18406),U_18408)),hAPP(hAPP(c_List_Onth(U_18405),U_18406),U_18407)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18405)),U_18406)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18407),U_18408))
      | ~ c_List_Olinorder__class_Osorted(U_18405,hAPP(c_List_Orev(U_18405),U_18406))
      | ~ class_Orderings_Olinorder(U_18405) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

cnf(f_4508_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18405),hAPP(hAPP(c_List_Onth(U_18405),U_18406),U_18408)),hAPP(hAPP(c_List_Onth(U_18405),U_18406),U_18407)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18405)),U_18406)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18407),U_18408))
    | ~ c_List_Olinorder__class_Osorted(U_18405,hAPP(c_List_Orev(U_18405),U_18406))
    | ~ class_Orderings_Olinorder(U_18405) ),
    inference(clausify,[status(thm)],[f_4508_2]) ).

fof(f_4509_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_4509_2,plain,
    ! [U_18411,U_18410,U_18409] :
      ( ( ( c_List_Ofoldr(U_18409,U_18409,c_Orderings_Oord__class_Omax(U_18409),U_18410,U_18411) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_18409),hAPP(hAPP(c_List_Onth(U_18409),U_18410),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_18411)
          | U_18410 = c_List_Olist_ONil(U_18409) )
        & ( c_List_Ofoldr(U_18409,U_18409,c_Orderings_Oord__class_Omax(U_18409),U_18410,U_18411) = U_18411
          | U_18410 != c_List_Olist_ONil(U_18409) ) )
      | ~ c_List_Olinorder__class_Osorted(U_18409,hAPP(c_List_Orev(U_18409),U_18410))
      | ~ class_Orderings_Olinorder(U_18409) ),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

cnf(f_4509_3,plain,
    ( c_List_Ofoldr(U_18409,U_18409,c_Orderings_Oord__class_Omax(U_18409),U_18410,U_18411) = U_18411
    | U_18410 != c_List_Olist_ONil(U_18409)
    | ~ c_List_Olinorder__class_Osorted(U_18409,hAPP(c_List_Orev(U_18409),U_18410))
    | ~ class_Orderings_Olinorder(U_18409) ),
    inference(clausify,[status(thm)],[f_4509_2]) ).

cnf(f_4509_4,plain,
    ( c_List_Ofoldr(U_18409,U_18409,c_Orderings_Oord__class_Omax(U_18409),U_18410,U_18411) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_18409),hAPP(hAPP(c_List_Onth(U_18409),U_18410),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_18411)
    | U_18410 = c_List_Olist_ONil(U_18409)
    | ~ c_List_Olinorder__class_Osorted(U_18409,hAPP(c_List_Orev(U_18409),U_18410))
    | ~ class_Orderings_Olinorder(U_18409) ),
    inference(clausify,[status(thm)],[f_4509_2]) ).

fof(f_4510_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_4510_2,plain,
    ! [U_18413,U_18412] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18412))),c_List_Otranspose(U_18412,U_18413)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18412)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18412)),U_18413),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_18413 = c_List_Olist_ONil(tc_List_Olist(U_18412)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18412))),c_List_Otranspose(U_18412,U_18413)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_18413 != c_List_Olist_ONil(tc_List_Olist(U_18412)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18412),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18412))),U_18413))) ),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

cnf(f_4510_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18412))),c_List_Otranspose(U_18412,U_18413)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_18413 != c_List_Olist_ONil(tc_List_Olist(U_18412))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18412),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18412))),U_18413))) ),
    inference(clausify,[status(thm)],[f_4510_2]) ).

cnf(f_4510_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18412))),c_List_Otranspose(U_18412,U_18413)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18412)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18412)),U_18413),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_18413 = c_List_Olist_ONil(tc_List_Olist(U_18412))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18412),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18412))),U_18413))) ),
    inference(clausify,[status(thm)],[f_4510_2]) ).

fof(f_4511_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_4511_2,plain,
    ! [U_18416,U_18415,U_18414] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18414))),hAPP(c_List_Ofilter(tc_List_Olist(U_18414),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18414)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18416)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18414)))),c_List_Otranspose(U_18414,U_18415))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18414)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18414)),U_18415),U_18416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18416),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18414))),U_18415)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18414),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18414))),U_18415))) ),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

cnf(f_4511_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18414))),hAPP(c_List_Ofilter(tc_List_Olist(U_18414),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18414)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18416)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18414)))),c_List_Otranspose(U_18414,U_18415))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18414)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18414)),U_18415),U_18416))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18416),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18414))),U_18415)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18414),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18414))),U_18415))) ),
    inference(clausify,[status(thm)],[f_4511_2]) ).

fof(f_4512_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_4512_2,plain,
    ! [U_18418,U_18417] :
      ( c_List_Otranspose(U_18417,c_List_Otranspose(U_18417,U_18418)) = c_List_OtakeWhile(tc_List_Olist(U_18417),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18417)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18417),tc_List_Olist(U_18417),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_18417))),U_18418)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18417),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18417))),U_18418))) ),
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

cnf(f_4512_3,plain,
    ( c_List_Otranspose(U_18417,c_List_Otranspose(U_18417,U_18418)) = c_List_OtakeWhile(tc_List_Olist(U_18417),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18417)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18417),tc_List_Olist(U_18417),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_18417))),U_18418)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18417),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18417))),U_18418))) ),
    inference(clausify,[status(thm)],[f_4512_2]) ).

fof(f_4513_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_4513_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_4513_1]) ).

fof(f_4514_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_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_4514_2,plain,
    ! [U_18421,U_18420,U_18419] :
      ( c_List_Olinorder__class_Osorted(U_18419,c_List_OtakeWhile(U_18419,U_18421,U_18420))
      | ~ c_List_Olinorder__class_Osorted(U_18419,U_18420)
      | ~ class_Orderings_Olinorder(U_18419) ),
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

cnf(f_4514_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18419,c_List_OtakeWhile(U_18419,U_18421,U_18420))
    | ~ c_List_Olinorder__class_Osorted(U_18419,U_18420)
    | ~ class_Orderings_Olinorder(U_18419) ),
    inference(clausify,[status(thm)],[f_4514_2]) ).

fof(f_4515_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_4515_2,plain,
    ! [U_18424,U_18423,U_18422] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),c_List_OtakeWhile(U_18422,U_18423,U_18424))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),U_18424))),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

cnf(f_4515_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),c_List_OtakeWhile(U_18422,U_18423,U_18424))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18422)),U_18424))),
    inference(clausify,[status(thm)],[f_4515_2]) ).

fof(f_4516_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv]) ).

fof(f_4516_2,plain,
    ! [U_18429,U_18428,U_18427] :
      ( ( c_List_OtakeWhile(U_18427,U_18428,U_18429) = U_18429
        | ? [U_18426] :
            ( ~ hBOOL(hAPP(U_18428,U_18426))
            & hBOOL(hAPP(hAPP(c_member(U_18427),U_18426),hAPP(c_List_Oset(U_18427),U_18429))) ) )
      & ( ! [U_18425] :
            ( hBOOL(hAPP(U_18428,U_18425))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18427),U_18425),hAPP(c_List_Oset(U_18427),U_18429))) )
        | c_List_OtakeWhile(U_18427,U_18428,U_18429) != U_18429 ) ),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

fof(f_4516_3,plain,
    ( ! [U_18435,U_18433,U_18431] :
        ( c_List_OtakeWhile(U_18431,U_18433,U_18435) = U_18435
        | ? [U_18426] :
            ( ~ hBOOL(hAPP(U_18433,U_18426))
            & hBOOL(hAPP(hAPP(c_member(U_18431),U_18426),hAPP(c_List_Oset(U_18431),U_18435))) ) )
    & ! [U_18434,U_18432,U_18430] :
        ( ! [U_18425] :
            ( hBOOL(hAPP(U_18432,U_18425))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18430),U_18425),hAPP(c_List_Oset(U_18430),U_18434))) )
        | c_List_OtakeWhile(U_18430,U_18432,U_18434) != U_18434 ) ),
    inference(miniscope,[status(thm)],[f_4516_2]) ).

fof(f_4516_4,plain,
    ( ! [U_18435,U_18433,U_18431] :
        ( c_List_OtakeWhile(U_18431,U_18433,U_18435) = U_18435
        | ( ~ hBOOL(hAPP(U_18433,sK448(U_18435,U_18433,U_18431)))
          & hBOOL(hAPP(hAPP(c_member(U_18431),sK448(U_18435,U_18433,U_18431)),hAPP(c_List_Oset(U_18431),U_18435))) ) )
    & ! [U_18434,U_18432,U_18430] :
        ( ! [U_18425] :
            ( hBOOL(hAPP(U_18432,U_18425))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18430),U_18425),hAPP(c_List_Oset(U_18430),U_18434))) )
        | c_List_OtakeWhile(U_18430,U_18432,U_18434) != U_18434 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_18426,sK448(U_18435,U_18433,U_18431))],[f_4516_3]) ).

cnf(f_4516_5,plain,
    ( hBOOL(hAPP(U_18432,U_18425))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18430),U_18425),hAPP(c_List_Oset(U_18430),U_18434)))
    | c_List_OtakeWhile(U_18430,U_18432,U_18434) != U_18434 ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18431),sK448(U_18435,U_18433,U_18431)),hAPP(c_List_Oset(U_18431),U_18435)))
    | c_List_OtakeWhile(U_18431,U_18433,U_18435) = U_18435 ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_7,plain,
    ( ~ hBOOL(hAPP(U_18433,sK448(U_18435,U_18433,U_18431)))
    | c_List_OtakeWhile(U_18431,U_18433,U_18435) = U_18435 ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

fof(f_4517_1,plain,
    ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__takeWhileD]) ).

fof(f_4517_2,plain,
    ! [U_18439,U_18438,U_18437,U_18436] :
      ( ( hBOOL(hAPP(U_18438,U_18437))
        & hBOOL(hAPP(hAPP(c_member(U_18436),U_18437),hAPP(c_List_Oset(U_18436),U_18439))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_18436),U_18437),hAPP(c_List_Oset(U_18436),c_List_OtakeWhile(U_18436,U_18438,U_18439)))) ),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

cnf(f_4517_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18436),U_18437),hAPP(c_List_Oset(U_18436),U_18439)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18436),U_18437),hAPP(c_List_Oset(U_18436),c_List_OtakeWhile(U_18436,U_18438,U_18439)))) ),
    inference(clausify,[status(thm)],[f_4517_2]) ).

cnf(f_4517_4,plain,
    ( hBOOL(hAPP(U_18438,U_18437))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18436),U_18437),hAPP(c_List_Oset(U_18436),c_List_OtakeWhile(U_18436,U_18438,U_18439)))) ),
    inference(clausify,[status(thm)],[f_4517_2]) ).

fof(f_4518_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_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_Pa_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_4518_2,plain,
    ! [U_18444,U_18443,U_18442,U_18441,U_18440] : hAPP(hAPP(c_List_Ozip(U_18440,U_18441),c_List_OtakeWhile(U_18440,U_18442,U_18443)),U_18444) = c_List_OtakeWhile(tc_prod(U_18440,U_18441),hAPP(c_Fun_Ocomp(U_18440,tc_HOL_Obool,tc_prod(U_18440,U_18441),U_18442),c_Product__Type_Ofst(U_18440,U_18441)),hAPP(hAPP(c_List_Ozip(U_18440,U_18441),U_18443),U_18444)),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

cnf(f_4518_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18440,U_18441),c_List_OtakeWhile(U_18440,U_18442,U_18443)),U_18444) = c_List_OtakeWhile(tc_prod(U_18440,U_18441),hAPP(c_Fun_Ocomp(U_18440,tc_HOL_Obool,tc_prod(U_18440,U_18441),U_18442),c_Product__Type_Ofst(U_18440,U_18441)),hAPP(hAPP(c_List_Ozip(U_18440,U_18441),U_18443),U_18444)),
    inference(clausify,[status(thm)],[f_4518_2]) ).

fof(f_4519_1,plain,
    ! [V_ys_2,V_Pa_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_Pa_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_Pa_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_4519_2,plain,
    ! [U_18449,U_18448,U_18447,U_18446,U_18445] : hAPP(hAPP(c_List_Ozip(U_18445,U_18446),U_18447),c_List_OtakeWhile(U_18446,U_18448,U_18449)) = c_List_OtakeWhile(tc_prod(U_18445,U_18446),hAPP(c_Fun_Ocomp(U_18446,tc_HOL_Obool,tc_prod(U_18445,U_18446),U_18448),c_Product__Type_Osnd(U_18445,U_18446)),hAPP(hAPP(c_List_Ozip(U_18445,U_18446),U_18447),U_18449)),
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

cnf(f_4519_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18445,U_18446),U_18447),c_List_OtakeWhile(U_18446,U_18448,U_18449)) = c_List_OtakeWhile(tc_prod(U_18445,U_18446),hAPP(c_Fun_Ocomp(U_18446,tc_HOL_Obool,tc_prod(U_18445,U_18446),U_18448),c_Product__Type_Osnd(U_18445,U_18446)),hAPP(hAPP(c_List_Ozip(U_18445,U_18446),U_18447),U_18449)),
    inference(clausify,[status(thm)],[f_4519_2]) ).

fof(f_4520_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_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_Pa_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__map]) ).

fof(f_4520_2,plain,
    ! [U_18454,U_18453,U_18452,U_18451,U_18450] : c_List_OtakeWhile(U_18450,U_18451,hAPP(hAPP(c_List_Omap(U_18452,U_18450),U_18453),U_18454)) = hAPP(hAPP(c_List_Omap(U_18452,U_18450),U_18453),c_List_OtakeWhile(U_18452,hAPP(c_Fun_Ocomp(U_18450,tc_HOL_Obool,U_18452,U_18451),U_18453),U_18454)),
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

cnf(f_4520_3,plain,
    c_List_OtakeWhile(U_18450,U_18451,hAPP(hAPP(c_List_Omap(U_18452,U_18450),U_18453),U_18454)) = hAPP(hAPP(c_List_Omap(U_18452,U_18450),U_18453),c_List_OtakeWhile(U_18452,hAPP(c_Fun_Ocomp(U_18450,tc_HOL_Obool,U_18452,U_18451),U_18453),U_18454)),
    inference(clausify,[status(thm)],[f_4520_2]) ).

fof(f_4521_1,plain,
    ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_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_4521_2,plain,
    ! [U_18456,U_18455] : c_List_OtakeWhile(U_18455,U_18456,c_List_Olist_ONil(U_18455)) = c_List_Olist_ONil(U_18455),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

cnf(f_4521_3,plain,
    c_List_OtakeWhile(U_18455,U_18456,c_List_Olist_ONil(U_18455)) = c_List_Olist_ONil(U_18455),
    inference(clausify,[status(thm)],[f_4521_2]) ).

fof(f_4522_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(f_4522_2,plain,
    ! [U_18460,U_18459,U_18458,U_18457] :
      ( ( c_List_OtakeWhile(U_18459,U_18457,hAPP(hAPP(c_List_Olist_OCons(U_18459),U_18458),U_18460)) = c_List_Olist_ONil(U_18459)
        | hBOOL(hAPP(U_18457,U_18458)) )
      & ( c_List_OtakeWhile(U_18459,U_18457,hAPP(hAPP(c_List_Olist_OCons(U_18459),U_18458),U_18460)) = hAPP(hAPP(c_List_Olist_OCons(U_18459),U_18458),c_List_OtakeWhile(U_18459,U_18457,U_18460))
        | ~ hBOOL(hAPP(U_18457,U_18458)) ) ),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

fof(f_4522_3,plain,
    ( ! [U_18468,U_18466,U_18464,U_18462] :
        ( c_List_OtakeWhile(U_18466,U_18462,hAPP(hAPP(c_List_Olist_OCons(U_18466),U_18464),U_18468)) = c_List_Olist_ONil(U_18466)
        | hBOOL(hAPP(U_18462,U_18464)) )
    & ! [U_18467,U_18465,U_18463,U_18461] :
        ( c_List_OtakeWhile(U_18465,U_18461,hAPP(hAPP(c_List_Olist_OCons(U_18465),U_18463),U_18467)) = hAPP(hAPP(c_List_Olist_OCons(U_18465),U_18463),c_List_OtakeWhile(U_18465,U_18461,U_18467))
        | ~ hBOOL(hAPP(U_18461,U_18463)) ) ),
    inference(miniscope,[status(thm)],[f_4522_2]) ).

cnf(f_4522_4,plain,
    ( c_List_OtakeWhile(U_18465,U_18461,hAPP(hAPP(c_List_Olist_OCons(U_18465),U_18463),U_18467)) = hAPP(hAPP(c_List_Olist_OCons(U_18465),U_18463),c_List_OtakeWhile(U_18465,U_18461,U_18467))
    | ~ hBOOL(hAPP(U_18461,U_18463)) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

cnf(f_4522_5,plain,
    ( c_List_OtakeWhile(U_18466,U_18462,hAPP(hAPP(c_List_Olist_OCons(U_18466),U_18464),U_18468)) = c_List_Olist_ONil(U_18466)
    | hBOOL(hAPP(U_18462,U_18464)) ),
    inference(clausify,[status(thm)],[f_4522_3]) ).

fof(f_4523_1,plain,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__tail]) ).

fof(f_4523_2,plain,
    ! [U_18473,U_18472,U_18471,U_18470,U_18469] :
      ( c_List_OtakeWhile(U_18471,U_18469,hAPP(hAPP(c_List_Oappend(U_18471),U_18472),hAPP(hAPP(c_List_Olist_OCons(U_18471),U_18470),U_18473))) = c_List_OtakeWhile(U_18471,U_18469,U_18472)
      | hBOOL(hAPP(U_18469,U_18470)) ),
    inference(variable_rename,[status(thm)],[f_4523_1]) ).

cnf(f_4523_3,plain,
    ( c_List_OtakeWhile(U_18471,U_18469,hAPP(hAPP(c_List_Oappend(U_18471),U_18472),hAPP(hAPP(c_List_Olist_OCons(U_18471),U_18470),U_18473))) = c_List_OtakeWhile(U_18471,U_18469,U_18472)
    | hBOOL(hAPP(U_18469,U_18470)) ),
    inference(clausify,[status(thm)],[f_4523_2]) ).

fof(f_4524_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(f_4524_2,plain,
    ! [U_18476,U_18475,U_18474] : c_List_OtakeWhile(U_18474,U_18475,U_18476) = hAPP(hAPP(c_List_Otake(U_18474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18474)),c_List_OtakeWhile(U_18474,U_18475,U_18476))),U_18476),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

cnf(f_4524_3,plain,
    c_List_OtakeWhile(U_18474,U_18475,U_18476) = hAPP(hAPP(c_List_Otake(U_18474),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18474)),c_List_OtakeWhile(U_18474,U_18475,U_18476))),U_18476),
    inference(clausify,[status(thm)],[f_4524_2]) ).

fof(f_4525_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile]) ).

fof(f_4525_2,plain,
    ! [U_18479,U_18478,U_18477] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18477),c_List_OtakeWhile(U_18477,U_18479,U_18478)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18477),U_18478)) ),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

cnf(f_4525_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18477),c_List_OtakeWhile(U_18477,U_18479,U_18478)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18477),U_18478)) ),
    inference(clausify,[status(thm)],[f_4525_2]) ).

fof(f_4526_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_4526_2,plain,
    ! [U_18480] : c_List_Oreturn__list(U_18480) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_18480),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

cnf(f_4526_3,plain,
    c_List_Oreturn__list(U_18480) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_18480),
    inference(clausify,[status(thm)],[f_4526_2]) ).

fof(f_4527_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)
      | hBOOL(hAPP(V_Pa_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_4527_2,plain,
    ! [U_18485,U_18484,U_18483,U_18482,U_18481] :
      ( c_List_OtakeWhile(U_18481,U_18484,hAPP(hAPP(c_List_Oappend(U_18481),U_18483),U_18485)) = c_List_OtakeWhile(U_18481,U_18484,U_18483)
      | hBOOL(hAPP(U_18484,U_18482))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18481),U_18482),hAPP(c_List_Oset(U_18481),U_18483))) ),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

cnf(f_4527_3,plain,
    ( c_List_OtakeWhile(U_18481,U_18484,hAPP(hAPP(c_List_Oappend(U_18481),U_18483),U_18485)) = c_List_OtakeWhile(U_18481,U_18484,U_18483)
    | hBOOL(hAPP(U_18484,U_18482))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18481),U_18482),hAPP(c_List_Oset(U_18481),U_18483))) ),
    inference(clausify,[status(thm)],[f_4527_2]) ).

fof(f_4528_1,plain,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__nth]) ).

fof(f_4528_2,plain,
    ! [U_18489,U_18488,U_18487,U_18486] :
      ( hAPP(hAPP(c_List_Onth(U_18487),c_List_OtakeWhile(U_18487,U_18488,U_18489)),U_18486) = hAPP(hAPP(c_List_Onth(U_18487),U_18489),U_18486)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18487)),c_List_OtakeWhile(U_18487,U_18488,U_18489)))) ),
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

cnf(f_4528_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18487),c_List_OtakeWhile(U_18487,U_18488,U_18489)),U_18486) = hAPP(hAPP(c_List_Onth(U_18487),U_18489),U_18486)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18487)),c_List_OtakeWhile(U_18487,U_18488,U_18489)))) ),
    inference(clausify,[status(thm)],[f_4528_2]) ).

fof(f_4529_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_4529_2,plain,
    ! [U_18492,U_18491,U_18490] :
      ( ~ hBOOL(hAPP(U_18491,hAPP(hAPP(c_List_Onth(U_18490),U_18492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),c_List_OtakeWhile(U_18490,U_18491,U_18492)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),c_List_OtakeWhile(U_18490,U_18491,U_18492))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),U_18492))) ),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

cnf(f_4529_3,plain,
    ( ~ hBOOL(hAPP(U_18491,hAPP(hAPP(c_List_Onth(U_18490),U_18492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),c_List_OtakeWhile(U_18490,U_18491,U_18492)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),c_List_OtakeWhile(U_18490,U_18491,U_18492))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18490)),U_18492))) ),
    inference(clausify,[status(thm)],[f_4529_2]) ).

fof(f_4530_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_4530_2,plain,
    ! [U_18494,U_18493] :
      ( c_List_OtakeWhile(U_18494,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18494),c_fNot),hAPP(hAPP(c_COMBC(U_18494,U_18494,tc_HOL_Obool),c_fequal),c_List_Olast(U_18494,U_18493))),U_18493) = c_List_Obutlast(U_18494,U_18493)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18494),U_18493))
      | U_18493 = c_List_Olist_ONil(U_18494) ),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

cnf(f_4530_3,plain,
    ( c_List_OtakeWhile(U_18494,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18494),c_fNot),hAPP(hAPP(c_COMBC(U_18494,U_18494,tc_HOL_Obool),c_fequal),c_List_Olast(U_18494,U_18493))),U_18493) = c_List_Obutlast(U_18494,U_18493)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18494),U_18493))
    | U_18493 = c_List_Olist_ONil(U_18494) ),
    inference(clausify,[status(thm)],[f_4530_2]) ).

fof(f_4531_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_4531_2,plain,
    ! [U_18499,U_18498,U_18497,U_18496,U_18495] :
      ( hAPP(c_List_Ofilter(U_18496,hAPP(hAPP(c_COMBB(U_18495,tc_HOL_Obool,U_18496),hAPP(c_Orderings_Oord__class_Oless(U_18495),U_18499)),U_18497)),U_18498) = c_List_OtakeWhile(U_18496,hAPP(hAPP(c_COMBB(U_18495,tc_HOL_Obool,U_18496),hAPP(c_Orderings_Oord__class_Oless(U_18495),U_18499)),U_18497),U_18498)
      | ~ c_List_Olinorder__class_Osorted(U_18495,hAPP(c_List_Orev(U_18495),hAPP(hAPP(c_List_Omap(U_18496,U_18495),U_18497),U_18498)))
      | ~ class_Orderings_Olinorder(U_18495) ),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

cnf(f_4531_3,plain,
    ( hAPP(c_List_Ofilter(U_18496,hAPP(hAPP(c_COMBB(U_18495,tc_HOL_Obool,U_18496),hAPP(c_Orderings_Oord__class_Oless(U_18495),U_18499)),U_18497)),U_18498) = c_List_OtakeWhile(U_18496,hAPP(hAPP(c_COMBB(U_18495,tc_HOL_Obool,U_18496),hAPP(c_Orderings_Oord__class_Oless(U_18495),U_18499)),U_18497),U_18498)
    | ~ c_List_Olinorder__class_Osorted(U_18495,hAPP(c_List_Orev(U_18495),hAPP(hAPP(c_List_Omap(U_18496,U_18495),U_18497),U_18498)))
    | ~ class_Orderings_Olinorder(U_18495) ),
    inference(clausify,[status(thm)],[f_4531_2]) ).

fof(f_4532_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_4532_2,plain,
    ! [U_18500] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_18500)) = U_18500
      | ~ c_List_Onat__list(U_18500) ),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

cnf(f_4532_3,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(U_18500)) = U_18500
    | ~ c_List_Onat__list(U_18500) ),
    inference(clausify,[status(thm)],[f_4532_2]) ).

fof(f_4533_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_4533_2,plain,
    ! [U_18502,U_18501] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_18501),U_18502) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_18501)),c_List_Oembed__list(U_18502))),
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

cnf(f_4533_3,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_18501),U_18502) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_18501)),c_List_Oembed__list(U_18502))),
    inference(clausify,[status(thm)],[f_4533_2]) ).

fof(f_4534_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_4534_2,plain,
    ! [U_18503] : c_List_Oembed__list(U_18503) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_18503),
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

cnf(f_4534_3,plain,
    c_List_Oembed__list(U_18503) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_18503),
    inference(clausify,[status(thm)],[f_4534_2]) ).

fof(f_4535_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_4535_2,plain,
    ! [U_18506,U_18505,U_18504] :
      ( c_List_OtakeWhile(U_18504,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18504),c_fNot),hAPP(hAPP(c_COMBC(U_18504,U_18504,tc_HOL_Obool),c_fequal),U_18506)),hAPP(c_List_Orev(U_18504),U_18505)) = hAPP(c_List_Orev(U_18504),hAPP(c_List_Otl(U_18504),c_List_OdropWhile(U_18504,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18504),c_fNot),hAPP(hAPP(c_COMBC(U_18504,U_18504,tc_HOL_Obool),c_fequal),U_18506)),U_18505)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18504),U_18506),hAPP(c_List_Oset(U_18504),U_18505)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18504),U_18505)) ),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

cnf(f_4535_3,plain,
    ( c_List_OtakeWhile(U_18504,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18504),c_fNot),hAPP(hAPP(c_COMBC(U_18504,U_18504,tc_HOL_Obool),c_fequal),U_18506)),hAPP(c_List_Orev(U_18504),U_18505)) = hAPP(c_List_Orev(U_18504),hAPP(c_List_Otl(U_18504),c_List_OdropWhile(U_18504,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18504),c_fNot),hAPP(hAPP(c_COMBC(U_18504,U_18504,tc_HOL_Obool),c_fequal),U_18506)),U_18505)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18504),U_18506),hAPP(c_List_Oset(U_18504),U_18505)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18504),U_18505)) ),
    inference(clausify,[status(thm)],[f_4535_2]) ).

fof(f_4536_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_4536_2,plain,
    ! [U_18509,U_18508,U_18507] :
      ( c_List_OdropWhile(U_18507,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18507),c_fNot),hAPP(hAPP(c_COMBC(U_18507,U_18507,tc_HOL_Obool),c_fequal),U_18509)),hAPP(c_List_Orev(U_18507),U_18508)) = hAPP(hAPP(c_List_Olist_OCons(U_18507),U_18509),hAPP(c_List_Orev(U_18507),c_List_OtakeWhile(U_18507,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18507),c_fNot),hAPP(hAPP(c_COMBC(U_18507,U_18507,tc_HOL_Obool),c_fequal),U_18509)),U_18508)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18507),U_18509),hAPP(c_List_Oset(U_18507),U_18508)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18507),U_18508)) ),
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

cnf(f_4536_3,plain,
    ( c_List_OdropWhile(U_18507,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18507),c_fNot),hAPP(hAPP(c_COMBC(U_18507,U_18507,tc_HOL_Obool),c_fequal),U_18509)),hAPP(c_List_Orev(U_18507),U_18508)) = hAPP(hAPP(c_List_Olist_OCons(U_18507),U_18509),hAPP(c_List_Orev(U_18507),c_List_OtakeWhile(U_18507,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18507),c_fNot),hAPP(hAPP(c_COMBC(U_18507,U_18507,tc_HOL_Obool),c_fequal),U_18509)),U_18508)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18507),U_18509),hAPP(c_List_Oset(U_18507),U_18508)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18507),U_18508)) ),
    inference(clausify,[status(thm)],[f_4536_2]) ).

fof(f_4537_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(f_4537_2,plain,
    ! [U_18512,U_18511,U_18510] : hAPP(hAPP(c_List_Oappend(U_18510),c_List_OtakeWhile(U_18510,U_18511,U_18512)),c_List_OdropWhile(U_18510,U_18511,U_18512)) = U_18512,
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

cnf(f_4537_3,plain,
    hAPP(hAPP(c_List_Oappend(U_18510),c_List_OtakeWhile(U_18510,U_18511,U_18512)),c_List_OdropWhile(U_18510,U_18511,U_18512)) = U_18512,
    inference(clausify,[status(thm)],[f_4537_2]) ).

fof(f_4538_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
      | c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__dropWhile]) ).

fof(f_4538_2,plain,
    ! [U_18515,U_18514,U_18513] :
      ( ~ hBOOL(hAPP(U_18514,hAPP(c_List_Ohd(U_18513),c_List_OdropWhile(U_18513,U_18514,U_18515))))
      | c_List_OdropWhile(U_18513,U_18514,U_18515) = c_List_Olist_ONil(U_18513) ),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

cnf(f_4538_3,plain,
    ( ~ hBOOL(hAPP(U_18514,hAPP(c_List_Ohd(U_18513),c_List_OdropWhile(U_18513,U_18514,U_18515))))
    | c_List_OdropWhile(U_18513,U_18514,U_18515) = c_List_Olist_ONil(U_18513) ),
    inference(clausify,[status(thm)],[f_4538_2]) ).

fof(f_4539_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_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_4539_2,plain,
    ! [U_18518,U_18517,U_18516] :
      ( c_List_Olinorder__class_Osorted(U_18516,c_List_OdropWhile(U_18516,U_18518,U_18517))
      | ~ c_List_Olinorder__class_Osorted(U_18516,U_18517)
      | ~ class_Orderings_Olinorder(U_18516) ),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

cnf(f_4539_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18516,c_List_OdropWhile(U_18516,U_18518,U_18517))
    | ~ c_List_Olinorder__class_Osorted(U_18516,U_18517)
    | ~ class_Orderings_Olinorder(U_18516) ),
    inference(clausify,[status(thm)],[f_4539_2]) ).

fof(f_4540_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_4540_2,plain,
    ! [U_18521,U_18520,U_18519] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),c_List_OdropWhile(U_18519,U_18520,U_18521))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),U_18521))),
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

cnf(f_4540_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),c_List_OdropWhile(U_18519,U_18520,U_18521))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),U_18521))),
    inference(clausify,[status(thm)],[f_4540_2]) ).

fof(f_4541_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Nil__conv]) ).

fof(f_4541_2,plain,
    ! [U_18526,U_18525,U_18524] :
      ( ( c_List_OdropWhile(U_18524,U_18525,U_18526) = c_List_Olist_ONil(U_18524)
        | ? [U_18523] :
            ( ~ hBOOL(hAPP(U_18525,U_18523))
            & hBOOL(hAPP(hAPP(c_member(U_18524),U_18523),hAPP(c_List_Oset(U_18524),U_18526))) ) )
      & ( ! [U_18522] :
            ( hBOOL(hAPP(U_18525,U_18522))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18524),U_18522),hAPP(c_List_Oset(U_18524),U_18526))) )
        | c_List_OdropWhile(U_18524,U_18525,U_18526) != c_List_Olist_ONil(U_18524) ) ),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

fof(f_4541_3,plain,
    ( ! [U_18532,U_18530,U_18528] :
        ( c_List_OdropWhile(U_18528,U_18530,U_18532) = c_List_Olist_ONil(U_18528)
        | ? [U_18523] :
            ( ~ hBOOL(hAPP(U_18530,U_18523))
            & hBOOL(hAPP(hAPP(c_member(U_18528),U_18523),hAPP(c_List_Oset(U_18528),U_18532))) ) )
    & ! [U_18531,U_18529,U_18527] :
        ( ! [U_18522] :
            ( hBOOL(hAPP(U_18529,U_18522))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18527),U_18522),hAPP(c_List_Oset(U_18527),U_18531))) )
        | c_List_OdropWhile(U_18527,U_18529,U_18531) != c_List_Olist_ONil(U_18527) ) ),
    inference(miniscope,[status(thm)],[f_4541_2]) ).

fof(f_4541_4,plain,
    ( ! [U_18532,U_18530,U_18528] :
        ( c_List_OdropWhile(U_18528,U_18530,U_18532) = c_List_Olist_ONil(U_18528)
        | ( ~ hBOOL(hAPP(U_18530,sK449(U_18532,U_18530,U_18528)))
          & hBOOL(hAPP(hAPP(c_member(U_18528),sK449(U_18532,U_18530,U_18528)),hAPP(c_List_Oset(U_18528),U_18532))) ) )
    & ! [U_18531,U_18529,U_18527] :
        ( ! [U_18522] :
            ( hBOOL(hAPP(U_18529,U_18522))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18527),U_18522),hAPP(c_List_Oset(U_18527),U_18531))) )
        | c_List_OdropWhile(U_18527,U_18529,U_18531) != c_List_Olist_ONil(U_18527) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_18523,sK449(U_18532,U_18530,U_18528))],[f_4541_3]) ).

cnf(f_4541_5,plain,
    ( hBOOL(hAPP(U_18529,U_18522))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18527),U_18522),hAPP(c_List_Oset(U_18527),U_18531)))
    | c_List_OdropWhile(U_18527,U_18529,U_18531) != c_List_Olist_ONil(U_18527) ),
    inference(clausify,[status(thm)],[f_4541_4]) ).

cnf(f_4541_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18528),sK449(U_18532,U_18530,U_18528)),hAPP(c_List_Oset(U_18528),U_18532)))
    | c_List_OdropWhile(U_18528,U_18530,U_18532) = c_List_Olist_ONil(U_18528) ),
    inference(clausify,[status(thm)],[f_4541_4]) ).

cnf(f_4541_7,plain,
    ( ~ hBOOL(hAPP(U_18530,sK449(U_18532,U_18530,U_18528)))
    | c_List_OdropWhile(U_18528,U_18530,U_18532) = c_List_Olist_ONil(U_18528) ),
    inference(clausify,[status(thm)],[f_4541_4]) ).

fof(f_4542_1,plain,
    ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_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_4542_2,plain,
    ! [U_18534,U_18533] : c_List_OdropWhile(U_18533,U_18534,c_List_Olist_ONil(U_18533)) = c_List_Olist_ONil(U_18533),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

cnf(f_4542_3,plain,
    c_List_OdropWhile(U_18533,U_18534,c_List_Olist_ONil(U_18533)) = c_List_Olist_ONil(U_18533),
    inference(clausify,[status(thm)],[f_4542_2]) ).

fof(f_4543_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_x_2)) )
      & ( c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(f_4543_2,plain,
    ! [U_18538,U_18537,U_18536,U_18535] :
      ( ( c_List_OdropWhile(U_18537,U_18535,hAPP(hAPP(c_List_Olist_OCons(U_18537),U_18536),U_18538)) = hAPP(hAPP(c_List_Olist_OCons(U_18537),U_18536),U_18538)
        | hBOOL(hAPP(U_18535,U_18536)) )
      & ( c_List_OdropWhile(U_18537,U_18535,hAPP(hAPP(c_List_Olist_OCons(U_18537),U_18536),U_18538)) = c_List_OdropWhile(U_18537,U_18535,U_18538)
        | ~ hBOOL(hAPP(U_18535,U_18536)) ) ),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

fof(f_4543_3,plain,
    ( ! [U_18546,U_18544,U_18542,U_18540] :
        ( c_List_OdropWhile(U_18544,U_18540,hAPP(hAPP(c_List_Olist_OCons(U_18544),U_18542),U_18546)) = hAPP(hAPP(c_List_Olist_OCons(U_18544),U_18542),U_18546)
        | hBOOL(hAPP(U_18540,U_18542)) )
    & ! [U_18545,U_18543,U_18541,U_18539] :
        ( c_List_OdropWhile(U_18543,U_18539,hAPP(hAPP(c_List_Olist_OCons(U_18543),U_18541),U_18545)) = c_List_OdropWhile(U_18543,U_18539,U_18545)
        | ~ hBOOL(hAPP(U_18539,U_18541)) ) ),
    inference(miniscope,[status(thm)],[f_4543_2]) ).

cnf(f_4543_4,plain,
    ( c_List_OdropWhile(U_18543,U_18539,hAPP(hAPP(c_List_Olist_OCons(U_18543),U_18541),U_18545)) = c_List_OdropWhile(U_18543,U_18539,U_18545)
    | ~ hBOOL(hAPP(U_18539,U_18541)) ),
    inference(clausify,[status(thm)],[f_4543_3]) ).

cnf(f_4543_5,plain,
    ( c_List_OdropWhile(U_18544,U_18540,hAPP(hAPP(c_List_Olist_OCons(U_18544),U_18542),U_18546)) = hAPP(hAPP(c_List_Olist_OCons(U_18544),U_18542),U_18546)
    | hBOOL(hAPP(U_18540,U_18542)) ),
    inference(clausify,[status(thm)],[f_4543_3]) ).

fof(f_4544_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile]) ).

fof(f_4544_2,plain,
    ! [U_18549,U_18548,U_18547] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18547),c_List_OdropWhile(U_18547,U_18549,U_18548)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18547),U_18548)) ),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

cnf(f_4544_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18547),c_List_OdropWhile(U_18547,U_18549,U_18548)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18547),U_18548)) ),
    inference(clausify,[status(thm)],[f_4544_2]) ).

fof(f_4545_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_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_Pa_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__map]) ).

fof(f_4545_2,plain,
    ! [U_18554,U_18553,U_18552,U_18551,U_18550] : c_List_OdropWhile(U_18550,U_18551,hAPP(hAPP(c_List_Omap(U_18552,U_18550),U_18553),U_18554)) = hAPP(hAPP(c_List_Omap(U_18552,U_18550),U_18553),c_List_OdropWhile(U_18552,hAPP(c_Fun_Ocomp(U_18550,tc_HOL_Obool,U_18552,U_18551),U_18553),U_18554)),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

cnf(f_4545_3,plain,
    c_List_OdropWhile(U_18550,U_18551,hAPP(hAPP(c_List_Omap(U_18552,U_18550),U_18553),U_18554)) = hAPP(hAPP(c_List_Omap(U_18552,U_18550),U_18553),c_List_OdropWhile(U_18552,hAPP(c_Fun_Ocomp(U_18550,tc_HOL_Obool,U_18552,U_18551),U_18553),U_18554)),
    inference(clausify,[status(thm)],[f_4545_2]) ).

fof(f_4546_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_xs_2)),V_ys_2)
      | hBOOL(hAPP(V_Pa_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_4546_2,plain,
    ! [U_18559,U_18558,U_18557,U_18556,U_18555] :
      ( c_List_OdropWhile(U_18555,U_18558,hAPP(hAPP(c_List_Oappend(U_18555),U_18557),U_18559)) = hAPP(hAPP(c_List_Oappend(U_18555),c_List_OdropWhile(U_18555,U_18558,U_18557)),U_18559)
      | hBOOL(hAPP(U_18558,U_18556))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18555),U_18556),hAPP(c_List_Oset(U_18555),U_18557))) ),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

cnf(f_4546_3,plain,
    ( c_List_OdropWhile(U_18555,U_18558,hAPP(hAPP(c_List_Oappend(U_18555),U_18557),U_18559)) = hAPP(hAPP(c_List_Oappend(U_18555),c_List_OdropWhile(U_18555,U_18558,U_18557)),U_18559)
    | hBOOL(hAPP(U_18558,U_18556))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18555),U_18556),hAPP(c_List_Oset(U_18555),U_18557))) ),
    inference(clausify,[status(thm)],[f_4546_2]) ).

fof(f_4547_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
        | hBOOL(hAPP(V_Pa_2,V_y_2))
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
      & ( ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
        | c_List_OdropWhile(T_b,V_Pa_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_4547_2,plain,
    ! [U_18564,U_18563,U_18562,U_18561,U_18560] :
      ( ( c_List_OdropWhile(U_18560,U_18561,U_18562) = hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18563),U_18564)
        | hBOOL(hAPP(U_18561,U_18563))
        | U_18562 != hAPP(hAPP(c_List_Oappend(U_18560),c_List_OtakeWhile(U_18560,U_18561,U_18562)),hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18563),U_18564)) )
      & ( ( ~ hBOOL(hAPP(U_18561,U_18563))
          & U_18562 = hAPP(hAPP(c_List_Oappend(U_18560),c_List_OtakeWhile(U_18560,U_18561,U_18562)),hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18563),U_18564)) )
        | c_List_OdropWhile(U_18560,U_18561,U_18562) != hAPP(hAPP(c_List_Olist_OCons(U_18560),U_18563),U_18564) ) ),
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

fof(f_4547_3,plain,
    ( ! [U_18574,U_18572,U_18570,U_18568,U_18566] :
        ( c_List_OdropWhile(U_18566,U_18568,U_18570) = hAPP(hAPP(c_List_Olist_OCons(U_18566),U_18572),U_18574)
        | hBOOL(hAPP(U_18568,U_18572))
        | U_18570 != hAPP(hAPP(c_List_Oappend(U_18566),c_List_OtakeWhile(U_18566,U_18568,U_18570)),hAPP(hAPP(c_List_Olist_OCons(U_18566),U_18572),U_18574)) )
    & ! [U_18573,U_18571,U_18569,U_18567,U_18565] :
        ( ( ~ hBOOL(hAPP(U_18567,U_18571))
          & U_18569 = hAPP(hAPP(c_List_Oappend(U_18565),c_List_OtakeWhile(U_18565,U_18567,U_18569)),hAPP(hAPP(c_List_Olist_OCons(U_18565),U_18571),U_18573)) )
        | c_List_OdropWhile(U_18565,U_18567,U_18569) != hAPP(hAPP(c_List_Olist_OCons(U_18565),U_18571),U_18573) ) ),
    inference(miniscope,[status(thm)],[f_4547_2]) ).

cnf(f_4547_4,plain,
    ( U_18569 = hAPP(hAPP(c_List_Oappend(U_18565),c_List_OtakeWhile(U_18565,U_18567,U_18569)),hAPP(hAPP(c_List_Olist_OCons(U_18565),U_18571),U_18573))
    | c_List_OdropWhile(U_18565,U_18567,U_18569) != hAPP(hAPP(c_List_Olist_OCons(U_18565),U_18571),U_18573) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

cnf(f_4547_5,plain,
    ( ~ hBOOL(hAPP(U_18567,U_18571))
    | c_List_OdropWhile(U_18565,U_18567,U_18569) != hAPP(hAPP(c_List_Olist_OCons(U_18565),U_18571),U_18573) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

cnf(f_4547_6,plain,
    ( c_List_OdropWhile(U_18566,U_18568,U_18570) = hAPP(hAPP(c_List_Olist_OCons(U_18566),U_18572),U_18574)
    | hBOOL(hAPP(U_18568,U_18572))
    | U_18570 != hAPP(hAPP(c_List_Oappend(U_18566),c_List_OtakeWhile(U_18566,U_18568,U_18570)),hAPP(hAPP(c_List_Olist_OCons(U_18566),U_18572),U_18574)) ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

fof(f_4548_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_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_Pa_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(f_4548_2,plain,
    ! [U_18577,U_18576,U_18575] : c_List_OdropWhile(U_18575,U_18576,U_18577) = hAPP(hAPP(c_List_Odrop(U_18575),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18575)),c_List_OtakeWhile(U_18575,U_18576,U_18577))),U_18577),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

cnf(f_4548_3,plain,
    c_List_OdropWhile(U_18575,U_18576,U_18577) = hAPP(hAPP(c_List_Odrop(U_18575),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18575)),c_List_OtakeWhile(U_18575,U_18576,U_18577))),U_18577),
    inference(clausify,[status(thm)],[f_4548_2]) ).

fof(f_4549_1,plain,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_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_Pa_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_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__nth]) ).

fof(f_4549_2,plain,
    ! [U_18581,U_18580,U_18579,U_18578] :
      ( hAPP(hAPP(c_List_Onth(U_18579),c_List_OdropWhile(U_18579,U_18580,U_18581)),U_18578) = hAPP(hAPP(c_List_Onth(U_18579),U_18581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18578),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),c_List_OtakeWhile(U_18579,U_18580,U_18581))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18578),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),c_List_OdropWhile(U_18579,U_18580,U_18581)))) ),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

cnf(f_4549_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18579),c_List_OdropWhile(U_18579,U_18580,U_18581)),U_18578) = hAPP(hAPP(c_List_Onth(U_18579),U_18581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18578),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),c_List_OtakeWhile(U_18579,U_18580,U_18581))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18578),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),c_List_OdropWhile(U_18579,U_18580,U_18581)))) ),
    inference(clausify,[status(thm)],[f_4549_2]) ).

fof(f_4550_1,plain,
    ! [V_f_2,V_Pa_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_Pa_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_Pa_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_4550_2,plain,
    ! [U_18587,U_18586,U_18585,U_18584,U_18583] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),hAPP(c_List_Ofilter(U_18584,U_18586),U_18585))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),U_18585))
      | ? [U_18582] :
          ( hAPP(U_18587,U_18582) != c_Groups_Ozero__class_Ozero(U_18583)
          & ~ hBOOL(hAPP(U_18586,U_18582))
          & hBOOL(hAPP(hAPP(c_member(U_18584),U_18582),hAPP(c_List_Oset(U_18584),U_18585))) )
      | ~ class_Groups_Omonoid__add(U_18583) ),
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

fof(f_4550_3,plain,
    ! [U_18587,U_18586,U_18585,U_18584,U_18583] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),hAPP(c_List_Ofilter(U_18584,U_18586),U_18585))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),U_18585))
      | ( hAPP(U_18587,sK450(U_18587,U_18586,U_18585,U_18584,U_18583)) != c_Groups_Ozero__class_Ozero(U_18583)
        & ~ hBOOL(hAPP(U_18586,sK450(U_18587,U_18586,U_18585,U_18584,U_18583)))
        & hBOOL(hAPP(hAPP(c_member(U_18584),sK450(U_18587,U_18586,U_18585,U_18584,U_18583)),hAPP(c_List_Oset(U_18584),U_18585))) )
      | ~ class_Groups_Omonoid__add(U_18583) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_18582,sK450(U_18587,U_18586,U_18585,U_18584,U_18583))],[f_4550_2]) ).

cnf(f_4550_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18584),sK450(U_18587,U_18586,U_18585,U_18584,U_18583)),hAPP(c_List_Oset(U_18584),U_18585)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),hAPP(c_List_Ofilter(U_18584,U_18586),U_18585))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),U_18585))
    | ~ class_Groups_Omonoid__add(U_18583) ),
    inference(clausify,[status(thm)],[f_4550_3]) ).

cnf(f_4550_5,plain,
    ( ~ hBOOL(hAPP(U_18586,sK450(U_18587,U_18586,U_18585,U_18584,U_18583)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),hAPP(c_List_Ofilter(U_18584,U_18586),U_18585))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),U_18585))
    | ~ class_Groups_Omonoid__add(U_18583) ),
    inference(clausify,[status(thm)],[f_4550_3]) ).

cnf(f_4550_6,plain,
    ( hAPP(U_18587,sK450(U_18587,U_18586,U_18585,U_18584,U_18583)) != c_Groups_Ozero__class_Ozero(U_18583)
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),hAPP(c_List_Ofilter(U_18584,U_18586),U_18585))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18583),hAPP(hAPP(c_List_Omap(U_18584,U_18583),U_18587),U_18585))
    | ~ class_Groups_Omonoid__add(U_18583) ),
    inference(clausify,[status(thm)],[f_4550_3]) ).

fof(f_4551_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_4551_2,plain,
    ! [U_18591,U_18590] :
      ( c_List_Olinorder__class_Osorted(U_18590,U_18591)
      | ? [U_18589,U_18588] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18590),hAPP(hAPP(c_List_Onth(U_18590),U_18591),U_18589)),hAPP(hAPP(c_List_Onth(U_18590),U_18591),U_18588)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18588),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18590)),U_18591)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18589),U_18588)) )
      | ~ class_Orderings_Olinorder(U_18590) ),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

fof(f_4551_3,plain,
    ! [U_18591,U_18590] :
      ( c_List_Olinorder__class_Osorted(U_18590,U_18591)
      | ? [U_18588] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18590),hAPP(hAPP(c_List_Onth(U_18590),U_18591),sK451(U_18591,U_18590))),hAPP(hAPP(c_List_Onth(U_18590),U_18591),U_18588)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18588),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18590)),U_18591)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK451(U_18591,U_18590)),U_18588)) )
      | ~ class_Orderings_Olinorder(U_18590) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_18589,sK451(U_18591,U_18590))],[f_4551_2]) ).

fof(f_4551_4,plain,
    ! [U_18591,U_18590] :
      ( c_List_Olinorder__class_Osorted(U_18590,U_18591)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18590),hAPP(hAPP(c_List_Onth(U_18590),U_18591),sK451(U_18591,U_18590))),hAPP(hAPP(c_List_Onth(U_18590),U_18591),sK452(U_18591,U_18590))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK452(U_18591,U_18590)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18590)),U_18591)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK451(U_18591,U_18590)),sK452(U_18591,U_18590))) )
      | ~ class_Orderings_Olinorder(U_18590) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_18588,sK452(U_18591,U_18590))],[f_4551_3]) ).

cnf(f_4551_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK451(U_18591,U_18590)),sK452(U_18591,U_18590)))
    | c_List_Olinorder__class_Osorted(U_18590,U_18591)
    | ~ class_Orderings_Olinorder(U_18590) ),
    inference(clausify,[status(thm)],[f_4551_4]) ).

cnf(f_4551_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK452(U_18591,U_18590)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18590)),U_18591)))
    | c_List_Olinorder__class_Osorted(U_18590,U_18591)
    | ~ class_Orderings_Olinorder(U_18590) ),
    inference(clausify,[status(thm)],[f_4551_4]) ).

cnf(f_4551_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18590),hAPP(hAPP(c_List_Onth(U_18590),U_18591),sK451(U_18591,U_18590))),hAPP(hAPP(c_List_Onth(U_18590),U_18591),sK452(U_18591,U_18590))))
    | c_List_Olinorder__class_Osorted(U_18590,U_18591)
    | ~ class_Orderings_Olinorder(U_18590) ),
    inference(clausify,[status(thm)],[f_4551_4]) ).

fof(f_4552_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
      | ? [B_x] :
          ( hBOOL(hAPP(V_Pa_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(f_4552_2,plain,
    ! [U_18595,U_18594,U_18593] :
      ( c_List_OtakeWhile(U_18593,U_18594,U_18595) = hAPP(c_List_Ofilter(U_18593,U_18594),U_18595)
      | ? [U_18592] :
          ( hBOOL(hAPP(U_18594,U_18592))
          & hBOOL(hAPP(hAPP(c_member(U_18593),U_18592),hAPP(c_List_Oset(U_18593),c_List_OdropWhile(U_18593,U_18594,U_18595)))) ) ),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

fof(f_4552_3,plain,
    ! [U_18595,U_18594,U_18593] :
      ( c_List_OtakeWhile(U_18593,U_18594,U_18595) = hAPP(c_List_Ofilter(U_18593,U_18594),U_18595)
      | ( hBOOL(hAPP(U_18594,sK453(U_18595,U_18594,U_18593)))
        & hBOOL(hAPP(hAPP(c_member(U_18593),sK453(U_18595,U_18594,U_18593)),hAPP(c_List_Oset(U_18593),c_List_OdropWhile(U_18593,U_18594,U_18595)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_18592,sK453(U_18595,U_18594,U_18593))],[f_4552_2]) ).

cnf(f_4552_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18593),sK453(U_18595,U_18594,U_18593)),hAPP(c_List_Oset(U_18593),c_List_OdropWhile(U_18593,U_18594,U_18595))))
    | c_List_OtakeWhile(U_18593,U_18594,U_18595) = hAPP(c_List_Ofilter(U_18593,U_18594),U_18595) ),
    inference(clausify,[status(thm)],[f_4552_3]) ).

cnf(f_4552_5,plain,
    ( hBOOL(hAPP(U_18594,sK453(U_18595,U_18594,U_18593)))
    | c_List_OtakeWhile(U_18593,U_18594,U_18595) = hAPP(c_List_Ofilter(U_18593,U_18594),U_18595) ),
    inference(clausify,[status(thm)],[f_4552_3]) ).

fof(f_4553_1,plain,
    ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
      ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)
      | ( hBOOL(hAPP(V_Pa_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_Pa_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_4553_2,plain,
    ! [U_18600,U_18599,U_18598,U_18597] :
      ( c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
      | ( hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18597)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599))) )
      | ? [U_18596] :
          ( ~ hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18596)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18596),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18596),U_18597)) ) ),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

fof(f_4553_3,plain,
    ! [U_18600,U_18599,U_18598,U_18597] :
      ( c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
      | ( hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18597)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599))) )
      | ( ~ hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),sK454(U_18600,U_18599,U_18598,U_18597))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),U_18597)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_18596,sK454(U_18600,U_18599,U_18598,U_18597))],[f_4553_2]) ).

cnf(f_4553_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),U_18597)) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

cnf(f_4553_5,plain,
    ( hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18597)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),U_18597)) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

cnf(f_4553_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599))) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

cnf(f_4553_7,plain,
    ( hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18597)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18600,U_18599,U_18598,U_18597)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599))) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

cnf(f_4553_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18597),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18598)),U_18599)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | ~ hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),sK454(U_18600,U_18599,U_18598,U_18597)))) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

cnf(f_4553_9,plain,
    ( hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18597)))
    | c_List_OtakeWhile(U_18598,U_18600,U_18599) = hAPP(hAPP(c_List_Otake(U_18598),U_18597),U_18599)
    | ~ hBOOL(hAPP(U_18600,hAPP(hAPP(c_List_Onth(U_18598),U_18599),sK454(U_18600,U_18599,U_18598,U_18597)))) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

fof(f_4554_1,plain,
    ! [V_xs_2,T_b,V_Pa_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_Pa_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_Pa_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_4554_2,plain,
    ! [U_18605,U_18604,U_18603,U_18602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),c_List_OtakeWhile(U_18604,U_18603,U_18605))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),U_18605)))
      | ? [U_18601] :
          ( ~ hBOOL(hAPP(U_18603,hAPP(hAPP(c_List_Onth(U_18604),U_18605),U_18601)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18601),U_18602)) ) ),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

fof(f_4554_3,plain,
    ! [U_18605,U_18604,U_18603,U_18602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),c_List_OtakeWhile(U_18604,U_18603,U_18605))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),U_18605)))
      | ( ~ hBOOL(hAPP(U_18603,hAPP(hAPP(c_List_Onth(U_18604),U_18605),sK455(U_18605,U_18604,U_18603,U_18602))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK455(U_18605,U_18604,U_18603,U_18602)),U_18602)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_18601,sK455(U_18605,U_18604,U_18603,U_18602))],[f_4554_2]) ).

cnf(f_4554_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK455(U_18605,U_18604,U_18603,U_18602)),U_18602))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),c_List_OtakeWhile(U_18604,U_18603,U_18605))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),U_18605))) ),
    inference(clausify,[status(thm)],[f_4554_3]) ).

cnf(f_4554_5,plain,
    ( ~ hBOOL(hAPP(U_18603,hAPP(hAPP(c_List_Onth(U_18604),U_18605),sK455(U_18605,U_18604,U_18603,U_18602))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),c_List_OtakeWhile(U_18604,U_18603,U_18605))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18604)),U_18605))) ),
    inference(clausify,[status(thm)],[f_4554_3]) ).

fof(f_4555_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_4555_2,plain,
    ! [U_18613,U_18612] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18612,U_18613)
          | ( ! [U_18611,U_18610] :
                ( ~ c_List_Olinorder__class_Osorted(U_18612,U_18611)
                | ? [U_18609] :
                    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),U_18609))
                    & hBOOL(hAPP(hAPP(c_member(U_18612),U_18609),hAPP(c_List_Oset(U_18612),U_18611))) )
                | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611) )
            & U_18613 != c_List_Olist_ONil(U_18612) ) )
        & ( ? [U_18608,U_18607] :
              ( c_List_Olinorder__class_Osorted(U_18612,U_18608)
              & ! [U_18606] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18607),U_18606))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),U_18608))) )
              & U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18607),U_18608) )
          | U_18613 = c_List_Olist_ONil(U_18612)
          | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613) ) )
      | ~ class_Orderings_Olinorder(U_18612) ),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

fof(f_4555_3,plain,
    ! [U_18613,U_18612] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18612,U_18613)
          | ( ! [U_18611] :
                ( ! [U_18610] :
                    ( ? [U_18609] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),U_18609))
                        & hBOOL(hAPP(hAPP(c_member(U_18612),U_18609),hAPP(c_List_Oset(U_18612),U_18611))) )
                    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611) )
                | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611) )
            & U_18613 != c_List_Olist_ONil(U_18612) ) )
        & ( ? [U_18608] :
              ( ? [U_18607] :
                  ( ! [U_18606] :
                      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18607),U_18606))
                      | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),U_18608))) )
                  & U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18607),U_18608) )
              & c_List_Olinorder__class_Osorted(U_18612,U_18608) )
          | U_18613 = c_List_Olist_ONil(U_18612)
          | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613) ) )
      | ~ class_Orderings_Olinorder(U_18612) ),
    inference(miniscope,[status(thm)],[f_4555_2]) ).

fof(f_4555_4,plain,
    ! [U_18613,U_18612] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18612,U_18613)
          | ( ! [U_18611] :
                ( ! [U_18610] :
                    ( ? [U_18609] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),U_18609))
                        & hBOOL(hAPP(hAPP(c_member(U_18612),U_18609),hAPP(c_List_Oset(U_18612),U_18611))) )
                    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611) )
                | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611) )
            & U_18613 != c_List_Olist_ONil(U_18612) ) )
        & ( ( ? [U_18607] :
                ( ! [U_18606] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18607),U_18606))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),sK456(U_18613,U_18612)))) )
                & U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18607),sK456(U_18613,U_18612)) )
            & c_List_Olinorder__class_Osorted(U_18612,sK456(U_18613,U_18612)) )
          | U_18613 = c_List_Olist_ONil(U_18612)
          | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613) ) )
      | ~ class_Orderings_Olinorder(U_18612) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_18608,sK456(U_18613,U_18612))],[f_4555_3]) ).

fof(f_4555_5,plain,
    ! [U_18613,U_18612] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18612,U_18613)
          | ( ! [U_18611] :
                ( ! [U_18610] :
                    ( ? [U_18609] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),U_18609))
                        & hBOOL(hAPP(hAPP(c_member(U_18612),U_18609),hAPP(c_List_Oset(U_18612),U_18611))) )
                    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611) )
                | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611) )
            & U_18613 != c_List_Olist_ONil(U_18612) ) )
        & ( ( ! [U_18606] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),sK457(U_18613,U_18612)),U_18606))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),sK456(U_18613,U_18612)))) )
            & U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),sK457(U_18613,U_18612)),sK456(U_18613,U_18612))
            & c_List_Olinorder__class_Osorted(U_18612,sK456(U_18613,U_18612)) )
          | U_18613 = c_List_Olist_ONil(U_18612)
          | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613) ) )
      | ~ class_Orderings_Olinorder(U_18612) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_18607,sK457(U_18613,U_18612))],[f_4555_4]) ).

fof(f_4555_6,plain,
    ! [U_18613,U_18612] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18612,U_18613)
          | ( ! [U_18611] :
                ( ! [U_18610] :
                    ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),sK458(U_18613,U_18612,U_18611,U_18610)))
                      & hBOOL(hAPP(hAPP(c_member(U_18612),sK458(U_18613,U_18612,U_18611,U_18610)),hAPP(c_List_Oset(U_18612),U_18611))) )
                    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611) )
                | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611) )
            & U_18613 != c_List_Olist_ONil(U_18612) ) )
        & ( ( ! [U_18606] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),sK457(U_18613,U_18612)),U_18606))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),sK456(U_18613,U_18612)))) )
            & U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),sK457(U_18613,U_18612)),sK456(U_18613,U_18612))
            & c_List_Olinorder__class_Osorted(U_18612,sK456(U_18613,U_18612)) )
          | U_18613 = c_List_Olist_ONil(U_18612)
          | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613) ) )
      | ~ class_Orderings_Olinorder(U_18612) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18609,sK458(U_18613,U_18612,U_18611,U_18610))],[f_4555_5]) ).

cnf(f_4555_7,plain,
    ( c_List_Olinorder__class_Osorted(U_18612,sK456(U_18613,U_18612))
    | U_18613 = c_List_Olist_ONil(U_18612)
    | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

cnf(f_4555_8,plain,
    ( U_18613 = hAPP(hAPP(c_List_Olist_OCons(U_18612),sK457(U_18613,U_18612)),sK456(U_18613,U_18612))
    | U_18613 = c_List_Olist_ONil(U_18612)
    | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

cnf(f_4555_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),sK457(U_18613,U_18612)),U_18606))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18612),U_18606),hAPP(c_List_Oset(U_18612),sK456(U_18613,U_18612))))
    | U_18613 = c_List_Olist_ONil(U_18612)
    | ~ c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

cnf(f_4555_10,plain,
    ( U_18613 != c_List_Olist_ONil(U_18612)
    | c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

cnf(f_4555_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18612),sK458(U_18613,U_18612,U_18611,U_18610)),hAPP(c_List_Oset(U_18612),U_18611)))
    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611)
    | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611)
    | c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

cnf(f_4555_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18612),U_18610),sK458(U_18613,U_18612,U_18611,U_18610)))
    | U_18613 != hAPP(hAPP(c_List_Olist_OCons(U_18612),U_18610),U_18611)
    | ~ c_List_Olinorder__class_Osorted(U_18612,U_18611)
    | c_List_Olinorder__class_Osorted(U_18612,U_18613)
    | ~ class_Orderings_Olinorder(U_18612) ),
    inference(clausify,[status(thm)],[f_4555_6]) ).

fof(f_4556_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_4556_2,plain,
    ! [U_18616,U_18615,U_18614] :
      ( ( c_List_Oinsert(U_18614,U_18615,U_18616) = hAPP(hAPP(c_List_Olist_OCons(U_18614),U_18615),U_18616)
        | hBOOL(hAPP(hAPP(c_member(U_18614),U_18615),hAPP(c_List_Oset(U_18614),U_18616))) )
      & ( c_List_Oinsert(U_18614,U_18615,U_18616) = U_18616
        | ~ hBOOL(hAPP(hAPP(c_member(U_18614),U_18615),hAPP(c_List_Oset(U_18614),U_18616))) ) ),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

fof(f_4556_3,plain,
    ( ! [U_18622,U_18620,U_18618] :
        ( c_List_Oinsert(U_18618,U_18620,U_18622) = hAPP(hAPP(c_List_Olist_OCons(U_18618),U_18620),U_18622)
        | hBOOL(hAPP(hAPP(c_member(U_18618),U_18620),hAPP(c_List_Oset(U_18618),U_18622))) )
    & ! [U_18621,U_18619,U_18617] :
        ( c_List_Oinsert(U_18617,U_18619,U_18621) = U_18621
        | ~ hBOOL(hAPP(hAPP(c_member(U_18617),U_18619),hAPP(c_List_Oset(U_18617),U_18621))) ) ),
    inference(miniscope,[status(thm)],[f_4556_2]) ).

cnf(f_4556_4,plain,
    ( c_List_Oinsert(U_18617,U_18619,U_18621) = U_18621
    | ~ hBOOL(hAPP(hAPP(c_member(U_18617),U_18619),hAPP(c_List_Oset(U_18617),U_18621))) ),
    inference(clausify,[status(thm)],[f_4556_3]) ).

cnf(f_4556_5,plain,
    ( c_List_Oinsert(U_18618,U_18620,U_18622) = hAPP(hAPP(c_List_Olist_OCons(U_18618),U_18620),U_18622)
    | hBOOL(hAPP(hAPP(c_member(U_18618),U_18620),hAPP(c_List_Oset(U_18618),U_18622))) ),
    inference(clausify,[status(thm)],[f_4556_3]) ).

fof(f_4557_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_4557_2,plain,
    ! [U_18625,U_18624,U_18623] :
      ( c_List_Oinsert(U_18623,U_18624,U_18625) = hAPP(hAPP(c_List_Olist_OCons(U_18623),U_18624),U_18625)
      | hBOOL(hAPP(hAPP(c_member(U_18623),U_18624),hAPP(c_List_Oset(U_18623),U_18625))) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

cnf(f_4557_3,plain,
    ( c_List_Oinsert(U_18623,U_18624,U_18625) = hAPP(hAPP(c_List_Olist_OCons(U_18623),U_18624),U_18625)
    | hBOOL(hAPP(hAPP(c_member(U_18623),U_18624),hAPP(c_List_Oset(U_18623),U_18625))) ),
    inference(clausify,[status(thm)],[f_4557_2]) ).

fof(f_4558_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_4558_2,plain,
    ! [U_18628,U_18627,U_18626] : c_List_Oinsert(U_18626,U_18627,c_List_Oremdups(U_18626,U_18628)) = c_List_Oremdups(U_18626,c_List_Oinsert(U_18626,U_18627,U_18628)),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

cnf(f_4558_3,plain,
    c_List_Oinsert(U_18626,U_18627,c_List_Oremdups(U_18626,U_18628)) = c_List_Oremdups(U_18626,c_List_Oinsert(U_18626,U_18627,U_18628)),
    inference(clausify,[status(thm)],[f_4558_2]) ).

fof(f_4559_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_4559_2,plain,
    ! [U_18631,U_18630,U_18629] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18629),c_List_Oinsert(U_18629,U_18631,U_18630)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18629),U_18630)) ),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

cnf(f_4559_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18629),c_List_Oinsert(U_18629,U_18631,U_18630)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18629),U_18630)) ),
    inference(clausify,[status(thm)],[f_4559_2]) ).

fof(f_4560_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_4560_2,plain,
    ! [U_18634,U_18633,U_18632] :
      ( c_List_Oinsert(U_18632,U_18633,U_18634) = U_18634
      | ~ hBOOL(hAPP(hAPP(c_member(U_18632),U_18633),hAPP(c_List_Oset(U_18632),U_18634))) ),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

cnf(f_4560_3,plain,
    ( c_List_Oinsert(U_18632,U_18633,U_18634) = U_18634
    | ~ hBOOL(hAPP(hAPP(c_member(U_18632),U_18633),hAPP(c_List_Oset(U_18632),U_18634))) ),
    inference(clausify,[status(thm)],[f_4560_2]) ).

fof(f_4561_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_4561_2,plain,
    ! [U_18637,U_18636,U_18635] : hAPP(c_List_Oset(U_18635),c_List_Oinsert(U_18635,U_18636,U_18637)) = hAPP(hAPP(c_Set_Oinsert(U_18635),U_18636),hAPP(c_List_Oset(U_18635),U_18637)),
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

cnf(f_4561_3,plain,
    hAPP(c_List_Oset(U_18635),c_List_Oinsert(U_18635,U_18636,U_18637)) = hAPP(hAPP(c_Set_Oinsert(U_18635),U_18636),hAPP(c_List_Oset(U_18635),U_18637)),
    inference(clausify,[status(thm)],[f_4561_2]) ).

fof(f_4562_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_4562_2,plain,
    ! [U_18639,U_18638] : c_List_Oinsert(U_18638,U_18639,c_List_Olist_ONil(U_18638)) = hAPP(hAPP(c_List_Olist_OCons(U_18638),U_18639),c_List_Olist_ONil(U_18638)),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

cnf(f_4562_3,plain,
    c_List_Oinsert(U_18638,U_18639,c_List_Olist_ONil(U_18638)) = hAPP(hAPP(c_List_Olist_OCons(U_18638),U_18639),c_List_Olist_ONil(U_18638)),
    inference(clausify,[status(thm)],[f_4562_2]) ).

fof(f_4563_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_4563_2,plain,
    ! [U_18643,U_18642,U_18641,U_18640] : c_List_Omaps(U_18640,U_18641,U_18642,U_18643) = c_List_Oconcat(U_18641,hAPP(hAPP(c_List_Omap(U_18640,tc_List_Olist(U_18641)),U_18642),U_18643)),
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

cnf(f_4563_3,plain,
    c_List_Omaps(U_18640,U_18641,U_18642,U_18643) = c_List_Oconcat(U_18641,hAPP(hAPP(c_List_Omap(U_18640,tc_List_Olist(U_18641)),U_18642),U_18643)),
    inference(clausify,[status(thm)],[f_4563_2]) ).

fof(f_4564_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_4564_2,plain,
    ! [U_18647,U_18646,U_18645,U_18644] : c_List_Oconcat(U_18644,hAPP(hAPP(c_List_Omap(U_18645,tc_List_Olist(U_18644)),U_18646),U_18647)) = c_List_Omaps(U_18645,U_18644,U_18646,U_18647),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

cnf(f_4564_3,plain,
    c_List_Oconcat(U_18644,hAPP(hAPP(c_List_Omap(U_18645,tc_List_Olist(U_18644)),U_18646),U_18647)) = c_List_Omaps(U_18645,U_18644,U_18646,U_18647),
    inference(clausify,[status(thm)],[f_4564_2]) ).

fof(f_4565_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_4565_2,plain,
    ! [U_18650,U_18649,U_18648] : c_List_Omaps(U_18648,U_18649,U_18650,c_List_Olist_ONil(U_18648)) = c_List_Olist_ONil(U_18649),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

cnf(f_4565_3,plain,
    c_List_Omaps(U_18648,U_18649,U_18650,c_List_Olist_ONil(U_18648)) = c_List_Olist_ONil(U_18649),
    inference(clausify,[status(thm)],[f_4565_2]) ).

fof(f_4566_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_4566_2,plain,
    ! [U_18655,U_18654,U_18653,U_18652,U_18651] : c_List_Omaps(U_18651,U_18652,U_18653,hAPP(hAPP(c_List_Olist_OCons(U_18651),U_18654),U_18655)) = hAPP(hAPP(c_List_Oappend(U_18652),hAPP(U_18653,U_18654)),c_List_Omaps(U_18651,U_18652,U_18653,U_18655)),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

cnf(f_4566_3,plain,
    c_List_Omaps(U_18651,U_18652,U_18653,hAPP(hAPP(c_List_Olist_OCons(U_18651),U_18654),U_18655)) = hAPP(hAPP(c_List_Oappend(U_18652),hAPP(U_18653,U_18654)),c_List_Omaps(U_18651,U_18652,U_18653,U_18655)),
    inference(clausify,[status(thm)],[f_4566_2]) ).

fof(f_4567_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_4567_2,plain,
    ! [U_18660,U_18659] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
      | ? [U_18658] :
          ( ? [U_18657] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),U_18658)),hAPP(c_List_Oset(U_18659),U_18657)) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
              & U_18658 != U_18657
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18657),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18658),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ? [U_18656] :
          ( ~ hBOOL(hAPP(c_List_Odistinct(U_18659),U_18656))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18656),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

fof(f_4567_3,plain,
    ! [U_18660,U_18659] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
      | ? [U_18658] :
          ( ? [U_18657] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),U_18658)),hAPP(c_List_Oset(U_18659),U_18657)) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
              & U_18658 != U_18657
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18657),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18658),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18656,sK459(U_18660,U_18659))],[f_4567_2]) ).

fof(f_4567_4,plain,
    ! [U_18660,U_18659] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
      | ( ? [U_18657] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),sK460(U_18660,U_18659))),hAPP(c_List_Oset(U_18659),U_18657)) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
            & sK460(U_18660,U_18659) != U_18657
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),U_18657),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK460(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18658,sK460(U_18660,U_18659))],[f_4567_3]) ).

fof(f_4567_5,plain,
    ! [U_18660,U_18659] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),sK460(U_18660,U_18659))),hAPP(c_List_Oset(U_18659),sK461(U_18660,U_18659))) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
        & sK460(U_18660,U_18659) != sK461(U_18660,U_18659)
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK461(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK460(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18657,sK461(U_18660,U_18659))],[f_4567_4]) ).

cnf(f_4567_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK460(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK461(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_8,plain,
    ( sK460(U_18660,U_18659) != sK461(U_18660,U_18659)
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),sK460(U_18660,U_18659))),hAPP(c_List_Oset(U_18659),sK461(U_18660,U_18659))) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK459(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK460(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18659)),sK461(U_18660,U_18659)),hAPP(c_List_Oset(tc_List_Olist(U_18659)),U_18660)))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_12,plain,
    ( sK460(U_18660,U_18659) != sK461(U_18660,U_18659)
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

cnf(f_4567_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18659,tc_HOL_Obool)),hAPP(c_List_Oset(U_18659),sK460(U_18660,U_18659))),hAPP(c_List_Oset(U_18659),sK461(U_18660,U_18659))) != c_Orderings_Obot__class_Obot(tc_fun(U_18659,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_18659),c_List_Oconcat(U_18659,U_18660)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18659),sK459(U_18660,U_18659)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18659)),U_18660)) ),
    inference(clausify,[status(thm)],[f_4567_5]) ).

fof(f_4568_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_4568_2,plain,
    ! [U_18665,U_18664,U_18663,U_18662,U_18661] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18664,U_18664)),hAPP(hAPP(c_Product__Type_OPair(U_18664,U_18664),U_18662),U_18663)),c_List_Omeasures(U_18664,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18664,tc_Nat_Onat)),U_18661),U_18665))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18664,U_18664)),hAPP(hAPP(c_Product__Type_OPair(U_18664,U_18664),U_18662),U_18663)),c_List_Omeasures(U_18664,U_18665)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_18661,U_18662)),hAPP(U_18661,U_18663))) ),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

cnf(f_4568_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18664,U_18664)),hAPP(hAPP(c_Product__Type_OPair(U_18664,U_18664),U_18662),U_18663)),c_List_Omeasures(U_18664,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18664,tc_Nat_Onat)),U_18661),U_18665))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18664,U_18664)),hAPP(hAPP(c_Product__Type_OPair(U_18664,U_18664),U_18662),U_18663)),c_List_Omeasures(U_18664,U_18665)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_18661,U_18662)),hAPP(U_18661,U_18663))) ),
    inference(clausify,[status(thm)],[f_4568_2]) ).

fof(f_4569_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_4569_2,plain,
    ! [U_18667,U_18666] : c_Wellfounded_Owf(U_18666,c_List_Omeasures(U_18666,U_18667)),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

cnf(f_4569_3,plain,
    c_Wellfounded_Owf(U_18666,c_List_Omeasures(U_18666,U_18667)),
    inference(clausify,[status(thm)],[f_4569_2]) ).

fof(f_4570_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_4570_2,plain,
    ! [U_18670,U_18669,U_18668] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18668,U_18668)),hAPP(hAPP(c_Product__Type_OPair(U_18668,U_18668),U_18669),U_18670)),c_List_Omeasures(U_18668,c_List_Olist_ONil(tc_fun(U_18668,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

cnf(f_4570_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18668,U_18668)),hAPP(hAPP(c_Product__Type_OPair(U_18668,U_18668),U_18669),U_18670)),c_List_Omeasures(U_18668,c_List_Olist_ONil(tc_fun(U_18668,tc_Nat_Onat))))),
    inference(clausify,[status(thm)],[f_4570_2]) ).

fof(f_4571_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_4571_2,plain,
    ! [U_18672,U_18671] : c_List_Omeasures(U_18671,U_18672) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_18671),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_18671,tc_List_Olist(tc_fun(U_18671,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_18671,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_18671,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_18671),c_List_Omap(tc_fun(U_18671,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_18671,tc_Nat_Onat),U_18671,tc_Nat_Onat),c_COMBI(tc_fun(U_18671,tc_Nat_Onat))))),U_18672)),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

cnf(f_4571_3,plain,
    c_List_Omeasures(U_18671,U_18672) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_18671),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_18671,tc_List_Olist(tc_fun(U_18671,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_18671,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_18671,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_18671),c_List_Omap(tc_fun(U_18671,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_18671,tc_Nat_Onat),U_18671,tc_Nat_Onat),c_COMBI(tc_fun(U_18671,tc_Nat_Onat))))),U_18672)),
    inference(clausify,[status(thm)],[f_4571_2]) ).

fof(f_4572_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_4572_2,plain,
    ! [U_18677,U_18676,U_18675,U_18674,U_18673] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18674),U_18675)),c_List_Omeasures(U_18673,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18673,tc_Nat_Onat)),U_18676),U_18677))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18674),U_18675)),c_List_Omeasures(U_18673,U_18677)))
            | hAPP(U_18676,U_18674) != hAPP(U_18676,U_18675) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18676,U_18674)),hAPP(U_18676,U_18675))) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18674),U_18675)),c_List_Omeasures(U_18673,U_18677)))
          & hAPP(U_18676,U_18674) = hAPP(U_18676,U_18675) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18676,U_18674)),hAPP(U_18676,U_18675)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18674),U_18675)),c_List_Omeasures(U_18673,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18673,tc_Nat_Onat)),U_18676),U_18677)))) ) ),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

fof(f_4572_3,plain,
    ( ! [U_18687,U_18685,U_18683,U_18681,U_18679] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18679,U_18679)),hAPP(hAPP(c_Product__Type_OPair(U_18679,U_18679),U_18681),U_18683)),c_List_Omeasures(U_18679,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18679,tc_Nat_Onat)),U_18685),U_18687))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18679,U_18679)),hAPP(hAPP(c_Product__Type_OPair(U_18679,U_18679),U_18681),U_18683)),c_List_Omeasures(U_18679,U_18687)))
            | hAPP(U_18685,U_18681) != hAPP(U_18685,U_18683) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18685,U_18681)),hAPP(U_18685,U_18683))) ) )
    & ! [U_18686,U_18684,U_18682,U_18680,U_18678] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18678,U_18678)),hAPP(hAPP(c_Product__Type_OPair(U_18678,U_18678),U_18680),U_18682)),c_List_Omeasures(U_18678,U_18686)))
          & hAPP(U_18684,U_18680) = hAPP(U_18684,U_18682) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18684,U_18680)),hAPP(U_18684,U_18682)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18678,U_18678)),hAPP(hAPP(c_Product__Type_OPair(U_18678,U_18678),U_18680),U_18682)),c_List_Omeasures(U_18678,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18678,tc_Nat_Onat)),U_18684),U_18686)))) ) ),
    inference(miniscope,[status(thm)],[f_4572_2]) ).

cnf(f_4572_4,plain,
    ( hAPP(U_18684,U_18680) = hAPP(U_18684,U_18682)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18684,U_18680)),hAPP(U_18684,U_18682)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18678,U_18678)),hAPP(hAPP(c_Product__Type_OPair(U_18678,U_18678),U_18680),U_18682)),c_List_Omeasures(U_18678,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18678,tc_Nat_Onat)),U_18684),U_18686)))) ),
    inference(clausify,[status(thm)],[f_4572_3]) ).

cnf(f_4572_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18678,U_18678)),hAPP(hAPP(c_Product__Type_OPair(U_18678,U_18678),U_18680),U_18682)),c_List_Omeasures(U_18678,U_18686)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18684,U_18680)),hAPP(U_18684,U_18682)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18678,U_18678)),hAPP(hAPP(c_Product__Type_OPair(U_18678,U_18678),U_18680),U_18682)),c_List_Omeasures(U_18678,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18678,tc_Nat_Onat)),U_18684),U_18686)))) ),
    inference(clausify,[status(thm)],[f_4572_3]) ).

cnf(f_4572_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18685,U_18681)),hAPP(U_18685,U_18683)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18679,U_18679)),hAPP(hAPP(c_Product__Type_OPair(U_18679,U_18679),U_18681),U_18683)),c_List_Omeasures(U_18679,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18679,tc_Nat_Onat)),U_18685),U_18687)))) ),
    inference(clausify,[status(thm)],[f_4572_3]) ).

cnf(f_4572_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18679,U_18679)),hAPP(hAPP(c_Product__Type_OPair(U_18679,U_18679),U_18681),U_18683)),c_List_Omeasures(U_18679,U_18687)))
    | hAPP(U_18685,U_18681) != hAPP(U_18685,U_18683)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18679,U_18679)),hAPP(hAPP(c_Product__Type_OPair(U_18679,U_18679),U_18681),U_18683)),c_List_Omeasures(U_18679,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18679,tc_Nat_Onat)),U_18685),U_18687)))) ),
    inference(clausify,[status(thm)],[f_4572_3]) ).

fof(f_4573_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_4573_2,plain,
    ! [U_18692,U_18691,U_18690,U_18689,U_18688] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18691,U_18691)),hAPP(hAPP(c_Product__Type_OPair(U_18691,U_18691),U_18689),U_18690)),c_List_Omeasures(U_18691,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18691,tc_Nat_Onat)),U_18688),U_18692))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18688,U_18689)),hAPP(U_18688,U_18690))) ),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

cnf(f_4573_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18691,U_18691)),hAPP(hAPP(c_Product__Type_OPair(U_18691,U_18691),U_18689),U_18690)),c_List_Omeasures(U_18691,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18691,tc_Nat_Onat)),U_18688),U_18692))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18688,U_18689)),hAPP(U_18688,U_18690))) ),
    inference(clausify,[status(thm)],[f_4573_2]) ).

fof(f_4574_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_4574_2,plain,
    ! [U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694] :
      ( hAPP(c_List_Ofoldl(U_18696,U_18694,hAPP(c_COMBC(U_18694,U_18696,U_18696),U_18698),hAPP(U_18699,U_18701)),U_18695) = hAPP(U_18699,hAPP(c_List_Ofoldl(U_18697,U_18694,hAPP(c_COMBC(U_18694,U_18697,U_18697),U_18700),U_18701),U_18695))
      | ? [U_18693] :
          ( hAPP(c_Fun_Ocomp(U_18696,U_18696,U_18697,hAPP(U_18698,U_18693)),U_18699) != hAPP(c_Fun_Ocomp(U_18697,U_18696,U_18697,U_18699),hAPP(U_18700,U_18693))
          & hBOOL(hAPP(hAPP(c_member(U_18694),U_18693),hAPP(c_List_Oset(U_18694),U_18695))) ) ),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

fof(f_4574_3,plain,
    ! [U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694] :
      ( hAPP(c_List_Ofoldl(U_18696,U_18694,hAPP(c_COMBC(U_18694,U_18696,U_18696),U_18698),hAPP(U_18699,U_18701)),U_18695) = hAPP(U_18699,hAPP(c_List_Ofoldl(U_18697,U_18694,hAPP(c_COMBC(U_18694,U_18697,U_18697),U_18700),U_18701),U_18695))
      | ( hAPP(c_Fun_Ocomp(U_18696,U_18696,U_18697,hAPP(U_18698,sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694))),U_18699) != hAPP(c_Fun_Ocomp(U_18697,U_18696,U_18697,U_18699),hAPP(U_18700,sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694)))
        & hBOOL(hAPP(hAPP(c_member(U_18694),sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694)),hAPP(c_List_Oset(U_18694),U_18695))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18693,sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694))],[f_4574_2]) ).

cnf(f_4574_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18694),sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694)),hAPP(c_List_Oset(U_18694),U_18695)))
    | hAPP(c_List_Ofoldl(U_18696,U_18694,hAPP(c_COMBC(U_18694,U_18696,U_18696),U_18698),hAPP(U_18699,U_18701)),U_18695) = hAPP(U_18699,hAPP(c_List_Ofoldl(U_18697,U_18694,hAPP(c_COMBC(U_18694,U_18697,U_18697),U_18700),U_18701),U_18695)) ),
    inference(clausify,[status(thm)],[f_4574_3]) ).

cnf(f_4574_5,plain,
    ( hAPP(c_Fun_Ocomp(U_18696,U_18696,U_18697,hAPP(U_18698,sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694))),U_18699) != hAPP(c_Fun_Ocomp(U_18697,U_18696,U_18697,U_18699),hAPP(U_18700,sK462(U_18701,U_18700,U_18699,U_18698,U_18697,U_18696,U_18695,U_18694)))
    | hAPP(c_List_Ofoldl(U_18696,U_18694,hAPP(c_COMBC(U_18694,U_18696,U_18696),U_18698),hAPP(U_18699,U_18701)),U_18695) = hAPP(U_18699,hAPP(c_List_Ofoldl(U_18697,U_18694,hAPP(c_COMBC(U_18694,U_18697,U_18697),U_18700),U_18701),U_18695)) ),
    inference(clausify,[status(thm)],[f_4574_3]) ).

fof(f_4575_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_4575_2,plain,
    ! [U_18705,U_18704,U_18703,U_18702] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18703,U_18702)),U_18704),U_18705))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18703),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18703),c_fNot),hAPP(hAPP(c_COMBS(U_18703,U_18702,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18702,tc_fun(U_18702,tc_HOL_Obool),U_18703),c_fequal),U_18704)),U_18705))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18703,U_18702)),U_18704),U_18705)) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18703),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18703),c_fNot),hAPP(hAPP(c_COMBS(U_18703,U_18702,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18702,tc_fun(U_18702,tc_HOL_Obool),U_18703),c_fequal),U_18704)),U_18705))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18703,U_18702)),U_18704),U_18705)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18703,U_18702)),U_18704),U_18705)) ) )
      | ~ class_Enum_Oenum(U_18703)
      | ~ class_Orderings_Oorder(U_18702) ),
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

cnf(f_4575_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18703,U_18702)),U_18704),U_18705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18703,U_18702)),U_18704),U_18705))
    | ~ class_Enum_Oenum(U_18703)
    | ~ class_Orderings_Oorder(U_18702) ),
    inference(clausify,[status(thm)],[f_4575_2]) ).

cnf(f_4575_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18703),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18703),c_fNot),hAPP(hAPP(c_COMBS(U_18703,U_18702,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18702,tc_fun(U_18702,tc_HOL_Obool),U_18703),c_fequal),U_18704)),U_18705))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18703,U_18702)),U_18704),U_18705))
    | ~ class_Enum_Oenum(U_18703)
    | ~ class_Orderings_Oorder(U_18702) ),
    inference(clausify,[status(thm)],[f_4575_2]) ).

cnf(f_4575_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18703,U_18702)),U_18704),U_18705))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18703),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18703),c_fNot),hAPP(hAPP(c_COMBS(U_18703,U_18702,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18702,tc_fun(U_18702,tc_HOL_Obool),U_18703),c_fequal),U_18704)),U_18705))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18703,U_18702)),U_18704),U_18705))
    | ~ class_Enum_Oenum(U_18703)
    | ~ class_Orderings_Oorder(U_18702) ),
    inference(clausify,[status(thm)],[f_4575_2]) ).

fof(f_4576_1,plain,
    ! [V_Pa_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_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_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def]) ).

fof(f_4576_2,plain,
    ! [U_18708,U_18707,U_18706] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18707,U_18706)),U_18708))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18707),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_HOL_Obool),tc_HOL_Obool,U_18707),c_Enum_Oenum__class_Oenum__ex(U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_prod(U_18707,U_18706)),tc_fun(U_18706,tc_HOL_Obool),U_18707),hAPP(c_COMBB(tc_prod(U_18707,U_18706),tc_HOL_Obool,U_18706),U_18708)),c_Product__Type_OPair(U_18707,U_18706))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18707),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_HOL_Obool),tc_HOL_Obool,U_18707),c_Enum_Oenum__class_Oenum__ex(U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_prod(U_18707,U_18706)),tc_fun(U_18706,tc_HOL_Obool),U_18707),hAPP(c_COMBB(tc_prod(U_18707,U_18706),tc_HOL_Obool,U_18706),U_18708)),c_Product__Type_OPair(U_18707,U_18706)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18707,U_18706)),U_18708)) ) )
      | ~ class_Enum_Oenum(U_18707)
      | ~ class_Enum_Oenum(U_18706) ),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

cnf(f_4576_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18707),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_HOL_Obool),tc_HOL_Obool,U_18707),c_Enum_Oenum__class_Oenum__ex(U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_prod(U_18707,U_18706)),tc_fun(U_18706,tc_HOL_Obool),U_18707),hAPP(c_COMBB(tc_prod(U_18707,U_18706),tc_HOL_Obool,U_18706),U_18708)),c_Product__Type_OPair(U_18707,U_18706)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18707,U_18706)),U_18708))
    | ~ class_Enum_Oenum(U_18707)
    | ~ class_Enum_Oenum(U_18706) ),
    inference(clausify,[status(thm)],[f_4576_2]) ).

cnf(f_4576_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18707,U_18706)),U_18708))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18707),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_HOL_Obool),tc_HOL_Obool,U_18707),c_Enum_Oenum__class_Oenum__ex(U_18706)),hAPP(hAPP(c_COMBB(tc_fun(U_18706,tc_prod(U_18707,U_18706)),tc_fun(U_18706,tc_HOL_Obool),U_18707),hAPP(c_COMBB(tc_prod(U_18707,U_18706),tc_HOL_Obool,U_18706),U_18708)),c_Product__Type_OPair(U_18707,U_18706)))))
    | ~ class_Enum_Oenum(U_18707)
    | ~ class_Enum_Oenum(U_18706) ),
    inference(clausify,[status(thm)],[f_4576_2]) ).

fof(f_4577_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) )
        & ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex]) ).

fof(f_4577_2,plain,
    ! [U_18712,U_18711] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712))
          | ! [U_18710] : ~ hBOOL(hAPP(U_18712,U_18710)) )
        & ( ? [U_18709] : hBOOL(hAPP(U_18712,U_18709))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712)) ) )
      | ~ class_Enum_Oenum(U_18711) ),
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ! [U_18712,U_18711] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712))
          | ! [U_18710] : ~ hBOOL(hAPP(U_18712,U_18710)) )
        & ( hBOOL(hAPP(U_18712,sK463(U_18712,U_18711)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712)) ) )
      | ~ class_Enum_Oenum(U_18711) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18709,sK463(U_18712,U_18711))],[f_4577_2]) ).

cnf(f_4577_4,plain,
    ( hBOOL(hAPP(U_18712,sK463(U_18712,U_18711)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712))
    | ~ class_Enum_Oenum(U_18711) ),
    inference(clausify,[status(thm)],[f_4577_3]) ).

cnf(f_4577_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18711),U_18712))
    | ~ hBOOL(hAPP(U_18712,U_18710))
    | ~ class_Enum_Oenum(U_18711) ),
    inference(clausify,[status(thm)],[f_4577_3]) ).

fof(f_4578_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_exists__code]) ).

fof(f_4578_2,plain,
    ! [U_18716,U_18715] :
      ( ( ( ? [U_18714] : hBOOL(hAPP(U_18716,U_18714))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716))
          | ! [U_18713] : ~ hBOOL(hAPP(U_18716,U_18713)) ) )
      | ~ class_Enum_Oenum(U_18715) ),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

fof(f_4578_3,plain,
    ! [U_18716,U_18715] :
      ( ( ( hBOOL(hAPP(U_18716,sK464(U_18716,U_18715)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716))
          | ! [U_18713] : ~ hBOOL(hAPP(U_18716,U_18713)) ) )
      | ~ class_Enum_Oenum(U_18715) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18714,sK464(U_18716,U_18715))],[f_4578_2]) ).

cnf(f_4578_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716))
    | ~ hBOOL(hAPP(U_18716,U_18713))
    | ~ class_Enum_Oenum(U_18715) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

cnf(f_4578_5,plain,
    ( hBOOL(hAPP(U_18716,sK464(U_18716,U_18715)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18715),U_18716))
    | ~ class_Enum_Oenum(U_18715) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

fof(f_4579_1,plain,
    ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))
      | ( ~ hBOOL(hAPP(V_Pa_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_4579_2,plain,
    ! [U_18721,U_18720,U_18719,U_18718,U_18717] :
      ( hBOOL(hAPP(U_18721,hAPP(hAPP(c_List_Ozip(U_18717,U_18719),U_18718),U_18720)))
      | ( ~ hBOOL(hAPP(U_18721,hAPP(hAPP(c_List_Ozip(U_18717,U_18719),hAPP(hAPP(c_List_Otake(U_18717),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18718)),hAPP(hAPP(c_List_Otake(U_18719),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18720))))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),hAPP(hAPP(c_List_Otake(U_18717),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18718)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),hAPP(hAPP(c_List_Otake(U_18719),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18720)) ) ),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

cnf(f_4579_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),hAPP(hAPP(c_List_Otake(U_18717),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18718)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),hAPP(hAPP(c_List_Otake(U_18719),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18720))
    | hBOOL(hAPP(U_18721,hAPP(hAPP(c_List_Ozip(U_18717,U_18719),U_18718),U_18720))) ),
    inference(clausify,[status(thm)],[f_4579_2]) ).

cnf(f_4579_4,plain,
    ( ~ hBOOL(hAPP(U_18721,hAPP(hAPP(c_List_Ozip(U_18717,U_18719),hAPP(hAPP(c_List_Otake(U_18717),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18718)),hAPP(hAPP(c_List_Otake(U_18719),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18718)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18719)),U_18720))),U_18720))))
    | hBOOL(hAPP(U_18721,hAPP(hAPP(c_List_Ozip(U_18717,U_18719),U_18718),U_18720))) ),
    inference(clausify,[status(thm)],[f_4579_2]) ).

fof(f_4580_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_4580_2,plain,
    ! [U_18725,U_18724,U_18723,U_18722] : c_New__Random__Sequence_Opos__not__random__dseq(U_18722,U_18723,U_18724,U_18725) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_18722,U_18723),U_18724),U_18725)),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

cnf(f_4580_3,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_18722,U_18723,U_18724,U_18725) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_18722,U_18723),U_18724),U_18725)),
    inference(clausify,[status(thm)],[f_4580_2]) ).

fof(f_4581_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Pa_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_4581_2,plain,
    ! [U_18730,U_18729,U_18728,U_18727] :
      ( c_List_OdropWhile(U_18727,U_18729,hAPP(hAPP(c_List_Oappend(U_18727),U_18728),U_18730)) = c_List_OdropWhile(U_18727,U_18729,U_18730)
      | ? [U_18726] :
          ( ~ hBOOL(hAPP(U_18729,U_18726))
          & hBOOL(hAPP(hAPP(c_member(U_18727),U_18726),hAPP(c_List_Oset(U_18727),U_18728))) ) ),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

fof(f_4581_3,plain,
    ! [U_18730,U_18729,U_18728,U_18727] :
      ( c_List_OdropWhile(U_18727,U_18729,hAPP(hAPP(c_List_Oappend(U_18727),U_18728),U_18730)) = c_List_OdropWhile(U_18727,U_18729,U_18730)
      | ( ~ hBOOL(hAPP(U_18729,sK465(U_18730,U_18729,U_18728,U_18727)))
        & hBOOL(hAPP(hAPP(c_member(U_18727),sK465(U_18730,U_18729,U_18728,U_18727)),hAPP(c_List_Oset(U_18727),U_18728))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18726,sK465(U_18730,U_18729,U_18728,U_18727))],[f_4581_2]) ).

cnf(f_4581_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18727),sK465(U_18730,U_18729,U_18728,U_18727)),hAPP(c_List_Oset(U_18727),U_18728)))
    | c_List_OdropWhile(U_18727,U_18729,hAPP(hAPP(c_List_Oappend(U_18727),U_18728),U_18730)) = c_List_OdropWhile(U_18727,U_18729,U_18730) ),
    inference(clausify,[status(thm)],[f_4581_3]) ).

cnf(f_4581_5,plain,
    ( ~ hBOOL(hAPP(U_18729,sK465(U_18730,U_18729,U_18728,U_18727)))
    | c_List_OdropWhile(U_18727,U_18729,hAPP(hAPP(c_List_Oappend(U_18727),U_18728),U_18730)) = c_List_OdropWhile(U_18727,U_18729,U_18730) ),
    inference(clausify,[status(thm)],[f_4581_3]) ).

fof(f_4582_1,plain,
    ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
      | ? [B_n] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_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_4582_2,plain,
    ! [U_18736,U_18735,U_18734,U_18733,U_18732] :
      ( c_List_Olist__all2(U_18732,U_18734,U_18736,U_18733,U_18735)
      | ? [U_18731] :
          ( ~ hBOOL(hAPP(hAPP(U_18736,hAPP(hAPP(c_List_Onth(U_18732),U_18733),U_18731)),hAPP(hAPP(c_List_Onth(U_18734),U_18735),U_18731)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18731),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18734)),U_18735) ),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

fof(f_4582_3,plain,
    ! [U_18736,U_18735,U_18734,U_18733,U_18732] :
      ( c_List_Olist__all2(U_18732,U_18734,U_18736,U_18733,U_18735)
      | ( ~ hBOOL(hAPP(hAPP(U_18736,hAPP(hAPP(c_List_Onth(U_18732),U_18733),sK466(U_18736,U_18735,U_18734,U_18733,U_18732))),hAPP(hAPP(c_List_Onth(U_18734),U_18735),sK466(U_18736,U_18735,U_18734,U_18733,U_18732))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK466(U_18736,U_18735,U_18734,U_18733,U_18732)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18734)),U_18735) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18731,sK466(U_18736,U_18735,U_18734,U_18733,U_18732))],[f_4582_2]) ).

cnf(f_4582_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK466(U_18736,U_18735,U_18734,U_18733,U_18732)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733)))
    | c_List_Olist__all2(U_18732,U_18734,U_18736,U_18733,U_18735)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18734)),U_18735) ),
    inference(clausify,[status(thm)],[f_4582_3]) ).

cnf(f_4582_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_18736,hAPP(hAPP(c_List_Onth(U_18732),U_18733),sK466(U_18736,U_18735,U_18734,U_18733,U_18732))),hAPP(hAPP(c_List_Onth(U_18734),U_18735),sK466(U_18736,U_18735,U_18734,U_18733,U_18732))))
    | c_List_Olist__all2(U_18732,U_18734,U_18736,U_18733,U_18735)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18732)),U_18733) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18734)),U_18735) ),
    inference(clausify,[status(thm)],[f_4582_3]) ).

fof(f_4583_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_4583_2,plain,
    ! [U_18740,U_18739] :
      ( ? [U_18738] :
          ( ! [U_18737] :
              ( U_18737 = U_18738
              | ~ hBOOL(hAPP(c_List_Odistinct(U_18739),U_18737))
              | ~ c_List_Olinorder__class_Osorted(U_18739,U_18737)
              | hAPP(c_List_Oset(U_18739),U_18737) != U_18740 )
          & hBOOL(hAPP(c_List_Odistinct(U_18739),U_18738))
          & c_List_Olinorder__class_Osorted(U_18739,U_18738)
          & hAPP(c_List_Oset(U_18739),U_18738) = U_18740 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
      | ~ class_Orderings_Olinorder(U_18739) ),
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

fof(f_4583_3,plain,
    ! [U_18740,U_18739] :
      ( ( ! [U_18737] :
            ( U_18737 = sK467(U_18740,U_18739)
            | ~ hBOOL(hAPP(c_List_Odistinct(U_18739),U_18737))
            | ~ c_List_Olinorder__class_Osorted(U_18739,U_18737)
            | hAPP(c_List_Oset(U_18739),U_18737) != U_18740 )
        & hBOOL(hAPP(c_List_Odistinct(U_18739),sK467(U_18740,U_18739)))
        & c_List_Olinorder__class_Osorted(U_18739,sK467(U_18740,U_18739))
        & hAPP(c_List_Oset(U_18739),sK467(U_18740,U_18739)) = U_18740 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
      | ~ class_Orderings_Olinorder(U_18739) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18738,sK467(U_18740,U_18739))],[f_4583_2]) ).

cnf(f_4583_4,plain,
    ( hAPP(c_List_Oset(U_18739),sK467(U_18740,U_18739)) = U_18740
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
    | ~ class_Orderings_Olinorder(U_18739) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18739,sK467(U_18740,U_18739))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
    | ~ class_Orderings_Olinorder(U_18739) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18739),sK467(U_18740,U_18739)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
    | ~ class_Orderings_Olinorder(U_18739) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_7,plain,
    ( U_18737 = sK467(U_18740,U_18739)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18739),U_18737))
    | ~ c_List_Olinorder__class_Osorted(U_18739,U_18737)
    | hAPP(c_List_Oset(U_18739),U_18737) != U_18740
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18739),U_18740))
    | ~ class_Orderings_Olinorder(U_18739) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

fof(f_4584_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,V_ys_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Pa_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_4584_2,plain,
    ! [U_18745,U_18744,U_18743,U_18742] :
      ( c_List_OtakeWhile(U_18742,U_18744,hAPP(hAPP(c_List_Oappend(U_18742),U_18743),U_18745)) = hAPP(hAPP(c_List_Oappend(U_18742),U_18743),c_List_OtakeWhile(U_18742,U_18744,U_18745))
      | ? [U_18741] :
          ( ~ hBOOL(hAPP(U_18744,U_18741))
          & hBOOL(hAPP(hAPP(c_member(U_18742),U_18741),hAPP(c_List_Oset(U_18742),U_18743))) ) ),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

fof(f_4584_3,plain,
    ! [U_18745,U_18744,U_18743,U_18742] :
      ( c_List_OtakeWhile(U_18742,U_18744,hAPP(hAPP(c_List_Oappend(U_18742),U_18743),U_18745)) = hAPP(hAPP(c_List_Oappend(U_18742),U_18743),c_List_OtakeWhile(U_18742,U_18744,U_18745))
      | ( ~ hBOOL(hAPP(U_18744,sK468(U_18745,U_18744,U_18743,U_18742)))
        & hBOOL(hAPP(hAPP(c_member(U_18742),sK468(U_18745,U_18744,U_18743,U_18742)),hAPP(c_List_Oset(U_18742),U_18743))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18741,sK468(U_18745,U_18744,U_18743,U_18742))],[f_4584_2]) ).

cnf(f_4584_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18742),sK468(U_18745,U_18744,U_18743,U_18742)),hAPP(c_List_Oset(U_18742),U_18743)))
    | c_List_OtakeWhile(U_18742,U_18744,hAPP(hAPP(c_List_Oappend(U_18742),U_18743),U_18745)) = hAPP(hAPP(c_List_Oappend(U_18742),U_18743),c_List_OtakeWhile(U_18742,U_18744,U_18745)) ),
    inference(clausify,[status(thm)],[f_4584_3]) ).

cnf(f_4584_5,plain,
    ( ~ hBOOL(hAPP(U_18744,sK468(U_18745,U_18744,U_18743,U_18742)))
    | c_List_OtakeWhile(U_18742,U_18744,hAPP(hAPP(c_List_Oappend(U_18742),U_18743),U_18745)) = hAPP(hAPP(c_List_Oappend(U_18742),U_18743),c_List_OtakeWhile(U_18742,U_18744,U_18745)) ),
    inference(clausify,[status(thm)],[f_4584_3]) ).

fof(f_4585_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_4585_2,plain,
    ! [U_18751,U_18750,U_18749,U_18748,U_18747] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18748,U_18747,U_18750),U_18751),U_18749) = hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18751),U_18749)
      | ? [U_18746] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18747),hAPP(U_18750,U_18751)),hAPP(U_18750,U_18746)))
          & hBOOL(hAPP(hAPP(c_member(U_18748),U_18746),hAPP(c_List_Oset(U_18748),U_18749))) )
      | ~ class_Orderings_Olinorder(U_18747) ),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

fof(f_4585_3,plain,
    ! [U_18751,U_18750,U_18749,U_18748,U_18747] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18748,U_18747,U_18750),U_18751),U_18749) = hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18751),U_18749)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18747),hAPP(U_18750,U_18751)),hAPP(U_18750,sK469(U_18751,U_18750,U_18749,U_18748,U_18747))))
        & hBOOL(hAPP(hAPP(c_member(U_18748),sK469(U_18751,U_18750,U_18749,U_18748,U_18747)),hAPP(c_List_Oset(U_18748),U_18749))) )
      | ~ class_Orderings_Olinorder(U_18747) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18746,sK469(U_18751,U_18750,U_18749,U_18748,U_18747))],[f_4585_2]) ).

cnf(f_4585_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18748),sK469(U_18751,U_18750,U_18749,U_18748,U_18747)),hAPP(c_List_Oset(U_18748),U_18749)))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18748,U_18747,U_18750),U_18751),U_18749) = hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18751),U_18749)
    | ~ class_Orderings_Olinorder(U_18747) ),
    inference(clausify,[status(thm)],[f_4585_3]) ).

cnf(f_4585_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18747),hAPP(U_18750,U_18751)),hAPP(U_18750,sK469(U_18751,U_18750,U_18749,U_18748,U_18747))))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18748,U_18747,U_18750),U_18751),U_18749) = hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18751),U_18749)
    | ~ class_Orderings_Olinorder(U_18747) ),
    inference(clausify,[status(thm)],[f_4585_3]) ).

fof(f_4586_1,plain,
    ! [V_ys_2,V_Pa_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_Pa_2),V_ys_2)
        | ! [B_us,B_vs] :
            ( V_xs_2 != hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs)
            | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_Pa_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_Pa_2),B_vs)
            & hBOOL(hAPP(V_Pa_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_Pa_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_Pa_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(f_4586_2,plain,
    ! [U_18762,U_18761,U_18760,U_18759,U_18758] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18758),U_18759),U_18760) = hAPP(c_List_Ofilter(U_18758,U_18761),U_18762)
        | ! [U_18757,U_18756] :
            ( U_18760 != hAPP(c_List_Ofilter(U_18758,U_18761),U_18756)
            | ~ hBOOL(hAPP(U_18761,U_18759))
            | ? [U_18755] :
                ( hBOOL(hAPP(U_18761,U_18755))
                & hBOOL(hAPP(hAPP(c_member(U_18758),U_18755),hAPP(c_List_Oset(U_18758),U_18757))) )
            | U_18762 != hAPP(hAPP(c_List_Oappend(U_18758),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18758),U_18759),U_18756)) ) )
      & ( ? [U_18754,U_18753] :
            ( U_18760 = hAPP(c_List_Ofilter(U_18758,U_18761),U_18753)
            & hBOOL(hAPP(U_18761,U_18759))
            & ! [U_18752] :
                ( ~ hBOOL(hAPP(U_18761,U_18752))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18758),U_18752),hAPP(c_List_Oset(U_18758),U_18754))) )
            & U_18762 = hAPP(hAPP(c_List_Oappend(U_18758),U_18754),hAPP(hAPP(c_List_Olist_OCons(U_18758),U_18759),U_18753)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18758),U_18759),U_18760) != hAPP(c_List_Ofilter(U_18758,U_18761),U_18762) ) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

fof(f_4586_3,plain,
    ( ! [U_18772,U_18770,U_18768,U_18766,U_18764] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772)
        | ! [U_18757] :
            ( ! [U_18756] :
                ( U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
                | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756)) )
            | ? [U_18755] :
                ( hBOOL(hAPP(U_18770,U_18755))
                & hBOOL(hAPP(hAPP(c_member(U_18764),U_18755),hAPP(c_List_Oset(U_18764),U_18757))) ) )
        | ~ hBOOL(hAPP(U_18770,U_18766)) )
    & ! [U_18771,U_18769,U_18767,U_18765,U_18763] :
        ( ( ? [U_18754] :
              ( ? [U_18753] :
                  ( U_18767 = hAPP(c_List_Ofilter(U_18763,U_18769),U_18753)
                  & U_18771 = hAPP(hAPP(c_List_Oappend(U_18763),U_18754),hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18753)) )
              & ! [U_18752] :
                  ( ~ hBOOL(hAPP(U_18769,U_18752))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18763),U_18752),hAPP(c_List_Oset(U_18763),U_18754))) ) )
          & hBOOL(hAPP(U_18769,U_18765)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ) ),
    inference(miniscope,[status(thm)],[f_4586_2]) ).

fof(f_4586_4,plain,
    ( ! [U_18772,U_18770,U_18768,U_18766,U_18764] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772)
        | ! [U_18757] :
            ( ! [U_18756] :
                ( U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
                | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756)) )
            | ? [U_18755] :
                ( hBOOL(hAPP(U_18770,U_18755))
                & hBOOL(hAPP(hAPP(c_member(U_18764),U_18755),hAPP(c_List_Oset(U_18764),U_18757))) ) )
        | ~ hBOOL(hAPP(U_18770,U_18766)) )
    & ! [U_18771,U_18769,U_18767,U_18765,U_18763] :
        ( ( ? [U_18753] :
              ( U_18767 = hAPP(c_List_Ofilter(U_18763,U_18769),U_18753)
              & U_18771 = hAPP(hAPP(c_List_Oappend(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)),hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18753)) )
          & ! [U_18752] :
              ( ~ hBOOL(hAPP(U_18769,U_18752))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18763),U_18752),hAPP(c_List_Oset(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)))) )
          & hBOOL(hAPP(U_18769,U_18765)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_18754,sK470(U_18771,U_18769,U_18767,U_18765,U_18763))],[f_4586_3]) ).

fof(f_4586_5,plain,
    ( ! [U_18772,U_18770,U_18768,U_18766,U_18764] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772)
        | ! [U_18757] :
            ( ! [U_18756] :
                ( U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
                | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756)) )
            | ? [U_18755] :
                ( hBOOL(hAPP(U_18770,U_18755))
                & hBOOL(hAPP(hAPP(c_member(U_18764),U_18755),hAPP(c_List_Oset(U_18764),U_18757))) ) )
        | ~ hBOOL(hAPP(U_18770,U_18766)) )
    & ! [U_18771,U_18769,U_18767,U_18765,U_18763] :
        ( ( U_18767 = hAPP(c_List_Ofilter(U_18763,U_18769),sK471(U_18771,U_18769,U_18767,U_18765,U_18763))
          & U_18771 = hAPP(hAPP(c_List_Oappend(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)),hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),sK471(U_18771,U_18769,U_18767,U_18765,U_18763)))
          & ! [U_18752] :
              ( ~ hBOOL(hAPP(U_18769,U_18752))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18763),U_18752),hAPP(c_List_Oset(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)))) )
          & hBOOL(hAPP(U_18769,U_18765)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_18753,sK471(U_18771,U_18769,U_18767,U_18765,U_18763))],[f_4586_4]) ).

fof(f_4586_6,plain,
    ( ! [U_18772,U_18770,U_18768,U_18766,U_18764] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772)
        | ! [U_18757] :
            ( ! [U_18756] :
                ( U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
                | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756)) )
            | ( hBOOL(hAPP(U_18770,sK472(U_18772,U_18770,U_18768,U_18766,U_18764,U_18757)))
              & hBOOL(hAPP(hAPP(c_member(U_18764),sK472(U_18772,U_18770,U_18768,U_18766,U_18764,U_18757)),hAPP(c_List_Oset(U_18764),U_18757))) ) )
        | ~ hBOOL(hAPP(U_18770,U_18766)) )
    & ! [U_18771,U_18769,U_18767,U_18765,U_18763] :
        ( ( U_18767 = hAPP(c_List_Ofilter(U_18763,U_18769),sK471(U_18771,U_18769,U_18767,U_18765,U_18763))
          & U_18771 = hAPP(hAPP(c_List_Oappend(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)),hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),sK471(U_18771,U_18769,U_18767,U_18765,U_18763)))
          & ! [U_18752] :
              ( ~ hBOOL(hAPP(U_18769,U_18752))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18763),U_18752),hAPP(c_List_Oset(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)))) )
          & hBOOL(hAPP(U_18769,U_18765)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_18755,sK472(U_18772,U_18770,U_18768,U_18766,U_18764,U_18757))],[f_4586_5]) ).

cnf(f_4586_7,plain,
    ( hBOOL(hAPP(U_18769,U_18765))
    | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

cnf(f_4586_8,plain,
    ( ~ hBOOL(hAPP(U_18769,U_18752))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18763),U_18752),hAPP(c_List_Oset(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763))))
    | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

cnf(f_4586_9,plain,
    ( U_18771 = hAPP(hAPP(c_List_Oappend(U_18763),sK470(U_18771,U_18769,U_18767,U_18765,U_18763)),hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),sK471(U_18771,U_18769,U_18767,U_18765,U_18763)))
    | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

cnf(f_4586_10,plain,
    ( U_18767 = hAPP(c_List_Ofilter(U_18763,U_18769),sK471(U_18771,U_18769,U_18767,U_18765,U_18763))
    | hAPP(hAPP(c_List_Olist_OCons(U_18763),U_18765),U_18767) != hAPP(c_List_Ofilter(U_18763,U_18769),U_18771) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

cnf(f_4586_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18764),sK472(U_18772,U_18770,U_18768,U_18766,U_18764,U_18757)),hAPP(c_List_Oset(U_18764),U_18757)))
    | U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
    | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756))
    | ~ hBOOL(hAPP(U_18770,U_18766))
    | hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

cnf(f_4586_12,plain,
    ( hBOOL(hAPP(U_18770,sK472(U_18772,U_18770,U_18768,U_18766,U_18764,U_18757)))
    | U_18768 != hAPP(c_List_Ofilter(U_18764,U_18770),U_18756)
    | U_18772 != hAPP(hAPP(c_List_Oappend(U_18764),U_18757),hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18756))
    | ~ hBOOL(hAPP(U_18770,U_18766))
    | hAPP(hAPP(c_List_Olist_OCons(U_18764),U_18766),U_18768) = hAPP(c_List_Ofilter(U_18764,U_18770),U_18772) ),
    inference(clausify,[status(thm)],[f_4586_6]) ).

fof(f_4587_1,plain,
    ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),B_vs)
            | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_Pa_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_Pa_2),B_vs)
            & hBOOL(hAPP(V_Pa_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_4587_2,plain,
    ! [U_18783,U_18782,U_18781,U_18780,U_18779] :
      ( ( hAPP(c_List_Ofilter(U_18779,U_18780),U_18781) = hAPP(hAPP(c_List_Olist_OCons(U_18779),U_18782),U_18783)
        | ! [U_18778,U_18777] :
            ( U_18783 != hAPP(c_List_Ofilter(U_18779,U_18780),U_18777)
            | ~ hBOOL(hAPP(U_18780,U_18782))
            | ? [U_18776] :
                ( hBOOL(hAPP(U_18780,U_18776))
                & hBOOL(hAPP(hAPP(c_member(U_18779),U_18776),hAPP(c_List_Oset(U_18779),U_18778))) )
            | U_18781 != hAPP(hAPP(c_List_Oappend(U_18779),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18779),U_18782),U_18777)) ) )
      & ( ? [U_18775,U_18774] :
            ( U_18783 = hAPP(c_List_Ofilter(U_18779,U_18780),U_18774)
            & hBOOL(hAPP(U_18780,U_18782))
            & ! [U_18773] :
                ( ~ hBOOL(hAPP(U_18780,U_18773))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18779),U_18773),hAPP(c_List_Oset(U_18779),U_18775))) )
            & U_18781 = hAPP(hAPP(c_List_Oappend(U_18779),U_18775),hAPP(hAPP(c_List_Olist_OCons(U_18779),U_18782),U_18774)) )
        | hAPP(c_List_Ofilter(U_18779,U_18780),U_18781) != hAPP(hAPP(c_List_Olist_OCons(U_18779),U_18782),U_18783) ) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

fof(f_4587_3,plain,
    ( ! [U_18793,U_18791,U_18789,U_18787,U_18785] :
        ( hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793)
        | ! [U_18778] :
            ( ! [U_18777] :
                ( U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
                | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777)) )
            | ? [U_18776] :
                ( hBOOL(hAPP(U_18787,U_18776))
                & hBOOL(hAPP(hAPP(c_member(U_18785),U_18776),hAPP(c_List_Oset(U_18785),U_18778))) ) )
        | ~ hBOOL(hAPP(U_18787,U_18791)) )
    & ! [U_18792,U_18790,U_18788,U_18786,U_18784] :
        ( ( ? [U_18775] :
              ( ? [U_18774] :
                  ( U_18792 = hAPP(c_List_Ofilter(U_18784,U_18786),U_18774)
                  & U_18788 = hAPP(hAPP(c_List_Oappend(U_18784),U_18775),hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18774)) )
              & ! [U_18773] :
                  ( ~ hBOOL(hAPP(U_18786,U_18773))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18784),U_18773),hAPP(c_List_Oset(U_18784),U_18775))) ) )
          & hBOOL(hAPP(U_18786,U_18790)) )
        | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ) ),
    inference(miniscope,[status(thm)],[f_4587_2]) ).

fof(f_4587_4,plain,
    ( ! [U_18793,U_18791,U_18789,U_18787,U_18785] :
        ( hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793)
        | ! [U_18778] :
            ( ! [U_18777] :
                ( U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
                | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777)) )
            | ? [U_18776] :
                ( hBOOL(hAPP(U_18787,U_18776))
                & hBOOL(hAPP(hAPP(c_member(U_18785),U_18776),hAPP(c_List_Oset(U_18785),U_18778))) ) )
        | ~ hBOOL(hAPP(U_18787,U_18791)) )
    & ! [U_18792,U_18790,U_18788,U_18786,U_18784] :
        ( ( ? [U_18774] :
              ( U_18792 = hAPP(c_List_Ofilter(U_18784,U_18786),U_18774)
              & U_18788 = hAPP(hAPP(c_List_Oappend(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)),hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18774)) )
          & ! [U_18773] :
              ( ~ hBOOL(hAPP(U_18786,U_18773))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18784),U_18773),hAPP(c_List_Oset(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)))) )
          & hBOOL(hAPP(U_18786,U_18790)) )
        | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_18775,sK473(U_18792,U_18790,U_18788,U_18786,U_18784))],[f_4587_3]) ).

fof(f_4587_5,plain,
    ( ! [U_18793,U_18791,U_18789,U_18787,U_18785] :
        ( hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793)
        | ! [U_18778] :
            ( ! [U_18777] :
                ( U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
                | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777)) )
            | ? [U_18776] :
                ( hBOOL(hAPP(U_18787,U_18776))
                & hBOOL(hAPP(hAPP(c_member(U_18785),U_18776),hAPP(c_List_Oset(U_18785),U_18778))) ) )
        | ~ hBOOL(hAPP(U_18787,U_18791)) )
    & ! [U_18792,U_18790,U_18788,U_18786,U_18784] :
        ( ( U_18792 = hAPP(c_List_Ofilter(U_18784,U_18786),sK474(U_18792,U_18790,U_18788,U_18786,U_18784))
          & U_18788 = hAPP(hAPP(c_List_Oappend(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)),hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),sK474(U_18792,U_18790,U_18788,U_18786,U_18784)))
          & ! [U_18773] :
              ( ~ hBOOL(hAPP(U_18786,U_18773))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18784),U_18773),hAPP(c_List_Oset(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)))) )
          & hBOOL(hAPP(U_18786,U_18790)) )
        | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_18774,sK474(U_18792,U_18790,U_18788,U_18786,U_18784))],[f_4587_4]) ).

fof(f_4587_6,plain,
    ( ! [U_18793,U_18791,U_18789,U_18787,U_18785] :
        ( hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793)
        | ! [U_18778] :
            ( ! [U_18777] :
                ( U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
                | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777)) )
            | ( hBOOL(hAPP(U_18787,sK475(U_18793,U_18791,U_18789,U_18787,U_18785,U_18778)))
              & hBOOL(hAPP(hAPP(c_member(U_18785),sK475(U_18793,U_18791,U_18789,U_18787,U_18785,U_18778)),hAPP(c_List_Oset(U_18785),U_18778))) ) )
        | ~ hBOOL(hAPP(U_18787,U_18791)) )
    & ! [U_18792,U_18790,U_18788,U_18786,U_18784] :
        ( ( U_18792 = hAPP(c_List_Ofilter(U_18784,U_18786),sK474(U_18792,U_18790,U_18788,U_18786,U_18784))
          & U_18788 = hAPP(hAPP(c_List_Oappend(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)),hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),sK474(U_18792,U_18790,U_18788,U_18786,U_18784)))
          & ! [U_18773] :
              ( ~ hBOOL(hAPP(U_18786,U_18773))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18784),U_18773),hAPP(c_List_Oset(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)))) )
          & hBOOL(hAPP(U_18786,U_18790)) )
        | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_18776,sK475(U_18793,U_18791,U_18789,U_18787,U_18785,U_18778))],[f_4587_5]) ).

cnf(f_4587_7,plain,
    ( hBOOL(hAPP(U_18786,U_18790))
    | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

cnf(f_4587_8,plain,
    ( ~ hBOOL(hAPP(U_18786,U_18773))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18784),U_18773),hAPP(c_List_Oset(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784))))
    | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

cnf(f_4587_9,plain,
    ( U_18788 = hAPP(hAPP(c_List_Oappend(U_18784),sK473(U_18792,U_18790,U_18788,U_18786,U_18784)),hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),sK474(U_18792,U_18790,U_18788,U_18786,U_18784)))
    | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

cnf(f_4587_10,plain,
    ( U_18792 = hAPP(c_List_Ofilter(U_18784,U_18786),sK474(U_18792,U_18790,U_18788,U_18786,U_18784))
    | hAPP(c_List_Ofilter(U_18784,U_18786),U_18788) != hAPP(hAPP(c_List_Olist_OCons(U_18784),U_18790),U_18792) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

cnf(f_4587_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18785),sK475(U_18793,U_18791,U_18789,U_18787,U_18785,U_18778)),hAPP(c_List_Oset(U_18785),U_18778)))
    | U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
    | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777))
    | ~ hBOOL(hAPP(U_18787,U_18791))
    | hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

cnf(f_4587_12,plain,
    ( hBOOL(hAPP(U_18787,sK475(U_18793,U_18791,U_18789,U_18787,U_18785,U_18778)))
    | U_18793 != hAPP(c_List_Ofilter(U_18785,U_18787),U_18777)
    | U_18789 != hAPP(hAPP(c_List_Oappend(U_18785),U_18778),hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18777))
    | ~ hBOOL(hAPP(U_18787,U_18791))
    | hAPP(c_List_Ofilter(U_18785,U_18787),U_18789) = hAPP(hAPP(c_List_Olist_OCons(U_18785),U_18791),U_18793) ),
    inference(clausify,[status(thm)],[f_4587_6]) ).

fof(f_4588_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_4588_2,plain,
    ! [U_18797,U_18796,U_18795,U_18794] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18795,U_18794)),U_18796),U_18797))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18795),hAPP(hAPP(c_COMBS(U_18795,U_18794,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18794,tc_fun(U_18794,tc_HOL_Obool),U_18795),c_Orderings_Oord__class_Oless__eq(U_18794)),U_18796)),U_18797))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18795),hAPP(hAPP(c_COMBS(U_18795,U_18794,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18794,tc_fun(U_18794,tc_HOL_Obool),U_18795),c_Orderings_Oord__class_Oless__eq(U_18794)),U_18796)),U_18797)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18795,U_18794)),U_18796),U_18797)) ) )
      | ~ class_Enum_Oenum(U_18795)
      | ~ class_Orderings_Oorder(U_18794) ),
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

cnf(f_4588_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18795),hAPP(hAPP(c_COMBS(U_18795,U_18794,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18794,tc_fun(U_18794,tc_HOL_Obool),U_18795),c_Orderings_Oord__class_Oless__eq(U_18794)),U_18796)),U_18797)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18795,U_18794)),U_18796),U_18797))
    | ~ class_Enum_Oenum(U_18795)
    | ~ class_Orderings_Oorder(U_18794) ),
    inference(clausify,[status(thm)],[f_4588_2]) ).

cnf(f_4588_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18795,U_18794)),U_18796),U_18797))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18795),hAPP(hAPP(c_COMBS(U_18795,U_18794,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18794,tc_fun(U_18794,tc_HOL_Obool),U_18795),c_Orderings_Oord__class_Oless__eq(U_18794)),U_18796)),U_18797)))
    | ~ class_Enum_Oenum(U_18795)
    | ~ class_Orderings_Oorder(U_18794) ),
    inference(clausify,[status(thm)],[f_4588_2]) ).

fof(f_4589_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_all__code]) ).

fof(f_4589_2,plain,
    ! [U_18801,U_18800] :
      ( ( ( ! [U_18799] : hBOOL(hAPP(U_18801,U_18799))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801))
          | ? [U_18798] : ~ hBOOL(hAPP(U_18801,U_18798)) ) )
      | ~ class_Enum_Oenum(U_18800) ),
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

fof(f_4589_3,plain,
    ! [U_18801,U_18800] :
      ( ( ( ! [U_18799] : hBOOL(hAPP(U_18801,U_18799))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801))
          | ~ hBOOL(hAPP(U_18801,sK476(U_18801,U_18800))) ) )
      | ~ class_Enum_Oenum(U_18800) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_18798,sK476(U_18801,U_18800))],[f_4589_2]) ).

cnf(f_4589_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801))
    | ~ hBOOL(hAPP(U_18801,sK476(U_18801,U_18800)))
    | ~ class_Enum_Oenum(U_18800) ),
    inference(clausify,[status(thm)],[f_4589_3]) ).

cnf(f_4589_5,plain,
    ( hBOOL(hAPP(U_18801,U_18799))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18800),U_18801))
    | ~ class_Enum_Oenum(U_18800) ),
    inference(clausify,[status(thm)],[f_4589_3]) ).

fof(f_4590_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) )
        & ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all]) ).

fof(f_4590_2,plain,
    ! [U_18805,U_18804] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805))
          | ? [U_18803] : ~ hBOOL(hAPP(U_18805,U_18803)) )
        & ( ! [U_18802] : hBOOL(hAPP(U_18805,U_18802))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805)) ) )
      | ~ class_Enum_Oenum(U_18804) ),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

fof(f_4590_3,plain,
    ! [U_18805,U_18804] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805))
          | ~ hBOOL(hAPP(U_18805,sK477(U_18805,U_18804))) )
        & ( ! [U_18802] : hBOOL(hAPP(U_18805,U_18802))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805)) ) )
      | ~ class_Enum_Oenum(U_18804) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_18803,sK477(U_18805,U_18804))],[f_4590_2]) ).

cnf(f_4590_4,plain,
    ( hBOOL(hAPP(U_18805,U_18802))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805))
    | ~ class_Enum_Oenum(U_18804) ),
    inference(clausify,[status(thm)],[f_4590_3]) ).

cnf(f_4590_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18804),U_18805))
    | ~ hBOOL(hAPP(U_18805,sK477(U_18805,U_18804)))
    | ~ class_Enum_Oenum(U_18804) ),
    inference(clausify,[status(thm)],[f_4590_3]) ).

fof(f_4591_1,plain,
    ! [V_Pa_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_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_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def]) ).

fof(f_4591_2,plain,
    ! [U_18808,U_18807,U_18806] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18807,U_18806)),U_18808))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18807),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_HOL_Obool),tc_HOL_Obool,U_18807),c_Enum_Oenum__class_Oenum__all(U_18806)),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_prod(U_18807,U_18806)),tc_fun(U_18806,tc_HOL_Obool),U_18807),hAPP(c_COMBB(tc_prod(U_18807,U_18806),tc_HOL_Obool,U_18806),U_18808)),c_Product__Type_OPair(U_18807,U_18806))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18807),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_HOL_Obool),tc_HOL_Obool,U_18807),c_Enum_Oenum__class_Oenum__all(U_18806)),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_prod(U_18807,U_18806)),tc_fun(U_18806,tc_HOL_Obool),U_18807),hAPP(c_COMBB(tc_prod(U_18807,U_18806),tc_HOL_Obool,U_18806),U_18808)),c_Product__Type_OPair(U_18807,U_18806)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18807,U_18806)),U_18808)) ) )
      | ~ class_Enum_Oenum(U_18807)
      | ~ class_Enum_Oenum(U_18806) ),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

cnf(f_4591_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18807),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_HOL_Obool),tc_HOL_Obool,U_18807),c_Enum_Oenum__class_Oenum__all(U_18806)),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_prod(U_18807,U_18806)),tc_fun(U_18806,tc_HOL_Obool),U_18807),hAPP(c_COMBB(tc_prod(U_18807,U_18806),tc_HOL_Obool,U_18806),U_18808)),c_Product__Type_OPair(U_18807,U_18806)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18807,U_18806)),U_18808))
    | ~ class_Enum_Oenum(U_18807)
    | ~ class_Enum_Oenum(U_18806) ),
    inference(clausify,[status(thm)],[f_4591_2]) ).

cnf(f_4591_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18807,U_18806)),U_18808))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18807),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_HOL_Obool),tc_HOL_Obool,U_18807),c_Enum_Oenum__class_Oenum__all(U_18806)),hAPP(hAPP(c_COMBB(tc_fun(U_18806,tc_prod(U_18807,U_18806)),tc_fun(U_18806,tc_HOL_Obool),U_18807),hAPP(c_COMBB(tc_prod(U_18807,U_18806),tc_HOL_Obool,U_18806),U_18808)),c_Product__Type_OPair(U_18807,U_18806)))))
    | ~ class_Enum_Oenum(U_18807)
    | ~ class_Enum_Oenum(U_18806) ),
    inference(clausify,[status(thm)],[f_4591_2]) ).

fof(f_4592_1,plain,
    ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Pa_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_4592_2,plain,
    ! [U_18813,U_18812,U_18811,U_18810] :
      ( hBOOL(hAPP(U_18813,hAPP(hAPP(c_List_Onth(U_18811),U_18812),U_18810)))
      | ? [U_18809] :
          ( ~ hBOOL(hAPP(U_18813,U_18809))
          & hBOOL(hAPP(hAPP(c_member(U_18811),U_18809),hAPP(c_List_Oset(U_18811),U_18812))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18812))) ),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

fof(f_4592_3,plain,
    ! [U_18813,U_18812,U_18811,U_18810] :
      ( hBOOL(hAPP(U_18813,hAPP(hAPP(c_List_Onth(U_18811),U_18812),U_18810)))
      | ( ~ hBOOL(hAPP(U_18813,sK478(U_18813,U_18812,U_18811,U_18810)))
        & hBOOL(hAPP(hAPP(c_member(U_18811),sK478(U_18813,U_18812,U_18811,U_18810)),hAPP(c_List_Oset(U_18811),U_18812))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18812))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_18809,sK478(U_18813,U_18812,U_18811,U_18810))],[f_4592_2]) ).

cnf(f_4592_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18811),sK478(U_18813,U_18812,U_18811,U_18810)),hAPP(c_List_Oset(U_18811),U_18812)))
    | hBOOL(hAPP(U_18813,hAPP(hAPP(c_List_Onth(U_18811),U_18812),U_18810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18812))) ),
    inference(clausify,[status(thm)],[f_4592_3]) ).

cnf(f_4592_5,plain,
    ( ~ hBOOL(hAPP(U_18813,sK478(U_18813,U_18812,U_18811,U_18810)))
    | hBOOL(hAPP(U_18813,hAPP(hAPP(c_List_Onth(U_18811),U_18812),U_18810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18812))) ),
    inference(clausify,[status(thm)],[f_4592_3]) ).

fof(f_4593_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_4593_2,plain,
    ! [U_18817,U_18816,U_18815] :
      ( c_List_Olinorder__class_Osorted(U_18815,hAPP(hAPP(c_List_Olist_OCons(U_18815),U_18817),U_18816))
      | ~ c_List_Olinorder__class_Osorted(U_18815,U_18816)
      | ? [U_18814] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18815),U_18817),U_18814))
          & hBOOL(hAPP(hAPP(c_member(U_18815),U_18814),hAPP(c_List_Oset(U_18815),U_18816))) )
      | ~ class_Orderings_Olinorder(U_18815) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

fof(f_4593_3,plain,
    ! [U_18817,U_18816,U_18815] :
      ( c_List_Olinorder__class_Osorted(U_18815,hAPP(hAPP(c_List_Olist_OCons(U_18815),U_18817),U_18816))
      | ~ c_List_Olinorder__class_Osorted(U_18815,U_18816)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18815),U_18817),sK479(U_18817,U_18816,U_18815)))
        & hBOOL(hAPP(hAPP(c_member(U_18815),sK479(U_18817,U_18816,U_18815)),hAPP(c_List_Oset(U_18815),U_18816))) )
      | ~ class_Orderings_Olinorder(U_18815) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_18814,sK479(U_18817,U_18816,U_18815))],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18815),sK479(U_18817,U_18816,U_18815)),hAPP(c_List_Oset(U_18815),U_18816)))
    | c_List_Olinorder__class_Osorted(U_18815,hAPP(hAPP(c_List_Olist_OCons(U_18815),U_18817),U_18816))
    | ~ c_List_Olinorder__class_Osorted(U_18815,U_18816)
    | ~ class_Orderings_Olinorder(U_18815) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

cnf(f_4593_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18815),U_18817),sK479(U_18817,U_18816,U_18815)))
    | c_List_Olinorder__class_Osorted(U_18815,hAPP(hAPP(c_List_Olist_OCons(U_18815),U_18817),U_18816))
    | ~ c_List_Olinorder__class_Osorted(U_18815,U_18816)
    | ~ class_Orderings_Olinorder(U_18815) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

fof(f_4594_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ! [B_n] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__length]) ).

fof(f_4594_2,plain,
    ! [U_18822,U_18821,U_18820] :
      ( ( c_List_Olist__ex(U_18820,U_18821,U_18822)
        | ! [U_18819] :
            ( ~ hBOOL(hAPP(U_18821,hAPP(hAPP(c_List_Onth(U_18820),U_18822),U_18819)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18819),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18820)),U_18822))) ) )
      & ( ? [U_18818] :
            ( hBOOL(hAPP(U_18821,hAPP(hAPP(c_List_Onth(U_18820),U_18822),U_18818)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18818),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18820)),U_18822))) )
        | ~ c_List_Olist__ex(U_18820,U_18821,U_18822) ) ),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

fof(f_4594_3,plain,
    ( ! [U_18828,U_18826,U_18824] :
        ( c_List_Olist__ex(U_18824,U_18826,U_18828)
        | ! [U_18819] :
            ( ~ hBOOL(hAPP(U_18826,hAPP(hAPP(c_List_Onth(U_18824),U_18828),U_18819)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18819),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18824)),U_18828))) ) )
    & ! [U_18827,U_18825,U_18823] :
        ( ? [U_18818] :
            ( hBOOL(hAPP(U_18825,hAPP(hAPP(c_List_Onth(U_18823),U_18827),U_18818)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18818),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18823)),U_18827))) )
        | ~ c_List_Olist__ex(U_18823,U_18825,U_18827) ) ),
    inference(miniscope,[status(thm)],[f_4594_2]) ).

fof(f_4594_4,plain,
    ( ! [U_18828,U_18826,U_18824] :
        ( c_List_Olist__ex(U_18824,U_18826,U_18828)
        | ! [U_18819] :
            ( ~ hBOOL(hAPP(U_18826,hAPP(hAPP(c_List_Onth(U_18824),U_18828),U_18819)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18819),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18824)),U_18828))) ) )
    & ! [U_18827,U_18825,U_18823] :
        ( ( hBOOL(hAPP(U_18825,hAPP(hAPP(c_List_Onth(U_18823),U_18827),sK480(U_18827,U_18825,U_18823))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK480(U_18827,U_18825,U_18823)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18823)),U_18827))) )
        | ~ c_List_Olist__ex(U_18823,U_18825,U_18827) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_18818,sK480(U_18827,U_18825,U_18823))],[f_4594_3]) ).

cnf(f_4594_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK480(U_18827,U_18825,U_18823)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18823)),U_18827)))
    | ~ c_List_Olist__ex(U_18823,U_18825,U_18827) ),
    inference(clausify,[status(thm)],[f_4594_4]) ).

cnf(f_4594_6,plain,
    ( hBOOL(hAPP(U_18825,hAPP(hAPP(c_List_Onth(U_18823),U_18827),sK480(U_18827,U_18825,U_18823))))
    | ~ c_List_Olist__ex(U_18823,U_18825,U_18827) ),
    inference(clausify,[status(thm)],[f_4594_4]) ).

cnf(f_4594_7,plain,
    ( c_List_Olist__ex(U_18824,U_18826,U_18828)
    | ~ hBOOL(hAPP(U_18826,hAPP(hAPP(c_List_Onth(U_18824),U_18828),U_18819)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18819),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18824)),U_18828))) ),
    inference(clausify,[status(thm)],[f_4594_4]) ).

fof(f_4595_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_4595_2,plain,
    ! [U_18835,U_18834,U_18833] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18833),U_18834),hAPP(c_List_Oset(U_18833),U_18835)))
        | ! [U_18832,U_18831] : U_18835 != hAPP(hAPP(c_List_Oappend(U_18833),U_18832),hAPP(hAPP(c_List_Olist_OCons(U_18833),U_18834),U_18831)) )
      & ( ? [U_18830,U_18829] : U_18835 = hAPP(hAPP(c_List_Oappend(U_18833),U_18830),hAPP(hAPP(c_List_Olist_OCons(U_18833),U_18834),U_18829))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18833),U_18834),hAPP(c_List_Oset(U_18833),U_18835))) ) ),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

fof(f_4595_3,plain,
    ( ! [U_18841,U_18839,U_18837] :
        ( hBOOL(hAPP(hAPP(c_member(U_18837),U_18839),hAPP(c_List_Oset(U_18837),U_18841)))
        | ! [U_18832,U_18831] : U_18841 != hAPP(hAPP(c_List_Oappend(U_18837),U_18832),hAPP(hAPP(c_List_Olist_OCons(U_18837),U_18839),U_18831)) )
    & ! [U_18840,U_18838,U_18836] :
        ( ? [U_18830,U_18829] : U_18840 = hAPP(hAPP(c_List_Oappend(U_18836),U_18830),hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18836),U_18838),hAPP(c_List_Oset(U_18836),U_18840))) ) ),
    inference(miniscope,[status(thm)],[f_4595_2]) ).

fof(f_4595_4,plain,
    ( ! [U_18841,U_18839,U_18837] :
        ( hBOOL(hAPP(hAPP(c_member(U_18837),U_18839),hAPP(c_List_Oset(U_18837),U_18841)))
        | ! [U_18832,U_18831] : U_18841 != hAPP(hAPP(c_List_Oappend(U_18837),U_18832),hAPP(hAPP(c_List_Olist_OCons(U_18837),U_18839),U_18831)) )
    & ! [U_18840,U_18838,U_18836] :
        ( ? [U_18829] : U_18840 = hAPP(hAPP(c_List_Oappend(U_18836),sK481(U_18840,U_18838,U_18836)),hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),U_18829))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18836),U_18838),hAPP(c_List_Oset(U_18836),U_18840))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_18830,sK481(U_18840,U_18838,U_18836))],[f_4595_3]) ).

fof(f_4595_5,plain,
    ( ! [U_18841,U_18839,U_18837] :
        ( hBOOL(hAPP(hAPP(c_member(U_18837),U_18839),hAPP(c_List_Oset(U_18837),U_18841)))
        | ! [U_18832,U_18831] : U_18841 != hAPP(hAPP(c_List_Oappend(U_18837),U_18832),hAPP(hAPP(c_List_Olist_OCons(U_18837),U_18839),U_18831)) )
    & ! [U_18840,U_18838,U_18836] :
        ( U_18840 = hAPP(hAPP(c_List_Oappend(U_18836),sK481(U_18840,U_18838,U_18836)),hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),sK482(U_18840,U_18838,U_18836)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18836),U_18838),hAPP(c_List_Oset(U_18836),U_18840))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_18829,sK482(U_18840,U_18838,U_18836))],[f_4595_4]) ).

cnf(f_4595_6,plain,
    ( U_18840 = hAPP(hAPP(c_List_Oappend(U_18836),sK481(U_18840,U_18838,U_18836)),hAPP(hAPP(c_List_Olist_OCons(U_18836),U_18838),sK482(U_18840,U_18838,U_18836)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18836),U_18838),hAPP(c_List_Oset(U_18836),U_18840))) ),
    inference(clausify,[status(thm)],[f_4595_5]) ).

cnf(f_4595_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18837),U_18839),hAPP(c_List_Oset(U_18837),U_18841)))
    | U_18841 != hAPP(hAPP(c_List_Oappend(U_18837),U_18832),hAPP(hAPP(c_List_Olist_OCons(U_18837),U_18839),U_18831)) ),
    inference(clausify,[status(thm)],[f_4595_5]) ).

fof(f_4596_1,plain,
    ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(f_4596_2,plain,
    ! [U_18843,U_18842] : ~ c_List_Olist__ex(U_18842,U_18843,c_List_Olist_ONil(U_18842)),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

cnf(f_4596_3,plain,
    ~ c_List_Olist__ex(U_18842,U_18843,c_List_Olist_ONil(U_18842)),
    inference(clausify,[status(thm)],[f_4596_2]) ).

fof(f_4597_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
        | ( ~ c_List_Olist__ex(T_b,V_Pa_2,V_ys_2)
          & ~ c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) )
      & ( c_List_Olist__ex(T_b,V_Pa_2,V_ys_2)
        | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ~ c_List_Olist__ex(T_b,V_Pa_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_4597_2,plain,
    ! [U_18847,U_18846,U_18845,U_18844] :
      ( ( c_List_Olist__ex(U_18844,U_18845,hAPP(hAPP(c_List_Oappend(U_18844),U_18846),U_18847))
        | ( ~ c_List_Olist__ex(U_18844,U_18845,U_18847)
          & ~ c_List_Olist__ex(U_18844,U_18845,U_18846) ) )
      & ( c_List_Olist__ex(U_18844,U_18845,U_18847)
        | c_List_Olist__ex(U_18844,U_18845,U_18846)
        | ~ c_List_Olist__ex(U_18844,U_18845,hAPP(hAPP(c_List_Oappend(U_18844),U_18846),U_18847)) ) ),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

fof(f_4597_3,plain,
    ( ! [U_18855,U_18853,U_18851,U_18849] :
        ( c_List_Olist__ex(U_18849,U_18851,hAPP(hAPP(c_List_Oappend(U_18849),U_18853),U_18855))
        | ( ~ c_List_Olist__ex(U_18849,U_18851,U_18855)
          & ~ c_List_Olist__ex(U_18849,U_18851,U_18853) ) )
    & ! [U_18854,U_18852,U_18850,U_18848] :
        ( c_List_Olist__ex(U_18848,U_18850,U_18854)
        | c_List_Olist__ex(U_18848,U_18850,U_18852)
        | ~ c_List_Olist__ex(U_18848,U_18850,hAPP(hAPP(c_List_Oappend(U_18848),U_18852),U_18854)) ) ),
    inference(miniscope,[status(thm)],[f_4597_2]) ).

cnf(f_4597_4,plain,
    ( c_List_Olist__ex(U_18848,U_18850,U_18854)
    | c_List_Olist__ex(U_18848,U_18850,U_18852)
    | ~ c_List_Olist__ex(U_18848,U_18850,hAPP(hAPP(c_List_Oappend(U_18848),U_18852),U_18854)) ),
    inference(clausify,[status(thm)],[f_4597_3]) ).

cnf(f_4597_5,plain,
    ( ~ c_List_Olist__ex(U_18849,U_18851,U_18853)
    | c_List_Olist__ex(U_18849,U_18851,hAPP(hAPP(c_List_Oappend(U_18849),U_18853),U_18855)) ),
    inference(clausify,[status(thm)],[f_4597_3]) ).

cnf(f_4597_6,plain,
    ( ~ c_List_Olist__ex(U_18849,U_18851,U_18855)
    | c_List_Olist__ex(U_18849,U_18851,hAPP(hAPP(c_List_Oappend(U_18849),U_18853),U_18855)) ),
    inference(clausify,[status(thm)],[f_4597_3]) ).

fof(f_4598_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff]) ).

fof(f_4598_2,plain,
    ! [U_18860,U_18859,U_18858] :
      ( ( c_List_Olist__ex(U_18858,U_18859,U_18860)
        | ! [U_18857] :
            ( ~ hBOOL(hAPP(U_18859,U_18857))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18858),U_18857),hAPP(c_List_Oset(U_18858),U_18860))) ) )
      & ( ? [U_18856] :
            ( hBOOL(hAPP(U_18859,U_18856))
            & hBOOL(hAPP(hAPP(c_member(U_18858),U_18856),hAPP(c_List_Oset(U_18858),U_18860))) )
        | ~ c_List_Olist__ex(U_18858,U_18859,U_18860) ) ),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

fof(f_4598_3,plain,
    ( ! [U_18866,U_18864,U_18862] :
        ( c_List_Olist__ex(U_18862,U_18864,U_18866)
        | ! [U_18857] :
            ( ~ hBOOL(hAPP(U_18864,U_18857))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18862),U_18857),hAPP(c_List_Oset(U_18862),U_18866))) ) )
    & ! [U_18865,U_18863,U_18861] :
        ( ? [U_18856] :
            ( hBOOL(hAPP(U_18863,U_18856))
            & hBOOL(hAPP(hAPP(c_member(U_18861),U_18856),hAPP(c_List_Oset(U_18861),U_18865))) )
        | ~ c_List_Olist__ex(U_18861,U_18863,U_18865) ) ),
    inference(miniscope,[status(thm)],[f_4598_2]) ).

fof(f_4598_4,plain,
    ( ! [U_18866,U_18864,U_18862] :
        ( c_List_Olist__ex(U_18862,U_18864,U_18866)
        | ! [U_18857] :
            ( ~ hBOOL(hAPP(U_18864,U_18857))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18862),U_18857),hAPP(c_List_Oset(U_18862),U_18866))) ) )
    & ! [U_18865,U_18863,U_18861] :
        ( ( hBOOL(hAPP(U_18863,sK483(U_18865,U_18863,U_18861)))
          & hBOOL(hAPP(hAPP(c_member(U_18861),sK483(U_18865,U_18863,U_18861)),hAPP(c_List_Oset(U_18861),U_18865))) )
        | ~ c_List_Olist__ex(U_18861,U_18863,U_18865) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_18856,sK483(U_18865,U_18863,U_18861))],[f_4598_3]) ).

cnf(f_4598_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18861),sK483(U_18865,U_18863,U_18861)),hAPP(c_List_Oset(U_18861),U_18865)))
    | ~ c_List_Olist__ex(U_18861,U_18863,U_18865) ),
    inference(clausify,[status(thm)],[f_4598_4]) ).

cnf(f_4598_6,plain,
    ( hBOOL(hAPP(U_18863,sK483(U_18865,U_18863,U_18861)))
    | ~ c_List_Olist__ex(U_18861,U_18863,U_18865) ),
    inference(clausify,[status(thm)],[f_4598_4]) ).

cnf(f_4598_7,plain,
    ( c_List_Olist__ex(U_18862,U_18864,U_18866)
    | ~ hBOOL(hAPP(U_18864,U_18857))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18862),U_18857),hAPP(c_List_Oset(U_18862),U_18866))) ),
    inference(clausify,[status(thm)],[f_4598_4]) ).

fof(f_4599_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
        | ~ c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) )
      & ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ~ c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__rev]) ).

fof(f_4599_2,plain,
    ! [U_18869,U_18868,U_18867] :
      ( ( c_List_Olist__ex(U_18867,U_18868,hAPP(c_List_Orev(U_18867),U_18869))
        | ~ c_List_Olist__ex(U_18867,U_18868,U_18869) )
      & ( c_List_Olist__ex(U_18867,U_18868,U_18869)
        | ~ c_List_Olist__ex(U_18867,U_18868,hAPP(c_List_Orev(U_18867),U_18869)) ) ),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ( ! [U_18875,U_18873,U_18871] :
        ( c_List_Olist__ex(U_18871,U_18873,hAPP(c_List_Orev(U_18871),U_18875))
        | ~ c_List_Olist__ex(U_18871,U_18873,U_18875) )
    & ! [U_18874,U_18872,U_18870] :
        ( c_List_Olist__ex(U_18870,U_18872,U_18874)
        | ~ c_List_Olist__ex(U_18870,U_18872,hAPP(c_List_Orev(U_18870),U_18874)) ) ),
    inference(miniscope,[status(thm)],[f_4599_2]) ).

cnf(f_4599_4,plain,
    ( c_List_Olist__ex(U_18870,U_18872,U_18874)
    | ~ c_List_Olist__ex(U_18870,U_18872,hAPP(c_List_Orev(U_18870),U_18874)) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_5,plain,
    ( c_List_Olist__ex(U_18871,U_18873,hAPP(c_List_Orev(U_18871),U_18875))
    | ~ c_List_Olist__ex(U_18871,U_18873,U_18875) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

fof(f_4600_1,plain,
    ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
          & ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) )
      & ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | hBOOL(hAPP(V_Pa_2,V_x_2))
        | ~ c_List_Olist__ex(T_b,V_Pa_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_4600_2,plain,
    ! [U_18879,U_18878,U_18877,U_18876] :
      ( ( c_List_Olist__ex(U_18876,U_18877,hAPP(hAPP(c_List_Olist_OCons(U_18876),U_18878),U_18879))
        | ( ~ c_List_Olist__ex(U_18876,U_18877,U_18879)
          & ~ hBOOL(hAPP(U_18877,U_18878)) ) )
      & ( c_List_Olist__ex(U_18876,U_18877,U_18879)
        | hBOOL(hAPP(U_18877,U_18878))
        | ~ c_List_Olist__ex(U_18876,U_18877,hAPP(hAPP(c_List_Olist_OCons(U_18876),U_18878),U_18879)) ) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ( ! [U_18887,U_18885,U_18883,U_18881] :
        ( c_List_Olist__ex(U_18881,U_18883,hAPP(hAPP(c_List_Olist_OCons(U_18881),U_18885),U_18887))
        | ( ~ c_List_Olist__ex(U_18881,U_18883,U_18887)
          & ~ hBOOL(hAPP(U_18883,U_18885)) ) )
    & ! [U_18886,U_18884,U_18882,U_18880] :
        ( c_List_Olist__ex(U_18880,U_18882,U_18886)
        | hBOOL(hAPP(U_18882,U_18884))
        | ~ c_List_Olist__ex(U_18880,U_18882,hAPP(hAPP(c_List_Olist_OCons(U_18880),U_18884),U_18886)) ) ),
    inference(miniscope,[status(thm)],[f_4600_2]) ).

cnf(f_4600_4,plain,
    ( c_List_Olist__ex(U_18880,U_18882,U_18886)
    | hBOOL(hAPP(U_18882,U_18884))
    | ~ c_List_Olist__ex(U_18880,U_18882,hAPP(hAPP(c_List_Olist_OCons(U_18880),U_18884),U_18886)) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

cnf(f_4600_5,plain,
    ( ~ hBOOL(hAPP(U_18883,U_18885))
    | c_List_Olist__ex(U_18881,U_18883,hAPP(hAPP(c_List_Olist_OCons(U_18881),U_18885),U_18887)) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

cnf(f_4600_6,plain,
    ( ~ c_List_Olist__ex(U_18881,U_18883,U_18887)
    | c_List_Olist__ex(U_18881,U_18883,hAPP(hAPP(c_List_Olist_OCons(U_18881),U_18885),U_18887)) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

fof(f_4601_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_4601_2,plain,
    ! [U_18894,U_18893,U_18892] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18892),U_18893),hAPP(c_List_Oset(U_18892),U_18894)))
        | ! [U_18891] :
            ( hBOOL(hAPP(hAPP(c_member(U_18892),U_18893),hAPP(c_List_Oset(U_18892),U_18891)))
            | ! [U_18890] : U_18894 != hAPP(hAPP(c_List_Oappend(U_18892),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18892),U_18893),U_18890)) ) )
      & ( ? [U_18889] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18892),U_18893),hAPP(c_List_Oset(U_18892),U_18889)))
            & ? [U_18888] : U_18894 = hAPP(hAPP(c_List_Oappend(U_18892),U_18889),hAPP(hAPP(c_List_Olist_OCons(U_18892),U_18893),U_18888)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18892),U_18893),hAPP(c_List_Oset(U_18892),U_18894))) ) ),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

fof(f_4601_3,plain,
    ( ! [U_18900,U_18898,U_18896] :
        ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18900)))
        | ! [U_18891] :
            ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18891)))
            | ! [U_18890] : U_18900 != hAPP(hAPP(c_List_Oappend(U_18896),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18896),U_18898),U_18890)) ) )
    & ! [U_18899,U_18897,U_18895] :
        ( ? [U_18889] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18889)))
            & ? [U_18888] : U_18899 = hAPP(hAPP(c_List_Oappend(U_18895),U_18889),hAPP(hAPP(c_List_Olist_OCons(U_18895),U_18897),U_18888)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18899))) ) ),
    inference(miniscope,[status(thm)],[f_4601_2]) ).

fof(f_4601_4,plain,
    ( ! [U_18900,U_18898,U_18896] :
        ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18900)))
        | ! [U_18891] :
            ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18891)))
            | ! [U_18890] : U_18900 != hAPP(hAPP(c_List_Oappend(U_18896),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18896),U_18898),U_18890)) ) )
    & ! [U_18899,U_18897,U_18895] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),sK484(U_18899,U_18897,U_18895))))
          & ? [U_18888] : U_18899 = hAPP(hAPP(c_List_Oappend(U_18895),sK484(U_18899,U_18897,U_18895)),hAPP(hAPP(c_List_Olist_OCons(U_18895),U_18897),U_18888)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18899))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_18889,sK484(U_18899,U_18897,U_18895))],[f_4601_3]) ).

fof(f_4601_5,plain,
    ( ! [U_18900,U_18898,U_18896] :
        ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18900)))
        | ! [U_18891] :
            ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18891)))
            | ! [U_18890] : U_18900 != hAPP(hAPP(c_List_Oappend(U_18896),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18896),U_18898),U_18890)) ) )
    & ! [U_18899,U_18897,U_18895] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),sK484(U_18899,U_18897,U_18895))))
          & U_18899 = hAPP(hAPP(c_List_Oappend(U_18895),sK484(U_18899,U_18897,U_18895)),hAPP(hAPP(c_List_Olist_OCons(U_18895),U_18897),sK485(U_18899,U_18897,U_18895))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18899))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_18888,sK485(U_18899,U_18897,U_18895))],[f_4601_4]) ).

cnf(f_4601_6,plain,
    ( U_18899 = hAPP(hAPP(c_List_Oappend(U_18895),sK484(U_18899,U_18897,U_18895)),hAPP(hAPP(c_List_Olist_OCons(U_18895),U_18897),sK485(U_18899,U_18897,U_18895)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18899))) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),sK484(U_18899,U_18897,U_18895))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18895),U_18897),hAPP(c_List_Oset(U_18895),U_18899))) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18900)))
    | hBOOL(hAPP(hAPP(c_member(U_18896),U_18898),hAPP(c_List_Oset(U_18896),U_18891)))
    | U_18900 != hAPP(hAPP(c_List_Oappend(U_18896),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18896),U_18898),U_18890)) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

fof(f_4602_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_4602_2,plain,
    ! [U_18907,U_18906,U_18905] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18905),U_18906),hAPP(c_List_Oset(U_18905),U_18907)))
        | ! [U_18904,U_18903] :
            ( hBOOL(hAPP(hAPP(c_member(U_18905),U_18906),hAPP(c_List_Oset(U_18905),U_18903)))
            | U_18907 != hAPP(hAPP(c_List_Oappend(U_18905),U_18904),hAPP(hAPP(c_List_Olist_OCons(U_18905),U_18906),U_18903)) ) )
      & ( ? [U_18902,U_18901] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18905),U_18906),hAPP(c_List_Oset(U_18905),U_18901)))
            & U_18907 = hAPP(hAPP(c_List_Oappend(U_18905),U_18902),hAPP(hAPP(c_List_Olist_OCons(U_18905),U_18906),U_18901)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18905),U_18906),hAPP(c_List_Oset(U_18905),U_18907))) ) ),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

fof(f_4602_3,plain,
    ( ! [U_18913,U_18911,U_18909] :
        ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18913)))
        | ! [U_18904,U_18903] :
            ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18903)))
            | U_18913 != hAPP(hAPP(c_List_Oappend(U_18909),U_18904),hAPP(hAPP(c_List_Olist_OCons(U_18909),U_18911),U_18903)) ) )
    & ! [U_18912,U_18910,U_18908] :
        ( ? [U_18902,U_18901] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18901)))
            & U_18912 = hAPP(hAPP(c_List_Oappend(U_18908),U_18902),hAPP(hAPP(c_List_Olist_OCons(U_18908),U_18910),U_18901)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18912))) ) ),
    inference(miniscope,[status(thm)],[f_4602_2]) ).

fof(f_4602_4,plain,
    ( ! [U_18913,U_18911,U_18909] :
        ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18913)))
        | ! [U_18904,U_18903] :
            ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18903)))
            | U_18913 != hAPP(hAPP(c_List_Oappend(U_18909),U_18904),hAPP(hAPP(c_List_Olist_OCons(U_18909),U_18911),U_18903)) ) )
    & ! [U_18912,U_18910,U_18908] :
        ( ? [U_18901] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18901)))
            & U_18912 = hAPP(hAPP(c_List_Oappend(U_18908),sK486(U_18912,U_18910,U_18908)),hAPP(hAPP(c_List_Olist_OCons(U_18908),U_18910),U_18901)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18912))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_18902,sK486(U_18912,U_18910,U_18908))],[f_4602_3]) ).

fof(f_4602_5,plain,
    ( ! [U_18913,U_18911,U_18909] :
        ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18913)))
        | ! [U_18904,U_18903] :
            ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18903)))
            | U_18913 != hAPP(hAPP(c_List_Oappend(U_18909),U_18904),hAPP(hAPP(c_List_Olist_OCons(U_18909),U_18911),U_18903)) ) )
    & ! [U_18912,U_18910,U_18908] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),sK487(U_18912,U_18910,U_18908))))
          & U_18912 = hAPP(hAPP(c_List_Oappend(U_18908),sK486(U_18912,U_18910,U_18908)),hAPP(hAPP(c_List_Olist_OCons(U_18908),U_18910),sK487(U_18912,U_18910,U_18908))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18912))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_18901,sK487(U_18912,U_18910,U_18908))],[f_4602_4]) ).

cnf(f_4602_6,plain,
    ( U_18912 = hAPP(hAPP(c_List_Oappend(U_18908),sK486(U_18912,U_18910,U_18908)),hAPP(hAPP(c_List_Olist_OCons(U_18908),U_18910),sK487(U_18912,U_18910,U_18908)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18912))) ),
    inference(clausify,[status(thm)],[f_4602_5]) ).

cnf(f_4602_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),sK487(U_18912,U_18910,U_18908))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18908),U_18910),hAPP(c_List_Oset(U_18908),U_18912))) ),
    inference(clausify,[status(thm)],[f_4602_5]) ).

cnf(f_4602_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18913)))
    | hBOOL(hAPP(hAPP(c_member(U_18909),U_18911),hAPP(c_List_Oset(U_18909),U_18903)))
    | U_18913 != hAPP(hAPP(c_List_Oappend(U_18909),U_18904),hAPP(hAPP(c_List_Olist_OCons(U_18909),U_18911),U_18903)) ),
    inference(clausify,[status(thm)],[f_4602_5]) ).

fof(f_4603_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__length]) ).

fof(f_4603_2,plain,
    ! [U_18918,U_18917,U_18916] :
      ( ( c_List_Olist__all(U_18916,U_18917,U_18918)
        | ? [U_18915] :
            ( ~ hBOOL(hAPP(U_18917,hAPP(hAPP(c_List_Onth(U_18916),U_18918),U_18915)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18915),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18916)),U_18918))) ) )
      & ( ! [U_18914] :
            ( hBOOL(hAPP(U_18917,hAPP(hAPP(c_List_Onth(U_18916),U_18918),U_18914)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18914),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18916)),U_18918))) )
        | ~ c_List_Olist__all(U_18916,U_18917,U_18918) ) ),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

fof(f_4603_3,plain,
    ( ! [U_18924,U_18922,U_18920] :
        ( c_List_Olist__all(U_18920,U_18922,U_18924)
        | ? [U_18915] :
            ( ~ hBOOL(hAPP(U_18922,hAPP(hAPP(c_List_Onth(U_18920),U_18924),U_18915)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18915),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18920)),U_18924))) ) )
    & ! [U_18923,U_18921,U_18919] :
        ( ! [U_18914] :
            ( hBOOL(hAPP(U_18921,hAPP(hAPP(c_List_Onth(U_18919),U_18923),U_18914)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18914),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18923))) )
        | ~ c_List_Olist__all(U_18919,U_18921,U_18923) ) ),
    inference(miniscope,[status(thm)],[f_4603_2]) ).

fof(f_4603_4,plain,
    ( ! [U_18924,U_18922,U_18920] :
        ( c_List_Olist__all(U_18920,U_18922,U_18924)
        | ( ~ hBOOL(hAPP(U_18922,hAPP(hAPP(c_List_Onth(U_18920),U_18924),sK488(U_18924,U_18922,U_18920))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_18924,U_18922,U_18920)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18920)),U_18924))) ) )
    & ! [U_18923,U_18921,U_18919] :
        ( ! [U_18914] :
            ( hBOOL(hAPP(U_18921,hAPP(hAPP(c_List_Onth(U_18919),U_18923),U_18914)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18914),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18923))) )
        | ~ c_List_Olist__all(U_18919,U_18921,U_18923) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_18915,sK488(U_18924,U_18922,U_18920))],[f_4603_3]) ).

cnf(f_4603_5,plain,
    ( hBOOL(hAPP(U_18921,hAPP(hAPP(c_List_Onth(U_18919),U_18923),U_18914)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18914),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18919)),U_18923)))
    | ~ c_List_Olist__all(U_18919,U_18921,U_18923) ),
    inference(clausify,[status(thm)],[f_4603_4]) ).

cnf(f_4603_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_18924,U_18922,U_18920)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18920)),U_18924)))
    | c_List_Olist__all(U_18920,U_18922,U_18924) ),
    inference(clausify,[status(thm)],[f_4603_4]) ).

cnf(f_4603_7,plain,
    ( ~ hBOOL(hAPP(U_18922,hAPP(hAPP(c_List_Onth(U_18920),U_18924),sK488(U_18924,U_18922,U_18920))))
    | c_List_Olist__all(U_18920,U_18922,U_18924) ),
    inference(clausify,[status(thm)],[f_4603_4]) ).

fof(f_4604_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_4604_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_4604_1]) ).

fof(f_4605_1,plain,
    ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(f_4605_2,plain,
    ! [U_18926,U_18925] : c_List_Olist__all(U_18925,U_18926,c_List_Olist_ONil(U_18925)),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

cnf(f_4605_3,plain,
    c_List_Olist__all(U_18925,U_18926,c_List_Olist_ONil(U_18925)),
    inference(clausify,[status(thm)],[f_4605_2]) ).

fof(f_4606_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
        | ~ c_List_Olist__all(T_b,V_Pa_2,V_ys_2)
        | ~ c_List_Olist__all(T_b,V_Pa_2,V_xs_2) )
      & ( ( c_List_Olist__all(T_b,V_Pa_2,V_ys_2)
          & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) )
        | ~ c_List_Olist__all(T_b,V_Pa_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_4606_2,plain,
    ! [U_18930,U_18929,U_18928,U_18927] :
      ( ( c_List_Olist__all(U_18927,U_18928,hAPP(hAPP(c_List_Oappend(U_18927),U_18929),U_18930))
        | ~ c_List_Olist__all(U_18927,U_18928,U_18930)
        | ~ c_List_Olist__all(U_18927,U_18928,U_18929) )
      & ( ( c_List_Olist__all(U_18927,U_18928,U_18930)
          & c_List_Olist__all(U_18927,U_18928,U_18929) )
        | ~ c_List_Olist__all(U_18927,U_18928,hAPP(hAPP(c_List_Oappend(U_18927),U_18929),U_18930)) ) ),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

fof(f_4606_3,plain,
    ( ! [U_18938,U_18936,U_18934,U_18932] :
        ( c_List_Olist__all(U_18932,U_18934,hAPP(hAPP(c_List_Oappend(U_18932),U_18936),U_18938))
        | ~ c_List_Olist__all(U_18932,U_18934,U_18938)
        | ~ c_List_Olist__all(U_18932,U_18934,U_18936) )
    & ! [U_18937,U_18935,U_18933,U_18931] :
        ( ( c_List_Olist__all(U_18931,U_18933,U_18937)
          & c_List_Olist__all(U_18931,U_18933,U_18935) )
        | ~ c_List_Olist__all(U_18931,U_18933,hAPP(hAPP(c_List_Oappend(U_18931),U_18935),U_18937)) ) ),
    inference(miniscope,[status(thm)],[f_4606_2]) ).

cnf(f_4606_4,plain,
    ( c_List_Olist__all(U_18931,U_18933,U_18935)
    | ~ c_List_Olist__all(U_18931,U_18933,hAPP(hAPP(c_List_Oappend(U_18931),U_18935),U_18937)) ),
    inference(clausify,[status(thm)],[f_4606_3]) ).

cnf(f_4606_5,plain,
    ( c_List_Olist__all(U_18931,U_18933,U_18937)
    | ~ c_List_Olist__all(U_18931,U_18933,hAPP(hAPP(c_List_Oappend(U_18931),U_18935),U_18937)) ),
    inference(clausify,[status(thm)],[f_4606_3]) ).

cnf(f_4606_6,plain,
    ( c_List_Olist__all(U_18932,U_18934,hAPP(hAPP(c_List_Oappend(U_18932),U_18936),U_18938))
    | ~ c_List_Olist__all(U_18932,U_18934,U_18938)
    | ~ c_List_Olist__all(U_18932,U_18934,U_18936) ),
    inference(clausify,[status(thm)],[f_4606_3]) ).

fof(f_4607_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_4607_2,plain,
    ! [U_18939] :
      ( c_FunDef_Ois__measure(U_18939,c_Nat_Osize__class_Osize(U_18939))
      | ~ class_Nat_Osize(U_18939) ),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

cnf(f_4607_3,plain,
    ( c_FunDef_Ois__measure(U_18939,c_Nat_Osize__class_Osize(U_18939))
    | ~ class_Nat_Osize(U_18939) ),
    inference(clausify,[status(thm)],[f_4607_2]) ).

fof(f_4608_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_4608_2,plain,
    ! [U_18941,U_18940] : c_FunDef_Ois__measure(U_18940,U_18941),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

cnf(f_4608_3,plain,
    c_FunDef_Ois__measure(U_18940,U_18941),
    inference(clausify,[status(thm)],[f_4608_2]) ).

fof(f_4609_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_4609_2,plain,
    ! [U_18943,U_18942] : c_FunDef_Ois__measure(U_18942,U_18943),
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

cnf(f_4609_3,plain,
    c_FunDef_Ois__measure(U_18942,U_18943),
    inference(clausify,[status(thm)],[f_4609_2]) ).

fof(f_4610_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_4610_2,plain,
    ! [U_18945,U_18944] : c_FunDef_Ois__measure(U_18944,U_18945),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

cnf(f_4610_3,plain,
    c_FunDef_Ois__measure(U_18944,U_18945),
    inference(clausify,[status(thm)],[f_4610_2]) ).

fof(f_4611_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff]) ).

fof(f_4611_2,plain,
    ! [U_18950,U_18949,U_18948] :
      ( ( c_List_Olist__all(U_18948,U_18949,U_18950)
        | ? [U_18947] :
            ( ~ hBOOL(hAPP(U_18949,U_18947))
            & hBOOL(hAPP(hAPP(c_member(U_18948),U_18947),hAPP(c_List_Oset(U_18948),U_18950))) ) )
      & ( ! [U_18946] :
            ( hBOOL(hAPP(U_18949,U_18946))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18948),U_18946),hAPP(c_List_Oset(U_18948),U_18950))) )
        | ~ c_List_Olist__all(U_18948,U_18949,U_18950) ) ),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

fof(f_4611_3,plain,
    ( ! [U_18956,U_18954,U_18952] :
        ( c_List_Olist__all(U_18952,U_18954,U_18956)
        | ? [U_18947] :
            ( ~ hBOOL(hAPP(U_18954,U_18947))
            & hBOOL(hAPP(hAPP(c_member(U_18952),U_18947),hAPP(c_List_Oset(U_18952),U_18956))) ) )
    & ! [U_18955,U_18953,U_18951] :
        ( ! [U_18946] :
            ( hBOOL(hAPP(U_18953,U_18946))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18951),U_18946),hAPP(c_List_Oset(U_18951),U_18955))) )
        | ~ c_List_Olist__all(U_18951,U_18953,U_18955) ) ),
    inference(miniscope,[status(thm)],[f_4611_2]) ).

fof(f_4611_4,plain,
    ( ! [U_18956,U_18954,U_18952] :
        ( c_List_Olist__all(U_18952,U_18954,U_18956)
        | ( ~ hBOOL(hAPP(U_18954,sK489(U_18956,U_18954,U_18952)))
          & hBOOL(hAPP(hAPP(c_member(U_18952),sK489(U_18956,U_18954,U_18952)),hAPP(c_List_Oset(U_18952),U_18956))) ) )
    & ! [U_18955,U_18953,U_18951] :
        ( ! [U_18946] :
            ( hBOOL(hAPP(U_18953,U_18946))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18951),U_18946),hAPP(c_List_Oset(U_18951),U_18955))) )
        | ~ c_List_Olist__all(U_18951,U_18953,U_18955) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_18947,sK489(U_18956,U_18954,U_18952))],[f_4611_3]) ).

cnf(f_4611_5,plain,
    ( hBOOL(hAPP(U_18953,U_18946))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18951),U_18946),hAPP(c_List_Oset(U_18951),U_18955)))
    | ~ c_List_Olist__all(U_18951,U_18953,U_18955) ),
    inference(clausify,[status(thm)],[f_4611_4]) ).

cnf(f_4611_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18952),sK489(U_18956,U_18954,U_18952)),hAPP(c_List_Oset(U_18952),U_18956)))
    | c_List_Olist__all(U_18952,U_18954,U_18956) ),
    inference(clausify,[status(thm)],[f_4611_4]) ).

cnf(f_4611_7,plain,
    ( ~ hBOOL(hAPP(U_18954,sK489(U_18956,U_18954,U_18952)))
    | c_List_Olist__all(U_18952,U_18954,U_18956) ),
    inference(clausify,[status(thm)],[f_4611_4]) ).

fof(f_4612_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_4612_2,plain,
    ! [U_18959,U_18958,U_18957] :
      ( c_FunDef_Ois__measure(tc_prod(U_18959,U_18957),hAPP(hAPP(c_COMBB(U_18957,tc_Nat_Onat,tc_prod(U_18959,U_18957)),U_18958),c_Product__Type_Osnd(U_18959,U_18957)))
      | ~ c_FunDef_Ois__measure(U_18957,U_18958) ),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

cnf(f_4612_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_18959,U_18957),hAPP(hAPP(c_COMBB(U_18957,tc_Nat_Onat,tc_prod(U_18959,U_18957)),U_18958),c_Product__Type_Osnd(U_18959,U_18957)))
    | ~ c_FunDef_Ois__measure(U_18957,U_18958) ),
    inference(clausify,[status(thm)],[f_4612_2]) ).

fof(f_4613_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_4613_2,plain,
    ! [U_18962,U_18961,U_18960] :
      ( c_FunDef_Ois__measure(tc_prod(U_18960,U_18962),hAPP(hAPP(c_COMBB(U_18960,tc_Nat_Onat,tc_prod(U_18960,U_18962)),U_18961),c_Product__Type_Ofst(U_18960,U_18962)))
      | ~ c_FunDef_Ois__measure(U_18960,U_18961) ),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

cnf(f_4613_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_18960,U_18962),hAPP(hAPP(c_COMBB(U_18960,tc_Nat_Onat,tc_prod(U_18960,U_18962)),U_18961),c_Product__Type_Ofst(U_18960,U_18962)))
    | ~ c_FunDef_Ois__measure(U_18960,U_18961) ),
    inference(clausify,[status(thm)],[f_4613_2]) ).

fof(f_4614_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
        | ~ c_List_Olist__all(T_b,V_Pa_2,V_xs_2) )
      & ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ~ c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__rev]) ).

fof(f_4614_2,plain,
    ! [U_18965,U_18964,U_18963] :
      ( ( c_List_Olist__all(U_18963,U_18964,hAPP(c_List_Orev(U_18963),U_18965))
        | ~ c_List_Olist__all(U_18963,U_18964,U_18965) )
      & ( c_List_Olist__all(U_18963,U_18964,U_18965)
        | ~ c_List_Olist__all(U_18963,U_18964,hAPP(c_List_Orev(U_18963),U_18965)) ) ),
    inference(variable_rename,[status(thm)],[f_4614_1]) ).

fof(f_4614_3,plain,
    ( ! [U_18971,U_18969,U_18967] :
        ( c_List_Olist__all(U_18967,U_18969,hAPP(c_List_Orev(U_18967),U_18971))
        | ~ c_List_Olist__all(U_18967,U_18969,U_18971) )
    & ! [U_18970,U_18968,U_18966] :
        ( c_List_Olist__all(U_18966,U_18968,U_18970)
        | ~ c_List_Olist__all(U_18966,U_18968,hAPP(c_List_Orev(U_18966),U_18970)) ) ),
    inference(miniscope,[status(thm)],[f_4614_2]) ).

cnf(f_4614_4,plain,
    ( c_List_Olist__all(U_18966,U_18968,U_18970)
    | ~ c_List_Olist__all(U_18966,U_18968,hAPP(c_List_Orev(U_18966),U_18970)) ),
    inference(clausify,[status(thm)],[f_4614_3]) ).

cnf(f_4614_5,plain,
    ( c_List_Olist__all(U_18967,U_18969,hAPP(c_List_Orev(U_18967),U_18971))
    | ~ c_List_Olist__all(U_18967,U_18969,U_18971) ),
    inference(clausify,[status(thm)],[f_4614_3]) ).

fof(f_4615_1,plain,
    ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ~ c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
          & hBOOL(hAPP(V_Pa_2,V_x_2)) )
        | ~ c_List_Olist__all(T_b,V_Pa_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_4615_2,plain,
    ! [U_18975,U_18974,U_18973,U_18972] :
      ( ( c_List_Olist__all(U_18972,U_18973,hAPP(hAPP(c_List_Olist_OCons(U_18972),U_18974),U_18975))
        | ~ c_List_Olist__all(U_18972,U_18973,U_18975)
        | ~ hBOOL(hAPP(U_18973,U_18974)) )
      & ( ( c_List_Olist__all(U_18972,U_18973,U_18975)
          & hBOOL(hAPP(U_18973,U_18974)) )
        | ~ c_List_Olist__all(U_18972,U_18973,hAPP(hAPP(c_List_Olist_OCons(U_18972),U_18974),U_18975)) ) ),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

fof(f_4615_3,plain,
    ( ! [U_18983,U_18981,U_18979,U_18977] :
        ( c_List_Olist__all(U_18977,U_18979,hAPP(hAPP(c_List_Olist_OCons(U_18977),U_18981),U_18983))
        | ~ c_List_Olist__all(U_18977,U_18979,U_18983)
        | ~ hBOOL(hAPP(U_18979,U_18981)) )
    & ! [U_18982,U_18980,U_18978,U_18976] :
        ( ( c_List_Olist__all(U_18976,U_18978,U_18982)
          & hBOOL(hAPP(U_18978,U_18980)) )
        | ~ c_List_Olist__all(U_18976,U_18978,hAPP(hAPP(c_List_Olist_OCons(U_18976),U_18980),U_18982)) ) ),
    inference(miniscope,[status(thm)],[f_4615_2]) ).

cnf(f_4615_4,plain,
    ( hBOOL(hAPP(U_18978,U_18980))
    | ~ c_List_Olist__all(U_18976,U_18978,hAPP(hAPP(c_List_Olist_OCons(U_18976),U_18980),U_18982)) ),
    inference(clausify,[status(thm)],[f_4615_3]) ).

cnf(f_4615_5,plain,
    ( c_List_Olist__all(U_18976,U_18978,U_18982)
    | ~ c_List_Olist__all(U_18976,U_18978,hAPP(hAPP(c_List_Olist_OCons(U_18976),U_18980),U_18982)) ),
    inference(clausify,[status(thm)],[f_4615_3]) ).

cnf(f_4615_6,plain,
    ( c_List_Olist__all(U_18977,U_18979,hAPP(hAPP(c_List_Olist_OCons(U_18977),U_18981),U_18983))
    | ~ c_List_Olist__all(U_18977,U_18979,U_18983)
    | ~ hBOOL(hAPP(U_18979,U_18981)) ),
    inference(clausify,[status(thm)],[f_4615_3]) ).

fof(f_4616_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2) )
      & ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_4616_2,plain,
    ! [U_18988,U_18987,U_18986] :
      ( ( ! [U_18985] :
            ( hBOOL(hAPP(U_18988,U_18985))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18986),U_18985),hAPP(c_List_Oset(U_18986),U_18987))) )
        | ~ c_List_Olist__all(U_18986,U_18988,U_18987) )
      & ( c_List_Olist__all(U_18986,U_18988,U_18987)
        | ? [U_18984] :
            ( ~ hBOOL(hAPP(U_18988,U_18984))
            & hBOOL(hAPP(hAPP(c_member(U_18986),U_18984),hAPP(c_List_Oset(U_18986),U_18987))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

fof(f_4616_3,plain,
    ( ! [U_18994,U_18992,U_18990] :
        ( ! [U_18985] :
            ( hBOOL(hAPP(U_18994,U_18985))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18990),U_18985),hAPP(c_List_Oset(U_18990),U_18992))) )
        | ~ c_List_Olist__all(U_18990,U_18994,U_18992) )
    & ! [U_18993,U_18991,U_18989] :
        ( c_List_Olist__all(U_18989,U_18993,U_18991)
        | ? [U_18984] :
            ( ~ hBOOL(hAPP(U_18993,U_18984))
            & hBOOL(hAPP(hAPP(c_member(U_18989),U_18984),hAPP(c_List_Oset(U_18989),U_18991))) ) ) ),
    inference(miniscope,[status(thm)],[f_4616_2]) ).

fof(f_4616_4,plain,
    ( ! [U_18994,U_18992,U_18990] :
        ( ! [U_18985] :
            ( hBOOL(hAPP(U_18994,U_18985))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18990),U_18985),hAPP(c_List_Oset(U_18990),U_18992))) )
        | ~ c_List_Olist__all(U_18990,U_18994,U_18992) )
    & ! [U_18993,U_18991,U_18989] :
        ( c_List_Olist__all(U_18989,U_18993,U_18991)
        | ( ~ hBOOL(hAPP(U_18993,sK490(U_18993,U_18991,U_18989)))
          & hBOOL(hAPP(hAPP(c_member(U_18989),sK490(U_18993,U_18991,U_18989)),hAPP(c_List_Oset(U_18989),U_18991))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_18984,sK490(U_18993,U_18991,U_18989))],[f_4616_3]) ).

cnf(f_4616_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18989),sK490(U_18993,U_18991,U_18989)),hAPP(c_List_Oset(U_18989),U_18991)))
    | c_List_Olist__all(U_18989,U_18993,U_18991) ),
    inference(clausify,[status(thm)],[f_4616_4]) ).

cnf(f_4616_6,plain,
    ( ~ hBOOL(hAPP(U_18993,sK490(U_18993,U_18991,U_18989)))
    | c_List_Olist__all(U_18989,U_18993,U_18991) ),
    inference(clausify,[status(thm)],[f_4616_4]) ).

cnf(f_4616_7,plain,
    ( hBOOL(hAPP(U_18994,U_18985))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18990),U_18985),hAPP(c_List_Oset(U_18990),U_18992)))
    | ~ c_List_Olist__all(U_18990,U_18994,U_18992) ),
    inference(clausify,[status(thm)],[f_4616_4]) ).

fof(f_4617_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__raw]) ).

fof(f_4617_2,plain,
    ! [U_18999,U_18998,U_18997] :
      ( ( c_List_Olist__all(U_18997,U_18998,U_18999)
        | ? [U_18996] :
            ( ~ hBOOL(hAPP(U_18998,U_18996))
            & hBOOL(hAPP(hAPP(c_member(U_18997),U_18996),hAPP(c_List_Oset(U_18997),U_18999))) ) )
      & ( ! [U_18995] :
            ( hBOOL(hAPP(U_18998,U_18995))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18997),U_18995),hAPP(c_List_Oset(U_18997),U_18999))) )
        | ~ c_List_Olist__all(U_18997,U_18998,U_18999) ) ),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

fof(f_4617_3,plain,
    ( ! [U_19005,U_19003,U_19001] :
        ( c_List_Olist__all(U_19001,U_19003,U_19005)
        | ? [U_18996] :
            ( ~ hBOOL(hAPP(U_19003,U_18996))
            & hBOOL(hAPP(hAPP(c_member(U_19001),U_18996),hAPP(c_List_Oset(U_19001),U_19005))) ) )
    & ! [U_19004,U_19002,U_19000] :
        ( ! [U_18995] :
            ( hBOOL(hAPP(U_19002,U_18995))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19000),U_18995),hAPP(c_List_Oset(U_19000),U_19004))) )
        | ~ c_List_Olist__all(U_19000,U_19002,U_19004) ) ),
    inference(miniscope,[status(thm)],[f_4617_2]) ).

fof(f_4617_4,plain,
    ( ! [U_19005,U_19003,U_19001] :
        ( c_List_Olist__all(U_19001,U_19003,U_19005)
        | ( ~ hBOOL(hAPP(U_19003,sK491(U_19005,U_19003,U_19001)))
          & hBOOL(hAPP(hAPP(c_member(U_19001),sK491(U_19005,U_19003,U_19001)),hAPP(c_List_Oset(U_19001),U_19005))) ) )
    & ! [U_19004,U_19002,U_19000] :
        ( ! [U_18995] :
            ( hBOOL(hAPP(U_19002,U_18995))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19000),U_18995),hAPP(c_List_Oset(U_19000),U_19004))) )
        | ~ c_List_Olist__all(U_19000,U_19002,U_19004) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_18996,sK491(U_19005,U_19003,U_19001))],[f_4617_3]) ).

cnf(f_4617_5,plain,
    ( hBOOL(hAPP(U_19002,U_18995))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19000),U_18995),hAPP(c_List_Oset(U_19000),U_19004)))
    | ~ c_List_Olist__all(U_19000,U_19002,U_19004) ),
    inference(clausify,[status(thm)],[f_4617_4]) ).

cnf(f_4617_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19001),sK491(U_19005,U_19003,U_19001)),hAPP(c_List_Oset(U_19001),U_19005)))
    | c_List_Olist__all(U_19001,U_19003,U_19005) ),
    inference(clausify,[status(thm)],[f_4617_4]) ).

cnf(f_4617_7,plain,
    ( ~ hBOOL(hAPP(U_19003,sK491(U_19005,U_19003,U_19001)))
    | c_List_Olist__all(U_19001,U_19003,U_19005) ),
    inference(clausify,[status(thm)],[f_4617_4]) ).

fof(f_4618_1,plain,
    ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
          & ~ hBOOL(hAPP(V_Pa_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_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
          & hBOOL(hAPP(V_Pa_2,V_x_2)) ) )
      & ( ( ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
            | hBOOL(hAPP(V_Pa_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_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
            | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) )
        | ~ c_List_Olist__ex1(T_b,V_Pa_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_4618_2,plain,
    ! [U_19009,U_19008,U_19007,U_19006] :
      ( ( c_List_Olist__ex1(U_19006,U_19007,hAPP(hAPP(c_List_Olist_OCons(U_19006),U_19008),U_19009))
        | ( ~ c_List_Olist__ex1(U_19006,U_19007,U_19009)
          & ~ hBOOL(hAPP(U_19007,U_19008)) )
        | ( ~ c_List_Olist__all(U_19006,hAPP(hAPP(c_COMBS(U_19006,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19006),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19006),c_fNot),U_19007))),hAPP(c_fequal,U_19008)),U_19009)
          & hBOOL(hAPP(U_19007,U_19008)) ) )
      & ( ( ( c_List_Olist__ex1(U_19006,U_19007,U_19009)
            | hBOOL(hAPP(U_19007,U_19008)) )
          & ( c_List_Olist__all(U_19006,hAPP(hAPP(c_COMBS(U_19006,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19006),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19006),c_fNot),U_19007))),hAPP(c_fequal,U_19008)),U_19009)
            | ~ hBOOL(hAPP(U_19007,U_19008)) ) )
        | ~ c_List_Olist__ex1(U_19006,U_19007,hAPP(hAPP(c_List_Olist_OCons(U_19006),U_19008),U_19009)) ) ),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

fof(f_4618_3,plain,
    ( ! [U_19017,U_19015,U_19013,U_19011] :
        ( c_List_Olist__ex1(U_19011,U_19013,hAPP(hAPP(c_List_Olist_OCons(U_19011),U_19015),U_19017))
        | ( ~ c_List_Olist__ex1(U_19011,U_19013,U_19017)
          & ~ hBOOL(hAPP(U_19013,U_19015)) )
        | ( ~ c_List_Olist__all(U_19011,hAPP(hAPP(c_COMBS(U_19011,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19011),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19011),c_fNot),U_19013))),hAPP(c_fequal,U_19015)),U_19017)
          & hBOOL(hAPP(U_19013,U_19015)) ) )
    & ! [U_19016,U_19014,U_19012,U_19010] :
        ( ( ( c_List_Olist__ex1(U_19010,U_19012,U_19016)
            | hBOOL(hAPP(U_19012,U_19014)) )
          & ( c_List_Olist__all(U_19010,hAPP(hAPP(c_COMBS(U_19010,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19010),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19010),c_fNot),U_19012))),hAPP(c_fequal,U_19014)),U_19016)
            | ~ hBOOL(hAPP(U_19012,U_19014)) ) )
        | ~ c_List_Olist__ex1(U_19010,U_19012,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19014),U_19016)) ) ),
    inference(miniscope,[status(thm)],[f_4618_2]) ).

cnf(f_4618_4,plain,
    ( c_List_Olist__all(U_19010,hAPP(hAPP(c_COMBS(U_19010,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19010),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19010),c_fNot),U_19012))),hAPP(c_fequal,U_19014)),U_19016)
    | ~ hBOOL(hAPP(U_19012,U_19014))
    | ~ c_List_Olist__ex1(U_19010,U_19012,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19014),U_19016)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

cnf(f_4618_5,plain,
    ( c_List_Olist__ex1(U_19010,U_19012,U_19016)
    | hBOOL(hAPP(U_19012,U_19014))
    | ~ c_List_Olist__ex1(U_19010,U_19012,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19014),U_19016)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

cnf(f_4618_6,plain,
    ( ~ hBOOL(hAPP(U_19013,U_19015))
    | hBOOL(hAPP(U_19013,U_19015))
    | c_List_Olist__ex1(U_19011,U_19013,hAPP(hAPP(c_List_Olist_OCons(U_19011),U_19015),U_19017)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

cnf(f_4618_7,plain,
    ( ~ c_List_Olist__ex1(U_19011,U_19013,U_19017)
    | hBOOL(hAPP(U_19013,U_19015))
    | c_List_Olist__ex1(U_19011,U_19013,hAPP(hAPP(c_List_Olist_OCons(U_19011),U_19015),U_19017)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

cnf(f_4618_8,plain,
    ( ~ hBOOL(hAPP(U_19013,U_19015))
    | ~ c_List_Olist__all(U_19011,hAPP(hAPP(c_COMBS(U_19011,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19011),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19011),c_fNot),U_19013))),hAPP(c_fequal,U_19015)),U_19017)
    | c_List_Olist__ex1(U_19011,U_19013,hAPP(hAPP(c_List_Olist_OCons(U_19011),U_19015),U_19017)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

cnf(f_4618_9,plain,
    ( ~ c_List_Olist__ex1(U_19011,U_19013,U_19017)
    | ~ c_List_Olist__all(U_19011,hAPP(hAPP(c_COMBS(U_19011,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19011),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19011),c_fNot),U_19013))),hAPP(c_fequal,U_19015)),U_19017)
    | c_List_Olist__ex1(U_19011,U_19013,hAPP(hAPP(c_List_Olist_OCons(U_19011),U_19015),U_19017)) ),
    inference(clausify,[status(thm)],[f_4618_3]) ).

fof(f_4619_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_4619_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_4619_1]) ).

fof(f_4620_1,plain,
    ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(f_4620_2,plain,
    ! [U_19019,U_19018] : ~ c_List_Olist__ex1(U_19018,U_19019,c_List_Olist_ONil(U_19018)),
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

cnf(f_4620_3,plain,
    ~ c_List_Olist__ex1(U_19018,U_19019,c_List_Olist_ONil(U_19018)),
    inference(clausify,[status(thm)],[f_4620_2]) ).

fof(f_4621_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_4621_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_4621_1]) ).

fof(f_4622_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_4622_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_4622_1]) ).

fof(f_4623_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_Pa_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            | ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_y))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__iff]) ).

fof(f_4623_2,plain,
    ! [U_19026,U_19025,U_19024] :
      ( ( c_List_Olist__ex1(U_19024,U_19025,U_19026)
        | ! [U_19023] :
            ( ? [U_19022] :
                ( U_19022 != U_19023
                & hBOOL(hAPP(U_19025,U_19022))
                & hBOOL(hAPP(hAPP(c_member(U_19024),U_19022),hAPP(c_List_Oset(U_19024),U_19026))) )
            | ~ hBOOL(hAPP(U_19025,U_19023))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19024),U_19023),hAPP(c_List_Oset(U_19024),U_19026))) ) )
      & ( ? [U_19021] :
            ( ! [U_19020] :
                ( U_19020 = U_19021
                | ~ hBOOL(hAPP(U_19025,U_19020))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19024),U_19020),hAPP(c_List_Oset(U_19024),U_19026))) )
            & hBOOL(hAPP(U_19025,U_19021))
            & hBOOL(hAPP(hAPP(c_member(U_19024),U_19021),hAPP(c_List_Oset(U_19024),U_19026))) )
        | ~ c_List_Olist__ex1(U_19024,U_19025,U_19026) ) ),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

fof(f_4623_3,plain,
    ( ! [U_19032,U_19030,U_19028] :
        ( c_List_Olist__ex1(U_19028,U_19030,U_19032)
        | ! [U_19023] :
            ( ? [U_19022] :
                ( U_19022 != U_19023
                & hBOOL(hAPP(U_19030,U_19022))
                & hBOOL(hAPP(hAPP(c_member(U_19028),U_19022),hAPP(c_List_Oset(U_19028),U_19032))) )
            | ~ hBOOL(hAPP(U_19030,U_19023))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032))) ) )
    & ! [U_19031,U_19029,U_19027] :
        ( ? [U_19021] :
            ( ! [U_19020] :
                ( U_19020 = U_19021
                | ~ hBOOL(hAPP(U_19029,U_19020))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19027),U_19020),hAPP(c_List_Oset(U_19027),U_19031))) )
            & hBOOL(hAPP(U_19029,U_19021))
            & hBOOL(hAPP(hAPP(c_member(U_19027),U_19021),hAPP(c_List_Oset(U_19027),U_19031))) )
        | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ) ),
    inference(miniscope,[status(thm)],[f_4623_2]) ).

fof(f_4623_4,plain,
    ( ! [U_19032,U_19030,U_19028] :
        ( c_List_Olist__ex1(U_19028,U_19030,U_19032)
        | ! [U_19023] :
            ( ? [U_19022] :
                ( U_19022 != U_19023
                & hBOOL(hAPP(U_19030,U_19022))
                & hBOOL(hAPP(hAPP(c_member(U_19028),U_19022),hAPP(c_List_Oset(U_19028),U_19032))) )
            | ~ hBOOL(hAPP(U_19030,U_19023))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032))) ) )
    & ! [U_19031,U_19029,U_19027] :
        ( ( ! [U_19020] :
              ( U_19020 = sK492(U_19031,U_19029,U_19027)
              | ~ hBOOL(hAPP(U_19029,U_19020))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19027),U_19020),hAPP(c_List_Oset(U_19027),U_19031))) )
          & hBOOL(hAPP(U_19029,sK492(U_19031,U_19029,U_19027)))
          & hBOOL(hAPP(hAPP(c_member(U_19027),sK492(U_19031,U_19029,U_19027)),hAPP(c_List_Oset(U_19027),U_19031))) )
        | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_19021,sK492(U_19031,U_19029,U_19027))],[f_4623_3]) ).

fof(f_4623_5,plain,
    ( ! [U_19032,U_19030,U_19028] :
        ( c_List_Olist__ex1(U_19028,U_19030,U_19032)
        | ! [U_19023] :
            ( ( sK493(U_19032,U_19030,U_19028,U_19023) != U_19023
              & hBOOL(hAPP(U_19030,sK493(U_19032,U_19030,U_19028,U_19023)))
              & hBOOL(hAPP(hAPP(c_member(U_19028),sK493(U_19032,U_19030,U_19028,U_19023)),hAPP(c_List_Oset(U_19028),U_19032))) )
            | ~ hBOOL(hAPP(U_19030,U_19023))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032))) ) )
    & ! [U_19031,U_19029,U_19027] :
        ( ( ! [U_19020] :
              ( U_19020 = sK492(U_19031,U_19029,U_19027)
              | ~ hBOOL(hAPP(U_19029,U_19020))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19027),U_19020),hAPP(c_List_Oset(U_19027),U_19031))) )
          & hBOOL(hAPP(U_19029,sK492(U_19031,U_19029,U_19027)))
          & hBOOL(hAPP(hAPP(c_member(U_19027),sK492(U_19031,U_19029,U_19027)),hAPP(c_List_Oset(U_19027),U_19031))) )
        | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_19022,sK493(U_19032,U_19030,U_19028,U_19023))],[f_4623_4]) ).

cnf(f_4623_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19027),sK492(U_19031,U_19029,U_19027)),hAPP(c_List_Oset(U_19027),U_19031)))
    | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

cnf(f_4623_7,plain,
    ( hBOOL(hAPP(U_19029,sK492(U_19031,U_19029,U_19027)))
    | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

cnf(f_4623_8,plain,
    ( U_19020 = sK492(U_19031,U_19029,U_19027)
    | ~ hBOOL(hAPP(U_19029,U_19020))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19027),U_19020),hAPP(c_List_Oset(U_19027),U_19031)))
    | ~ c_List_Olist__ex1(U_19027,U_19029,U_19031) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

cnf(f_4623_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19028),sK493(U_19032,U_19030,U_19028,U_19023)),hAPP(c_List_Oset(U_19028),U_19032)))
    | ~ hBOOL(hAPP(U_19030,U_19023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032)))
    | c_List_Olist__ex1(U_19028,U_19030,U_19032) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

cnf(f_4623_10,plain,
    ( hBOOL(hAPP(U_19030,sK493(U_19032,U_19030,U_19028,U_19023)))
    | ~ hBOOL(hAPP(U_19030,U_19023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032)))
    | c_List_Olist__ex1(U_19028,U_19030,U_19032) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

cnf(f_4623_11,plain,
    ( sK493(U_19032,U_19030,U_19028,U_19023) != U_19023
    | ~ hBOOL(hAPP(U_19030,U_19023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19028),U_19023),hAPP(c_List_Oset(U_19028),U_19032)))
    | c_List_Olist__ex1(U_19028,U_19030,U_19032) ),
    inference(clausify,[status(thm)],[f_4623_5]) ).

fof(f_4624_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_4624_2,plain,
    ! [U_19037,U_19036,U_19035,U_19034,U_19033] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19034,U_19035,U_19036,U_19037),U_19033) = c_Lazy__Sequence_Ohb__bind(U_19034,U_19035,hAPP(U_19036,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19033),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19034,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19035))),U_19037),U_19033))
        | U_19033 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19034,U_19035,U_19036,U_19037),U_19033) = c_Lazy__Sequence_Ohit__bound(U_19035)
        | U_19033 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

fof(f_4624_3,plain,
    ( ! [U_19047,U_19045,U_19043,U_19041,U_19039] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19041,U_19043,U_19045,U_19047),U_19039) = c_Lazy__Sequence_Ohb__bind(U_19041,U_19043,hAPP(U_19045,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19039),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19041,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19043))),U_19047),U_19039))
        | U_19039 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19046,U_19044,U_19042,U_19040,U_19038] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19040,U_19042,U_19044,U_19046),U_19038) = c_Lazy__Sequence_Ohit__bound(U_19042)
        | U_19038 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4624_2]) ).

cnf(f_4624_4,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19040,U_19042,U_19044,U_19046),U_19038) = c_Lazy__Sequence_Ohit__bound(U_19042)
    | U_19038 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

cnf(f_4624_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19041,U_19043,U_19045,U_19047),U_19039) = c_Lazy__Sequence_Ohb__bind(U_19041,U_19043,hAPP(U_19045,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19039),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19041,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19043))),U_19047),U_19039))
    | U_19039 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

fof(f_4625_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_4625_2,plain,
    ! [U_19052,U_19051,U_19050,U_19049,U_19048] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_19049,U_19050,U_19051,U_19052),U_19048) = hAPP(c_Lazy__Sequence_Obind(U_19049,U_19050,hAPP(U_19051,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19048),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19049,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19050)),U_19052),U_19048))
        | U_19048 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_19049,U_19050,U_19051,U_19052),U_19048) = c_Lazy__Sequence_Oempty(U_19050)
        | U_19048 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

fof(f_4625_3,plain,
    ( ! [U_19062,U_19060,U_19058,U_19056,U_19054] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_19056,U_19058,U_19060,U_19062),U_19054) = hAPP(c_Lazy__Sequence_Obind(U_19056,U_19058,hAPP(U_19060,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19054),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19056,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19058)),U_19062),U_19054))
        | U_19054 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19061,U_19059,U_19057,U_19055,U_19053] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_19055,U_19057,U_19059,U_19061),U_19053) = c_Lazy__Sequence_Oempty(U_19057)
        | U_19053 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4625_2]) ).

cnf(f_4625_4,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_19055,U_19057,U_19059,U_19061),U_19053) = c_Lazy__Sequence_Oempty(U_19057)
    | U_19053 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4625_3]) ).

cnf(f_4625_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_19056,U_19058,U_19060,U_19062),U_19054) = hAPP(c_Lazy__Sequence_Obind(U_19056,U_19058,hAPP(U_19060,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19054),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19056,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19058)),U_19062),U_19054))
    | U_19054 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4625_3]) ).

fof(f_4626_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_4626_2,plain,
    ! [U_19069,U_19068,U_19067,U_19066,U_19065,U_19064,U_19063] : c_New__Random__Sequence_Opos__decr__bind(U_19063,U_19064,U_19065,U_19066,U_19067,U_19068,U_19069) = c_New__DSequence_Opos__decr__bind(U_19063,U_19064,hAPP(hAPP(hAPP(U_19065,U_19067),U_19068),U_19069),hAPP(hAPP(c_COMBC(U_19063,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_19064))),hAPP(hAPP(c_COMBC(U_19063,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_19064)))),hAPP(hAPP(c_COMBC(U_19063,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_19064))))),U_19066),U_19067)),U_19068)),U_19069)),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

cnf(f_4626_3,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_19063,U_19064,U_19065,U_19066,U_19067,U_19068,U_19069) = c_New__DSequence_Opos__decr__bind(U_19063,U_19064,hAPP(hAPP(hAPP(U_19065,U_19067),U_19068),U_19069),hAPP(hAPP(c_COMBC(U_19063,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_19064))),hAPP(hAPP(c_COMBC(U_19063,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_19064)))),hAPP(hAPP(c_COMBC(U_19063,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_19064))))),U_19066),U_19067)),U_19068)),U_19069)),
    inference(clausify,[status(thm)],[f_4626_2]) ).

fof(f_4627_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_4627_2,plain,
    ! [U_19076,U_19075,U_19074,U_19073,U_19072,U_19071,U_19070] : c_New__Random__Sequence_Oneg__decr__bind(U_19070,U_19071,U_19072,U_19073,U_19074,U_19075,U_19076) = c_New__DSequence_Oneg__decr__bind(U_19070,U_19071,hAPP(hAPP(hAPP(U_19072,U_19074),U_19075),U_19076),hAPP(hAPP(c_COMBC(U_19070,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_19071)))),hAPP(hAPP(c_COMBC(U_19070,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_19071))))),hAPP(hAPP(c_COMBC(U_19070,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_19071)))))),U_19073),U_19074)),U_19075)),U_19076)),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

cnf(f_4627_3,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_19070,U_19071,U_19072,U_19073,U_19074,U_19075,U_19076) = c_New__DSequence_Oneg__decr__bind(U_19070,U_19071,hAPP(hAPP(hAPP(U_19072,U_19074),U_19075),U_19076),hAPP(hAPP(c_COMBC(U_19070,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_19071)))),hAPP(hAPP(c_COMBC(U_19070,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_19071))))),hAPP(hAPP(c_COMBC(U_19070,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_19071)))))),U_19073),U_19074)),U_19075)),U_19076)),
    inference(clausify,[status(thm)],[f_4627_2]) ).

fof(f_4628_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_4628_2,plain,
    ! [U_19081,U_19080,U_19079,U_19078,U_19077] : hAPP(c_New__DSequence_Oneg__bind(U_19077,U_19078,U_19079,U_19080),U_19081) = c_Lazy__Sequence_Ohb__bind(U_19077,U_19078,hAPP(U_19079,U_19081),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078))),U_19080),U_19081)),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

cnf(f_4628_3,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_19077,U_19078,U_19079,U_19080),U_19081) = c_Lazy__Sequence_Ohb__bind(U_19077,U_19078,hAPP(U_19079,U_19081),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078))),U_19080),U_19081)),
    inference(clausify,[status(thm)],[f_4628_2]) ).

fof(f_4629_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_4629_2,plain,
    ! [U_19083,U_19082] : hAPP(c_New__DSequence_Opos__empty(U_19082),U_19083) = c_Lazy__Sequence_Oempty(U_19082),
    inference(variable_rename,[status(thm)],[f_4629_1]) ).

cnf(f_4629_3,plain,
    hAPP(c_New__DSequence_Opos__empty(U_19082),U_19083) = c_Lazy__Sequence_Oempty(U_19082),
    inference(clausify,[status(thm)],[f_4629_2]) ).

fof(f_4630_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_4630_2,plain,
    ! [U_19087,U_19086,U_19085,U_19084] : c_New__Random__Sequence_Opos__empty(U_19084,U_19085,U_19086,U_19087) = c_New__DSequence_Opos__empty(U_19084),
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

cnf(f_4630_3,plain,
    c_New__Random__Sequence_Opos__empty(U_19084,U_19085,U_19086,U_19087) = c_New__DSequence_Opos__empty(U_19084),
    inference(clausify,[status(thm)],[f_4630_2]) ).

fof(f_4631_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_4631_2,plain,
    ! [U_19094,U_19093,U_19092,U_19091,U_19090,U_19089,U_19088] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_19088,U_19089,U_19090,U_19091),U_19092),U_19093),U_19094) = c_New__DSequence_Oneg__bind(U_19088,U_19089,hAPP(hAPP(hAPP(U_19090,U_19092),U_19093),U_19094),hAPP(hAPP(c_COMBC(U_19088,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_19089)))),hAPP(hAPP(c_COMBC(U_19088,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_19089))))),hAPP(hAPP(c_COMBC(U_19088,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_19089)))))),U_19091),U_19092)),U_19093)),U_19094)),
    inference(variable_rename,[status(thm)],[f_4631_1]) ).

cnf(f_4631_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_19088,U_19089,U_19090,U_19091),U_19092),U_19093),U_19094) = c_New__DSequence_Oneg__bind(U_19088,U_19089,hAPP(hAPP(hAPP(U_19090,U_19092),U_19093),U_19094),hAPP(hAPP(c_COMBC(U_19088,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_19089)))),hAPP(hAPP(c_COMBC(U_19088,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_19089))))),hAPP(hAPP(c_COMBC(U_19088,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_19089)))))),U_19091),U_19092)),U_19093)),U_19094)),
    inference(clausify,[status(thm)],[f_4631_2]) ).

fof(f_4632_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_4632_2,plain,
    ! [U_19099,U_19098,U_19097,U_19096,U_19095] : hAPP(c_New__DSequence_Opos__bind(U_19095,U_19096,U_19097,U_19098),U_19099) = hAPP(c_Lazy__Sequence_Obind(U_19095,U_19096,hAPP(U_19097,U_19099)),hAPP(hAPP(c_COMBC(U_19095,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19096)),U_19098),U_19099)),
    inference(variable_rename,[status(thm)],[f_4632_1]) ).

cnf(f_4632_3,plain,
    hAPP(c_New__DSequence_Opos__bind(U_19095,U_19096,U_19097,U_19098),U_19099) = hAPP(c_Lazy__Sequence_Obind(U_19095,U_19096,hAPP(U_19097,U_19099)),hAPP(hAPP(c_COMBC(U_19095,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19096)),U_19098),U_19099)),
    inference(clausify,[status(thm)],[f_4632_2]) ).

fof(f_4633_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_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_4633_2,plain,
    ! [U_19103,U_19102,U_19101,U_19100] : c_New__Random__Sequence_Oneg__map(U_19100,U_19101,U_19102,U_19103) = c_New__Random__Sequence_Oneg__bind(U_19100,U_19101,U_19103,hAPP(c_Fun_Ocomp(U_19101,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_19101)))))),U_19100,c_New__Random__Sequence_Oneg__single(U_19101)),U_19102)),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

cnf(f_4633_3,plain,
    c_New__Random__Sequence_Oneg__map(U_19100,U_19101,U_19102,U_19103) = c_New__Random__Sequence_Oneg__bind(U_19100,U_19101,U_19103,hAPP(c_Fun_Ocomp(U_19101,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_19101)))))),U_19100,c_New__Random__Sequence_Oneg__single(U_19101)),U_19102)),
    inference(clausify,[status(thm)],[f_4633_2]) ).

fof(f_4634_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_4634_2,plain,
    ! [U_19108,U_19107,U_19106,U_19105,U_19104] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_19104),U_19105),U_19106),U_19107),U_19108) = c_New__DSequence_Oneg__single(U_19104,U_19105),
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

cnf(f_4634_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_19104),U_19105),U_19106),U_19107),U_19108) = c_New__DSequence_Oneg__single(U_19104,U_19105),
    inference(clausify,[status(thm)],[f_4634_2]) ).

fof(f_4635_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_4635_2,plain,
    ! [U_19115,U_19114,U_19113,U_19112,U_19111,U_19110,U_19109] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_19109,U_19110,U_19111,U_19112),U_19113),U_19114),U_19115) = c_New__DSequence_Opos__bind(U_19109,U_19110,hAPP(hAPP(hAPP(U_19111,U_19113),U_19114),U_19115),hAPP(hAPP(c_COMBC(U_19109,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_19110))),hAPP(hAPP(c_COMBC(U_19109,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_19110)))),hAPP(hAPP(c_COMBC(U_19109,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_19110))))),U_19112),U_19113)),U_19114)),U_19115)),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

cnf(f_4635_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_19109,U_19110,U_19111,U_19112),U_19113),U_19114),U_19115) = c_New__DSequence_Opos__bind(U_19109,U_19110,hAPP(hAPP(hAPP(U_19111,U_19113),U_19114),U_19115),hAPP(hAPP(c_COMBC(U_19109,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_19110))),hAPP(hAPP(c_COMBC(U_19109,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_19110)))),hAPP(hAPP(c_COMBC(U_19109,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_19110))))),U_19112),U_19113)),U_19114)),U_19115)),
    inference(clausify,[status(thm)],[f_4635_2]) ).

fof(f_4636_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_4636_2,plain,
    ! [U_19118,U_19117,U_19116] : hAPP(c_New__DSequence_Oneg__single(U_19116,U_19117),U_19118) = c_Lazy__Sequence_Ohb__single(U_19116,U_19117),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

cnf(f_4636_3,plain,
    hAPP(c_New__DSequence_Oneg__single(U_19116,U_19117),U_19118) = c_Lazy__Sequence_Ohb__single(U_19116,U_19117),
    inference(clausify,[status(thm)],[f_4636_2]) ).

fof(f_4637_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_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_4637_2,plain,
    ! [U_19122,U_19121,U_19120,U_19119] : c_New__Random__Sequence_Opos__map(U_19119,U_19120,U_19121,U_19122) = c_New__Random__Sequence_Opos__bind(U_19119,U_19120,U_19122,hAPP(c_Fun_Ocomp(U_19120,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_19120))))),U_19119,c_New__Random__Sequence_Opos__single(U_19120)),U_19121)),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

cnf(f_4637_3,plain,
    c_New__Random__Sequence_Opos__map(U_19119,U_19120,U_19121,U_19122) = c_New__Random__Sequence_Opos__bind(U_19119,U_19120,U_19122,hAPP(c_Fun_Ocomp(U_19120,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_19120))))),U_19119,c_New__Random__Sequence_Opos__single(U_19120)),U_19121)),
    inference(clausify,[status(thm)],[f_4637_2]) ).

fof(f_4638_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_4638_2,plain,
    ! [U_19127,U_19126,U_19125,U_19124,U_19123] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_19123),U_19124),U_19125),U_19126),U_19127) = c_New__DSequence_Opos__single(U_19123,U_19124),
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

cnf(f_4638_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_19123),U_19124),U_19125),U_19126),U_19127) = c_New__DSequence_Opos__single(U_19123,U_19124),
    inference(clausify,[status(thm)],[f_4638_2]) ).

fof(f_4639_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_4639_2,plain,
    ! [U_19130,U_19129,U_19128] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),c_List_Osplice(U_19128,U_19129,U_19130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),U_19129)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),U_19130)),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

cnf(f_4639_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),c_List_Osplice(U_19128,U_19129,U_19130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),U_19129)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19128)),U_19130)),
    inference(clausify,[status(thm)],[f_4639_2]) ).

fof(f_4640_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_4640_2,plain,
    ! [U_19135,U_19134,U_19133,U_19132,U_19131] : c_List_Osplice(U_19131,hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),U_19133),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),U_19135)) = hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),c_List_Osplice(U_19131,U_19133,U_19135))),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

cnf(f_4640_3,plain,
    c_List_Osplice(U_19131,hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),U_19133),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),U_19135)) = hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),c_List_Osplice(U_19131,U_19133,U_19135))),
    inference(clausify,[status(thm)],[f_4640_2]) ).

fof(f_4641_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_4641_2,plain,
    ! [U_19137,U_19136] : c_List_Osplice(U_19136,c_List_Olist_ONil(U_19136),U_19137) = U_19137,
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

cnf(f_4641_3,plain,
    c_List_Osplice(U_19136,c_List_Olist_ONil(U_19136),U_19137) = U_19137,
    inference(clausify,[status(thm)],[f_4641_2]) ).

fof(f_4642_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_4642_2,plain,
    ! [U_19139,U_19138] : c_List_Osplice(U_19138,U_19139,c_List_Olist_ONil(U_19138)) = U_19139,
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

cnf(f_4642_3,plain,
    c_List_Osplice(U_19138,U_19139,c_List_Olist_ONil(U_19138)) = U_19139,
    inference(clausify,[status(thm)],[f_4642_2]) ).

fof(f_4643_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_4643_2,plain,
    ! [U_19142,U_19141,U_19140] : c_List_Osplice(U_19140,hAPP(hAPP(c_List_Olist_OCons(U_19140),U_19141),U_19142),c_List_Olist_ONil(U_19140)) = hAPP(hAPP(c_List_Olist_OCons(U_19140),U_19141),U_19142),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

cnf(f_4643_3,plain,
    c_List_Osplice(U_19140,hAPP(hAPP(c_List_Olist_OCons(U_19140),U_19141),U_19142),c_List_Olist_ONil(U_19140)) = hAPP(hAPP(c_List_Olist_OCons(U_19140),U_19141),U_19142),
    inference(clausify,[status(thm)],[f_4643_2]) ).

fof(f_4644_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_4644_2,plain,
    ! [U_19145,U_19144,U_19143] : hAPP(c_New__DSequence_Opos__single(U_19143,U_19144),U_19145) = hAPP(c_Lazy__Sequence_Osingle(U_19143),U_19144),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

cnf(f_4644_3,plain,
    hAPP(c_New__DSequence_Opos__single(U_19143,U_19144),U_19145) = hAPP(c_Lazy__Sequence_Osingle(U_19143),U_19144),
    inference(clausify,[status(thm)],[f_4644_2]) ).

fof(f_4645_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_4645_2,plain,
    ! [U_19147,U_19146] :
      ( ( c_Wellfounded_Oacyclic(U_19146,hAPP(c_Set_OCollect(tc_prod(U_19146,U_19146)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19146,U_19146,tc_HOL_Obool),c_Predicate_Oconversep(U_19146,U_19146,U_19147))))
        | ~ c_Wellfounded_Oacyclic(U_19146,hAPP(c_Set_OCollect(tc_prod(U_19146,U_19146)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19146,U_19146,tc_HOL_Obool),U_19147))) )
      & ( c_Wellfounded_Oacyclic(U_19146,hAPP(c_Set_OCollect(tc_prod(U_19146,U_19146)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19146,U_19146,tc_HOL_Obool),U_19147)))
        | ~ c_Wellfounded_Oacyclic(U_19146,hAPP(c_Set_OCollect(tc_prod(U_19146,U_19146)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19146,U_19146,tc_HOL_Obool),c_Predicate_Oconversep(U_19146,U_19146,U_19147)))) ) ),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

fof(f_4645_3,plain,
    ( ! [U_19151,U_19149] :
        ( c_Wellfounded_Oacyclic(U_19149,hAPP(c_Set_OCollect(tc_prod(U_19149,U_19149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19149,U_19149,tc_HOL_Obool),c_Predicate_Oconversep(U_19149,U_19149,U_19151))))
        | ~ c_Wellfounded_Oacyclic(U_19149,hAPP(c_Set_OCollect(tc_prod(U_19149,U_19149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19149,U_19149,tc_HOL_Obool),U_19151))) )
    & ! [U_19150,U_19148] :
        ( c_Wellfounded_Oacyclic(U_19148,hAPP(c_Set_OCollect(tc_prod(U_19148,U_19148)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19148,U_19148,tc_HOL_Obool),U_19150)))
        | ~ c_Wellfounded_Oacyclic(U_19148,hAPP(c_Set_OCollect(tc_prod(U_19148,U_19148)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19148,U_19148,tc_HOL_Obool),c_Predicate_Oconversep(U_19148,U_19148,U_19150)))) ) ),
    inference(miniscope,[status(thm)],[f_4645_2]) ).

cnf(f_4645_4,plain,
    ( c_Wellfounded_Oacyclic(U_19148,hAPP(c_Set_OCollect(tc_prod(U_19148,U_19148)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19148,U_19148,tc_HOL_Obool),U_19150)))
    | ~ c_Wellfounded_Oacyclic(U_19148,hAPP(c_Set_OCollect(tc_prod(U_19148,U_19148)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19148,U_19148,tc_HOL_Obool),c_Predicate_Oconversep(U_19148,U_19148,U_19150)))) ),
    inference(clausify,[status(thm)],[f_4645_3]) ).

cnf(f_4645_5,plain,
    ( c_Wellfounded_Oacyclic(U_19149,hAPP(c_Set_OCollect(tc_prod(U_19149,U_19149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19149,U_19149,tc_HOL_Obool),c_Predicate_Oconversep(U_19149,U_19149,U_19151))))
    | ~ c_Wellfounded_Oacyclic(U_19149,hAPP(c_Set_OCollect(tc_prod(U_19149,U_19149)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19149,U_19149,tc_HOL_Obool),U_19151))) ),
    inference(clausify,[status(thm)],[f_4645_3]) ).

fof(f_4646_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_4646_2,plain,
    ! [U_19155,U_19154,U_19153,U_19152] : c_Predicate_Oconversep(U_19152,U_19153,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19152,tc_fun(U_19153,tc_HOL_Obool))),U_19154),U_19155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19153,tc_fun(U_19152,tc_HOL_Obool))),c_Predicate_Oconversep(U_19152,U_19153,U_19154)),c_Predicate_Oconversep(U_19152,U_19153,U_19155)),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

cnf(f_4646_3,plain,
    c_Predicate_Oconversep(U_19152,U_19153,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19152,tc_fun(U_19153,tc_HOL_Obool))),U_19154),U_19155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19153,tc_fun(U_19152,tc_HOL_Obool))),c_Predicate_Oconversep(U_19152,U_19153,U_19154)),c_Predicate_Oconversep(U_19152,U_19153,U_19155)),
    inference(clausify,[status(thm)],[f_4646_2]) ).

fof(f_4647_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_4647_2,plain,
    ! [U_19159,U_19158,U_19157,U_19156] : c_Predicate_Oconversep(U_19156,U_19157,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19156,tc_fun(U_19157,tc_HOL_Obool))),U_19158),U_19159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19157,tc_fun(U_19156,tc_HOL_Obool))),c_Predicate_Oconversep(U_19156,U_19157,U_19158)),c_Predicate_Oconversep(U_19156,U_19157,U_19159)),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

cnf(f_4647_3,plain,
    c_Predicate_Oconversep(U_19156,U_19157,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19156,tc_fun(U_19157,tc_HOL_Obool))),U_19158),U_19159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19157,tc_fun(U_19156,tc_HOL_Obool))),c_Predicate_Oconversep(U_19156,U_19157,U_19158)),c_Predicate_Oconversep(U_19156,U_19157,U_19159)),
    inference(clausify,[status(thm)],[f_4647_2]) ).

fof(f_4648_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_4648_2,plain,
    ! [U_19164,U_19163,U_19162,U_19161,U_19160] : c_Predicate_Oconversep(U_19160,U_19161,c_Predicate_Opred__comp(U_19160,U_19162,U_19161,U_19163,U_19164)) = c_Predicate_Opred__comp(U_19161,U_19162,U_19160,c_Predicate_Oconversep(U_19162,U_19161,U_19164),c_Predicate_Oconversep(U_19160,U_19162,U_19163)),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

cnf(f_4648_3,plain,
    c_Predicate_Oconversep(U_19160,U_19161,c_Predicate_Opred__comp(U_19160,U_19162,U_19161,U_19163,U_19164)) = c_Predicate_Opred__comp(U_19161,U_19162,U_19160,c_Predicate_Oconversep(U_19162,U_19161,U_19164),c_Predicate_Oconversep(U_19160,U_19162,U_19163)),
    inference(clausify,[status(thm)],[f_4648_2]) ).

fof(f_4649_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_4649_2,plain,
    ! [U_19169,U_19168,U_19167,U_19166,U_19165] :
      ( hBOOL(hAPP(hAPP(U_19167,U_19169),U_19168))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19165,U_19166,U_19167),U_19168),U_19169)) ),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

fof(f_4649_3,plain,
    ! [U_19169,U_19168,U_19167] :
      ( ! [U_19166,U_19165] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19165,U_19166,U_19167),U_19168),U_19169))
      | hBOOL(hAPP(hAPP(U_19167,U_19169),U_19168)) ),
    inference(miniscope,[status(thm)],[f_4649_2]) ).

cnf(f_4649_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19165,U_19166,U_19167),U_19168),U_19169))
    | hBOOL(hAPP(hAPP(U_19167,U_19169),U_19168)) ),
    inference(clausify,[status(thm)],[f_4649_3]) ).

fof(f_4650_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_4650_2,plain,
    ! [U_19174,U_19173,U_19172,U_19171,U_19170] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19173,U_19174,U_19170),U_19172),U_19171))
      | ~ hBOOL(hAPP(hAPP(U_19170,U_19171),U_19172)) ),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

cnf(f_4650_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19173,U_19174,U_19170),U_19172),U_19171))
    | ~ hBOOL(hAPP(hAPP(U_19170,U_19171),U_19172)) ),
    inference(clausify,[status(thm)],[f_4650_2]) ).

fof(f_4651_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_4651_2,plain,
    ! [U_19179,U_19178,U_19177,U_19176,U_19175] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19175,U_19176,U_19177),U_19178),U_19179))
        | ~ hBOOL(hAPP(hAPP(U_19177,U_19179),U_19178)) )
      & ( hBOOL(hAPP(hAPP(U_19177,U_19179),U_19178))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19175,U_19176,U_19177),U_19178),U_19179)) ) ),
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

fof(f_4651_3,plain,
    ( ! [U_19189,U_19187,U_19185] :
        ( ! [U_19183,U_19181] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19181,U_19183,U_19185),U_19187),U_19189))
        | ~ hBOOL(hAPP(hAPP(U_19185,U_19189),U_19187)) )
    & ! [U_19188,U_19186,U_19184] :
        ( ! [U_19182,U_19180] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19180,U_19182,U_19184),U_19186),U_19188))
        | hBOOL(hAPP(hAPP(U_19184,U_19188),U_19186)) ) ),
    inference(miniscope,[status(thm)],[f_4651_2]) ).

cnf(f_4651_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19180,U_19182,U_19184),U_19186),U_19188))
    | hBOOL(hAPP(hAPP(U_19184,U_19188),U_19186)) ),
    inference(clausify,[status(thm)],[f_4651_3]) ).

cnf(f_4651_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19181,U_19183,U_19185),U_19187),U_19189))
    | ~ hBOOL(hAPP(hAPP(U_19185,U_19189),U_19187)) ),
    inference(clausify,[status(thm)],[f_4651_3]) ).

fof(f_4652_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_4652_2,plain,
    ! [U_19194,U_19193,U_19192,U_19191,U_19190] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19190,U_19191,U_19192),U_19193),U_19194))
        | ~ hBOOL(hAPP(hAPP(U_19192,U_19194),U_19193)) )
      & ( hBOOL(hAPP(hAPP(U_19192,U_19194),U_19193))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19190,U_19191,U_19192),U_19193),U_19194)) ) ),
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

fof(f_4652_3,plain,
    ( ! [U_19204,U_19202,U_19200] :
        ( ! [U_19198,U_19196] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19196,U_19198,U_19200),U_19202),U_19204))
        | ~ hBOOL(hAPP(hAPP(U_19200,U_19204),U_19202)) )
    & ! [U_19203,U_19201,U_19199] :
        ( ! [U_19197,U_19195] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19195,U_19197,U_19199),U_19201),U_19203))
        | hBOOL(hAPP(hAPP(U_19199,U_19203),U_19201)) ) ),
    inference(miniscope,[status(thm)],[f_4652_2]) ).

cnf(f_4652_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19195,U_19197,U_19199),U_19201),U_19203))
    | hBOOL(hAPP(hAPP(U_19199,U_19203),U_19201)) ),
    inference(clausify,[status(thm)],[f_4652_3]) ).

cnf(f_4652_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19196,U_19198,U_19200),U_19202),U_19204))
    | ~ hBOOL(hAPP(hAPP(U_19200,U_19204),U_19202)) ),
    inference(clausify,[status(thm)],[f_4652_3]) ).

fof(f_4653_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_4653_2,plain,
    ! [U_19207,U_19206,U_19205] : c_Predicate_Oconversep(U_19205,U_19206,c_Predicate_Oconversep(U_19206,U_19205,U_19207)) = U_19207,
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

cnf(f_4653_3,plain,
    c_Predicate_Oconversep(U_19205,U_19206,c_Predicate_Oconversep(U_19206,U_19205,U_19207)) = U_19207,
    inference(clausify,[status(thm)],[f_4653_2]) ).

fof(f_4654_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_4654_2,plain,
    ! [U_19208] : c_Predicate_Oconversep(U_19208,U_19208,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

cnf(f_4654_3,plain,
    c_Predicate_Oconversep(U_19208,U_19208,c_fequal) = c_fequal,
    inference(clausify,[status(thm)],[f_4654_2]) ).

fof(f_4655_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_4655_2,plain,
    ! [U_19211,U_19210,U_19209] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19209,U_19209,hAPP(hAPP(c_COMBB(tc_fun(U_19209,tc_HOL_Obool),tc_fun(U_19209,tc_HOL_Obool),U_19209),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19209),c_fNot)),c_fequal)),U_19210),U_19211))
        | U_19210 = U_19211 )
      & ( U_19210 != U_19211
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19209,U_19209,hAPP(hAPP(c_COMBB(tc_fun(U_19209,tc_HOL_Obool),tc_fun(U_19209,tc_HOL_Obool),U_19209),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19209),c_fNot)),c_fequal)),U_19210),U_19211)) ) ),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

fof(f_4655_3,plain,
    ( ! [U_19217,U_19215] :
        ( ! [U_19213] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19213,U_19213,hAPP(hAPP(c_COMBB(tc_fun(U_19213,tc_HOL_Obool),tc_fun(U_19213,tc_HOL_Obool),U_19213),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19213),c_fNot)),c_fequal)),U_19215),U_19217))
        | U_19215 = U_19217 )
    & ! [U_19216,U_19214] :
        ( ! [U_19212] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19212,U_19212,hAPP(hAPP(c_COMBB(tc_fun(U_19212,tc_HOL_Obool),tc_fun(U_19212,tc_HOL_Obool),U_19212),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19212),c_fNot)),c_fequal)),U_19214),U_19216))
        | U_19214 != U_19216 ) ),
    inference(miniscope,[status(thm)],[f_4655_2]) ).

cnf(f_4655_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19212,U_19212,hAPP(hAPP(c_COMBB(tc_fun(U_19212,tc_HOL_Obool),tc_fun(U_19212,tc_HOL_Obool),U_19212),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19212),c_fNot)),c_fequal)),U_19214),U_19216))
    | U_19214 != U_19216 ),
    inference(clausify,[status(thm)],[f_4655_3]) ).

cnf(f_4655_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19213,U_19213,hAPP(hAPP(c_COMBB(tc_fun(U_19213,tc_HOL_Obool),tc_fun(U_19213,tc_HOL_Obool),U_19213),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19213),c_fNot)),c_fequal)),U_19215),U_19217))
    | U_19215 = U_19217 ),
    inference(clausify,[status(thm)],[f_4655_3]) ).

fof(f_4656_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_4656_2,plain,
    ! [U_19222,U_19221,U_19220,U_19219,U_19218] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19218,U_19219,hAPP(hAPP(c_COMBC(U_19218,tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_fun(U_19219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19219,tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_fun(U_19219,tc_HOL_Obool)),U_19218),c_COMBC(U_19219,tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19219,tc_prod(U_19218,U_19219)),tc_fun(U_19219,tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),U_19218),hAPP(c_COMBB(tc_prod(U_19218,U_19219),tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool),U_19219),c_member(tc_prod(U_19218,U_19219)))),c_Product__Type_OPair(U_19218,U_19219)))),U_19220)),U_19221),U_19222))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19219,U_19218)),hAPP(hAPP(c_Product__Type_OPair(U_19219,U_19218),U_19221),U_19222)),hAPP(c_Relation_Oconverse(U_19218,U_19219),U_19220))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19219,U_19218)),hAPP(hAPP(c_Product__Type_OPair(U_19219,U_19218),U_19221),U_19222)),hAPP(c_Relation_Oconverse(U_19218,U_19219),U_19220)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19218,U_19219,hAPP(hAPP(c_COMBC(U_19218,tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_fun(U_19219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19219,tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_fun(U_19219,tc_HOL_Obool)),U_19218),c_COMBC(U_19219,tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19219,tc_prod(U_19218,U_19219)),tc_fun(U_19219,tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool)),U_19218),hAPP(c_COMBB(tc_prod(U_19218,U_19219),tc_fun(tc_fun(tc_prod(U_19218,U_19219),tc_HOL_Obool),tc_HOL_Obool),U_19219),c_member(tc_prod(U_19218,U_19219)))),c_Product__Type_OPair(U_19218,U_19219)))),U_19220)),U_19221),U_19222)) ) ),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

fof(f_4656_3,plain,
    ( ! [U_19232,U_19230,U_19228,U_19226,U_19224] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19224,U_19226,hAPP(hAPP(c_COMBC(U_19224,tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_fun(U_19226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19226,tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_fun(U_19226,tc_HOL_Obool)),U_19224),c_COMBC(U_19226,tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19226,tc_prod(U_19224,U_19226)),tc_fun(U_19226,tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),U_19224),hAPP(c_COMBB(tc_prod(U_19224,U_19226),tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool),U_19226),c_member(tc_prod(U_19224,U_19226)))),c_Product__Type_OPair(U_19224,U_19226)))),U_19228)),U_19230),U_19232))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19226,U_19224)),hAPP(hAPP(c_Product__Type_OPair(U_19226,U_19224),U_19230),U_19232)),hAPP(c_Relation_Oconverse(U_19224,U_19226),U_19228))) )
    & ! [U_19231,U_19229,U_19227,U_19225,U_19223] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19225,U_19223)),hAPP(hAPP(c_Product__Type_OPair(U_19225,U_19223),U_19229),U_19231)),hAPP(c_Relation_Oconverse(U_19223,U_19225),U_19227)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19223,U_19225,hAPP(hAPP(c_COMBC(U_19223,tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_fun(U_19225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19225,tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_fun(U_19225,tc_HOL_Obool)),U_19223),c_COMBC(U_19225,tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19225,tc_prod(U_19223,U_19225)),tc_fun(U_19225,tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),U_19223),hAPP(c_COMBB(tc_prod(U_19223,U_19225),tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool),U_19225),c_member(tc_prod(U_19223,U_19225)))),c_Product__Type_OPair(U_19223,U_19225)))),U_19227)),U_19229),U_19231)) ) ),
    inference(miniscope,[status(thm)],[f_4656_2]) ).

cnf(f_4656_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19225,U_19223)),hAPP(hAPP(c_Product__Type_OPair(U_19225,U_19223),U_19229),U_19231)),hAPP(c_Relation_Oconverse(U_19223,U_19225),U_19227)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19223,U_19225,hAPP(hAPP(c_COMBC(U_19223,tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_fun(U_19225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19225,tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_fun(U_19225,tc_HOL_Obool)),U_19223),c_COMBC(U_19225,tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19225,tc_prod(U_19223,U_19225)),tc_fun(U_19225,tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool)),U_19223),hAPP(c_COMBB(tc_prod(U_19223,U_19225),tc_fun(tc_fun(tc_prod(U_19223,U_19225),tc_HOL_Obool),tc_HOL_Obool),U_19225),c_member(tc_prod(U_19223,U_19225)))),c_Product__Type_OPair(U_19223,U_19225)))),U_19227)),U_19229),U_19231)) ),
    inference(clausify,[status(thm)],[f_4656_3]) ).

cnf(f_4656_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19224,U_19226,hAPP(hAPP(c_COMBC(U_19224,tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_fun(U_19226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19226,tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_fun(U_19226,tc_HOL_Obool)),U_19224),c_COMBC(U_19226,tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19226,tc_prod(U_19224,U_19226)),tc_fun(U_19226,tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool)),U_19224),hAPP(c_COMBB(tc_prod(U_19224,U_19226),tc_fun(tc_fun(tc_prod(U_19224,U_19226),tc_HOL_Obool),tc_HOL_Obool),U_19226),c_member(tc_prod(U_19224,U_19226)))),c_Product__Type_OPair(U_19224,U_19226)))),U_19228)),U_19230),U_19232))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19226,U_19224)),hAPP(hAPP(c_Product__Type_OPair(U_19226,U_19224),U_19230),U_19232)),hAPP(c_Relation_Oconverse(U_19224,U_19226),U_19228))) ),
    inference(clausify,[status(thm)],[f_4656_3]) ).

fof(f_4657_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_4657_2,plain,
    ! [U_19236,U_19235,U_19234,U_19233] : c_Lazy__Sequence_Oproduct(U_19233,U_19234,U_19235,U_19236) = hAPP(c_Lazy__Sequence_Obind(U_19233,tc_prod(U_19233,U_19234),U_19235),hAPP(hAPP(c_COMBB(tc_fun(U_19234,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234)),U_19233),c_Lazy__Sequence_Obind(U_19234,tc_prod(U_19233,U_19234),U_19236)),hAPP(hAPP(c_COMBB(tc_fun(U_19234,tc_prod(U_19233,U_19234)),tc_fun(U_19234,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234))),U_19233),hAPP(c_COMBB(tc_prod(U_19233,U_19234),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234)),U_19234),c_Lazy__Sequence_Osingle(tc_prod(U_19233,U_19234)))),c_Product__Type_OPair(U_19233,U_19234)))),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

cnf(f_4657_3,plain,
    c_Lazy__Sequence_Oproduct(U_19233,U_19234,U_19235,U_19236) = hAPP(c_Lazy__Sequence_Obind(U_19233,tc_prod(U_19233,U_19234),U_19235),hAPP(hAPP(c_COMBB(tc_fun(U_19234,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234)),U_19233),c_Lazy__Sequence_Obind(U_19234,tc_prod(U_19233,U_19234),U_19236)),hAPP(hAPP(c_COMBB(tc_fun(U_19234,tc_prod(U_19233,U_19234)),tc_fun(U_19234,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234))),U_19233),hAPP(c_COMBB(tc_prod(U_19233,U_19234),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19233,U_19234)),U_19234),c_Lazy__Sequence_Osingle(tc_prod(U_19233,U_19234)))),c_Product__Type_OPair(U_19233,U_19234)))),
    inference(clausify,[status(thm)],[f_4657_2]) ).

fof(f_4658_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_4658_2,plain,
    ! [U_19239,U_19238,U_19237] :
      ( hAPP(c_List_Otl(U_19238),c_List_Oreplicate(U_19238,U_19237,U_19239)) = c_List_Oreplicate(U_19238,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19237),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19239)
      | U_19237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

cnf(f_4658_3,plain,
    ( hAPP(c_List_Otl(U_19238),c_List_Oreplicate(U_19238,U_19237,U_19239)) = c_List_Oreplicate(U_19238,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19237),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19239)
    | U_19237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4658_2]) ).

fof(f_4659_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_4659_2,plain,
    ! [U_19242,U_19241,U_19240] : c_List_Oreplicate(U_19240,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19240)),hAPP(c_List_Ofilter(U_19240,hAPP(c_fequal,U_19241)),U_19242)),U_19241) = hAPP(c_List_Ofilter(U_19240,hAPP(c_fequal,U_19241)),U_19242),
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

cnf(f_4659_3,plain,
    c_List_Oreplicate(U_19240,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19240)),hAPP(c_List_Ofilter(U_19240,hAPP(c_fequal,U_19241)),U_19242)),U_19241) = hAPP(c_List_Ofilter(U_19240,hAPP(c_fequal,U_19241)),U_19242),
    inference(clausify,[status(thm)],[f_4659_2]) ).

fof(f_4660_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_4660_2,plain,
    ! [U_19245,U_19244,U_19243] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19243)),c_List_Oreplicate(U_19243,U_19244,U_19245)) = U_19244,
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

cnf(f_4660_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19243)),c_List_Oreplicate(U_19243,U_19244,U_19245)) = U_19244,
    inference(clausify,[status(thm)],[f_4660_2]) ).

fof(f_4661_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_4661_2,plain,
    ! [U_19249,U_19248,U_19247,U_19246] : hAPP(hAPP(c_List_Omap(U_19246,U_19247),hAPP(c_COMBK(U_19247,U_19246),U_19248)),U_19249) = c_List_Oreplicate(U_19247,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19246)),U_19249),U_19248),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

cnf(f_4661_3,plain,
    hAPP(hAPP(c_List_Omap(U_19246,U_19247),hAPP(c_COMBK(U_19247,U_19246),U_19248)),U_19249) = c_List_Oreplicate(U_19247,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19246)),U_19249),U_19248),
    inference(clausify,[status(thm)],[f_4661_2]) ).

fof(f_4662_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_4662_2,plain,
    ! [U_19253,U_19252,U_19251,U_19250] : hAPP(hAPP(c_List_Oappend(U_19250),c_List_Oreplicate(U_19250,U_19251,U_19252)),hAPP(hAPP(c_List_Olist_OCons(U_19250),U_19252),U_19253)) = hAPP(hAPP(c_List_Olist_OCons(U_19250),U_19252),hAPP(hAPP(c_List_Oappend(U_19250),c_List_Oreplicate(U_19250,U_19251,U_19252)),U_19253)),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

cnf(f_4662_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19250),c_List_Oreplicate(U_19250,U_19251,U_19252)),hAPP(hAPP(c_List_Olist_OCons(U_19250),U_19252),U_19253)) = hAPP(hAPP(c_List_Olist_OCons(U_19250),U_19252),hAPP(hAPP(c_List_Oappend(U_19250),c_List_Oreplicate(U_19250,U_19251,U_19252)),U_19253)),
    inference(clausify,[status(thm)],[f_4662_2]) ).

fof(f_4663_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_4663_2,plain,
    ! [U_19256,U_19255,U_19254] : c_List_Oreplicate(U_19254,hAPP(c_Nat_OSuc,U_19255),U_19256) = hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19256),c_List_Oreplicate(U_19254,U_19255,U_19256)),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

cnf(f_4663_3,plain,
    c_List_Oreplicate(U_19254,hAPP(c_Nat_OSuc,U_19255),U_19256) = hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19256),c_List_Oreplicate(U_19254,U_19255,U_19256)),
    inference(clausify,[status(thm)],[f_4663_2]) ).

fof(f_4664_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_4664_2,plain,
    ! [U_19259,U_19258,U_19257] : hAPP(c_List_Orev(U_19257),c_List_Oreplicate(U_19257,U_19258,U_19259)) = c_List_Oreplicate(U_19257,U_19258,U_19259),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

cnf(f_4664_3,plain,
    hAPP(c_List_Orev(U_19257),c_List_Oreplicate(U_19257,U_19258,U_19259)) = c_List_Oreplicate(U_19257,U_19258,U_19259),
    inference(clausify,[status(thm)],[f_4664_2]) ).

fof(f_4665_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_4665_2,plain,
    ! [U_19263,U_19262,U_19261,U_19260] : hAPP(hAPP(c_List_Otake(U_19260),U_19261),c_List_Oreplicate(U_19260,U_19262,U_19263)) = c_List_Oreplicate(U_19260,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19261),U_19262),U_19263),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

cnf(f_4665_3,plain,
    hAPP(hAPP(c_List_Otake(U_19260),U_19261),c_List_Oreplicate(U_19260,U_19262,U_19263)) = c_List_Oreplicate(U_19260,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19261),U_19262),U_19263),
    inference(clausify,[status(thm)],[f_4665_2]) ).

fof(f_4666_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_4666_2,plain,
    ! [U_19266,U_19265,U_19264] :
      ( hAPP(c_List_Ohd(U_19265),c_List_Oreplicate(U_19265,U_19264,U_19266)) = U_19266
      | U_19264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

cnf(f_4666_3,plain,
    ( hAPP(c_List_Ohd(U_19265),c_List_Oreplicate(U_19265,U_19264,U_19266)) = U_19266
    | U_19264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4666_2]) ).

fof(f_4667_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_4667_2,plain,
    ! [U_19270,U_19269,U_19268,U_19267] : hAPP(hAPP(c_List_Odrop(U_19267),U_19268),c_List_Oreplicate(U_19267,U_19269,U_19270)) = c_List_Oreplicate(U_19267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19269),U_19268),U_19270),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

cnf(f_4667_3,plain,
    hAPP(hAPP(c_List_Odrop(U_19267),U_19268),c_List_Oreplicate(U_19267,U_19269,U_19270)) = c_List_Oreplicate(U_19267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19269),U_19268),U_19270),
    inference(clausify,[status(thm)],[f_4667_2]) ).

fof(f_4668_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_4668_2,plain,
    ! [U_19273,U_19272,U_19271] :
      ( c_List_Olast(U_19272,c_List_Oreplicate(U_19272,U_19271,U_19273)) = U_19273
      | U_19271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

cnf(f_4668_3,plain,
    ( c_List_Olast(U_19272,c_List_Oreplicate(U_19272,U_19271,U_19273)) = U_19273
    | U_19271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4668_2]) ).

fof(f_4669_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_4669_2,plain,
    ! [U_19279,U_19278,U_19277,U_19276,U_19275,U_19274] : hAPP(hAPP(c_List_Ozip(U_19274,U_19275),c_List_Oreplicate(U_19274,U_19276,U_19277)),c_List_Oreplicate(U_19275,U_19278,U_19279)) = c_List_Oreplicate(tc_prod(U_19274,U_19275),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19276),U_19278),hAPP(hAPP(c_Product__Type_OPair(U_19274,U_19275),U_19277),U_19279)),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

cnf(f_4669_3,plain,
    hAPP(hAPP(c_List_Ozip(U_19274,U_19275),c_List_Oreplicate(U_19274,U_19276,U_19277)),c_List_Oreplicate(U_19275,U_19278,U_19279)) = c_List_Oreplicate(tc_prod(U_19274,U_19275),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19276),U_19278),hAPP(hAPP(c_Product__Type_OPair(U_19274,U_19275),U_19277),U_19279)),
    inference(clausify,[status(thm)],[f_4669_2]) ).

fof(f_4670_1,plain,
    ! [V_Pa_2,V_a_2,V_n_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,V_a_2)) )
      & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(V_Pa_2,V_a_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_4670_2,plain,
    ! [U_19285,U_19284,U_19283,U_19282] :
      ( ( ? [U_19281] :
            ( hBOOL(hAPP(U_19285,U_19281))
            & hBOOL(hAPP(hAPP(c_member(U_19282),U_19281),hAPP(c_List_Oset(U_19282),c_List_Oreplicate(U_19282,U_19283,U_19284)))) )
        | U_19283 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19285,U_19284)) )
      & ( ( U_19283 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19285,U_19284)) )
        | ! [U_19280] :
            ( ~ hBOOL(hAPP(U_19285,U_19280))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19282),U_19280),hAPP(c_List_Oset(U_19282),c_List_Oreplicate(U_19282,U_19283,U_19284)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

fof(f_4670_3,plain,
    ( ! [U_19293,U_19291,U_19289] :
        ( ! [U_19287] :
          ? [U_19281] :
            ( hBOOL(hAPP(U_19293,U_19281))
            & hBOOL(hAPP(hAPP(c_member(U_19287),U_19281),hAPP(c_List_Oset(U_19287),c_List_Oreplicate(U_19287,U_19289,U_19291)))) )
        | U_19289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19293,U_19291)) )
    & ! [U_19292,U_19290,U_19288] :
        ( ! [U_19286,U_19280] :
            ( ~ hBOOL(hAPP(U_19292,U_19280))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19286),U_19280),hAPP(c_List_Oset(U_19286),c_List_Oreplicate(U_19286,U_19288,U_19290)))) )
        | ( U_19288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19292,U_19290)) ) ) ),
    inference(miniscope,[status(thm)],[f_4670_2]) ).

fof(f_4670_4,plain,
    ( ! [U_19293,U_19291,U_19289] :
        ( ! [U_19287] :
            ( hBOOL(hAPP(U_19293,sK494(U_19293,U_19291,U_19289,U_19287)))
            & hBOOL(hAPP(hAPP(c_member(U_19287),sK494(U_19293,U_19291,U_19289,U_19287)),hAPP(c_List_Oset(U_19287),c_List_Oreplicate(U_19287,U_19289,U_19291)))) )
        | U_19289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19293,U_19291)) )
    & ! [U_19292,U_19290,U_19288] :
        ( ! [U_19286,U_19280] :
            ( ~ hBOOL(hAPP(U_19292,U_19280))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19286),U_19280),hAPP(c_List_Oset(U_19286),c_List_Oreplicate(U_19286,U_19288,U_19290)))) )
        | ( U_19288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19292,U_19290)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_19281,sK494(U_19293,U_19291,U_19289,U_19287))],[f_4670_3]) ).

cnf(f_4670_5,plain,
    ( hBOOL(hAPP(U_19292,U_19290))
    | ~ hBOOL(hAPP(U_19292,U_19280))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19286),U_19280),hAPP(c_List_Oset(U_19286),c_List_Oreplicate(U_19286,U_19288,U_19290)))) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

cnf(f_4670_6,plain,
    ( U_19288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19292,U_19280))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19286),U_19280),hAPP(c_List_Oset(U_19286),c_List_Oreplicate(U_19286,U_19288,U_19290)))) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

cnf(f_4670_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19287),sK494(U_19293,U_19291,U_19289,U_19287)),hAPP(c_List_Oset(U_19287),c_List_Oreplicate(U_19287,U_19289,U_19291))))
    | U_19289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19293,U_19291)) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

cnf(f_4670_8,plain,
    ( hBOOL(hAPP(U_19293,sK494(U_19293,U_19291,U_19289,U_19287)))
    | U_19289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19293,U_19291)) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

fof(f_4671_1,plain,
    ! [V_Pa_2,V_a_2,V_n_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,V_a_2)) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_Pa_2,V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_4671_2,plain,
    ! [U_19299,U_19298,U_19297,U_19296] :
      ( ( ! [U_19295] :
            ( hBOOL(hAPP(U_19299,U_19295))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19296),U_19295),hAPP(c_List_Oset(U_19296),c_List_Oreplicate(U_19296,U_19297,U_19298)))) )
        | ( U_19297 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19299,U_19298)) ) )
      & ( U_19297 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19299,U_19298))
        | ? [U_19294] :
            ( ~ hBOOL(hAPP(U_19299,U_19294))
            & hBOOL(hAPP(hAPP(c_member(U_19296),U_19294),hAPP(c_List_Oset(U_19296),c_List_Oreplicate(U_19296,U_19297,U_19298)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

fof(f_4671_3,plain,
    ( ! [U_19307,U_19305,U_19303] :
        ( ! [U_19301,U_19295] :
            ( hBOOL(hAPP(U_19307,U_19295))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19301),U_19295),hAPP(c_List_Oset(U_19301),c_List_Oreplicate(U_19301,U_19303,U_19305)))) )
        | ( U_19303 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19307,U_19305)) ) )
    & ! [U_19306,U_19304,U_19302] :
        ( ! [U_19300] :
          ? [U_19294] :
            ( ~ hBOOL(hAPP(U_19306,U_19294))
            & hBOOL(hAPP(hAPP(c_member(U_19300),U_19294),hAPP(c_List_Oset(U_19300),c_List_Oreplicate(U_19300,U_19302,U_19304)))) )
        | U_19302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19306,U_19304)) ) ),
    inference(miniscope,[status(thm)],[f_4671_2]) ).

fof(f_4671_4,plain,
    ( ! [U_19307,U_19305,U_19303] :
        ( ! [U_19301,U_19295] :
            ( hBOOL(hAPP(U_19307,U_19295))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19301),U_19295),hAPP(c_List_Oset(U_19301),c_List_Oreplicate(U_19301,U_19303,U_19305)))) )
        | ( U_19303 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19307,U_19305)) ) )
    & ! [U_19306,U_19304,U_19302] :
        ( ! [U_19300] :
            ( ~ hBOOL(hAPP(U_19306,sK495(U_19306,U_19304,U_19302,U_19300)))
            & hBOOL(hAPP(hAPP(c_member(U_19300),sK495(U_19306,U_19304,U_19302,U_19300)),hAPP(c_List_Oset(U_19300),c_List_Oreplicate(U_19300,U_19302,U_19304)))) )
        | U_19302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19306,U_19304)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_19294,sK495(U_19306,U_19304,U_19302,U_19300))],[f_4671_3]) ).

cnf(f_4671_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19300),sK495(U_19306,U_19304,U_19302,U_19300)),hAPP(c_List_Oset(U_19300),c_List_Oreplicate(U_19300,U_19302,U_19304))))
    | U_19302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19306,U_19304)) ),
    inference(clausify,[status(thm)],[f_4671_4]) ).

cnf(f_4671_6,plain,
    ( ~ hBOOL(hAPP(U_19306,sK495(U_19306,U_19304,U_19302,U_19300)))
    | U_19302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19306,U_19304)) ),
    inference(clausify,[status(thm)],[f_4671_4]) ).

cnf(f_4671_7,plain,
    ( ~ hBOOL(hAPP(U_19307,U_19305))
    | hBOOL(hAPP(U_19307,U_19295))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19301),U_19295),hAPP(c_List_Oset(U_19301),c_List_Oreplicate(U_19301,U_19303,U_19305)))) ),
    inference(clausify,[status(thm)],[f_4671_4]) ).

cnf(f_4671_8,plain,
    ( U_19303 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19307,U_19295))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19301),U_19295),hAPP(c_List_Oset(U_19301),c_List_Oreplicate(U_19301,U_19303,U_19305)))) ),
    inference(clausify,[status(thm)],[f_4671_4]) ).

fof(f_4672_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_4672_2,plain,
    ! [U_19312,U_19311,U_19310,U_19309,U_19308] :
      ( ( c_List_Oreplicate(U_19308,U_19309,U_19310) = c_List_Oreplicate(U_19308,U_19311,U_19312)
        | ( U_19310 != U_19312
          & U_19309 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_19309 != U_19311 )
      & ( ( ( U_19310 = U_19312
            | U_19309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_19309 = U_19311 )
        | c_List_Oreplicate(U_19308,U_19309,U_19310) != c_List_Oreplicate(U_19308,U_19311,U_19312) ) ),
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

fof(f_4672_3,plain,
    ( ! [U_19322,U_19320,U_19318,U_19316] :
        ( ! [U_19314] : c_List_Oreplicate(U_19314,U_19316,U_19318) = c_List_Oreplicate(U_19314,U_19320,U_19322)
        | ( U_19318 != U_19322
          & U_19316 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_19316 != U_19320 )
    & ! [U_19321,U_19319,U_19317,U_19315] :
        ( ! [U_19313] : c_List_Oreplicate(U_19313,U_19315,U_19317) != c_List_Oreplicate(U_19313,U_19319,U_19321)
        | ( ( U_19317 = U_19321
            | U_19315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_19315 = U_19319 ) ) ),
    inference(miniscope,[status(thm)],[f_4672_2]) ).

cnf(f_4672_4,plain,
    ( U_19315 = U_19319
    | c_List_Oreplicate(U_19313,U_19315,U_19317) != c_List_Oreplicate(U_19313,U_19319,U_19321) ),
    inference(clausify,[status(thm)],[f_4672_3]) ).

cnf(f_4672_5,plain,
    ( U_19317 = U_19321
    | U_19315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oreplicate(U_19313,U_19315,U_19317) != c_List_Oreplicate(U_19313,U_19319,U_19321) ),
    inference(clausify,[status(thm)],[f_4672_3]) ).

cnf(f_4672_6,plain,
    ( U_19316 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_19316 != U_19320
    | c_List_Oreplicate(U_19314,U_19316,U_19318) = c_List_Oreplicate(U_19314,U_19320,U_19322) ),
    inference(clausify,[status(thm)],[f_4672_3]) ).

cnf(f_4672_7,plain,
    ( U_19318 != U_19322
    | U_19316 != U_19320
    | c_List_Oreplicate(U_19314,U_19316,U_19318) = c_List_Oreplicate(U_19314,U_19320,U_19322) ),
    inference(clausify,[status(thm)],[f_4672_3]) ).

fof(f_4673_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_4673_2,plain,
    ! [U_19326,U_19325,U_19324,U_19323] :
      ( hAPP(hAPP(c_List_Onth(U_19325),c_List_Oreplicate(U_19325,U_19324,U_19326)),U_19323) = U_19326
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19323),U_19324)) ),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

cnf(f_4673_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19325),c_List_Oreplicate(U_19325,U_19324,U_19326)),U_19323) = U_19326
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19323),U_19324)) ),
    inference(clausify,[status(thm)],[f_4673_2]) ).

fof(f_4674_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_4674_2,plain,
    ! [U_19330,U_19329,U_19328,U_19327] : c_List_Oreplicate(U_19327,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19328),U_19329),U_19330) = hAPP(hAPP(c_List_Oappend(U_19327),c_List_Oreplicate(U_19327,U_19328,U_19330)),c_List_Oreplicate(U_19327,U_19329,U_19330)),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

cnf(f_4674_3,plain,
    c_List_Oreplicate(U_19327,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19328),U_19329),U_19330) = hAPP(hAPP(c_List_Oappend(U_19327),c_List_Oreplicate(U_19327,U_19328,U_19330)),c_List_Oreplicate(U_19327,U_19329,U_19330)),
    inference(clausify,[status(thm)],[f_4674_2]) ).

fof(f_4675_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_4675_2,plain,
    ! [U_19334,U_19333,U_19332,U_19331] : hAPP(hAPP(c_List_Oappend(U_19331),c_List_Oreplicate(U_19331,U_19332,U_19333)),c_List_Oreplicate(U_19331,U_19334,U_19333)) = hAPP(hAPP(c_List_Oappend(U_19331),c_List_Oreplicate(U_19331,U_19334,U_19333)),c_List_Oreplicate(U_19331,U_19332,U_19333)),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

cnf(f_4675_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19331),c_List_Oreplicate(U_19331,U_19332,U_19333)),c_List_Oreplicate(U_19331,U_19334,U_19333)) = hAPP(hAPP(c_List_Oappend(U_19331),c_List_Oreplicate(U_19331,U_19334,U_19333)),c_List_Oreplicate(U_19331,U_19332,U_19333)),
    inference(clausify,[status(thm)],[f_4675_2]) ).

fof(f_4676_1,plain,
    ! [V_n_2,T_b,V_x_2,V_Pa_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__replicate]) ).

fof(f_4676_2,plain,
    ! [U_19338,U_19337,U_19336,U_19335] :
      ( ( hAPP(c_List_Ofilter(U_19337,U_19335),c_List_Oreplicate(U_19337,U_19338,U_19336)) = c_List_Olist_ONil(U_19337)
        | hBOOL(hAPP(U_19335,U_19336)) )
      & ( hAPP(c_List_Ofilter(U_19337,U_19335),c_List_Oreplicate(U_19337,U_19338,U_19336)) = c_List_Oreplicate(U_19337,U_19338,U_19336)
        | ~ hBOOL(hAPP(U_19335,U_19336)) ) ),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

fof(f_4676_3,plain,
    ( ! [U_19346,U_19344,U_19342,U_19340] :
        ( hAPP(c_List_Ofilter(U_19344,U_19340),c_List_Oreplicate(U_19344,U_19346,U_19342)) = c_List_Olist_ONil(U_19344)
        | hBOOL(hAPP(U_19340,U_19342)) )
    & ! [U_19345,U_19343,U_19341,U_19339] :
        ( hAPP(c_List_Ofilter(U_19343,U_19339),c_List_Oreplicate(U_19343,U_19345,U_19341)) = c_List_Oreplicate(U_19343,U_19345,U_19341)
        | ~ hBOOL(hAPP(U_19339,U_19341)) ) ),
    inference(miniscope,[status(thm)],[f_4676_2]) ).

cnf(f_4676_4,plain,
    ( hAPP(c_List_Ofilter(U_19343,U_19339),c_List_Oreplicate(U_19343,U_19345,U_19341)) = c_List_Oreplicate(U_19343,U_19345,U_19341)
    | ~ hBOOL(hAPP(U_19339,U_19341)) ),
    inference(clausify,[status(thm)],[f_4676_3]) ).

cnf(f_4676_5,plain,
    ( hAPP(c_List_Ofilter(U_19344,U_19340),c_List_Oreplicate(U_19344,U_19346,U_19342)) = c_List_Olist_ONil(U_19344)
    | hBOOL(hAPP(U_19340,U_19342)) ),
    inference(clausify,[status(thm)],[f_4676_3]) ).

fof(f_4677_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_4677_2,plain,
    ! [U_19348,U_19347] : c_List_Oconcat(U_19347,c_List_Oreplicate(tc_List_Olist(U_19347),U_19348,c_List_Olist_ONil(U_19347))) = c_List_Olist_ONil(U_19347),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

cnf(f_4677_3,plain,
    c_List_Oconcat(U_19347,c_List_Oreplicate(tc_List_Olist(U_19347),U_19348,c_List_Olist_ONil(U_19347))) = c_List_Olist_ONil(U_19347),
    inference(clausify,[status(thm)],[f_4677_2]) ).

fof(f_4678_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_4678_2,plain,
    ! [U_19350,U_19349] : c_List_Oreplicate(U_19349,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19350) = c_List_Olist_ONil(U_19349),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

cnf(f_4678_3,plain,
    c_List_Oreplicate(U_19349,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19350) = c_List_Olist_ONil(U_19349),
    inference(clausify,[status(thm)],[f_4678_2]) ).

fof(f_4679_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_4679_2,plain,
    ! [U_19353,U_19352,U_19351] :
      ( ( c_List_Olist_ONil(U_19351) = c_List_Oreplicate(U_19351,U_19352,U_19353)
        | U_19352 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_19352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(U_19351) != c_List_Oreplicate(U_19351,U_19352,U_19353) ) ),
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

fof(f_4679_3,plain,
    ( ! [U_19359,U_19357] :
        ( ! [U_19355] : c_List_Olist_ONil(U_19355) = c_List_Oreplicate(U_19355,U_19357,U_19359)
        | U_19357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19358,U_19356] :
        ( ! [U_19354] : c_List_Olist_ONil(U_19354) != c_List_Oreplicate(U_19354,U_19356,U_19358)
        | U_19356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4679_2]) ).

cnf(f_4679_4,plain,
    ( c_List_Olist_ONil(U_19354) != c_List_Oreplicate(U_19354,U_19356,U_19358)
    | U_19356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

cnf(f_4679_5,plain,
    ( c_List_Olist_ONil(U_19355) = c_List_Oreplicate(U_19355,U_19357,U_19359)
    | U_19357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

fof(f_4680_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_4680_2,plain,
    ! [U_19362,U_19361,U_19360] :
      ( ( c_List_Oreplicate(U_19360,U_19361,U_19362) = c_List_Olist_ONil(U_19360)
        | U_19361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_19361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(U_19360,U_19361,U_19362) != c_List_Olist_ONil(U_19360) ) ),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

fof(f_4680_3,plain,
    ( ! [U_19368,U_19366] :
        ( ! [U_19364] : c_List_Oreplicate(U_19364,U_19366,U_19368) = c_List_Olist_ONil(U_19364)
        | U_19366 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19367,U_19365] :
        ( ! [U_19363] : c_List_Oreplicate(U_19363,U_19365,U_19367) != c_List_Olist_ONil(U_19363)
        | U_19365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4680_2]) ).

cnf(f_4680_4,plain,
    ( c_List_Oreplicate(U_19363,U_19365,U_19367) != c_List_Olist_ONil(U_19363)
    | U_19365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4680_3]) ).

cnf(f_4680_5,plain,
    ( c_List_Oreplicate(U_19364,U_19366,U_19368) = c_List_Olist_ONil(U_19364)
    | U_19366 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4680_3]) ).

fof(f_4681_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_4681_2,plain,
    ! [U_19373,U_19372,U_19371,U_19370,U_19369] : hAPP(hAPP(c_List_Omap(U_19369,U_19370),U_19371),c_List_Oreplicate(U_19369,U_19372,U_19373)) = c_List_Oreplicate(U_19370,U_19372,hAPP(U_19371,U_19373)),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

cnf(f_4681_3,plain,
    hAPP(hAPP(c_List_Omap(U_19369,U_19370),U_19371),c_List_Oreplicate(U_19369,U_19372,U_19373)) = c_List_Oreplicate(U_19370,U_19372,hAPP(U_19371,U_19373)),
    inference(clausify,[status(thm)],[f_4681_2]) ).

fof(f_4682_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_4682_2,plain,
    ! [U_19377,U_19376,U_19375,U_19374] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_19374),U_19375),hAPP(c_List_Oset(U_19374),c_List_Oreplicate(U_19374,U_19376,U_19377))))
        | U_19376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_19375 != U_19377 )
      & ( ( U_19376 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_19375 = U_19377 )
        | ~ hBOOL(hAPP(hAPP(c_member(U_19374),U_19375),hAPP(c_List_Oset(U_19374),c_List_Oreplicate(U_19374,U_19376,U_19377)))) ) ),
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

fof(f_4682_3,plain,
    ( ! [U_19385,U_19383,U_19381] :
        ( ! [U_19379] : hBOOL(hAPP(hAPP(c_member(U_19379),U_19381),hAPP(c_List_Oset(U_19379),c_List_Oreplicate(U_19379,U_19383,U_19385))))
        | U_19383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_19381 != U_19385 )
    & ! [U_19384,U_19382,U_19380] :
        ( ! [U_19378] : ~ hBOOL(hAPP(hAPP(c_member(U_19378),U_19380),hAPP(c_List_Oset(U_19378),c_List_Oreplicate(U_19378,U_19382,U_19384))))
        | ( U_19382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_19380 = U_19384 ) ) ),
    inference(miniscope,[status(thm)],[f_4682_2]) ).

cnf(f_4682_4,plain,
    ( U_19380 = U_19384
    | ~ hBOOL(hAPP(hAPP(c_member(U_19378),U_19380),hAPP(c_List_Oset(U_19378),c_List_Oreplicate(U_19378,U_19382,U_19384)))) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

cnf(f_4682_5,plain,
    ( U_19382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19378),U_19380),hAPP(c_List_Oset(U_19378),c_List_Oreplicate(U_19378,U_19382,U_19384)))) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

cnf(f_4682_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19379),U_19381),hAPP(c_List_Oset(U_19379),c_List_Oreplicate(U_19379,U_19383,U_19385))))
    | U_19383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_19381 != U_19385 ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

fof(f_4683_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_4683_2,plain,
    ! [U_19388,U_19387,U_19386] : hAPP(hAPP(c_List_Oappend(U_19386),c_List_Oreplicate(U_19386,U_19387,U_19388)),hAPP(hAPP(c_List_Olist_OCons(U_19386),U_19388),c_List_Olist_ONil(U_19386))) = hAPP(hAPP(c_List_Olist_OCons(U_19386),U_19388),c_List_Oreplicate(U_19386,U_19387,U_19388)),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

cnf(f_4683_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19386),c_List_Oreplicate(U_19386,U_19387,U_19388)),hAPP(hAPP(c_List_Olist_OCons(U_19386),U_19388),c_List_Olist_ONil(U_19386))) = hAPP(hAPP(c_List_Olist_OCons(U_19386),U_19388),c_List_Oreplicate(U_19386,U_19387,U_19388)),
    inference(clausify,[status(thm)],[f_4683_2]) ).

fof(f_4684_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_4684_2,plain,
    ! [U_19391,U_19390,U_19389] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19389),hAPP(c_COMBK(U_19389,tc_Nat_Onat),U_19390)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19391)) = c_List_Oreplicate(U_19389,U_19391,U_19390),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

cnf(f_4684_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19389),hAPP(c_COMBK(U_19389,tc_Nat_Onat),U_19390)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19391)) = c_List_Oreplicate(U_19389,U_19391,U_19390),
    inference(clausify,[status(thm)],[f_4684_2]) ).

fof(f_4685_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_4685_2,plain,
    ! [U_19394,U_19393,U_19392] :
      ( ( hAPP(c_List_Oset(U_19393),c_List_Oreplicate(U_19393,U_19392,U_19394)) = hAPP(hAPP(c_Set_Oinsert(U_19393),U_19394),c_Orderings_Obot__class_Obot(tc_fun(U_19393,tc_HOL_Obool)))
        | U_19392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_List_Oset(U_19393),c_List_Oreplicate(U_19393,U_19392,U_19394)) = c_Orderings_Obot__class_Obot(tc_fun(U_19393,tc_HOL_Obool))
        | U_19392 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

fof(f_4685_3,plain,
    ( ! [U_19400,U_19398,U_19396] :
        ( hAPP(c_List_Oset(U_19398),c_List_Oreplicate(U_19398,U_19396,U_19400)) = hAPP(hAPP(c_Set_Oinsert(U_19398),U_19400),c_Orderings_Obot__class_Obot(tc_fun(U_19398,tc_HOL_Obool)))
        | U_19396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19399,U_19397,U_19395] :
        ( hAPP(c_List_Oset(U_19397),c_List_Oreplicate(U_19397,U_19395,U_19399)) = c_Orderings_Obot__class_Obot(tc_fun(U_19397,tc_HOL_Obool))
        | U_19395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4685_2]) ).

cnf(f_4685_4,plain,
    ( hAPP(c_List_Oset(U_19397),c_List_Oreplicate(U_19397,U_19395,U_19399)) = c_Orderings_Obot__class_Obot(tc_fun(U_19397,tc_HOL_Obool))
    | U_19395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4685_3]) ).

cnf(f_4685_5,plain,
    ( hAPP(c_List_Oset(U_19398),c_List_Oreplicate(U_19398,U_19396,U_19400)) = hAPP(hAPP(c_Set_Oinsert(U_19398),U_19400),c_Orderings_Obot__class_Obot(tc_fun(U_19398,tc_HOL_Obool)))
    | U_19396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4685_3]) ).

fof(f_4686_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_4686_2,plain,
    ! [U_19403,U_19402,U_19401] :
      ( hAPP(c_List_Oset(U_19402),c_List_Oreplicate(U_19402,U_19401,U_19403)) = hAPP(hAPP(c_Set_Oinsert(U_19402),U_19403),c_Orderings_Obot__class_Obot(tc_fun(U_19402,tc_HOL_Obool)))
      | U_19401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

cnf(f_4686_3,plain,
    ( hAPP(c_List_Oset(U_19402),c_List_Oreplicate(U_19402,U_19401,U_19403)) = hAPP(hAPP(c_Set_Oinsert(U_19402),U_19403),c_Orderings_Obot__class_Obot(tc_fun(U_19402,tc_HOL_Obool)))
    | U_19401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4686_2]) ).

fof(f_4687_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_4687_2,plain,
    ! [U_19406,U_19405,U_19404] : hAPP(c_List_Oset(U_19404),c_List_Oreplicate(U_19404,hAPP(c_Nat_OSuc,U_19405),U_19406)) = hAPP(hAPP(c_Set_Oinsert(U_19404),U_19406),c_Orderings_Obot__class_Obot(tc_fun(U_19404,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

cnf(f_4687_3,plain,
    hAPP(c_List_Oset(U_19404),c_List_Oreplicate(U_19404,hAPP(c_Nat_OSuc,U_19405),U_19406)) = hAPP(hAPP(c_Set_Oinsert(U_19404),U_19406),c_Orderings_Obot__class_Obot(tc_fun(U_19404,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4687_2]) ).

fof(f_4688_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_4688_2,plain,
    ! [U_19408,U_19407] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19407),U_19408) = c_Lazy__Sequence_Oappend(tc_List_Olist(U_19407),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(U_19407)),c_List_Olist_ONil(U_19407)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_19408)),hAPP(c_Lazy__Sequence_Obind(tc_prod(U_19407,tc_List_Olist(U_19407)),tc_List_Olist(U_19407),c_Lazy__Sequence_Oproduct(U_19407,tc_List_Olist(U_19407),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19407,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19408),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19408),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(U_19407,tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19407),tc_List_Olist(U_19407)),tc_fun(tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),U_19407),hAPP(c_COMBB(tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407)),tc_List_Olist(U_19407)),c_Lazy__Sequence_Osingle(tc_List_Olist(U_19407)))),c_List_Olist_OCons(U_19407))))),c_Lazy__Sequence_Oempty(tc_List_Olist(U_19407))))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19407) ),
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

cnf(f_4688_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19407),U_19408) = c_Lazy__Sequence_Oappend(tc_List_Olist(U_19407),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(U_19407)),c_List_Olist_ONil(U_19407)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_19408)),hAPP(c_Lazy__Sequence_Obind(tc_prod(U_19407,tc_List_Olist(U_19407)),tc_List_Olist(U_19407),c_Lazy__Sequence_Oproduct(U_19407,tc_List_Olist(U_19407),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19407,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19408),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19408),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(U_19407,tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19407),tc_List_Olist(U_19407)),tc_fun(tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407))),U_19407),hAPP(c_COMBB(tc_List_Olist(U_19407),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19407)),tc_List_Olist(U_19407)),c_Lazy__Sequence_Osingle(tc_List_Olist(U_19407)))),c_List_Olist_OCons(U_19407))))),c_Lazy__Sequence_Oempty(tc_List_Olist(U_19407))))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19407) ),
    inference(clausify,[status(thm)],[f_4688_2]) ).

fof(f_4689_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_4689_2,plain,
    ! [U_19410,U_19409] : c_Predicate_Opred__comp(U_19409,U_19409,U_19409,c_fequal,c_Predicate_Opred__comp(U_19409,U_19409,U_19409,U_19410,c_fequal)) = U_19410,
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

cnf(f_4689_3,plain,
    c_Predicate_Opred__comp(U_19409,U_19409,U_19409,c_fequal,c_Predicate_Opred__comp(U_19409,U_19409,U_19409,U_19410,c_fequal)) = U_19410,
    inference(clausify,[status(thm)],[f_4689_2]) ).

fof(f_4690_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_4690_2,plain,
    ! [U_19413,U_19412,U_19411] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(U_19411,U_19412),U_19413) = c_Lazy__Sequence_Oproduct(U_19411,U_19412,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19411,U_19413),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19412,U_19413))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19412)
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19411) ),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

cnf(f_4690_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(U_19411,U_19412),U_19413) = c_Lazy__Sequence_Oproduct(U_19411,U_19412,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19411,U_19413),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19412,U_19413))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19412)
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19411) ),
    inference(clausify,[status(thm)],[f_4690_2]) ).

fof(f_4691_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_4691_2,plain,
    ! [U_19417,U_19416,U_19415,U_19414] : hAPP(c_New__DSequence_Opos__union(U_19414,U_19415,U_19416),U_19417) = c_Lazy__Sequence_Oappend(U_19414,hAPP(U_19415,U_19417),hAPP(U_19416,U_19417)),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

cnf(f_4691_3,plain,
    hAPP(c_New__DSequence_Opos__union(U_19414,U_19415,U_19416),U_19417) = c_Lazy__Sequence_Oappend(U_19414,hAPP(U_19415,U_19417),hAPP(U_19416,U_19417)),
    inference(clausify,[status(thm)],[f_4691_2]) ).

fof(f_4692_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_4692_2,plain,
    ! [U_19420,U_19419,U_19418] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19418)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19418,U_19419,U_19420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19418)),U_19420)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

cnf(f_4692_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19418)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19418,U_19419,U_19420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19418)),U_19420)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4692_2]) ).

fof(f_4693_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_4693_2,plain,
    ! [U_19424,U_19423,U_19422,U_19421] : c_Lazy__Sequence_Oappend(U_19421,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19421,U_19422,U_19423),U_19424) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19421,U_19422,c_Lazy__Sequence_Oappend(U_19421,U_19423,U_19424)),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

cnf(f_4693_3,plain,
    c_Lazy__Sequence_Oappend(U_19421,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19421,U_19422,U_19423),U_19424) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19421,U_19422,c_Lazy__Sequence_Oappend(U_19421,U_19423,U_19424)),
    inference(clausify,[status(thm)],[f_4693_2]) ).

fof(f_4694_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_4694_2,plain,
    ! [U_19429,U_19428,U_19427,U_19426,U_19425] :
      ( ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_19425,U_19426,U_19427) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19425,U_19428,U_19429)
        | U_19427 != U_19429
        | U_19426 != U_19428 )
      & ( ( U_19427 = U_19429
          & U_19426 = U_19428 )
        | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19425,U_19426,U_19427) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19425,U_19428,U_19429) ) ),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

fof(f_4694_3,plain,
    ( ! [U_19439,U_19437,U_19435,U_19433] :
        ( ! [U_19431] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19431,U_19433,U_19435) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19431,U_19437,U_19439)
        | U_19435 != U_19439
        | U_19433 != U_19437 )
    & ! [U_19438,U_19436,U_19434,U_19432] :
        ( ! [U_19430] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19432,U_19434) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19436,U_19438)
        | ( U_19434 = U_19438
          & U_19432 = U_19436 ) ) ),
    inference(miniscope,[status(thm)],[f_4694_2]) ).

cnf(f_4694_4,plain,
    ( U_19432 = U_19436
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19432,U_19434) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19436,U_19438) ),
    inference(clausify,[status(thm)],[f_4694_3]) ).

cnf(f_4694_5,plain,
    ( U_19434 = U_19438
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19432,U_19434) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19430,U_19436,U_19438) ),
    inference(clausify,[status(thm)],[f_4694_3]) ).

cnf(f_4694_6,plain,
    ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_19431,U_19433,U_19435) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19431,U_19437,U_19439)
    | U_19435 != U_19439
    | U_19433 != U_19437 ),
    inference(clausify,[status(thm)],[f_4694_3]) ).

fof(f_4695_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_4695_2,plain,
    ! [U_19445,U_19444,U_19443,U_19442,U_19441,U_19440] : c_New__Random__Sequence_Opos__union(U_19440,U_19441,U_19442,U_19443,U_19444,U_19445) = c_New__DSequence_Opos__union(U_19440,hAPP(hAPP(hAPP(U_19441,U_19443),U_19444),U_19445),hAPP(hAPP(hAPP(U_19442,U_19443),U_19444),U_19445)),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

cnf(f_4695_3,plain,
    c_New__Random__Sequence_Opos__union(U_19440,U_19441,U_19442,U_19443,U_19444,U_19445) = c_New__DSequence_Opos__union(U_19440,hAPP(hAPP(hAPP(U_19441,U_19443),U_19444),U_19445),hAPP(hAPP(hAPP(U_19442,U_19443),U_19444),U_19445)),
    inference(clausify,[status(thm)],[f_4695_2]) ).

fof(f_4696_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_4696_2,plain,
    ! [U_19449,U_19448,U_19447,U_19446] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19446,U_19447),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19446,U_19448,U_19449)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19447,U_19448)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19446,U_19447),U_19449))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

cnf(f_4696_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19446,U_19447),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19446,U_19448,U_19449)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19447,U_19448)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19446,U_19447),U_19449))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4696_2]) ).

fof(f_4697_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_4697_2,plain,
    ! [U_19451,U_19450] :
      ( ( c_Lazy__Sequence_Osmall__lazy_H(U_19450,U_19451) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19451),c_Lazy__Sequence_Osmall__lazy_H(U_19450,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19451),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19450),U_19451)) )
      & ( c_Lazy__Sequence_Osmall__lazy_H(U_19450,U_19451) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19450),U_19451)) ) ),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

fof(f_4697_3,plain,
    ( ! [U_19455,U_19453] :
        ( c_Lazy__Sequence_Osmall__lazy_H(U_19453,U_19455) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19455),c_Lazy__Sequence_Osmall__lazy_H(U_19453,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19455),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19453),U_19455)) )
    & ! [U_19454,U_19452] :
        ( c_Lazy__Sequence_Osmall__lazy_H(U_19452,U_19454) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19452),U_19454)) ) ),
    inference(miniscope,[status(thm)],[f_4697_2]) ).

cnf(f_4697_4,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19452,U_19454) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19452),U_19454)) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

cnf(f_4697_5,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19453,U_19455) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19455),c_Lazy__Sequence_Osmall__lazy_H(U_19453,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19455),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19453),U_19455)) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

fof(f_4698_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_4698_2,plain,
    ! [U_19457,U_19456] :
      ( ( ( c_Lazy__Sequence_Osmall__lazy_H(U_19456,U_19457) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19457),c_Lazy__Sequence_Osmall__lazy_H(U_19456,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19457),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19456),U_19457)) )
        & ( c_Lazy__Sequence_Osmall__lazy_H(U_19456,U_19457) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19456),U_19457)) ) )
      | ~ 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_19456),U_19457))) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

cnf(f_4698_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19456,U_19457) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19456),U_19457))
    | ~ 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_19456),U_19457))) ),
    inference(clausify,[status(thm)],[f_4698_2]) ).

cnf(f_4698_4,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19456,U_19457) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19457),c_Lazy__Sequence_Osmall__lazy_H(U_19456,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19457),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19456),U_19457))
    | ~ 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_19456),U_19457))) ),
    inference(clausify,[status(thm)],[f_4698_2]) ).

fof(f_4699_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_4699_2,plain,
    ! [U_19458] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,U_19458) = c_Lazy__Sequence_Osmall__lazy_H(U_19458,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_19458)),
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

cnf(f_4699_3,plain,
    c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,U_19458) = c_Lazy__Sequence_Osmall__lazy_H(U_19458,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_19458)),
    inference(clausify,[status(thm)],[f_4699_2]) ).

fof(f_4700_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_d,B_i] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_4700_2,plain,
    ! [U_19463,U_19462,U_19461] :
      ( hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
      | ? [U_19460,U_19459] :
          ( ~ hBOOL(hAPP(hAPP(U_19463,U_19460),U_19459))
          & ( hBOOL(hAPP(hAPP(U_19463,U_19460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19459),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19460),U_19459)) )
          & 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_19460),U_19459))) )
      | ~ 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_19461),U_19462))) ),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

fof(f_4700_3,plain,
    ! [U_19463,U_19462,U_19461] :
      ( hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
      | ? [U_19459] :
          ( ~ hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),U_19459))
          & ( hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19459),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK496(U_19463,U_19462,U_19461)),U_19459)) )
          & 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),sK496(U_19463,U_19462,U_19461)),U_19459))) )
      | ~ 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_19461),U_19462))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_19460,sK496(U_19463,U_19462,U_19461))],[f_4700_2]) ).

fof(f_4700_4,plain,
    ! [U_19463,U_19462,U_19461] :
      ( hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
      | ( ~ hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461)))
        & ( hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK497(U_19463,U_19462,U_19461)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461))) )
        & 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),sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461)))) )
      | ~ 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_19461),U_19462))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_19459,sK497(U_19463,U_19462,U_19461))],[f_4700_3]) ).

cnf(f_4700_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),sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461))))
    | hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
    | ~ 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_19461),U_19462))) ),
    inference(clausify,[status(thm)],[f_4700_4]) ).

cnf(f_4700_6,plain,
    ( hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK497(U_19463,U_19462,U_19461)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461)))
    | hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
    | ~ 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_19461),U_19462))) ),
    inference(clausify,[status(thm)],[f_4700_4]) ).

cnf(f_4700_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19463,sK496(U_19463,U_19462,U_19461)),sK497(U_19463,U_19462,U_19461)))
    | hBOOL(hAPP(hAPP(U_19463,U_19461),U_19462))
    | ~ 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_19461),U_19462))) ),
    inference(clausify,[status(thm)],[f_4700_4]) ).

fof(f_4701_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_4701_2,plain,
    ! [U_19465,U_19464] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19464)),U_19465) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19464,tc_Lazy__Sequence_Olazy__sequence(U_19464)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19464,tc_Lazy__Sequence_Olazy__sequence(U_19464),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19464),tc_Nat_Onat),U_19464),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19464),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_19464)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19464)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_19464),U_19465)),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

cnf(f_4701_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19464)),U_19465) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19464,tc_Lazy__Sequence_Olazy__sequence(U_19464)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19464,tc_Lazy__Sequence_Olazy__sequence(U_19464),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19464),tc_Nat_Onat),U_19464),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19464),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_19464)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19464)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_19464),U_19465)),
    inference(clausify,[status(thm)],[f_4701_2]) ).

fof(f_4702_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_4702_2,plain,
    ! [U_19468,U_19467,U_19466] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19466,U_19467),U_19468) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19466,tc_Lazy__Sequence_Olazy__sequence(U_19466)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19466,tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_19466,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),U_19466),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_19466),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19466)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_19466,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),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_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),U_19466),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_19466))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_19466),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_19467))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19466,U_19467))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(U_19466),U_19468)),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

cnf(f_4702_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19466,U_19467),U_19468) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19466,tc_Lazy__Sequence_Olazy__sequence(U_19466)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19466,tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_19466,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),U_19466),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_19466),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19466)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_19466,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),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_19466),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19466),tc_Nat_Onat)),U_19466),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_19466))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_19466),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_19467))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19466,U_19467))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(U_19466),U_19468)),
    inference(clausify,[status(thm)],[f_4702_2]) ).

fof(f_4703_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_4703_2,plain,
    ! [U_19473,U_19472,U_19471,U_19470,U_19469] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19469,U_19470,U_19471,U_19472,U_19473) = c_Option_Ooption_Ooption__case(U_19469,tc_prod(U_19470,tc_Lazy__Sequence_Olazy__sequence(U_19470)),U_19471,hAPP(c_Product__Type_Oprod_Oprod__case(U_19470,tc_Lazy__Sequence_Olazy__sequence(U_19470),U_19469),U_19472),hAPP(c_Lazy__Sequence_Oyield(U_19470),U_19473)),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

cnf(f_4703_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19469,U_19470,U_19471,U_19472,U_19473) = c_Option_Ooption_Ooption__case(U_19469,tc_prod(U_19470,tc_Lazy__Sequence_Olazy__sequence(U_19470)),U_19471,hAPP(c_Product__Type_Oprod_Oprod__case(U_19470,tc_Lazy__Sequence_Olazy__sequence(U_19470),U_19469),U_19472),hAPP(c_Lazy__Sequence_Oyield(U_19470),U_19473)),
    inference(clausify,[status(thm)],[f_4703_2]) ).

fof(f_4704_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_4704_2,plain,
    ! [U_19474] : c_Lazy__Sequence_Oyieldn(U_19474) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_19474),U_19474,c_Lazy__Sequence_Oyield(U_19474)),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

cnf(f_4704_3,plain,
    c_Lazy__Sequence_Oyieldn(U_19474) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_19474),U_19474,c_Lazy__Sequence_Oyield(U_19474)),
    inference(clausify,[status(thm)],[f_4704_2]) ).

fof(f_4705_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_4705_2,plain,
    ! [U_19480,U_19479,U_19478,U_19477,U_19476,U_19475] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19475,U_19476,U_19477,U_19478,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19476,U_19479,U_19480)) = hAPP(hAPP(U_19478,U_19479),U_19480),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

cnf(f_4705_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19475,U_19476,U_19477,U_19478,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19476,U_19479,U_19480)) = hAPP(hAPP(U_19478,U_19479),U_19480),
    inference(clausify,[status(thm)],[f_4705_2]) ).

fof(f_4706_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_4706_2,plain,
    ! [U_19486,U_19485,U_19484,U_19483,U_19482] :
      ( c_Relation_Orefl__on(U_19484,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(U_19484,tc_HOL_Obool)),U_19483),U_19485),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(tc_prod(U_19484,U_19484),tc_HOL_Obool)),U_19483),U_19486))
      | ? [U_19481] :
          ( ~ c_Relation_Orefl__on(U_19484,hAPP(U_19485,U_19481),hAPP(U_19486,U_19481))
          & hBOOL(hAPP(hAPP(c_member(U_19482),U_19481),U_19483)) ) ),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

fof(f_4706_3,plain,
    ! [U_19486,U_19485,U_19484,U_19483,U_19482] :
      ( c_Relation_Orefl__on(U_19484,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(U_19484,tc_HOL_Obool)),U_19483),U_19485),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(tc_prod(U_19484,U_19484),tc_HOL_Obool)),U_19483),U_19486))
      | ( ~ c_Relation_Orefl__on(U_19484,hAPP(U_19485,sK498(U_19486,U_19485,U_19484,U_19483,U_19482)),hAPP(U_19486,sK498(U_19486,U_19485,U_19484,U_19483,U_19482)))
        & hBOOL(hAPP(hAPP(c_member(U_19482),sK498(U_19486,U_19485,U_19484,U_19483,U_19482)),U_19483)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_19481,sK498(U_19486,U_19485,U_19484,U_19483,U_19482))],[f_4706_2]) ).

cnf(f_4706_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19482),sK498(U_19486,U_19485,U_19484,U_19483,U_19482)),U_19483))
    | c_Relation_Orefl__on(U_19484,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(U_19484,tc_HOL_Obool)),U_19483),U_19485),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(tc_prod(U_19484,U_19484),tc_HOL_Obool)),U_19483),U_19486)) ),
    inference(clausify,[status(thm)],[f_4706_3]) ).

cnf(f_4706_5,plain,
    ( ~ c_Relation_Orefl__on(U_19484,hAPP(U_19485,sK498(U_19486,U_19485,U_19484,U_19483,U_19482)),hAPP(U_19486,sK498(U_19486,U_19485,U_19484,U_19483,U_19482)))
    | c_Relation_Orefl__on(U_19484,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(U_19484,tc_HOL_Obool)),U_19483),U_19485),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19482,tc_fun(tc_prod(U_19484,U_19484),tc_HOL_Obool)),U_19483),U_19486)) ),
    inference(clausify,[status(thm)],[f_4706_3]) ).

fof(f_4707_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_4707_2,plain,
    ! [U_19489,U_19488,U_19487] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(U_19487),U_19488),U_19489))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19487),U_19489),hAPP(c_List_Oset(U_19487),U_19488))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_19487),U_19489),hAPP(c_List_Oset(U_19487),U_19488)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19487),U_19488),U_19489)) ) ),
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

fof(f_4707_3,plain,
    ( ! [U_19495,U_19493,U_19491] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19491),U_19493),U_19495))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19491),U_19495),hAPP(c_List_Oset(U_19491),U_19493))) )
    & ! [U_19494,U_19492,U_19490] :
        ( hBOOL(hAPP(hAPP(c_member(U_19490),U_19494),hAPP(c_List_Oset(U_19490),U_19492)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19490),U_19492),U_19494)) ) ),
    inference(miniscope,[status(thm)],[f_4707_2]) ).

cnf(f_4707_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19490),U_19494),hAPP(c_List_Oset(U_19490),U_19492)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19490),U_19492),U_19494)) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

cnf(f_4707_5,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19491),U_19493),U_19495))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19491),U_19495),hAPP(c_List_Oset(U_19491),U_19493))) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

fof(f_4708_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_4708_2,plain,
    ! [U_19497,U_19496] : ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19496),c_List_Olist_ONil(U_19496)),U_19497)),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

cnf(f_4708_3,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19496),c_List_Olist_ONil(U_19496)),U_19497)),
    inference(clausify,[status(thm)],[f_4708_2]) ).

fof(f_4709_1,plain,
    ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b),
    inference(fof_nnf,[status(thm)],[fact_member__set]) ).

fof(f_4709_2,plain,
    ! [U_19498] : c_List_Omember(U_19498) = c_List_Oset(U_19498),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

cnf(f_4709_3,plain,
    c_List_Omember(U_19498) = c_List_Oset(U_19498),
    inference(clausify,[status(thm)],[f_4709_2]) ).

fof(f_4710_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_4710_2,plain,
    ! [U_19502,U_19501,U_19500,U_19499] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(U_19499),hAPP(hAPP(c_List_Olist_OCons(U_19499),U_19500),U_19501)),U_19502))
        | ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19499),U_19501),U_19502))
          & U_19500 != U_19502 ) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(U_19499),U_19501),U_19502))
        | U_19500 = U_19502
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19499),hAPP(hAPP(c_List_Olist_OCons(U_19499),U_19500),U_19501)),U_19502)) ) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

fof(f_4710_3,plain,
    ( ! [U_19510,U_19508,U_19506,U_19504] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19504),hAPP(hAPP(c_List_Olist_OCons(U_19504),U_19506),U_19508)),U_19510))
        | ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19504),U_19508),U_19510))
          & U_19506 != U_19510 ) )
    & ! [U_19509,U_19507,U_19505,U_19503] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19503),U_19507),U_19509))
        | U_19505 = U_19509
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19503),hAPP(hAPP(c_List_Olist_OCons(U_19503),U_19505),U_19507)),U_19509)) ) ),
    inference(miniscope,[status(thm)],[f_4710_2]) ).

cnf(f_4710_4,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19503),U_19507),U_19509))
    | U_19505 = U_19509
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19503),hAPP(hAPP(c_List_Olist_OCons(U_19503),U_19505),U_19507)),U_19509)) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

cnf(f_4710_5,plain,
    ( U_19506 != U_19510
    | hBOOL(hAPP(hAPP(c_List_Omember(U_19504),hAPP(hAPP(c_List_Olist_OCons(U_19504),U_19506),U_19508)),U_19510)) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

cnf(f_4710_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19504),U_19508),U_19510))
    | hBOOL(hAPP(hAPP(c_List_Omember(U_19504),hAPP(hAPP(c_List_Olist_OCons(U_19504),U_19506),U_19508)),U_19510)) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

fof(f_4711_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_4711_2,plain,
    ! [U_19513,U_19512,U_19511] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_19511),U_19512),hAPP(c_List_Oset(U_19511),U_19513)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19511),U_19513),U_19512)) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(U_19511),U_19513),U_19512))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19511),U_19512),hAPP(c_List_Oset(U_19511),U_19513))) ) ),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

fof(f_4711_3,plain,
    ( ! [U_19519,U_19517,U_19515] :
        ( hBOOL(hAPP(hAPP(c_member(U_19515),U_19517),hAPP(c_List_Oset(U_19515),U_19519)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19515),U_19519),U_19517)) )
    & ! [U_19518,U_19516,U_19514] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19514),U_19518),U_19516))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19514),U_19516),hAPP(c_List_Oset(U_19514),U_19518))) ) ),
    inference(miniscope,[status(thm)],[f_4711_2]) ).

cnf(f_4711_4,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19514),U_19518),U_19516))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19514),U_19516),hAPP(c_List_Oset(U_19514),U_19518))) ),
    inference(clausify,[status(thm)],[f_4711_3]) ).

cnf(f_4711_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19515),U_19517),hAPP(c_List_Oset(U_19515),U_19519)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19515),U_19519),U_19517)) ),
    inference(clausify,[status(thm)],[f_4711_3]) ).

fof(f_4712_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_Pa_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            | ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_y))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__iff__raw]) ).

fof(f_4712_2,plain,
    ! [U_19526,U_19525,U_19524] :
      ( ( c_List_Olist__ex1(U_19524,U_19525,U_19526)
        | ! [U_19523] :
            ( ? [U_19522] :
                ( U_19522 != U_19523
                & hBOOL(hAPP(U_19525,U_19522))
                & hBOOL(hAPP(hAPP(c_member(U_19524),U_19522),hAPP(c_List_Oset(U_19524),U_19526))) )
            | ~ hBOOL(hAPP(U_19525,U_19523))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19524),U_19523),hAPP(c_List_Oset(U_19524),U_19526))) ) )
      & ( ? [U_19521] :
            ( ! [U_19520] :
                ( U_19520 = U_19521
                | ~ hBOOL(hAPP(U_19525,U_19520))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19524),U_19520),hAPP(c_List_Oset(U_19524),U_19526))) )
            & hBOOL(hAPP(U_19525,U_19521))
            & hBOOL(hAPP(hAPP(c_member(U_19524),U_19521),hAPP(c_List_Oset(U_19524),U_19526))) )
        | ~ c_List_Olist__ex1(U_19524,U_19525,U_19526) ) ),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

fof(f_4712_3,plain,
    ( ! [U_19532,U_19530,U_19528] :
        ( c_List_Olist__ex1(U_19528,U_19530,U_19532)
        | ! [U_19523] :
            ( ? [U_19522] :
                ( U_19522 != U_19523
                & hBOOL(hAPP(U_19530,U_19522))
                & hBOOL(hAPP(hAPP(c_member(U_19528),U_19522),hAPP(c_List_Oset(U_19528),U_19532))) )
            | ~ hBOOL(hAPP(U_19530,U_19523))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532))) ) )
    & ! [U_19531,U_19529,U_19527] :
        ( ? [U_19521] :
            ( ! [U_19520] :
                ( U_19520 = U_19521
                | ~ hBOOL(hAPP(U_19529,U_19520))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19527),U_19520),hAPP(c_List_Oset(U_19527),U_19531))) )
            & hBOOL(hAPP(U_19529,U_19521))
            & hBOOL(hAPP(hAPP(c_member(U_19527),U_19521),hAPP(c_List_Oset(U_19527),U_19531))) )
        | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ) ),
    inference(miniscope,[status(thm)],[f_4712_2]) ).

fof(f_4712_4,plain,
    ( ! [U_19532,U_19530,U_19528] :
        ( c_List_Olist__ex1(U_19528,U_19530,U_19532)
        | ! [U_19523] :
            ( ? [U_19522] :
                ( U_19522 != U_19523
                & hBOOL(hAPP(U_19530,U_19522))
                & hBOOL(hAPP(hAPP(c_member(U_19528),U_19522),hAPP(c_List_Oset(U_19528),U_19532))) )
            | ~ hBOOL(hAPP(U_19530,U_19523))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532))) ) )
    & ! [U_19531,U_19529,U_19527] :
        ( ( ! [U_19520] :
              ( U_19520 = sK499(U_19531,U_19529,U_19527)
              | ~ hBOOL(hAPP(U_19529,U_19520))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19527),U_19520),hAPP(c_List_Oset(U_19527),U_19531))) )
          & hBOOL(hAPP(U_19529,sK499(U_19531,U_19529,U_19527)))
          & hBOOL(hAPP(hAPP(c_member(U_19527),sK499(U_19531,U_19529,U_19527)),hAPP(c_List_Oset(U_19527),U_19531))) )
        | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_19521,sK499(U_19531,U_19529,U_19527))],[f_4712_3]) ).

fof(f_4712_5,plain,
    ( ! [U_19532,U_19530,U_19528] :
        ( c_List_Olist__ex1(U_19528,U_19530,U_19532)
        | ! [U_19523] :
            ( ( sK500(U_19532,U_19530,U_19528,U_19523) != U_19523
              & hBOOL(hAPP(U_19530,sK500(U_19532,U_19530,U_19528,U_19523)))
              & hBOOL(hAPP(hAPP(c_member(U_19528),sK500(U_19532,U_19530,U_19528,U_19523)),hAPP(c_List_Oset(U_19528),U_19532))) )
            | ~ hBOOL(hAPP(U_19530,U_19523))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532))) ) )
    & ! [U_19531,U_19529,U_19527] :
        ( ( ! [U_19520] :
              ( U_19520 = sK499(U_19531,U_19529,U_19527)
              | ~ hBOOL(hAPP(U_19529,U_19520))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19527),U_19520),hAPP(c_List_Oset(U_19527),U_19531))) )
          & hBOOL(hAPP(U_19529,sK499(U_19531,U_19529,U_19527)))
          & hBOOL(hAPP(hAPP(c_member(U_19527),sK499(U_19531,U_19529,U_19527)),hAPP(c_List_Oset(U_19527),U_19531))) )
        | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_19522,sK500(U_19532,U_19530,U_19528,U_19523))],[f_4712_4]) ).

cnf(f_4712_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19527),sK499(U_19531,U_19529,U_19527)),hAPP(c_List_Oset(U_19527),U_19531)))
    | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

cnf(f_4712_7,plain,
    ( hBOOL(hAPP(U_19529,sK499(U_19531,U_19529,U_19527)))
    | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

cnf(f_4712_8,plain,
    ( U_19520 = sK499(U_19531,U_19529,U_19527)
    | ~ hBOOL(hAPP(U_19529,U_19520))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19527),U_19520),hAPP(c_List_Oset(U_19527),U_19531)))
    | ~ c_List_Olist__ex1(U_19527,U_19529,U_19531) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

cnf(f_4712_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19528),sK500(U_19532,U_19530,U_19528,U_19523)),hAPP(c_List_Oset(U_19528),U_19532)))
    | ~ hBOOL(hAPP(U_19530,U_19523))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532)))
    | c_List_Olist__ex1(U_19528,U_19530,U_19532) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

cnf(f_4712_10,plain,
    ( hBOOL(hAPP(U_19530,sK500(U_19532,U_19530,U_19528,U_19523)))
    | ~ hBOOL(hAPP(U_19530,U_19523))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532)))
    | c_List_Olist__ex1(U_19528,U_19530,U_19532) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

cnf(f_4712_11,plain,
    ( sK500(U_19532,U_19530,U_19528,U_19523) != U_19523
    | ~ hBOOL(hAPP(U_19530,U_19523))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19528),U_19523),hAPP(c_List_Oset(U_19528),U_19532)))
    | c_List_Olist__ex1(U_19528,U_19530,U_19532) ),
    inference(clausify,[status(thm)],[f_4712_5]) ).

fof(f_4713_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_4713_2,plain,
    ! [U_19540,U_19539,U_19538,U_19537] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
      | ? [U_19536] :
          ( ? [U_19535] :
              ( ? [U_19534] :
                  ( hAPP(U_19540,U_19534) != c_Groups_Ozero__class_Ozero(U_19537)
                  & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),U_19535))
                  & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),U_19536)) )
              & U_19536 != U_19535
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19535),U_19539)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19536),U_19539)) )
      | ? [U_19533] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),U_19533))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19533),U_19539)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
      | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

fof(f_4713_3,plain,
    ! [U_19540,U_19539,U_19538,U_19537] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
      | ? [U_19536] :
          ( ? [U_19535] :
              ( ? [U_19534] :
                  ( hAPP(U_19540,U_19534) != c_Groups_Ozero__class_Ozero(U_19537)
                  & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),U_19535))
                  & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),U_19536)) )
              & U_19536 != U_19535
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19535),U_19539)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19536),U_19539)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
      | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_19533,sK501(U_19540,U_19539,U_19538,U_19537))],[f_4713_2]) ).

fof(f_4713_4,plain,
    ! [U_19540,U_19539,U_19538,U_19537] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
      | ( ? [U_19535] :
            ( ? [U_19534] :
                ( hAPP(U_19540,U_19534) != c_Groups_Ozero__class_Ozero(U_19537)
                & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),U_19535))
                & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),sK502(U_19540,U_19539,U_19538,U_19537))) )
            & sK502(U_19540,U_19539,U_19538,U_19537) != U_19535
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),U_19535),U_19539)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK502(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
      | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_19536,sK502(U_19540,U_19539,U_19538,U_19537))],[f_4713_3]) ).

fof(f_4713_5,plain,
    ! [U_19540,U_19539,U_19538,U_19537] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
      | ( ? [U_19534] :
            ( hAPP(U_19540,U_19534) != c_Groups_Ozero__class_Ozero(U_19537)
            & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),sK503(U_19540,U_19539,U_19538,U_19537)))
            & hBOOL(hAPP(hAPP(c_member(U_19538),U_19534),sK502(U_19540,U_19539,U_19538,U_19537))) )
        & sK502(U_19540,U_19539,U_19538,U_19537) != sK503(U_19540,U_19539,U_19538,U_19537)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK503(U_19540,U_19539,U_19538,U_19537)),U_19539))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK502(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
      | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_19535,sK503(U_19540,U_19539,U_19538,U_19537))],[f_4713_4]) ).

fof(f_4713_6,plain,
    ! [U_19540,U_19539,U_19538,U_19537] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
      | ( hAPP(U_19540,sK504(U_19540,U_19539,U_19538,U_19537)) != c_Groups_Ozero__class_Ozero(U_19537)
        & hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK503(U_19540,U_19539,U_19538,U_19537)))
        & hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK502(U_19540,U_19539,U_19538,U_19537)))
        & sK502(U_19540,U_19539,U_19538,U_19537) != sK503(U_19540,U_19539,U_19538,U_19537)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK503(U_19540,U_19539,U_19538,U_19537)),U_19539))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK502(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
      | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_19534,sK504(U_19540,U_19539,U_19538,U_19537))],[f_4713_5]) ).

cnf(f_4713_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK502(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK503(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_9,plain,
    ( sK502(U_19540,U_19539,U_19538,U_19537) != sK503(U_19540,U_19539,U_19538,U_19537)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK502(U_19540,U_19539,U_19538,U_19537)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK503(U_19540,U_19539,U_19538,U_19537)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_12,plain,
    ( hAPP(U_19540,sK504(U_19540,U_19539,U_19538,U_19537)) != c_Groups_Ozero__class_Ozero(U_19537)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK501(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK502(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19538,tc_HOL_Obool)),sK503(U_19540,U_19539,U_19538,U_19537)),U_19539))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_15,plain,
    ( sK502(U_19540,U_19539,U_19538,U_19537) != sK503(U_19540,U_19539,U_19538,U_19537)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK502(U_19540,U_19539,U_19538,U_19537)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_17,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19538),sK504(U_19540,U_19539,U_19538,U_19537)),sK503(U_19540,U_19539,U_19538,U_19537)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

cnf(f_4713_18,plain,
    ( hAPP(U_19540,sK504(U_19540,U_19539,U_19538,U_19537)) != c_Groups_Ozero__class_Ozero(U_19537)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19538,tc_HOL_Obool),U_19539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19538,tc_HOL_Obool),U_19537),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19538,U_19537),U_19540)),U_19539)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19538),sK501(U_19540,U_19539,U_19538,U_19537)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19538,tc_HOL_Obool)),U_19539))
    | ~ class_Groups_Ocomm__monoid__add(U_19537) ),
    inference(clausify,[status(thm)],[f_4713_6]) ).

fof(f_4714_1,plain,
    ! [V_d_2,T_b,V_Pa_2] :
      ( ( c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2
        | ? [B_x] :
            ( ! [B_y] :
                ( B_y = B_x
                | ~ hBOOL(hAPP(V_Pa_2,B_y)) )
            & hBOOL(hAPP(V_Pa_2,B_x)) ) )
      & ( c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_Pa_2,B_y)) )
            | ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_THE__default__def]) ).

fof(f_4714_2,plain,
    ! [U_19547,U_19546,U_19545] :
      ( ( c_FunDef_OTHE__default(U_19546,U_19547,U_19545) = U_19547
        | ? [U_19544] :
            ( ! [U_19543] :
                ( U_19543 = U_19544
                | ~ hBOOL(hAPP(U_19545,U_19543)) )
            & hBOOL(hAPP(U_19545,U_19544)) ) )
      & ( c_FunDef_OTHE__default(U_19546,U_19547,U_19545) = c_HOL_OThe(U_19546,U_19545)
        | ! [U_19542] :
            ( ? [U_19541] :
                ( U_19541 != U_19542
                & hBOOL(hAPP(U_19545,U_19541)) )
            | ~ hBOOL(hAPP(U_19545,U_19542)) ) ) ),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

fof(f_4714_3,plain,
    ( ! [U_19553,U_19551,U_19549] :
        ( c_FunDef_OTHE__default(U_19551,U_19553,U_19549) = U_19553
        | ? [U_19544] :
            ( ! [U_19543] :
                ( U_19543 = U_19544
                | ~ hBOOL(hAPP(U_19549,U_19543)) )
            & hBOOL(hAPP(U_19549,U_19544)) ) )
    & ! [U_19552,U_19550,U_19548] :
        ( c_FunDef_OTHE__default(U_19550,U_19552,U_19548) = c_HOL_OThe(U_19550,U_19548)
        | ! [U_19542] :
            ( ? [U_19541] :
                ( U_19541 != U_19542
                & hBOOL(hAPP(U_19548,U_19541)) )
            | ~ hBOOL(hAPP(U_19548,U_19542)) ) ) ),
    inference(miniscope,[status(thm)],[f_4714_2]) ).

fof(f_4714_4,plain,
    ( ! [U_19553,U_19551,U_19549] :
        ( c_FunDef_OTHE__default(U_19551,U_19553,U_19549) = U_19553
        | ? [U_19544] :
            ( ! [U_19543] :
                ( U_19543 = U_19544
                | ~ hBOOL(hAPP(U_19549,U_19543)) )
            & hBOOL(hAPP(U_19549,U_19544)) ) )
    & ! [U_19552,U_19550,U_19548] :
        ( c_FunDef_OTHE__default(U_19550,U_19552,U_19548) = c_HOL_OThe(U_19550,U_19548)
        | ! [U_19542] :
            ( ( sK505(U_19552,U_19550,U_19548,U_19542) != U_19542
              & hBOOL(hAPP(U_19548,sK505(U_19552,U_19550,U_19548,U_19542))) )
            | ~ hBOOL(hAPP(U_19548,U_19542)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_19541,sK505(U_19552,U_19550,U_19548,U_19542))],[f_4714_3]) ).

fof(f_4714_5,plain,
    ( ! [U_19553,U_19551,U_19549] :
        ( c_FunDef_OTHE__default(U_19551,U_19553,U_19549) = U_19553
        | ( ! [U_19543] :
              ( U_19543 = sK506(U_19553,U_19551,U_19549)
              | ~ hBOOL(hAPP(U_19549,U_19543)) )
          & hBOOL(hAPP(U_19549,sK506(U_19553,U_19551,U_19549))) ) )
    & ! [U_19552,U_19550,U_19548] :
        ( c_FunDef_OTHE__default(U_19550,U_19552,U_19548) = c_HOL_OThe(U_19550,U_19548)
        | ! [U_19542] :
            ( ( sK505(U_19552,U_19550,U_19548,U_19542) != U_19542
              & hBOOL(hAPP(U_19548,sK505(U_19552,U_19550,U_19548,U_19542))) )
            | ~ hBOOL(hAPP(U_19548,U_19542)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_19544,sK506(U_19553,U_19551,U_19549))],[f_4714_4]) ).

cnf(f_4714_6,plain,
    ( hBOOL(hAPP(U_19548,sK505(U_19552,U_19550,U_19548,U_19542)))
    | ~ hBOOL(hAPP(U_19548,U_19542))
    | c_FunDef_OTHE__default(U_19550,U_19552,U_19548) = c_HOL_OThe(U_19550,U_19548) ),
    inference(clausify,[status(thm)],[f_4714_5]) ).

cnf(f_4714_7,plain,
    ( sK505(U_19552,U_19550,U_19548,U_19542) != U_19542
    | ~ hBOOL(hAPP(U_19548,U_19542))
    | c_FunDef_OTHE__default(U_19550,U_19552,U_19548) = c_HOL_OThe(U_19550,U_19548) ),
    inference(clausify,[status(thm)],[f_4714_5]) ).

cnf(f_4714_8,plain,
    ( hBOOL(hAPP(U_19549,sK506(U_19553,U_19551,U_19549)))
    | c_FunDef_OTHE__default(U_19551,U_19553,U_19549) = U_19553 ),
    inference(clausify,[status(thm)],[f_4714_5]) ).

cnf(f_4714_9,plain,
    ( U_19543 = sK506(U_19553,U_19551,U_19549)
    | ~ hBOOL(hAPP(U_19549,U_19543))
    | c_FunDef_OTHE__default(U_19551,U_19553,U_19549) = U_19553 ),
    inference(clausify,[status(thm)],[f_4714_5]) ).

fof(f_4715_1,plain,
    ! [V_ca_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_ca_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_ca_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__E]) ).

fof(f_4715_2,plain,
    ! [U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555] :
      ( ? [U_19554] :
          ( hBOOL(hAPP(hAPP(hAPP(U_19559,U_19554),U_19560),U_19561))
          & hBOOL(hAPP(hAPP(c_member(U_19555),U_19554),U_19558)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19555,tc_fun(U_19556,tc_fun(U_19557,tc_HOL_Obool))),U_19558),U_19559),U_19560),U_19561)) ),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

fof(f_4715_3,plain,
    ! [U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555] :
      ( ( hBOOL(hAPP(hAPP(hAPP(U_19559,sK507(U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555)),U_19560),U_19561))
        & hBOOL(hAPP(hAPP(c_member(U_19555),sK507(U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555)),U_19558)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19555,tc_fun(U_19556,tc_fun(U_19557,tc_HOL_Obool))),U_19558),U_19559),U_19560),U_19561)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_19554,sK507(U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555))],[f_4715_2]) ).

cnf(f_4715_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19555),sK507(U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555)),U_19558))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19555,tc_fun(U_19556,tc_fun(U_19557,tc_HOL_Obool))),U_19558),U_19559),U_19560),U_19561)) ),
    inference(clausify,[status(thm)],[f_4715_3]) ).

cnf(f_4715_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_19559,sK507(U_19561,U_19560,U_19559,U_19558,U_19557,U_19556,U_19555)),U_19560),U_19561))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19555,tc_fun(U_19556,tc_fun(U_19557,tc_HOL_Obool))),U_19558),U_19559),U_19560),U_19561)) ),
    inference(clausify,[status(thm)],[f_4715_3]) ).

fof(f_4716_1,plain,
    ! [T_d,T_c,V_ca_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_ca_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__I]) ).

fof(f_4716_2,plain,
    ! [U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19563,tc_fun(U_19568,tc_fun(U_19569,tc_HOL_Obool))),U_19564),U_19565),U_19566),U_19567))
      | ? [U_19562] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_19565,U_19562),U_19566),U_19567))
          & hBOOL(hAPP(hAPP(c_member(U_19563),U_19562),U_19564)) ) ),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

fof(f_4716_3,plain,
    ! [U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19563,tc_fun(U_19568,tc_fun(U_19569,tc_HOL_Obool))),U_19564),U_19565),U_19566),U_19567))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_19565,sK508(U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563)),U_19566),U_19567))
        & hBOOL(hAPP(hAPP(c_member(U_19563),sK508(U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563)),U_19564)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_19562,sK508(U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563))],[f_4716_2]) ).

cnf(f_4716_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19563),sK508(U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563)),U_19564))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19563,tc_fun(U_19568,tc_fun(U_19569,tc_HOL_Obool))),U_19564),U_19565),U_19566),U_19567)) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

cnf(f_4716_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_19565,sK508(U_19569,U_19568,U_19567,U_19566,U_19565,U_19564,U_19563)),U_19566),U_19567))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19563,tc_fun(U_19568,tc_fun(U_19569,tc_HOL_Obool))),U_19564),U_19565),U_19566),U_19567)) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

fof(f_4717_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_4717_2,plain,
    ! [U_19573,U_19572] :
      ( ? [U_19571] :
        ! [U_19570] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19572)),U_19570)),U_19571))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19572)),U_19570),U_19573)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19572)),U_19573)) ),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

fof(f_4717_3,plain,
    ! [U_19573,U_19572] :
      ( ! [U_19570] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19572)),U_19570)),sK509(U_19573,U_19572)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19572)),U_19570),U_19573)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19572)),U_19573)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK509]),skolemize(U_19571,sK509(U_19573,U_19572))],[f_4717_2]) ).

cnf(f_4717_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19572)),U_19570)),sK509(U_19573,U_19572)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19572)),U_19570),U_19573))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19572)),U_19573)) ),
    inference(clausify,[status(thm)],[f_4717_3]) ).

fof(f_4718_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_4718_2,plain,
    ! [U_19574] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19574)),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19574)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

cnf(f_4718_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19574)),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19574)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4718_2]) ).

fof(f_4719_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_4719_2,plain,
    ! [U_19576,U_19575] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19575,U_19576),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19575)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

cnf(f_4719_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19575,U_19576),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19575)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4719_2]) ).

fof(f_4720_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_4720_2,plain,
    ! [U_19578,U_19577] : c_Lazy__Sequence_Oappend(U_19577,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19577),U_19578) = U_19578,
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

cnf(f_4720_3,plain,
    c_Lazy__Sequence_Oappend(U_19577,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19577),U_19578) = U_19578,
    inference(clausify,[status(thm)],[f_4720_2]) ).

fof(f_4721_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_4721_2,plain,
    ! [U_19581,U_19580,U_19579] : c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19579) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19579,U_19580,U_19581),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

cnf(f_4721_3,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19579) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19579,U_19580,U_19581),
    inference(clausify,[status(thm)],[f_4721_2]) ).

fof(f_4722_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_4722_2,plain,
    ! [U_19584,U_19583,U_19582] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19582,U_19583,U_19584) != c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19582),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

cnf(f_4722_3,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(U_19582,U_19583,U_19584) != c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19582),
    inference(clausify,[status(thm)],[f_4722_2]) ).

fof(f_4723_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_4723_2,plain,
    ! [U_19588,U_19587,U_19586,U_19585] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19585,U_19586,U_19587,U_19588,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19586)) = U_19587,
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

cnf(f_4723_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19585,U_19586,U_19587,U_19588,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19586)) = U_19587,
    inference(clausify,[status(thm)],[f_4723_2]) ).

fof(f_4724_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
        | ~ c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) )
      & ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
        | ~ c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int]) ).

fof(f_4724_2,plain,
    ! [U_19591,U_19590,U_19589] :
      ( ( c_List_Olist__all(tc_Int_Oint,U_19589,c_List_Oupto(U_19590,U_19591))
        | ~ c_List_Oall__interval__int(U_19589,U_19590,U_19591) )
      & ( c_List_Oall__interval__int(U_19589,U_19590,U_19591)
        | ~ c_List_Olist__all(tc_Int_Oint,U_19589,c_List_Oupto(U_19590,U_19591)) ) ),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ( ! [U_19597,U_19595,U_19593] :
        ( c_List_Olist__all(tc_Int_Oint,U_19593,c_List_Oupto(U_19595,U_19597))
        | ~ c_List_Oall__interval__int(U_19593,U_19595,U_19597) )
    & ! [U_19596,U_19594,U_19592] :
        ( c_List_Oall__interval__int(U_19592,U_19594,U_19596)
        | ~ c_List_Olist__all(tc_Int_Oint,U_19592,c_List_Oupto(U_19594,U_19596)) ) ),
    inference(miniscope,[status(thm)],[f_4724_2]) ).

cnf(f_4724_4,plain,
    ( c_List_Oall__interval__int(U_19592,U_19594,U_19596)
    | ~ c_List_Olist__all(tc_Int_Oint,U_19592,c_List_Oupto(U_19594,U_19596)) ),
    inference(clausify,[status(thm)],[f_4724_3]) ).

cnf(f_4724_5,plain,
    ( c_List_Olist__all(tc_Int_Oint,U_19593,c_List_Oupto(U_19595,U_19597))
    | ~ c_List_Oall__interval__int(U_19593,U_19595,U_19597) ),
    inference(clausify,[status(thm)],[f_4724_3]) ).

fof(f_4725_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Olist__ex(tc_Int_Oint,V_Pa_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_Pa_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_Pa_2),V_i_2,V_j_2)
        | ~ c_List_Olist__ex(tc_Int_Oint,V_Pa_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_4725_2,plain,
    ! [U_19600,U_19599,U_19598] :
      ( ( c_List_Olist__ex(tc_Int_Oint,U_19598,c_List_Oupto(U_19599,U_19600))
        | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19598),U_19599,U_19600) )
      & ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19598),U_19599,U_19600)
        | ~ c_List_Olist__ex(tc_Int_Oint,U_19598,c_List_Oupto(U_19599,U_19600)) ) ),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

fof(f_4725_3,plain,
    ( ! [U_19606,U_19604,U_19602] :
        ( c_List_Olist__ex(tc_Int_Oint,U_19602,c_List_Oupto(U_19604,U_19606))
        | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19602),U_19604,U_19606) )
    & ! [U_19605,U_19603,U_19601] :
        ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19601),U_19603,U_19605)
        | ~ c_List_Olist__ex(tc_Int_Oint,U_19601,c_List_Oupto(U_19603,U_19605)) ) ),
    inference(miniscope,[status(thm)],[f_4725_2]) ).

cnf(f_4725_4,plain,
    ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19601),U_19603,U_19605)
    | ~ c_List_Olist__ex(tc_Int_Oint,U_19601,c_List_Oupto(U_19603,U_19605)) ),
    inference(clausify,[status(thm)],[f_4725_3]) ).

cnf(f_4725_5,plain,
    ( c_List_Olist__ex(tc_Int_Oint,U_19602,c_List_Oupto(U_19604,U_19606))
    | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19602),U_19604,U_19606) ),
    inference(clausify,[status(thm)],[f_4725_3]) ).

fof(f_4726_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_i_2,V_j_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__interval__int__def]) ).

fof(f_4726_2,plain,
    ! [U_19611,U_19610,U_19609] :
      ( ( c_List_Oall__interval__int(U_19609,U_19610,U_19611)
        | ? [U_19608] :
            ( ~ hBOOL(hAPP(U_19609,U_19608))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19608),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19610,U_19611))) ) )
      & ( ! [U_19607] :
            ( hBOOL(hAPP(U_19609,U_19607))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19610,U_19611))) )
        | ~ c_List_Oall__interval__int(U_19609,U_19610,U_19611) ) ),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

fof(f_4726_3,plain,
    ( ! [U_19617,U_19615,U_19613] :
        ( c_List_Oall__interval__int(U_19613,U_19615,U_19617)
        | ? [U_19608] :
            ( ~ hBOOL(hAPP(U_19613,U_19608))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19608),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19615,U_19617))) ) )
    & ! [U_19616,U_19614,U_19612] :
        ( ! [U_19607] :
            ( hBOOL(hAPP(U_19612,U_19607))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19614,U_19616))) )
        | ~ c_List_Oall__interval__int(U_19612,U_19614,U_19616) ) ),
    inference(miniscope,[status(thm)],[f_4726_2]) ).

fof(f_4726_4,plain,
    ( ! [U_19617,U_19615,U_19613] :
        ( c_List_Oall__interval__int(U_19613,U_19615,U_19617)
        | ( ~ hBOOL(hAPP(U_19613,sK510(U_19617,U_19615,U_19613)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK510(U_19617,U_19615,U_19613)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19615,U_19617))) ) )
    & ! [U_19616,U_19614,U_19612] :
        ( ! [U_19607] :
            ( hBOOL(hAPP(U_19612,U_19607))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19614,U_19616))) )
        | ~ c_List_Oall__interval__int(U_19612,U_19614,U_19616) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK510]),skolemize(U_19608,sK510(U_19617,U_19615,U_19613))],[f_4726_3]) ).

cnf(f_4726_5,plain,
    ( hBOOL(hAPP(U_19612,U_19607))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19614,U_19616)))
    | ~ c_List_Oall__interval__int(U_19612,U_19614,U_19616) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

cnf(f_4726_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK510(U_19617,U_19615,U_19613)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19615,U_19617)))
    | c_List_Oall__interval__int(U_19613,U_19615,U_19617) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

cnf(f_4726_7,plain,
    ( ~ hBOOL(hAPP(U_19613,sK510(U_19617,U_19615,U_19613)))
    | c_List_Oall__interval__int(U_19613,U_19615,U_19617) ),
    inference(clausify,[status(thm)],[f_4726_4]) ).

fof(f_4727_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_4727_2,plain,
    ! [U_19621,U_19620,U_19619,U_19618] :
      ( ( c_Random__Sequence_ORandom(U_19619,U_19620,U_19618,U_19621) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19619,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_19619)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19620,U_19621)),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_19619)))),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_19619)))),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_19619)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19619,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_19619)))),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_19619)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19619,U_19620,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19618),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19621))),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_19619)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19619))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19619)))),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_19619)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19619,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_19619)))),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_19619)))),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_19619))))),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_19619)))),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_19619)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19619)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19619))))),tc_prod(U_19619,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19619)),hAPP(hAPP(c_COMBB(U_19619,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19619)))),tc_prod(U_19619,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19619)),c_Product__Type_Ofst(U_19619,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_19618),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(U_19619,U_19620,U_19618,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_19619)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19618),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

fof(f_4727_3,plain,
    ( ! [U_19629,U_19627,U_19625,U_19623] :
        ( c_Random__Sequence_ORandom(U_19625,U_19627,U_19623,U_19629) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19625,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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19627,U_19629)),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_19625)))),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_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19625,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_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19625,U_19627,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19623),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19629))),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_19625)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19625,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_19625)))),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_19625)))),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_19625))))),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_19625)))),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_19625)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625))))),tc_prod(U_19625,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19625)),hAPP(hAPP(c_COMBB(U_19625,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),tc_prod(U_19625,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19625)),c_Product__Type_Ofst(U_19625,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_19623),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_19628,U_19626,U_19624,U_19622] :
        ( c_Random__Sequence_ORandom(U_19624,U_19626,U_19622,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_19624)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19624))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19622),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(miniscope,[status(thm)],[f_4727_2]) ).

cnf(f_4727_4,plain,
    ( c_Random__Sequence_ORandom(U_19624,U_19626,U_19622,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_19624)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19622),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_4727_3]) ).

cnf(f_4727_5,plain,
    ( c_Random__Sequence_ORandom(U_19625,U_19627,U_19623,U_19629) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19625,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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19627,U_19629)),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_19625)))),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_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19625,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_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19625,U_19627,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19623),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19629))),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_19625)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),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_19625)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19625,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_19625)))),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_19625)))),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_19625))))),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_19625)))),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_19625)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625))))),tc_prod(U_19625,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19625)),hAPP(hAPP(c_COMBB(U_19625,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19625)))),tc_prod(U_19625,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19625)),c_Product__Type_Ofst(U_19625,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_19623),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_4727_3]) ).

fof(f_4728_1,plain,
    ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
      ( hBOOL(hAPP(V_Qa_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_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y)))
          & hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) )
      | ~ hBOOL(hAPP(hAPP(V_Pa_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_4728_2,plain,
    ! [U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632] :
      ( hBOOL(hAPP(U_19636,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19633,U_19634,U_19638),U_19637),U_19635)))
      | ? [U_19631,U_19630] :
          ( ~ hBOOL(hAPP(U_19636,hAPP(hAPP(U_19637,U_19631),U_19630)))
          & hBOOL(hAPP(hAPP(U_19632,U_19630),U_19631)) )
      | ~ hBOOL(hAPP(hAPP(U_19632,hAPP(c_Product__Type_Osnd(U_19633,U_19634),U_19635)),hAPP(c_Product__Type_Ofst(U_19633,U_19634),U_19635))) ),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

fof(f_4728_3,plain,
    ! [U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632] :
      ( hBOOL(hAPP(U_19636,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19633,U_19634,U_19638),U_19637),U_19635)))
      | ? [U_19630] :
          ( ~ hBOOL(hAPP(U_19636,hAPP(hAPP(U_19637,sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)),U_19630)))
          & hBOOL(hAPP(hAPP(U_19632,U_19630),sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))) )
      | ~ hBOOL(hAPP(hAPP(U_19632,hAPP(c_Product__Type_Osnd(U_19633,U_19634),U_19635)),hAPP(c_Product__Type_Ofst(U_19633,U_19634),U_19635))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK511]),skolemize(U_19631,sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))],[f_4728_2]) ).

fof(f_4728_4,plain,
    ! [U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632] :
      ( hBOOL(hAPP(U_19636,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19633,U_19634,U_19638),U_19637),U_19635)))
      | ( ~ hBOOL(hAPP(U_19636,hAPP(hAPP(U_19637,sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)),sK512(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))))
        & hBOOL(hAPP(hAPP(U_19632,sK512(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)),sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))) )
      | ~ hBOOL(hAPP(hAPP(U_19632,hAPP(c_Product__Type_Osnd(U_19633,U_19634),U_19635)),hAPP(c_Product__Type_Ofst(U_19633,U_19634),U_19635))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK512]),skolemize(U_19630,sK512(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))],[f_4728_3]) ).

cnf(f_4728_5,plain,
    ( hBOOL(hAPP(hAPP(U_19632,sK512(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)),sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)))
    | hBOOL(hAPP(U_19636,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19633,U_19634,U_19638),U_19637),U_19635)))
    | ~ hBOOL(hAPP(hAPP(U_19632,hAPP(c_Product__Type_Osnd(U_19633,U_19634),U_19635)),hAPP(c_Product__Type_Ofst(U_19633,U_19634),U_19635))) ),
    inference(clausify,[status(thm)],[f_4728_4]) ).

cnf(f_4728_6,plain,
    ( ~ hBOOL(hAPP(U_19636,hAPP(hAPP(U_19637,sK511(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632)),sK512(U_19638,U_19637,U_19636,U_19635,U_19634,U_19633,U_19632))))
    | hBOOL(hAPP(U_19636,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19633,U_19634,U_19638),U_19637),U_19635)))
    | ~ hBOOL(hAPP(hAPP(U_19632,hAPP(c_Product__Type_Osnd(U_19633,U_19634),U_19635)),hAPP(c_Product__Type_Ofst(U_19633,U_19634),U_19635))) ),
    inference(clausify,[status(thm)],[f_4728_4]) ).

fof(f_4729_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_4729_2,plain,
    ! [U_19641,U_19640,U_19639] : c_Random__Sequence_Oempty(U_19639,U_19640,U_19641) = 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_19639)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19639)),
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

cnf(f_4729_3,plain,
    c_Random__Sequence_Oempty(U_19639,U_19640,U_19641) = 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_19639)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19639)),
    inference(clausify,[status(thm)],[f_4729_2]) ).

fof(f_4730_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_4730_2,plain,
    ! [U_19645,U_19644,U_19643,U_19642] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_19642),U_19643),U_19644),U_19645) = 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_19642)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_19642),U_19643)),
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

cnf(f_4730_3,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_19642),U_19643),U_19644),U_19645) = 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_19642)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_19642),U_19643)),
    inference(clausify,[status(thm)],[f_4730_2]) ).

fof(f_4731_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_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_4731_2,plain,
    ! [U_19649,U_19648,U_19647,U_19646] : c_Random__Sequence_Omap(U_19646,U_19647,U_19648,U_19649) = c_Random__Sequence_Obind(U_19646,U_19647,U_19649,hAPP(c_Fun_Ocomp(U_19647,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_19647)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_19646,c_Random__Sequence_Osingle(U_19647)),U_19648)),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

cnf(f_4731_3,plain,
    c_Random__Sequence_Omap(U_19646,U_19647,U_19648,U_19649) = c_Random__Sequence_Obind(U_19646,U_19647,U_19649,hAPP(c_Fun_Ocomp(U_19647,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_19647)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_19646,c_Random__Sequence_Osingle(U_19647)),U_19648)),
    inference(clausify,[status(thm)],[f_4731_2]) ).

fof(f_4732_1,plain,
    ! [V_A_2,V_Pa_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_Pa_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_Pa_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__Collect__split]) ).

fof(f_4732_2,plain,
    ! [U_19653,U_19652,U_19651,U_19650] : hAPP(c_Relation_OImage(U_19650,U_19651,hAPP(c_Set_OCollect(tc_prod(U_19650,U_19651)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19650,U_19651,tc_HOL_Obool),U_19652))),U_19653) = hAPP(c_Set_OCollect(U_19651),hAPP(hAPP(c_COMBB(tc_fun(U_19650,tc_HOL_Obool),tc_HOL_Obool,U_19651),c_HOL_OEx(U_19650)),hAPP(hAPP(c_COMBB(tc_fun(U_19650,tc_HOL_Obool),tc_fun(U_19650,tc_HOL_Obool),U_19651),hAPP(c_COMBS(U_19650,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19650),c_fconj),hAPP(hAPP(c_COMBC(U_19650,tc_fun(U_19650,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19650)),U_19653)))),hAPP(c_COMBC(U_19650,U_19651,tc_HOL_Obool),U_19652)))),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

cnf(f_4732_3,plain,
    hAPP(c_Relation_OImage(U_19650,U_19651,hAPP(c_Set_OCollect(tc_prod(U_19650,U_19651)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19650,U_19651,tc_HOL_Obool),U_19652))),U_19653) = hAPP(c_Set_OCollect(U_19651),hAPP(hAPP(c_COMBB(tc_fun(U_19650,tc_HOL_Obool),tc_HOL_Obool,U_19651),c_HOL_OEx(U_19650)),hAPP(hAPP(c_COMBB(tc_fun(U_19650,tc_HOL_Obool),tc_fun(U_19650,tc_HOL_Obool),U_19651),hAPP(c_COMBS(U_19650,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19650),c_fconj),hAPP(hAPP(c_COMBC(U_19650,tc_fun(U_19650,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19650)),U_19653)))),hAPP(c_COMBC(U_19650,U_19651,tc_HOL_Obool),U_19652)))),
    inference(clausify,[status(thm)],[f_4732_2]) ).

fof(f_4733_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff__raw]) ).

fof(f_4733_2,plain,
    ! [U_19658,U_19657,U_19656] :
      ( ( c_List_Olist__ex(U_19656,U_19657,U_19658)
        | ! [U_19655] :
            ( ~ hBOOL(hAPP(U_19657,U_19655))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19656),U_19655),hAPP(c_List_Oset(U_19656),U_19658))) ) )
      & ( ? [U_19654] :
            ( hBOOL(hAPP(U_19657,U_19654))
            & hBOOL(hAPP(hAPP(c_member(U_19656),U_19654),hAPP(c_List_Oset(U_19656),U_19658))) )
        | ~ c_List_Olist__ex(U_19656,U_19657,U_19658) ) ),
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

fof(f_4733_3,plain,
    ( ! [U_19664,U_19662,U_19660] :
        ( c_List_Olist__ex(U_19660,U_19662,U_19664)
        | ! [U_19655] :
            ( ~ hBOOL(hAPP(U_19662,U_19655))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19660),U_19655),hAPP(c_List_Oset(U_19660),U_19664))) ) )
    & ! [U_19663,U_19661,U_19659] :
        ( ? [U_19654] :
            ( hBOOL(hAPP(U_19661,U_19654))
            & hBOOL(hAPP(hAPP(c_member(U_19659),U_19654),hAPP(c_List_Oset(U_19659),U_19663))) )
        | ~ c_List_Olist__ex(U_19659,U_19661,U_19663) ) ),
    inference(miniscope,[status(thm)],[f_4733_2]) ).

fof(f_4733_4,plain,
    ( ! [U_19664,U_19662,U_19660] :
        ( c_List_Olist__ex(U_19660,U_19662,U_19664)
        | ! [U_19655] :
            ( ~ hBOOL(hAPP(U_19662,U_19655))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19660),U_19655),hAPP(c_List_Oset(U_19660),U_19664))) ) )
    & ! [U_19663,U_19661,U_19659] :
        ( ( hBOOL(hAPP(U_19661,sK513(U_19663,U_19661,U_19659)))
          & hBOOL(hAPP(hAPP(c_member(U_19659),sK513(U_19663,U_19661,U_19659)),hAPP(c_List_Oset(U_19659),U_19663))) )
        | ~ c_List_Olist__ex(U_19659,U_19661,U_19663) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK513]),skolemize(U_19654,sK513(U_19663,U_19661,U_19659))],[f_4733_3]) ).

cnf(f_4733_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19659),sK513(U_19663,U_19661,U_19659)),hAPP(c_List_Oset(U_19659),U_19663)))
    | ~ c_List_Olist__ex(U_19659,U_19661,U_19663) ),
    inference(clausify,[status(thm)],[f_4733_4]) ).

cnf(f_4733_6,plain,
    ( hBOOL(hAPP(U_19661,sK513(U_19663,U_19661,U_19659)))
    | ~ c_List_Olist__ex(U_19659,U_19661,U_19663) ),
    inference(clausify,[status(thm)],[f_4733_4]) ).

cnf(f_4733_7,plain,
    ( c_List_Olist__ex(U_19660,U_19662,U_19664)
    | ~ hBOOL(hAPP(U_19662,U_19655))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19660),U_19655),hAPP(c_List_Oset(U_19660),U_19664))) ),
    inference(clausify,[status(thm)],[f_4733_4]) ).

fof(f_4734_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,V_xs_2) )
      & ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_4734_2,plain,
    ! [U_19669,U_19668,U_19667] :
      ( ( ? [U_19666] :
            ( hBOOL(hAPP(U_19669,U_19666))
            & hBOOL(hAPP(hAPP(c_member(U_19667),U_19666),hAPP(c_List_Oset(U_19667),U_19668))) )
        | ~ c_List_Olist__ex(U_19667,U_19669,U_19668) )
      & ( c_List_Olist__ex(U_19667,U_19669,U_19668)
        | ! [U_19665] :
            ( ~ hBOOL(hAPP(U_19669,U_19665))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19667),U_19665),hAPP(c_List_Oset(U_19667),U_19668))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ( ! [U_19675,U_19673,U_19671] :
        ( ? [U_19666] :
            ( hBOOL(hAPP(U_19675,U_19666))
            & hBOOL(hAPP(hAPP(c_member(U_19671),U_19666),hAPP(c_List_Oset(U_19671),U_19673))) )
        | ~ c_List_Olist__ex(U_19671,U_19675,U_19673) )
    & ! [U_19674,U_19672,U_19670] :
        ( c_List_Olist__ex(U_19670,U_19674,U_19672)
        | ! [U_19665] :
            ( ~ hBOOL(hAPP(U_19674,U_19665))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19670),U_19665),hAPP(c_List_Oset(U_19670),U_19672))) ) ) ),
    inference(miniscope,[status(thm)],[f_4734_2]) ).

fof(f_4734_4,plain,
    ( ! [U_19675,U_19673,U_19671] :
        ( ( hBOOL(hAPP(U_19675,sK514(U_19675,U_19673,U_19671)))
          & hBOOL(hAPP(hAPP(c_member(U_19671),sK514(U_19675,U_19673,U_19671)),hAPP(c_List_Oset(U_19671),U_19673))) )
        | ~ c_List_Olist__ex(U_19671,U_19675,U_19673) )
    & ! [U_19674,U_19672,U_19670] :
        ( c_List_Olist__ex(U_19670,U_19674,U_19672)
        | ! [U_19665] :
            ( ~ hBOOL(hAPP(U_19674,U_19665))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19670),U_19665),hAPP(c_List_Oset(U_19670),U_19672))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK514]),skolemize(U_19666,sK514(U_19675,U_19673,U_19671))],[f_4734_3]) ).

cnf(f_4734_5,plain,
    ( c_List_Olist__ex(U_19670,U_19674,U_19672)
    | ~ hBOOL(hAPP(U_19674,U_19665))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19670),U_19665),hAPP(c_List_Oset(U_19670),U_19672))) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

cnf(f_4734_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19671),sK514(U_19675,U_19673,U_19671)),hAPP(c_List_Oset(U_19671),U_19673)))
    | ~ c_List_Olist__ex(U_19671,U_19675,U_19673) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

cnf(f_4734_7,plain,
    ( hBOOL(hAPP(U_19675,sK514(U_19675,U_19673,U_19671)))
    | ~ c_List_Olist__ex(U_19671,U_19675,U_19673) ),
    inference(clausify,[status(thm)],[f_4734_4]) ).

fof(f_4735_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_4735_2,plain,
    ! [U_19676] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19676,tc_HOL_Obool) = c_Set_OBex(U_19676),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

cnf(f_4735_3,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19676,tc_HOL_Obool) = c_Set_OBex(U_19676),
    inference(clausify,[status(thm)],[f_4735_2]) ).

fof(f_4736_1,plain,
    ! [V_Pa_2,T_b,B_x] :
      ( ~ hBOOL(hAPP(V_Pa_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_4736_2,plain,
    ! [U_19679,U_19678,U_19677] :
      ( ~ hBOOL(hAPP(U_19679,U_19677))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19678),U_19677),c_Orderings_Obot__class_Obot(tc_fun(U_19678,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

cnf(f_4736_3,plain,
    ( ~ hBOOL(hAPP(U_19679,U_19677))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19678),U_19677),c_Orderings_Obot__class_Obot(tc_fun(U_19678,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4736_2]) ).

fof(f_4737_1,plain,
    ! [V_Qa_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_Qa_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_Qa_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_Qa_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_Qa_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bex]) ).

fof(f_4737_2,plain,
    ! [U_19685,U_19684,U_19683,U_19682] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685)))))
          | ? [U_19681] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),U_19681))))
              & hBOOL(hAPP(hAPP(c_member(U_19682),U_19681),U_19683)) ) )
        & ( ! [U_19680] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),U_19680))))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19682),U_19680),U_19683)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19682),U_19683)) ),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

fof(f_4737_3,plain,
    ! [U_19685,U_19684,U_19683,U_19682] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),sK515(U_19685,U_19684,U_19683,U_19682)))))
            & hBOOL(hAPP(hAPP(c_member(U_19682),sK515(U_19685,U_19684,U_19683,U_19682)),U_19683)) ) )
        & ( ! [U_19680] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),U_19680))))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19682),U_19680),U_19683)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19682),U_19683)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK515]),skolemize(U_19681,sK515(U_19685,U_19684,U_19683,U_19682))],[f_4737_2]) ).

cnf(f_4737_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),U_19680))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19682),U_19680),U_19683))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19682),U_19683)) ),
    inference(clausify,[status(thm)],[f_4737_3]) ).

cnf(f_4737_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19682),sK515(U_19685,U_19684,U_19683,U_19682)),U_19683))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19682),U_19683)) ),
    inference(clausify,[status(thm)],[f_4737_3]) ).

cnf(f_4737_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBC(U_19684,U_19682,tc_HOL_Obool),U_19685),sK515(U_19685,U_19684,U_19683,U_19682)))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_19684),hAPP(c_Set_OCollect(U_19684),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool,U_19684),c_HOL_OEx(U_19682)),hAPP(hAPP(c_COMBB(tc_fun(U_19682,tc_HOL_Obool),tc_fun(U_19682,tc_HOL_Obool),U_19684),hAPP(c_COMBS(U_19682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19682),c_fconj),hAPP(hAPP(c_COMBC(U_19682,tc_fun(U_19682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19682)),U_19683)))),U_19685)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19682),U_19683)) ),
    inference(clausify,[status(thm)],[f_4737_3]) ).

fof(f_4738_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_4738_2,plain,
    ! [U_19691,U_19690] :
      ( ( ? [U_19689] :
            ( hBOOL(hAPP(U_19691,U_19689))
            & hBOOL(hAPP(hAPP(c_member(U_19690),U_19689),c_Orderings_Otop__class_Otop(tc_fun(U_19690,tc_HOL_Obool)))) )
        | ! [U_19688] : ~ hBOOL(hAPP(U_19691,U_19688)) )
      & ( ? [U_19687] : hBOOL(hAPP(U_19691,U_19687))
        | ! [U_19686] :
            ( ~ hBOOL(hAPP(U_19691,U_19686))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19690),U_19686),c_Orderings_Otop__class_Otop(tc_fun(U_19690,tc_HOL_Obool)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ( ! [U_19695] :
        ( ! [U_19693] :
          ? [U_19689] :
            ( hBOOL(hAPP(U_19695,U_19689))
            & hBOOL(hAPP(hAPP(c_member(U_19693),U_19689),c_Orderings_Otop__class_Otop(tc_fun(U_19693,tc_HOL_Obool)))) )
        | ! [U_19688] : ~ hBOOL(hAPP(U_19695,U_19688)) )
    & ! [U_19694] :
        ( ! [U_19692,U_19686] :
            ( ~ hBOOL(hAPP(U_19694,U_19686))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19692),U_19686),c_Orderings_Otop__class_Otop(tc_fun(U_19692,tc_HOL_Obool)))) )
        | ? [U_19687] : hBOOL(hAPP(U_19694,U_19687)) ) ),
    inference(miniscope,[status(thm)],[f_4738_2]) ).

fof(f_4738_4,plain,
    ( ! [U_19695] :
        ( ! [U_19693] :
          ? [U_19689] :
            ( hBOOL(hAPP(U_19695,U_19689))
            & hBOOL(hAPP(hAPP(c_member(U_19693),U_19689),c_Orderings_Otop__class_Otop(tc_fun(U_19693,tc_HOL_Obool)))) )
        | ! [U_19688] : ~ hBOOL(hAPP(U_19695,U_19688)) )
    & ! [U_19694] :
        ( ! [U_19692,U_19686] :
            ( ~ hBOOL(hAPP(U_19694,U_19686))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19692),U_19686),c_Orderings_Otop__class_Otop(tc_fun(U_19692,tc_HOL_Obool)))) )
        | hBOOL(hAPP(U_19694,sK516(U_19694))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK516]),skolemize(U_19687,sK516(U_19694))],[f_4738_3]) ).

fof(f_4738_5,plain,
    ( ! [U_19695] :
        ( ! [U_19693] :
            ( hBOOL(hAPP(U_19695,sK517(U_19695,U_19693)))
            & hBOOL(hAPP(hAPP(c_member(U_19693),sK517(U_19695,U_19693)),c_Orderings_Otop__class_Otop(tc_fun(U_19693,tc_HOL_Obool)))) )
        | ! [U_19688] : ~ hBOOL(hAPP(U_19695,U_19688)) )
    & ! [U_19694] :
        ( ! [U_19692,U_19686] :
            ( ~ hBOOL(hAPP(U_19694,U_19686))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19692),U_19686),c_Orderings_Otop__class_Otop(tc_fun(U_19692,tc_HOL_Obool)))) )
        | hBOOL(hAPP(U_19694,sK516(U_19694))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK517]),skolemize(U_19689,sK517(U_19695,U_19693))],[f_4738_4]) ).

cnf(f_4738_6,plain,
    ( ~ hBOOL(hAPP(U_19694,U_19686))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19692),U_19686),c_Orderings_Otop__class_Otop(tc_fun(U_19692,tc_HOL_Obool))))
    | hBOOL(hAPP(U_19694,sK516(U_19694))) ),
    inference(clausify,[status(thm)],[f_4738_5]) ).

cnf(f_4738_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19693),sK517(U_19695,U_19693)),c_Orderings_Otop__class_Otop(tc_fun(U_19693,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_19695,U_19688)) ),
    inference(clausify,[status(thm)],[f_4738_5]) ).

cnf(f_4738_8,plain,
    ( hBOOL(hAPP(U_19695,sK517(U_19695,U_19693)))
    | ~ hBOOL(hAPP(U_19695,U_19688)) ),
    inference(clausify,[status(thm)],[f_4738_5]) ).

fof(f_4739_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_4739_2,plain,
    ! [U_19697,U_19696] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19696,tc_HOL_Obool),U_19697) = hAPP(c_Set_OCollect(U_19696),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_19696),c_HOL_OEx(tc_fun(U_19696,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),U_19696),hAPP(c_COMBS(tc_fun(U_19696,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_19696,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19696,tc_HOL_Obool),tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19696,tc_HOL_Obool))),U_19697)))),c_member(U_19696)))),
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

cnf(f_4739_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19696,tc_HOL_Obool),U_19697) = hAPP(c_Set_OCollect(U_19696),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_19696),c_HOL_OEx(tc_fun(U_19696,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),U_19696),hAPP(c_COMBS(tc_fun(U_19696,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_19696,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19696,tc_HOL_Obool),tc_fun(tc_fun(U_19696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19696,tc_HOL_Obool))),U_19697)))),c_member(U_19696)))),
    inference(clausify,[status(thm)],[f_4739_2]) ).

fof(f_4740_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_4740_2,plain,
    ! [U_19701,U_19700,U_19699,U_19698] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19698,tc_fun(U_19699,tc_HOL_Obool)),U_19700),U_19701) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19699,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19698,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19699,tc_HOL_Obool)),c_HOL_OEx(U_19698)),hAPP(hAPP(c_COMBB(tc_fun(U_19698,tc_HOL_Obool),tc_fun(U_19698,tc_HOL_Obool),tc_fun(U_19699,tc_HOL_Obool)),hAPP(c_COMBS(U_19698,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19698),c_fconj),hAPP(hAPP(c_COMBC(U_19698,tc_fun(U_19698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19698)),U_19700)))),hAPP(hAPP(c_COMBC(tc_fun(U_19699,tc_HOL_Obool),tc_fun(U_19698,tc_fun(U_19699,tc_HOL_Obool)),tc_fun(U_19698,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19699,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19698,tc_fun(U_19699,tc_HOL_Obool)),tc_fun(U_19698,tc_HOL_Obool)),tc_fun(U_19699,tc_HOL_Obool)),c_COMBB(tc_fun(U_19699,tc_HOL_Obool),tc_HOL_Obool,U_19698)),c_fequal)),U_19701))))),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

cnf(f_4740_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19698,tc_fun(U_19699,tc_HOL_Obool)),U_19700),U_19701) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19699,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19698,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19699,tc_HOL_Obool)),c_HOL_OEx(U_19698)),hAPP(hAPP(c_COMBB(tc_fun(U_19698,tc_HOL_Obool),tc_fun(U_19698,tc_HOL_Obool),tc_fun(U_19699,tc_HOL_Obool)),hAPP(c_COMBS(U_19698,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19698),c_fconj),hAPP(hAPP(c_COMBC(U_19698,tc_fun(U_19698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19698)),U_19700)))),hAPP(hAPP(c_COMBC(tc_fun(U_19699,tc_HOL_Obool),tc_fun(U_19698,tc_fun(U_19699,tc_HOL_Obool)),tc_fun(U_19698,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19699,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19698,tc_fun(U_19699,tc_HOL_Obool)),tc_fun(U_19698,tc_HOL_Obool)),tc_fun(U_19699,tc_HOL_Obool)),c_COMBB(tc_fun(U_19699,tc_HOL_Obool),tc_HOL_Obool,U_19698)),c_fequal)),U_19701))))),
    inference(clausify,[status(thm)],[f_4740_2]) ).

fof(f_4741_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_4741_2,plain,
    ! [U_19705,U_19704,U_19703,U_19702] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19702,tc_fun(U_19703,tc_HOL_Obool)),U_19704),U_19705) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19703,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19702,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19703,tc_HOL_Obool)),c_HOL_OEx(U_19702)),hAPP(hAPP(c_COMBB(tc_fun(U_19702,tc_HOL_Obool),tc_fun(U_19702,tc_HOL_Obool),tc_fun(U_19703,tc_HOL_Obool)),hAPP(c_COMBS(U_19702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19702),c_fconj),hAPP(hAPP(c_COMBC(U_19702,tc_fun(U_19702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19702)),U_19704)))),hAPP(hAPP(c_COMBC(tc_fun(U_19703,tc_HOL_Obool),tc_fun(U_19702,tc_fun(U_19703,tc_HOL_Obool)),tc_fun(U_19702,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19703,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19702,tc_fun(U_19703,tc_HOL_Obool)),tc_fun(U_19702,tc_HOL_Obool)),tc_fun(U_19703,tc_HOL_Obool)),c_COMBB(tc_fun(U_19703,tc_HOL_Obool),tc_HOL_Obool,U_19702)),c_fequal)),U_19705))))),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

cnf(f_4741_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19702,tc_fun(U_19703,tc_HOL_Obool)),U_19704),U_19705) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19703,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19702,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19703,tc_HOL_Obool)),c_HOL_OEx(U_19702)),hAPP(hAPP(c_COMBB(tc_fun(U_19702,tc_HOL_Obool),tc_fun(U_19702,tc_HOL_Obool),tc_fun(U_19703,tc_HOL_Obool)),hAPP(c_COMBS(U_19702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19702),c_fconj),hAPP(hAPP(c_COMBC(U_19702,tc_fun(U_19702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19702)),U_19704)))),hAPP(hAPP(c_COMBC(tc_fun(U_19703,tc_HOL_Obool),tc_fun(U_19702,tc_fun(U_19703,tc_HOL_Obool)),tc_fun(U_19702,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19703,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19702,tc_fun(U_19703,tc_HOL_Obool)),tc_fun(U_19702,tc_HOL_Obool)),tc_fun(U_19703,tc_HOL_Obool)),c_COMBB(tc_fun(U_19703,tc_HOL_Obool),tc_HOL_Obool,U_19702)),c_fequal)),U_19705))))),
    inference(clausify,[status(thm)],[f_4741_2]) ).

fof(f_4742_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_4742_2,plain,
    ! [U_19709,U_19708,U_19707,U_19706] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19707,U_19706),U_19708),U_19709) = c_Complete__Lattice_OSup__class_OSup(U_19706,hAPP(c_Set_OCollect(U_19706),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_HOL_Obool,U_19706),c_HOL_OEx(tc_fun(U_19707,U_19706))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),U_19706),hAPP(c_COMBS(tc_fun(U_19707,U_19706),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19707,U_19706)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19707,U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19707,U_19706))),U_19708)))),hAPP(hAPP(c_COMBC(U_19706,tc_fun(tc_fun(U_19707,U_19706),U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19706,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19707,U_19706),U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool)),U_19706),c_COMBB(U_19706,tc_HOL_Obool,tc_fun(U_19707,U_19706))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19707,U_19706),U_19707,U_19706),c_COMBI(tc_fun(U_19707,U_19706))),U_19709))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19706) ),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

cnf(f_4742_3,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19707,U_19706),U_19708),U_19709) = c_Complete__Lattice_OSup__class_OSup(U_19706,hAPP(c_Set_OCollect(U_19706),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_HOL_Obool,U_19706),c_HOL_OEx(tc_fun(U_19707,U_19706))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),U_19706),hAPP(c_COMBS(tc_fun(U_19707,U_19706),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19707,U_19706)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19707,U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19707,U_19706))),U_19708)))),hAPP(hAPP(c_COMBC(U_19706,tc_fun(tc_fun(U_19707,U_19706),U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19706,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19707,U_19706),U_19706),tc_fun(tc_fun(U_19707,U_19706),tc_HOL_Obool)),U_19706),c_COMBB(U_19706,tc_HOL_Obool,tc_fun(U_19707,U_19706))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19707,U_19706),U_19707,U_19706),c_COMBI(tc_fun(U_19707,U_19706))),U_19709))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19706) ),
    inference(clausify,[status(thm)],[f_4742_2]) ).

fof(f_4743_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_4743_2,plain,
    ! [U_19713,U_19712,U_19711,U_19710] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19711,U_19710),U_19712),U_19713) = c_Complete__Lattice_OSup__class_OSup(U_19710,hAPP(c_Set_OCollect(U_19710),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_HOL_Obool,U_19710),c_HOL_OEx(tc_fun(U_19711,U_19710))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),U_19710),hAPP(c_COMBS(tc_fun(U_19711,U_19710),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19711,U_19710)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19711,U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19711,U_19710))),U_19712)))),hAPP(hAPP(c_COMBC(U_19710,tc_fun(tc_fun(U_19711,U_19710),U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19710,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19711,U_19710),U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool)),U_19710),c_COMBB(U_19710,tc_HOL_Obool,tc_fun(U_19711,U_19710))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19711,U_19710),U_19711,U_19710),c_COMBI(tc_fun(U_19711,U_19710))),U_19713))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19710) ),
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

cnf(f_4743_3,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19711,U_19710),U_19712),U_19713) = c_Complete__Lattice_OSup__class_OSup(U_19710,hAPP(c_Set_OCollect(U_19710),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_HOL_Obool,U_19710),c_HOL_OEx(tc_fun(U_19711,U_19710))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),U_19710),hAPP(c_COMBS(tc_fun(U_19711,U_19710),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19711,U_19710)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19711,U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19711,U_19710))),U_19712)))),hAPP(hAPP(c_COMBC(U_19710,tc_fun(tc_fun(U_19711,U_19710),U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19710,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19711,U_19710),U_19710),tc_fun(tc_fun(U_19711,U_19710),tc_HOL_Obool)),U_19710),c_COMBB(U_19710,tc_HOL_Obool,tc_fun(U_19711,U_19710))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19711,U_19710),U_19711,U_19710),c_COMBI(tc_fun(U_19711,U_19710))),U_19713))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19710) ),
    inference(clausify,[status(thm)],[f_4743_2]) ).

fof(f_4744_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_4744_2,plain,
    ! [U_19717,U_19716,U_19715,U_19714] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19715,U_19714),U_19716),U_19717) = c_Complete__Lattice_OInf__class_OInf(U_19714,hAPP(c_Set_OCollect(U_19714),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_HOL_Obool,U_19714),c_HOL_OEx(tc_fun(U_19715,U_19714))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),U_19714),hAPP(c_COMBS(tc_fun(U_19715,U_19714),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19715,U_19714)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19715,U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19715,U_19714))),U_19716)))),hAPP(hAPP(c_COMBC(U_19714,tc_fun(tc_fun(U_19715,U_19714),U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19714,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19715,U_19714),U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool)),U_19714),c_COMBB(U_19714,tc_HOL_Obool,tc_fun(U_19715,U_19714))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19715,U_19714),U_19715,U_19714),c_COMBI(tc_fun(U_19715,U_19714))),U_19717))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19714) ),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

cnf(f_4744_3,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19715,U_19714),U_19716),U_19717) = c_Complete__Lattice_OInf__class_OInf(U_19714,hAPP(c_Set_OCollect(U_19714),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_HOL_Obool,U_19714),c_HOL_OEx(tc_fun(U_19715,U_19714))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),U_19714),hAPP(c_COMBS(tc_fun(U_19715,U_19714),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19715,U_19714)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19715,U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19715,U_19714))),U_19716)))),hAPP(hAPP(c_COMBC(U_19714,tc_fun(tc_fun(U_19715,U_19714),U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19714,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19715,U_19714),U_19714),tc_fun(tc_fun(U_19715,U_19714),tc_HOL_Obool)),U_19714),c_COMBB(U_19714,tc_HOL_Obool,tc_fun(U_19715,U_19714))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19715,U_19714),U_19715,U_19714),c_COMBI(tc_fun(U_19715,U_19714))),U_19717))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19714) ),
    inference(clausify,[status(thm)],[f_4744_2]) ).

fof(f_4745_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_4745_2,plain,
    ! [U_19721,U_19720,U_19719,U_19718] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19719,U_19718),U_19720),U_19721) = c_Complete__Lattice_OInf__class_OInf(U_19718,hAPP(c_Set_OCollect(U_19718),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_HOL_Obool,U_19718),c_HOL_OEx(tc_fun(U_19719,U_19718))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),U_19718),hAPP(c_COMBS(tc_fun(U_19719,U_19718),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19719,U_19718)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19719,U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19719,U_19718))),U_19720)))),hAPP(hAPP(c_COMBC(U_19718,tc_fun(tc_fun(U_19719,U_19718),U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19718,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19719,U_19718),U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool)),U_19718),c_COMBB(U_19718,tc_HOL_Obool,tc_fun(U_19719,U_19718))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19719,U_19718),U_19719,U_19718),c_COMBI(tc_fun(U_19719,U_19718))),U_19721))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19718) ),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

cnf(f_4745_3,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19719,U_19718),U_19720),U_19721) = c_Complete__Lattice_OInf__class_OInf(U_19718,hAPP(c_Set_OCollect(U_19718),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_HOL_Obool,U_19718),c_HOL_OEx(tc_fun(U_19719,U_19718))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),U_19718),hAPP(c_COMBS(tc_fun(U_19719,U_19718),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19719,U_19718)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19719,U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19719,U_19718))),U_19720)))),hAPP(hAPP(c_COMBC(U_19718,tc_fun(tc_fun(U_19719,U_19718),U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19718,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19719,U_19718),U_19718),tc_fun(tc_fun(U_19719,U_19718),tc_HOL_Obool)),U_19718),c_COMBB(U_19718,tc_HOL_Obool,tc_fun(U_19719,U_19718))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19719,U_19718),U_19719,U_19718),c_COMBI(tc_fun(U_19719,U_19718))),U_19721))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19718) ),
    inference(clausify,[status(thm)],[f_4745_2]) ).

fof(f_4746_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_4746_2,plain,
    ! [U_19727,U_19726,U_19725,U_19724] :
      ( c_Wellfounded_Omax__extp(U_19724,U_19727,U_19725,U_19726)
      | ? [U_19723] :
          ( ! [U_19722] :
              ( ~ hBOOL(hAPP(hAPP(U_19727,U_19723),U_19722))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19724),U_19722),U_19726)) )
          & hBOOL(hAPP(hAPP(c_member(U_19724),U_19723),U_19725)) )
      | U_19726 = c_Orderings_Obot__class_Obot(tc_fun(U_19724,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19726))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19725)) ),
    inference(variable_rename,[status(thm)],[f_4746_1]) ).

fof(f_4746_3,plain,
    ! [U_19727,U_19726,U_19725,U_19724] :
      ( c_Wellfounded_Omax__extp(U_19724,U_19727,U_19725,U_19726)
      | ( ! [U_19722] :
            ( ~ hBOOL(hAPP(hAPP(U_19727,sK518(U_19727,U_19726,U_19725,U_19724)),U_19722))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19724),U_19722),U_19726)) )
        & hBOOL(hAPP(hAPP(c_member(U_19724),sK518(U_19727,U_19726,U_19725,U_19724)),U_19725)) )
      | U_19726 = c_Orderings_Obot__class_Obot(tc_fun(U_19724,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19726))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19725)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK518]),skolemize(U_19723,sK518(U_19727,U_19726,U_19725,U_19724))],[f_4746_2]) ).

cnf(f_4746_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19724),sK518(U_19727,U_19726,U_19725,U_19724)),U_19725))
    | c_Wellfounded_Omax__extp(U_19724,U_19727,U_19725,U_19726)
    | U_19726 = c_Orderings_Obot__class_Obot(tc_fun(U_19724,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19726))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19725)) ),
    inference(clausify,[status(thm)],[f_4746_3]) ).

cnf(f_4746_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19727,sK518(U_19727,U_19726,U_19725,U_19724)),U_19722))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19724),U_19722),U_19726))
    | c_Wellfounded_Omax__extp(U_19724,U_19727,U_19725,U_19726)
    | U_19726 = c_Orderings_Obot__class_Obot(tc_fun(U_19724,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19726))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19724),U_19725)) ),
    inference(clausify,[status(thm)],[f_4746_3]) ).

fof(f_4747_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_4747_2,plain,
    ! [U_19735,U_19734,U_19733,U_19732] :
      ( ( c_Wellfounded_Omax__extp(U_19732,U_19733,U_19734,U_19735)
        | ? [U_19731] :
            ( ! [U_19730] :
                ( ~ hBOOL(hAPP(hAPP(U_19733,U_19731),U_19730))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19732),U_19730),U_19735)) )
            & hBOOL(hAPP(hAPP(c_member(U_19732),U_19731),U_19734)) )
        | U_19735 = c_Orderings_Obot__class_Obot(tc_fun(U_19732,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19732),U_19735))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19732),U_19734)) )
      & ( ( ! [U_19729] :
              ( ? [U_19728] :
                  ( hBOOL(hAPP(hAPP(U_19733,U_19729),U_19728))
                  & hBOOL(hAPP(hAPP(c_member(U_19732),U_19728),U_19735)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19732),U_19729),U_19734)) )
          & U_19735 != c_Orderings_Obot__class_Obot(tc_fun(U_19732,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19732),U_19735))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19732),U_19734)) )
        | ~ c_Wellfounded_Omax__extp(U_19732,U_19733,U_19734,U_19735) ) ),
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

fof(f_4747_3,plain,
    ( ! [U_19743,U_19741,U_19739,U_19737] :
        ( c_Wellfounded_Omax__extp(U_19737,U_19739,U_19741,U_19743)
        | ? [U_19731] :
            ( ! [U_19730] :
                ( ~ hBOOL(hAPP(hAPP(U_19739,U_19731),U_19730))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19737),U_19730),U_19743)) )
            & hBOOL(hAPP(hAPP(c_member(U_19737),U_19731),U_19741)) )
        | U_19743 = c_Orderings_Obot__class_Obot(tc_fun(U_19737,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19743))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19741)) )
    & ! [U_19742,U_19740,U_19738,U_19736] :
        ( ( ! [U_19729] :
              ( ? [U_19728] :
                  ( hBOOL(hAPP(hAPP(U_19738,U_19729),U_19728))
                  & hBOOL(hAPP(hAPP(c_member(U_19736),U_19728),U_19742)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19736),U_19729),U_19740)) )
          & U_19742 != c_Orderings_Obot__class_Obot(tc_fun(U_19736,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19742))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19740)) )
        | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ) ),
    inference(miniscope,[status(thm)],[f_4747_2]) ).

fof(f_4747_4,plain,
    ( ! [U_19743,U_19741,U_19739,U_19737] :
        ( c_Wellfounded_Omax__extp(U_19737,U_19739,U_19741,U_19743)
        | ? [U_19731] :
            ( ! [U_19730] :
                ( ~ hBOOL(hAPP(hAPP(U_19739,U_19731),U_19730))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19737),U_19730),U_19743)) )
            & hBOOL(hAPP(hAPP(c_member(U_19737),U_19731),U_19741)) )
        | U_19743 = c_Orderings_Obot__class_Obot(tc_fun(U_19737,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19743))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19741)) )
    & ! [U_19742,U_19740,U_19738,U_19736] :
        ( ( ! [U_19729] :
              ( ( hBOOL(hAPP(hAPP(U_19738,U_19729),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)))
                & hBOOL(hAPP(hAPP(c_member(U_19736),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)),U_19742)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19736),U_19729),U_19740)) )
          & U_19742 != c_Orderings_Obot__class_Obot(tc_fun(U_19736,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19742))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19740)) )
        | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK519]),skolemize(U_19728,sK519(U_19742,U_19740,U_19738,U_19736,U_19729))],[f_4747_3]) ).

fof(f_4747_5,plain,
    ( ! [U_19743,U_19741,U_19739,U_19737] :
        ( c_Wellfounded_Omax__extp(U_19737,U_19739,U_19741,U_19743)
        | ( ! [U_19730] :
              ( ~ hBOOL(hAPP(hAPP(U_19739,sK520(U_19743,U_19741,U_19739,U_19737)),U_19730))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19737),U_19730),U_19743)) )
          & hBOOL(hAPP(hAPP(c_member(U_19737),sK520(U_19743,U_19741,U_19739,U_19737)),U_19741)) )
        | U_19743 = c_Orderings_Obot__class_Obot(tc_fun(U_19737,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19743))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19741)) )
    & ! [U_19742,U_19740,U_19738,U_19736] :
        ( ( ! [U_19729] :
              ( ( hBOOL(hAPP(hAPP(U_19738,U_19729),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)))
                & hBOOL(hAPP(hAPP(c_member(U_19736),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)),U_19742)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19736),U_19729),U_19740)) )
          & U_19742 != c_Orderings_Obot__class_Obot(tc_fun(U_19736,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19742))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19740)) )
        | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK520]),skolemize(U_19731,sK520(U_19743,U_19741,U_19739,U_19737))],[f_4747_4]) ).

cnf(f_4747_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19740))
    | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19736),U_19742))
    | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_8,plain,
    ( U_19742 != c_Orderings_Obot__class_Obot(tc_fun(U_19736,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19736),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)),U_19742))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19736),U_19729),U_19740))
    | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_10,plain,
    ( hBOOL(hAPP(hAPP(U_19738,U_19729),sK519(U_19742,U_19740,U_19738,U_19736,U_19729)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19736),U_19729),U_19740))
    | ~ c_Wellfounded_Omax__extp(U_19736,U_19738,U_19740,U_19742) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19737),sK520(U_19743,U_19741,U_19739,U_19737)),U_19741))
    | U_19743 = c_Orderings_Obot__class_Obot(tc_fun(U_19737,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19743))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19741))
    | c_Wellfounded_Omax__extp(U_19737,U_19739,U_19741,U_19743) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

cnf(f_4747_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19739,sK520(U_19743,U_19741,U_19739,U_19737)),U_19730))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19737),U_19730),U_19743))
    | U_19743 = c_Orderings_Obot__class_Obot(tc_fun(U_19737,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19743))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19737),U_19741))
    | c_Wellfounded_Omax__extp(U_19737,U_19739,U_19741,U_19743) ),
    inference(clausify,[status(thm)],[f_4747_5]) ).

fof(f_4748_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_4748_2,plain,
    ! [U_19749,U_19748,U_19747,U_19746,U_19745,U_19744] : c_Partial__Function_Ofun__lub(U_19744,U_19745,U_19746,U_19747,U_19748,U_19749) = hAPP(U_19747,hAPP(c_Set_OCollect(U_19744),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_HOL_Obool,U_19744),c_HOL_OEx(tc_fun(U_19746,U_19744))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),U_19744),hAPP(c_COMBS(tc_fun(U_19746,U_19744),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19746,U_19744)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19746,U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19746,U_19744))),U_19748)))),hAPP(hAPP(c_COMBC(U_19744,tc_fun(tc_fun(U_19746,U_19744),U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19744,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19746,U_19744),U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool)),U_19744),c_COMBB(U_19744,tc_HOL_Obool,tc_fun(U_19746,U_19744))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19746,U_19744),U_19746,U_19744),c_COMBI(tc_fun(U_19746,U_19744))),U_19749)))))),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

cnf(f_4748_3,plain,
    c_Partial__Function_Ofun__lub(U_19744,U_19745,U_19746,U_19747,U_19748,U_19749) = hAPP(U_19747,hAPP(c_Set_OCollect(U_19744),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_HOL_Obool,U_19744),c_HOL_OEx(tc_fun(U_19746,U_19744))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),U_19744),hAPP(c_COMBS(tc_fun(U_19746,U_19744),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19746,U_19744)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19746,U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19746,U_19744))),U_19748)))),hAPP(hAPP(c_COMBC(U_19744,tc_fun(tc_fun(U_19746,U_19744),U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19744,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19746,U_19744),U_19744),tc_fun(tc_fun(U_19746,U_19744),tc_HOL_Obool)),U_19744),c_COMBB(U_19744,tc_HOL_Obool,tc_fun(U_19746,U_19744))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19746,U_19744),U_19746,U_19744),c_COMBI(tc_fun(U_19746,U_19744))),U_19749)))))),
    inference(clausify,[status(thm)],[f_4748_2]) ).

fof(f_4749_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_4749_2,plain,
    ! [U_19754,U_19753,U_19752,U_19751,U_19750] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19751),U_19754)),c_List_Olexord(U_19750,U_19753)))
      | ~ c_Relation_Otrans(U_19750,U_19753)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19754)),c_List_Olexord(U_19750,U_19753)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19751),U_19752)),c_List_Olexord(U_19750,U_19753))) ),
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

cnf(f_4749_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19751),U_19754)),c_List_Olexord(U_19750,U_19753)))
    | ~ c_Relation_Otrans(U_19750,U_19753)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19754)),c_List_Olexord(U_19750,U_19753)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19751),U_19752)),c_List_Olexord(U_19750,U_19753))) ),
    inference(clausify,[status(thm)],[f_4749_2]) ).

fof(f_4750_1,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_trans__less__than]) ).

cnf(f_4750_2,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_4750_1]) ).

fof(f_4751_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_4751_2,plain,
    ! [U_19758,U_19757,U_19756,U_19755] :
      ( c_Relation_Otrans(tc_prod(U_19755,U_19757),c_Wellfounded_Olex__prod(U_19755,U_19757,U_19756,U_19758))
      | ~ c_Relation_Otrans(U_19757,U_19758)
      | ~ c_Relation_Otrans(U_19755,U_19756) ),
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

cnf(f_4751_3,plain,
    ( c_Relation_Otrans(tc_prod(U_19755,U_19757),c_Wellfounded_Olex__prod(U_19755,U_19757,U_19756,U_19758))
    | ~ c_Relation_Otrans(U_19757,U_19758)
    | ~ c_Relation_Otrans(U_19755,U_19756) ),
    inference(clausify,[status(thm)],[f_4751_2]) ).

fof(f_4752_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_4752_2,plain,
    ! [U_19762,U_19761,U_19760,U_19759] :
      ( c_Relation_Otrans(U_19761,hAPP(hAPP(c_Relation_Oinv__image(U_19759,U_19761),U_19760),U_19762))
      | ~ c_Relation_Otrans(U_19759,U_19760) ),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

cnf(f_4752_3,plain,
    ( c_Relation_Otrans(U_19761,hAPP(hAPP(c_Relation_Oinv__image(U_19759,U_19761),U_19760),U_19762))
    | ~ c_Relation_Otrans(U_19759,U_19760) ),
    inference(clausify,[status(thm)],[f_4752_2]) ).

fof(f_4753_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_4753_2,plain,
    ! [U_19764,U_19763] :
      ( c_Relation_Otrans(U_19763,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19763,U_19763),tc_HOL_Obool)),U_19764),c_Relation_OId(U_19763)))
      | ~ c_Relation_Otrans(U_19763,U_19764) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

cnf(f_4753_3,plain,
    ( c_Relation_Otrans(U_19763,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19763,U_19763),tc_HOL_Obool)),U_19764),c_Relation_OId(U_19763)))
    | ~ c_Relation_Otrans(U_19763,U_19764) ),
    inference(clausify,[status(thm)],[f_4753_2]) ).

fof(f_4754_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_4754_2,plain,
    ! [U_19767,U_19766,U_19765] :
      ( c_Relation_Otrans(U_19765,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19765,U_19765),tc_HOL_Obool)),U_19766),U_19767))
      | ~ c_Relation_Otrans(U_19765,U_19767)
      | ~ c_Relation_Otrans(U_19765,U_19766) ),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

cnf(f_4754_3,plain,
    ( c_Relation_Otrans(U_19765,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19765,U_19765),tc_HOL_Obool)),U_19766),U_19767))
    | ~ c_Relation_Otrans(U_19765,U_19767)
    | ~ c_Relation_Otrans(U_19765,U_19766) ),
    inference(clausify,[status(thm)],[f_4754_2]) ).

fof(f_4755_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_4755_2,plain,
    ! [U_19769,U_19768] : c_Relation_Otrans(U_19768,c_Transitive__Closure_Ortrancl(U_19768,U_19769)),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

cnf(f_4755_3,plain,
    c_Relation_Otrans(U_19768,c_Transitive__Closure_Ortrancl(U_19768,U_19769)),
    inference(clausify,[status(thm)],[f_4755_2]) ).

fof(f_4756_1,plain,
    ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_trans__Id]) ).

fof(f_4756_2,plain,
    ! [U_19770] : c_Relation_Otrans(U_19770,c_Relation_OId(U_19770)),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

cnf(f_4756_3,plain,
    c_Relation_Otrans(U_19770,c_Relation_OId(U_19770)),
    inference(clausify,[status(thm)],[f_4756_2]) ).

fof(f_4757_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_4757_2,plain,
    ! [U_19772,U_19771] : c_Relation_Otrans(U_19771,c_Transitive__Closure_Otrancl(U_19771,U_19772)),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

cnf(f_4757_3,plain,
    c_Relation_Otrans(U_19771,c_Transitive__Closure_Otrancl(U_19771,U_19772)),
    inference(clausify,[status(thm)],[f_4757_2]) ).

fof(f_4758_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_4758_2,plain,
    ! [U_19774,U_19773] :
      ( c_Transitive__Closure_Otrancl(U_19773,U_19774) = U_19774
      | ~ c_Relation_Otrans(U_19773,U_19774) ),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

cnf(f_4758_3,plain,
    ( c_Transitive__Closure_Otrancl(U_19773,U_19774) = U_19774
    | ~ c_Relation_Otrans(U_19773,U_19774) ),
    inference(clausify,[status(thm)],[f_4758_2]) ).

fof(f_4759_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_4759_2,plain,
    ! [U_19776,U_19775] : c_Relation_Otrans(U_19775,c_Relation_OId__on(U_19775,U_19776)),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

cnf(f_4759_3,plain,
    c_Relation_Otrans(U_19775,c_Relation_OId__on(U_19775,U_19776)),
    inference(clausify,[status(thm)],[f_4759_2]) ).

fof(f_4760_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_4760_2,plain,
    ! [U_19777] : c_Relation_Otrans(tc_fun(U_19777,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_19777)),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

cnf(f_4760_3,plain,
    c_Relation_Otrans(tc_fun(U_19777,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_19777)),
    inference(clausify,[status(thm)],[f_4760_2]) ).

fof(f_4761_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_4761_2,plain,
    ! [U_19779,U_19778] :
      ( c_Relation_Otrans(tc_List_Olist(U_19778),c_List_Olexord(U_19778,U_19779))
      | ~ c_Relation_Otrans(U_19778,U_19779) ),
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

cnf(f_4761_3,plain,
    ( c_Relation_Otrans(tc_List_Olist(U_19778),c_List_Olexord(U_19778,U_19779))
    | ~ c_Relation_Otrans(U_19778,U_19779) ),
    inference(clausify,[status(thm)],[f_4761_2]) ).

fof(f_4762_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_4762_2,plain,
    ! [U_19781,U_19780] :
      ( c_Relation_Otrans(tc_List_Olist(U_19780),c_List_Olistrel(U_19780,U_19781))
      | ~ c_Relation_Otrans(U_19780,U_19781) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

cnf(f_4762_3,plain,
    ( c_Relation_Otrans(tc_List_Olist(U_19780),c_List_Olistrel(U_19780,U_19781))
    | ~ c_Relation_Otrans(U_19780,U_19781) ),
    inference(clausify,[status(thm)],[f_4762_2]) ).

fof(f_4763_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_4763_2,plain,
    ! [U_19783,U_19782] :
      ( ( c_Relation_Otrans(U_19782,hAPP(c_Relation_Oconverse(U_19782,U_19782),U_19783))
        | ~ c_Relation_Otrans(U_19782,U_19783) )
      & ( c_Relation_Otrans(U_19782,U_19783)
        | ~ c_Relation_Otrans(U_19782,hAPP(c_Relation_Oconverse(U_19782,U_19782),U_19783)) ) ),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

fof(f_4763_3,plain,
    ( ! [U_19787,U_19785] :
        ( c_Relation_Otrans(U_19785,hAPP(c_Relation_Oconverse(U_19785,U_19785),U_19787))
        | ~ c_Relation_Otrans(U_19785,U_19787) )
    & ! [U_19786,U_19784] :
        ( c_Relation_Otrans(U_19784,U_19786)
        | ~ c_Relation_Otrans(U_19784,hAPP(c_Relation_Oconverse(U_19784,U_19784),U_19786)) ) ),
    inference(miniscope,[status(thm)],[f_4763_2]) ).

cnf(f_4763_4,plain,
    ( c_Relation_Otrans(U_19784,U_19786)
    | ~ c_Relation_Otrans(U_19784,hAPP(c_Relation_Oconverse(U_19784,U_19784),U_19786)) ),
    inference(clausify,[status(thm)],[f_4763_3]) ).

cnf(f_4763_5,plain,
    ( c_Relation_Otrans(U_19785,hAPP(c_Relation_Oconverse(U_19785,U_19785),U_19787))
    | ~ c_Relation_Otrans(U_19785,U_19787) ),
    inference(clausify,[status(thm)],[f_4763_3]) ).

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_19789,U_19788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19788,U_19788),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19788,U_19788,U_19788),U_19789),U_19789)),U_19789))
      | ~ c_Relation_Otrans(U_19788,U_19789) ),
    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_19788,U_19788),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19788,U_19788,U_19788),U_19789),U_19789)),U_19789))
    | ~ c_Relation_Otrans(U_19788,U_19789) ),
    inference(clausify,[status(thm)],[f_4764_2]) ).

fof(f_4765_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_4765_2,plain,
    ! [U_19797,U_19796] :
      ( ( c_Relation_Otrans(U_19796,U_19797)
        | ? [U_19795,U_19794] :
            ( ? [U_19793] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19795),U_19793)),U_19797))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19794),U_19793)),U_19797)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19795),U_19794)),U_19797)) ) )
      & ( ! [U_19792,U_19791] :
            ( ! [U_19790] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19792),U_19790)),U_19797))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19791),U_19790)),U_19797)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19796,U_19796)),hAPP(hAPP(c_Product__Type_OPair(U_19796,U_19796),U_19792),U_19791)),U_19797)) )
        | ~ c_Relation_Otrans(U_19796,U_19797) ) ),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

fof(f_4765_3,plain,
    ( ! [U_19801,U_19799] :
        ( c_Relation_Otrans(U_19799,U_19801)
        | ? [U_19795,U_19794] :
            ( ? [U_19793] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),U_19795),U_19793)),U_19801))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),U_19794),U_19793)),U_19801)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),U_19795),U_19794)),U_19801)) ) )
    & ! [U_19800,U_19798] :
        ( ! [U_19792,U_19791] :
            ( ! [U_19790] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19790)),U_19800))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19791),U_19790)),U_19800)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19791)),U_19800)) )
        | ~ c_Relation_Otrans(U_19798,U_19800) ) ),
    inference(miniscope,[status(thm)],[f_4765_2]) ).

fof(f_4765_4,plain,
    ( ! [U_19801,U_19799] :
        ( c_Relation_Otrans(U_19799,U_19801)
        | ? [U_19794] :
            ( ? [U_19793] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),U_19793)),U_19801))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),U_19794),U_19793)),U_19801)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),U_19794)),U_19801)) ) )
    & ! [U_19800,U_19798] :
        ( ! [U_19792,U_19791] :
            ( ! [U_19790] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19790)),U_19800))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19791),U_19790)),U_19800)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19791)),U_19800)) )
        | ~ c_Relation_Otrans(U_19798,U_19800) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK521]),skolemize(U_19795,sK521(U_19801,U_19799))],[f_4765_3]) ).

fof(f_4765_5,plain,
    ( ! [U_19801,U_19799] :
        ( c_Relation_Otrans(U_19799,U_19801)
        | ( ? [U_19793] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),U_19793)),U_19801))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK522(U_19801,U_19799)),U_19793)),U_19801)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),sK522(U_19801,U_19799))),U_19801)) ) )
    & ! [U_19800,U_19798] :
        ( ! [U_19792,U_19791] :
            ( ! [U_19790] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19790)),U_19800))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19791),U_19790)),U_19800)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19791)),U_19800)) )
        | ~ c_Relation_Otrans(U_19798,U_19800) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK522]),skolemize(U_19794,sK522(U_19801,U_19799))],[f_4765_4]) ).

fof(f_4765_6,plain,
    ( ! [U_19801,U_19799] :
        ( c_Relation_Otrans(U_19799,U_19801)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),sK523(U_19801,U_19799))),U_19801))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK522(U_19801,U_19799)),sK523(U_19801,U_19799))),U_19801))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),sK522(U_19801,U_19799))),U_19801)) ) )
    & ! [U_19800,U_19798] :
        ( ! [U_19792,U_19791] :
            ( ! [U_19790] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19790)),U_19800))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19791),U_19790)),U_19800)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19791)),U_19800)) )
        | ~ c_Relation_Otrans(U_19798,U_19800) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK523]),skolemize(U_19793,sK523(U_19801,U_19799))],[f_4765_5]) ).

cnf(f_4765_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19790)),U_19800))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19791),U_19790)),U_19800))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19798,U_19798)),hAPP(hAPP(c_Product__Type_OPair(U_19798,U_19798),U_19792),U_19791)),U_19800))
    | ~ c_Relation_Otrans(U_19798,U_19800) ),
    inference(clausify,[status(thm)],[f_4765_6]) ).

cnf(f_4765_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),sK522(U_19801,U_19799))),U_19801))
    | c_Relation_Otrans(U_19799,U_19801) ),
    inference(clausify,[status(thm)],[f_4765_6]) ).

cnf(f_4765_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK522(U_19801,U_19799)),sK523(U_19801,U_19799))),U_19801))
    | c_Relation_Otrans(U_19799,U_19801) ),
    inference(clausify,[status(thm)],[f_4765_6]) ).

cnf(f_4765_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19799,U_19799)),hAPP(hAPP(c_Product__Type_OPair(U_19799,U_19799),sK521(U_19801,U_19799)),sK523(U_19801,U_19799))),U_19801))
    | c_Relation_Otrans(U_19799,U_19801) ),
    inference(clausify,[status(thm)],[f_4765_6]) ).

fof(f_4766_1,plain,
    ! [V_ca_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_ca_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_ca_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_4766_2,plain,
    ! [U_19806,U_19805,U_19804,U_19803,U_19802] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19804),U_19806)),U_19803))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19805),U_19806)),U_19803))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19804),U_19805)),U_19803))
      | ~ c_Relation_Otrans(U_19802,U_19803) ),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

cnf(f_4766_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19804),U_19806)),U_19803))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19805),U_19806)),U_19803))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19802,U_19802)),hAPP(hAPP(c_Product__Type_OPair(U_19802,U_19802),U_19804),U_19805)),U_19803))
    | ~ c_Relation_Otrans(U_19802,U_19803) ),
    inference(clausify,[status(thm)],[f_4766_2]) ).

fof(f_4767_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_4767_2,plain,
    ! [U_19808,U_19807] :
      ( ( c_Predicate_Otransp(U_19807,U_19808)
        | ~ c_Relation_Otrans(U_19807,hAPP(c_Set_OCollect(tc_prod(U_19807,U_19807)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19807,U_19807,tc_HOL_Obool),U_19808))) )
      & ( c_Relation_Otrans(U_19807,hAPP(c_Set_OCollect(tc_prod(U_19807,U_19807)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19807,U_19807,tc_HOL_Obool),U_19808)))
        | ~ c_Predicate_Otransp(U_19807,U_19808) ) ),
    inference(variable_rename,[status(thm)],[f_4767_1]) ).

fof(f_4767_3,plain,
    ( ! [U_19812,U_19810] :
        ( c_Predicate_Otransp(U_19810,U_19812)
        | ~ c_Relation_Otrans(U_19810,hAPP(c_Set_OCollect(tc_prod(U_19810,U_19810)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19810,U_19810,tc_HOL_Obool),U_19812))) )
    & ! [U_19811,U_19809] :
        ( c_Relation_Otrans(U_19809,hAPP(c_Set_OCollect(tc_prod(U_19809,U_19809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19809,U_19809,tc_HOL_Obool),U_19811)))
        | ~ c_Predicate_Otransp(U_19809,U_19811) ) ),
    inference(miniscope,[status(thm)],[f_4767_2]) ).

cnf(f_4767_4,plain,
    ( c_Relation_Otrans(U_19809,hAPP(c_Set_OCollect(tc_prod(U_19809,U_19809)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19809,U_19809,tc_HOL_Obool),U_19811)))
    | ~ c_Predicate_Otransp(U_19809,U_19811) ),
    inference(clausify,[status(thm)],[f_4767_3]) ).

cnf(f_4767_5,plain,
    ( c_Predicate_Otransp(U_19810,U_19812)
    | ~ c_Relation_Otrans(U_19810,hAPP(c_Set_OCollect(tc_prod(U_19810,U_19810)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19810,U_19810,tc_HOL_Obool),U_19812))) ),
    inference(clausify,[status(thm)],[f_4767_3]) ).

fof(f_4768_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_4768_2,plain,
    ! [U_19814,U_19813] :
      ( c_Relation_Otrans(U_19813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_19813,U_19813),tc_HOL_Obool)),U_19814),c_Relation_OId(U_19813)))
      | ~ c_Relation_Oantisym(U_19813,U_19814)
      | ~ c_Relation_Otrans(U_19813,U_19814) ),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

cnf(f_4768_3,plain,
    ( c_Relation_Otrans(U_19813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_19813,U_19813),tc_HOL_Obool)),U_19814),c_Relation_OId(U_19813)))
    | ~ c_Relation_Oantisym(U_19813,U_19814)
    | ~ c_Relation_Otrans(U_19813,U_19814) ),
    inference(clausify,[status(thm)],[f_4768_2]) ).

fof(f_4769_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_4769_2,plain,
    ! [U_19816,U_19815] : c_Relation_Oantisym(U_19815,c_Relation_OId__on(U_19815,U_19816)),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

cnf(f_4769_3,plain,
    c_Relation_Oantisym(U_19815,c_Relation_OId__on(U_19815,U_19816)),
    inference(clausify,[status(thm)],[f_4769_2]) ).

fof(f_4770_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_4770_2,plain,
    ! [U_19818,U_19817] :
      ( ( c_Relation_Oantisym(U_19817,hAPP(c_Relation_Oconverse(U_19817,U_19817),U_19818))
        | ~ c_Relation_Oantisym(U_19817,U_19818) )
      & ( c_Relation_Oantisym(U_19817,U_19818)
        | ~ c_Relation_Oantisym(U_19817,hAPP(c_Relation_Oconverse(U_19817,U_19817),U_19818)) ) ),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

fof(f_4770_3,plain,
    ( ! [U_19822,U_19820] :
        ( c_Relation_Oantisym(U_19820,hAPP(c_Relation_Oconverse(U_19820,U_19820),U_19822))
        | ~ c_Relation_Oantisym(U_19820,U_19822) )
    & ! [U_19821,U_19819] :
        ( c_Relation_Oantisym(U_19819,U_19821)
        | ~ c_Relation_Oantisym(U_19819,hAPP(c_Relation_Oconverse(U_19819,U_19819),U_19821)) ) ),
    inference(miniscope,[status(thm)],[f_4770_2]) ).

cnf(f_4770_4,plain,
    ( c_Relation_Oantisym(U_19819,U_19821)
    | ~ c_Relation_Oantisym(U_19819,hAPP(c_Relation_Oconverse(U_19819,U_19819),U_19821)) ),
    inference(clausify,[status(thm)],[f_4770_3]) ).

cnf(f_4770_5,plain,
    ( c_Relation_Oantisym(U_19820,hAPP(c_Relation_Oconverse(U_19820,U_19820),U_19822))
    | ~ c_Relation_Oantisym(U_19820,U_19822) ),
    inference(clausify,[status(thm)],[f_4770_3]) ).

fof(f_4771_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_4771_2,plain,
    ! [U_19823] : c_Relation_Oantisym(U_19823,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_19823,U_19823),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

cnf(f_4771_3,plain,
    c_Relation_Oantisym(U_19823,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_19823,U_19823),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4771_2]) ).

fof(f_4772_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_4772_2,plain,
    ! [U_19828,U_19827,U_19826,U_19825,U_19824] :
      ( hBOOL(hAPP(hAPP(U_19825,U_19826),U_19828))
      | ~ hBOOL(hAPP(hAPP(U_19825,U_19827),U_19828))
      | ~ hBOOL(hAPP(hAPP(U_19825,U_19826),U_19827))
      | ~ c_Predicate_Otransp(U_19824,U_19825) ),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

fof(f_4772_3,plain,
    ! [U_19828,U_19827,U_19826,U_19825] :
      ( ! [U_19824] : ~ c_Predicate_Otransp(U_19824,U_19825)
      | hBOOL(hAPP(hAPP(U_19825,U_19826),U_19828))
      | ~ hBOOL(hAPP(hAPP(U_19825,U_19827),U_19828))
      | ~ hBOOL(hAPP(hAPP(U_19825,U_19826),U_19827)) ),
    inference(miniscope,[status(thm)],[f_4772_2]) ).

cnf(f_4772_4,plain,
    ( ~ c_Predicate_Otransp(U_19824,U_19825)
    | hBOOL(hAPP(hAPP(U_19825,U_19826),U_19828))
    | ~ hBOOL(hAPP(hAPP(U_19825,U_19827),U_19828))
    | ~ hBOOL(hAPP(hAPP(U_19825,U_19826),U_19827)) ),
    inference(clausify,[status(thm)],[f_4772_3]) ).

fof(f_4773_1,plain,
    ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_antisym__Id]) ).

fof(f_4773_2,plain,
    ! [U_19829] : c_Relation_Oantisym(U_19829,c_Relation_OId(U_19829)),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

cnf(f_4773_3,plain,
    c_Relation_Oantisym(U_19829,c_Relation_OId(U_19829)),
    inference(clausify,[status(thm)],[f_4773_2]) ).

fof(f_4774_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_4774_2,plain,
    ! [U_19832,U_19831,U_19830] :
      ( c_Relation_Oantisym(U_19830,U_19831)
      | ~ c_Relation_Oantisym(U_19830,U_19832)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19830,U_19830),tc_HOL_Obool)),U_19831),U_19832)) ),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

cnf(f_4774_3,plain,
    ( c_Relation_Oantisym(U_19830,U_19831)
    | ~ c_Relation_Oantisym(U_19830,U_19832)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19830,U_19830),tc_HOL_Obool)),U_19831),U_19832)) ),
    inference(clausify,[status(thm)],[f_4774_2]) ).

fof(f_4775_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_4775_2,plain,
    ! [U_19838,U_19837] :
      ( ( c_Relation_Oantisym(U_19837,U_19838)
        | ? [U_19836,U_19835] :
            ( U_19836 != U_19835
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),U_19835),U_19836)),U_19838))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),U_19836),U_19835)),U_19838)) ) )
      & ( ! [U_19834,U_19833] :
            ( U_19834 = U_19833
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),U_19833),U_19834)),U_19838))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19837,U_19837)),hAPP(hAPP(c_Product__Type_OPair(U_19837,U_19837),U_19834),U_19833)),U_19838)) )
        | ~ c_Relation_Oantisym(U_19837,U_19838) ) ),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

fof(f_4775_3,plain,
    ( ! [U_19842,U_19840] :
        ( c_Relation_Oantisym(U_19840,U_19842)
        | ? [U_19836,U_19835] :
            ( U_19836 != U_19835
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),U_19835),U_19836)),U_19842))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),U_19836),U_19835)),U_19842)) ) )
    & ! [U_19841,U_19839] :
        ( ! [U_19834,U_19833] :
            ( U_19834 = U_19833
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19833),U_19834)),U_19841))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19834),U_19833)),U_19841)) )
        | ~ c_Relation_Oantisym(U_19839,U_19841) ) ),
    inference(miniscope,[status(thm)],[f_4775_2]) ).

fof(f_4775_4,plain,
    ( ! [U_19842,U_19840] :
        ( c_Relation_Oantisym(U_19840,U_19842)
        | ? [U_19835] :
            ( sK524(U_19842,U_19840) != U_19835
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),U_19835),sK524(U_19842,U_19840))),U_19842))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),sK524(U_19842,U_19840)),U_19835)),U_19842)) ) )
    & ! [U_19841,U_19839] :
        ( ! [U_19834,U_19833] :
            ( U_19834 = U_19833
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19833),U_19834)),U_19841))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19834),U_19833)),U_19841)) )
        | ~ c_Relation_Oantisym(U_19839,U_19841) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK524]),skolemize(U_19836,sK524(U_19842,U_19840))],[f_4775_3]) ).

fof(f_4775_5,plain,
    ( ! [U_19842,U_19840] :
        ( c_Relation_Oantisym(U_19840,U_19842)
        | ( sK524(U_19842,U_19840) != sK525(U_19842,U_19840)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),sK525(U_19842,U_19840)),sK524(U_19842,U_19840))),U_19842))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),sK524(U_19842,U_19840)),sK525(U_19842,U_19840))),U_19842)) ) )
    & ! [U_19841,U_19839] :
        ( ! [U_19834,U_19833] :
            ( U_19834 = U_19833
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19833),U_19834)),U_19841))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19834),U_19833)),U_19841)) )
        | ~ c_Relation_Oantisym(U_19839,U_19841) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK525]),skolemize(U_19835,sK525(U_19842,U_19840))],[f_4775_4]) ).

cnf(f_4775_6,plain,
    ( U_19834 = U_19833
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19833),U_19834)),U_19841))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19839,U_19839)),hAPP(hAPP(c_Product__Type_OPair(U_19839,U_19839),U_19834),U_19833)),U_19841))
    | ~ c_Relation_Oantisym(U_19839,U_19841) ),
    inference(clausify,[status(thm)],[f_4775_5]) ).

cnf(f_4775_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),sK524(U_19842,U_19840)),sK525(U_19842,U_19840))),U_19842))
    | c_Relation_Oantisym(U_19840,U_19842) ),
    inference(clausify,[status(thm)],[f_4775_5]) ).

cnf(f_4775_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19840,U_19840)),hAPP(hAPP(c_Product__Type_OPair(U_19840,U_19840),sK525(U_19842,U_19840)),sK524(U_19842,U_19840))),U_19842))
    | c_Relation_Oantisym(U_19840,U_19842) ),
    inference(clausify,[status(thm)],[f_4775_5]) ).

cnf(f_4775_9,plain,
    ( sK524(U_19842,U_19840) != sK525(U_19842,U_19840)
    | c_Relation_Oantisym(U_19840,U_19842) ),
    inference(clausify,[status(thm)],[f_4775_5]) ).

fof(f_4776_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_4776_2,plain,
    ! [U_19846,U_19845,U_19844,U_19843] :
      ( U_19845 = U_19846
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19846),U_19845)),U_19844))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19845),U_19846)),U_19844))
      | ~ c_Relation_Oantisym(U_19843,U_19844) ),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

cnf(f_4776_3,plain,
    ( U_19845 = U_19846
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19846),U_19845)),U_19844))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19845),U_19846)),U_19844))
    | ~ c_Relation_Oantisym(U_19843,U_19844) ),
    inference(clausify,[status(thm)],[f_4776_2]) ).

fof(f_4777_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_4777_2,plain,
    ! [U_19848,U_19847] :
      ( ( c_Relation_Oantisym(U_19847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19847,U_19847),tc_HOL_Obool)),U_19848),c_Relation_OId(U_19847)))
        | ~ c_Relation_Oantisym(U_19847,U_19848) )
      & ( c_Relation_Oantisym(U_19847,U_19848)
        | ~ c_Relation_Oantisym(U_19847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19847,U_19847),tc_HOL_Obool)),U_19848),c_Relation_OId(U_19847))) ) ),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

fof(f_4777_3,plain,
    ( ! [U_19852,U_19850] :
        ( c_Relation_Oantisym(U_19850,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19850,U_19850),tc_HOL_Obool)),U_19852),c_Relation_OId(U_19850)))
        | ~ c_Relation_Oantisym(U_19850,U_19852) )
    & ! [U_19851,U_19849] :
        ( c_Relation_Oantisym(U_19849,U_19851)
        | ~ c_Relation_Oantisym(U_19849,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19849,U_19849),tc_HOL_Obool)),U_19851),c_Relation_OId(U_19849))) ) ),
    inference(miniscope,[status(thm)],[f_4777_2]) ).

cnf(f_4777_4,plain,
    ( c_Relation_Oantisym(U_19849,U_19851)
    | ~ c_Relation_Oantisym(U_19849,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19849,U_19849),tc_HOL_Obool)),U_19851),c_Relation_OId(U_19849))) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

cnf(f_4777_5,plain,
    ( c_Relation_Oantisym(U_19850,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19850,U_19850),tc_HOL_Obool)),U_19852),c_Relation_OId(U_19850)))
    | ~ c_Relation_Oantisym(U_19850,U_19852) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

fof(f_4778_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_4778_2,plain,
    ! [U_19854,U_19853] :
      ( c_Relation_Oantisym(U_19853,c_Transitive__Closure_Ortrancl(U_19853,U_19854))
      | ~ c_Wellfounded_Oacyclic(U_19853,U_19854) ),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

cnf(f_4778_3,plain,
    ( c_Relation_Oantisym(U_19853,c_Transitive__Closure_Ortrancl(U_19853,U_19854))
    | ~ c_Wellfounded_Oacyclic(U_19853,U_19854) ),
    inference(clausify,[status(thm)],[f_4778_2]) ).

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_19856,U_19855] :
      ( ( c_Equiv__Relations_Oequivp(U_19855,U_19856)
        | ~ c_Predicate_Otransp(U_19855,U_19856)
        | ~ c_Predicate_Osymp(U_19855,U_19856)
        | ~ c_Predicate_Oreflp(U_19855,U_19856) )
      & ( ( c_Predicate_Otransp(U_19855,U_19856)
          & c_Predicate_Osymp(U_19855,U_19856)
          & c_Predicate_Oreflp(U_19855,U_19856) )
        | ~ c_Equiv__Relations_Oequivp(U_19855,U_19856) ) ),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

fof(f_4779_3,plain,
    ( ! [U_19860,U_19858] :
        ( c_Equiv__Relations_Oequivp(U_19858,U_19860)
        | ~ c_Predicate_Otransp(U_19858,U_19860)
        | ~ c_Predicate_Osymp(U_19858,U_19860)
        | ~ c_Predicate_Oreflp(U_19858,U_19860) )
    & ! [U_19859,U_19857] :
        ( ( c_Predicate_Otransp(U_19857,U_19859)
          & c_Predicate_Osymp(U_19857,U_19859)
          & c_Predicate_Oreflp(U_19857,U_19859) )
        | ~ c_Equiv__Relations_Oequivp(U_19857,U_19859) ) ),
    inference(miniscope,[status(thm)],[f_4779_2]) ).

cnf(f_4779_4,plain,
    ( c_Predicate_Oreflp(U_19857,U_19859)
    | ~ c_Equiv__Relations_Oequivp(U_19857,U_19859) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_5,plain,
    ( c_Predicate_Osymp(U_19857,U_19859)
    | ~ c_Equiv__Relations_Oequivp(U_19857,U_19859) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_6,plain,
    ( c_Predicate_Otransp(U_19857,U_19859)
    | ~ c_Equiv__Relations_Oequivp(U_19857,U_19859) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_7,plain,
    ( c_Equiv__Relations_Oequivp(U_19858,U_19860)
    | ~ c_Predicate_Otransp(U_19858,U_19860)
    | ~ c_Predicate_Osymp(U_19858,U_19860)
    | ~ c_Predicate_Oreflp(U_19858,U_19860) ),
    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_19862,U_19861] :
      ( c_Equiv__Relations_Oequivp(U_19861,U_19862)
      | ~ c_Predicate_Otransp(U_19861,U_19862)
      | ~ c_Predicate_Osymp(U_19861,U_19862)
      | ~ c_Predicate_Oreflp(U_19861,U_19862) ),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

cnf(f_4780_3,plain,
    ( c_Equiv__Relations_Oequivp(U_19861,U_19862)
    | ~ c_Predicate_Otransp(U_19861,U_19862)
    | ~ c_Predicate_Osymp(U_19861,U_19862)
    | ~ c_Predicate_Oreflp(U_19861,U_19862) ),
    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_19866,U_19865,U_19864,U_19863] :
      ( hBOOL(hAPP(hAPP(U_19864,U_19866),U_19865))
      | ~ hBOOL(hAPP(hAPP(U_19864,U_19865),U_19866))
      | ~ c_Predicate_Osymp(U_19863,U_19864) ),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

fof(f_4781_3,plain,
    ! [U_19866,U_19865,U_19864] :
      ( ! [U_19863] : ~ c_Predicate_Osymp(U_19863,U_19864)
      | hBOOL(hAPP(hAPP(U_19864,U_19866),U_19865))
      | ~ hBOOL(hAPP(hAPP(U_19864,U_19865),U_19866)) ),
    inference(miniscope,[status(thm)],[f_4781_2]) ).

cnf(f_4781_4,plain,
    ( ~ c_Predicate_Osymp(U_19863,U_19864)
    | hBOOL(hAPP(hAPP(U_19864,U_19866),U_19865))
    | ~ hBOOL(hAPP(hAPP(U_19864,U_19865),U_19866)) ),
    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_19868,U_19867] :
      ( ( c_Predicate_Otransp(U_19867,U_19868)
        & c_Predicate_Osymp(U_19867,U_19868)
        & c_Predicate_Oreflp(U_19867,U_19868) )
      | ~ c_Equiv__Relations_Oequivp(U_19867,U_19868) ),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

cnf(f_4782_3,plain,
    ( c_Predicate_Oreflp(U_19867,U_19868)
    | ~ c_Equiv__Relations_Oequivp(U_19867,U_19868) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

cnf(f_4782_4,plain,
    ( c_Predicate_Osymp(U_19867,U_19868)
    | ~ c_Equiv__Relations_Oequivp(U_19867,U_19868) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

cnf(f_4782_5,plain,
    ( c_Predicate_Otransp(U_19867,U_19868)
    | ~ c_Equiv__Relations_Oequivp(U_19867,U_19868) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

fof(f_4783_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_4783_2,plain,
    ! [U_19870,U_19869] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19869,U_19869),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19869,U_19869,U_19869),hAPP(c_Relation_Oconverse(U_19869,U_19869),U_19870)),U_19870)),U_19870))
      | ~ c_Relation_Otrans(U_19869,U_19870)
      | ~ c_Relation_Osym(U_19869,U_19870) ),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

cnf(f_4783_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19869,U_19869),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19869,U_19869,U_19869),hAPP(c_Relation_Oconverse(U_19869,U_19869),U_19870)),U_19870)),U_19870))
    | ~ c_Relation_Otrans(U_19869,U_19870)
    | ~ c_Relation_Osym(U_19869,U_19870) ),
    inference(clausify,[status(thm)],[f_4783_2]) ).

fof(f_4784_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_4784_2,plain,
    ! [U_19874,U_19873] :
      ( ( c_Equiv__Relations_Opart__equivp(U_19873,U_19874)
        | ~ c_Predicate_Otransp(U_19873,U_19874)
        | ~ c_Predicate_Osymp(U_19873,U_19874)
        | ! [U_19872] : ~ hBOOL(hAPP(hAPP(U_19874,U_19872),U_19872)) )
      & ( ( c_Predicate_Otransp(U_19873,U_19874)
          & c_Predicate_Osymp(U_19873,U_19874)
          & ? [U_19871] : hBOOL(hAPP(hAPP(U_19874,U_19871),U_19871)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19873,U_19874) ) ),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

fof(f_4784_3,plain,
    ( ! [U_19878,U_19876] :
        ( c_Equiv__Relations_Opart__equivp(U_19876,U_19878)
        | ~ c_Predicate_Otransp(U_19876,U_19878)
        | ~ c_Predicate_Osymp(U_19876,U_19878)
        | ! [U_19872] : ~ hBOOL(hAPP(hAPP(U_19878,U_19872),U_19872)) )
    & ! [U_19877,U_19875] :
        ( ( c_Predicate_Otransp(U_19875,U_19877)
          & c_Predicate_Osymp(U_19875,U_19877)
          & ? [U_19871] : hBOOL(hAPP(hAPP(U_19877,U_19871),U_19871)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19875,U_19877) ) ),
    inference(miniscope,[status(thm)],[f_4784_2]) ).

fof(f_4784_4,plain,
    ( ! [U_19878,U_19876] :
        ( c_Equiv__Relations_Opart__equivp(U_19876,U_19878)
        | ~ c_Predicate_Otransp(U_19876,U_19878)
        | ~ c_Predicate_Osymp(U_19876,U_19878)
        | ! [U_19872] : ~ hBOOL(hAPP(hAPP(U_19878,U_19872),U_19872)) )
    & ! [U_19877,U_19875] :
        ( ( c_Predicate_Otransp(U_19875,U_19877)
          & c_Predicate_Osymp(U_19875,U_19877)
          & hBOOL(hAPP(hAPP(U_19877,sK526(U_19877,U_19875)),sK526(U_19877,U_19875))) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19875,U_19877) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK526]),skolemize(U_19871,sK526(U_19877,U_19875))],[f_4784_3]) ).

cnf(f_4784_5,plain,
    ( hBOOL(hAPP(hAPP(U_19877,sK526(U_19877,U_19875)),sK526(U_19877,U_19875)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19875,U_19877) ),
    inference(clausify,[status(thm)],[f_4784_4]) ).

cnf(f_4784_6,plain,
    ( c_Predicate_Osymp(U_19875,U_19877)
    | ~ c_Equiv__Relations_Opart__equivp(U_19875,U_19877) ),
    inference(clausify,[status(thm)],[f_4784_4]) ).

cnf(f_4784_7,plain,
    ( c_Predicate_Otransp(U_19875,U_19877)
    | ~ c_Equiv__Relations_Opart__equivp(U_19875,U_19877) ),
    inference(clausify,[status(thm)],[f_4784_4]) ).

cnf(f_4784_8,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19876,U_19878)
    | ~ c_Predicate_Otransp(U_19876,U_19878)
    | ~ c_Predicate_Osymp(U_19876,U_19878)
    | ~ hBOOL(hAPP(hAPP(U_19878,U_19872),U_19872)) ),
    inference(clausify,[status(thm)],[f_4784_4]) ).

fof(f_4785_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_4785_2,plain,
    ! [U_19882,U_19881,U_19880,U_19879] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19879,U_19879)),hAPP(hAPP(c_Product__Type_OPair(U_19879,U_19879),U_19882),U_19881)),U_19880))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19879,U_19879)),hAPP(hAPP(c_Product__Type_OPair(U_19879,U_19879),U_19881),U_19882)),U_19880))
      | ~ c_Relation_Osym(U_19879,U_19880) ),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

cnf(f_4785_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19879,U_19879)),hAPP(hAPP(c_Product__Type_OPair(U_19879,U_19879),U_19882),U_19881)),U_19880))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19879,U_19879)),hAPP(hAPP(c_Product__Type_OPair(U_19879,U_19879),U_19881),U_19882)),U_19880))
    | ~ c_Relation_Osym(U_19879,U_19880) ),
    inference(clausify,[status(thm)],[f_4785_2]) ).

fof(f_4786_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_4786_2,plain,
    ! [U_19888,U_19887] :
      ( ( c_Relation_Osym(U_19887,U_19888)
        | ? [U_19886,U_19885] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19887,U_19887)),hAPP(hAPP(c_Product__Type_OPair(U_19887,U_19887),U_19885),U_19886)),U_19888))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19887,U_19887)),hAPP(hAPP(c_Product__Type_OPair(U_19887,U_19887),U_19886),U_19885)),U_19888)) ) )
      & ( ! [U_19884,U_19883] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19887,U_19887)),hAPP(hAPP(c_Product__Type_OPair(U_19887,U_19887),U_19883),U_19884)),U_19888))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19887,U_19887)),hAPP(hAPP(c_Product__Type_OPair(U_19887,U_19887),U_19884),U_19883)),U_19888)) )
        | ~ c_Relation_Osym(U_19887,U_19888) ) ),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

fof(f_4786_3,plain,
    ( ! [U_19892,U_19890] :
        ( c_Relation_Osym(U_19890,U_19892)
        | ? [U_19886,U_19885] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),U_19885),U_19886)),U_19892))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),U_19886),U_19885)),U_19892)) ) )
    & ! [U_19891,U_19889] :
        ( ! [U_19884,U_19883] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19883),U_19884)),U_19891))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19884),U_19883)),U_19891)) )
        | ~ c_Relation_Osym(U_19889,U_19891) ) ),
    inference(miniscope,[status(thm)],[f_4786_2]) ).

fof(f_4786_4,plain,
    ( ! [U_19892,U_19890] :
        ( c_Relation_Osym(U_19890,U_19892)
        | ? [U_19885] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),U_19885),sK527(U_19892,U_19890))),U_19892))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),sK527(U_19892,U_19890)),U_19885)),U_19892)) ) )
    & ! [U_19891,U_19889] :
        ( ! [U_19884,U_19883] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19883),U_19884)),U_19891))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19884),U_19883)),U_19891)) )
        | ~ c_Relation_Osym(U_19889,U_19891) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK527]),skolemize(U_19886,sK527(U_19892,U_19890))],[f_4786_3]) ).

fof(f_4786_5,plain,
    ( ! [U_19892,U_19890] :
        ( c_Relation_Osym(U_19890,U_19892)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),sK528(U_19892,U_19890)),sK527(U_19892,U_19890))),U_19892))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),sK527(U_19892,U_19890)),sK528(U_19892,U_19890))),U_19892)) ) )
    & ! [U_19891,U_19889] :
        ( ! [U_19884,U_19883] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19883),U_19884)),U_19891))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19884),U_19883)),U_19891)) )
        | ~ c_Relation_Osym(U_19889,U_19891) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK528]),skolemize(U_19885,sK528(U_19892,U_19890))],[f_4786_4]) ).

cnf(f_4786_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19883),U_19884)),U_19891))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19889,U_19889)),hAPP(hAPP(c_Product__Type_OPair(U_19889,U_19889),U_19884),U_19883)),U_19891))
    | ~ c_Relation_Osym(U_19889,U_19891) ),
    inference(clausify,[status(thm)],[f_4786_5]) ).

cnf(f_4786_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),sK527(U_19892,U_19890)),sK528(U_19892,U_19890))),U_19892))
    | c_Relation_Osym(U_19890,U_19892) ),
    inference(clausify,[status(thm)],[f_4786_5]) ).

cnf(f_4786_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19890,U_19890)),hAPP(hAPP(c_Product__Type_OPair(U_19890,U_19890),sK528(U_19892,U_19890)),sK527(U_19892,U_19890))),U_19892))
    | c_Relation_Osym(U_19890,U_19892) ),
    inference(clausify,[status(thm)],[f_4786_5]) ).

fof(f_4787_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_4787_2,plain,
    ! [U_19894,U_19893] :
      ( ( c_Relation_Osym(U_19893,U_19894)
        | hAPP(c_Relation_Oconverse(U_19893,U_19893),U_19894) != U_19894 )
      & ( hAPP(c_Relation_Oconverse(U_19893,U_19893),U_19894) = U_19894
        | ~ c_Relation_Osym(U_19893,U_19894) ) ),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

fof(f_4787_3,plain,
    ( ! [U_19898,U_19896] :
        ( c_Relation_Osym(U_19896,U_19898)
        | hAPP(c_Relation_Oconverse(U_19896,U_19896),U_19898) != U_19898 )
    & ! [U_19897,U_19895] :
        ( hAPP(c_Relation_Oconverse(U_19895,U_19895),U_19897) = U_19897
        | ~ c_Relation_Osym(U_19895,U_19897) ) ),
    inference(miniscope,[status(thm)],[f_4787_2]) ).

cnf(f_4787_4,plain,
    ( hAPP(c_Relation_Oconverse(U_19895,U_19895),U_19897) = U_19897
    | ~ c_Relation_Osym(U_19895,U_19897) ),
    inference(clausify,[status(thm)],[f_4787_3]) ).

cnf(f_4787_5,plain,
    ( c_Relation_Osym(U_19896,U_19898)
    | hAPP(c_Relation_Oconverse(U_19896,U_19896),U_19898) != U_19898 ),
    inference(clausify,[status(thm)],[f_4787_3]) ).

fof(f_4788_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_4788_2,plain,
    ! [U_19900,U_19899] :
      ( ( c_Relation_Osym(U_19899,hAPP(c_Relation_Oconverse(U_19899,U_19899),U_19900))
        | ~ c_Relation_Osym(U_19899,U_19900) )
      & ( c_Relation_Osym(U_19899,U_19900)
        | ~ c_Relation_Osym(U_19899,hAPP(c_Relation_Oconverse(U_19899,U_19899),U_19900)) ) ),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

fof(f_4788_3,plain,
    ( ! [U_19904,U_19902] :
        ( c_Relation_Osym(U_19902,hAPP(c_Relation_Oconverse(U_19902,U_19902),U_19904))
        | ~ c_Relation_Osym(U_19902,U_19904) )
    & ! [U_19903,U_19901] :
        ( c_Relation_Osym(U_19901,U_19903)
        | ~ c_Relation_Osym(U_19901,hAPP(c_Relation_Oconverse(U_19901,U_19901),U_19903)) ) ),
    inference(miniscope,[status(thm)],[f_4788_2]) ).

cnf(f_4788_4,plain,
    ( c_Relation_Osym(U_19901,U_19903)
    | ~ c_Relation_Osym(U_19901,hAPP(c_Relation_Oconverse(U_19901,U_19901),U_19903)) ),
    inference(clausify,[status(thm)],[f_4788_3]) ).

cnf(f_4788_5,plain,
    ( c_Relation_Osym(U_19902,hAPP(c_Relation_Oconverse(U_19902,U_19902),U_19904))
    | ~ c_Relation_Osym(U_19902,U_19904) ),
    inference(clausify,[status(thm)],[f_4788_3]) ).

fof(f_4789_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_4789_2,plain,
    ! [U_19906,U_19905] :
      ( c_Relation_Osym(tc_List_Olist(U_19905),c_List_Olistrel(U_19905,U_19906))
      | ~ c_Relation_Osym(U_19905,U_19906) ),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

cnf(f_4789_3,plain,
    ( c_Relation_Osym(tc_List_Olist(U_19905),c_List_Olistrel(U_19905,U_19906))
    | ~ c_Relation_Osym(U_19905,U_19906) ),
    inference(clausify,[status(thm)],[f_4789_2]) ).

fof(f_4790_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_4790_2,plain,
    ! [U_19908,U_19907] : c_Relation_Osym(U_19907,c_Relation_OId__on(U_19907,U_19908)),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

cnf(f_4790_3,plain,
    c_Relation_Osym(U_19907,c_Relation_OId__on(U_19907,U_19908)),
    inference(clausify,[status(thm)],[f_4790_2]) ).

fof(f_4791_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_4791_2,plain,
    ! [U_19916,U_19915] :
      ( ( c_Equiv__Relations_Opart__equivp(U_19915,U_19916)
        | ? [U_19914,U_19913] :
            ( ( ~ hBOOL(hAPP(hAPP(U_19916,U_19914),U_19913))
              & hAPP(U_19916,U_19914) = hAPP(U_19916,U_19913)
              & hBOOL(hAPP(hAPP(U_19916,U_19913),U_19913))
              & hBOOL(hAPP(hAPP(U_19916,U_19914),U_19914)) )
            | ( ( hAPP(U_19916,U_19914) != hAPP(U_19916,U_19913)
                | ~ hBOOL(hAPP(hAPP(U_19916,U_19913),U_19913))
                | ~ hBOOL(hAPP(hAPP(U_19916,U_19914),U_19914)) )
              & hBOOL(hAPP(hAPP(U_19916,U_19914),U_19913)) ) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19916,U_19912),U_19912)) )
      & ( ( ! [U_19911,U_19910] :
              ( ( hBOOL(hAPP(hAPP(U_19916,U_19911),U_19910))
                | hAPP(U_19916,U_19911) != hAPP(U_19916,U_19910)
                | ~ hBOOL(hAPP(hAPP(U_19916,U_19910),U_19910))
                | ~ hBOOL(hAPP(hAPP(U_19916,U_19911),U_19911)) )
              & ( ( hAPP(U_19916,U_19911) = hAPP(U_19916,U_19910)
                  & hBOOL(hAPP(hAPP(U_19916,U_19910),U_19910))
                  & hBOOL(hAPP(hAPP(U_19916,U_19911),U_19911)) )
                | ~ hBOOL(hAPP(hAPP(U_19916,U_19911),U_19910)) ) )
          & ? [U_19909] : hBOOL(hAPP(hAPP(U_19916,U_19909),U_19909)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19915,U_19916) ) ),
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

fof(f_4791_3,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ? [U_19924,U_19922] :
            ( ~ hBOOL(hAPP(hAPP(U_19928,U_19924),U_19922))
            & hAPP(U_19928,U_19924) = hAPP(U_19928,U_19922)
            & hBOOL(hAPP(hAPP(U_19928,U_19922),U_19922))
            & hBOOL(hAPP(hAPP(U_19928,U_19924),U_19924)) )
        | ? [U_19923,U_19921] :
            ( ( hAPP(U_19928,U_19923) != hAPP(U_19928,U_19921)
              | ~ hBOOL(hAPP(hAPP(U_19928,U_19921),U_19921))
              | ~ hBOOL(hAPP(hAPP(U_19928,U_19923),U_19923)) )
            & hBOOL(hAPP(hAPP(U_19928,U_19923),U_19921)) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & ? [U_19909] : hBOOL(hAPP(hAPP(U_19927,U_19909),U_19909)) ) ) ),
    inference(miniscope,[status(thm)],[f_4791_2]) ).

fof(f_4791_4,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ? [U_19924,U_19922] :
            ( ~ hBOOL(hAPP(hAPP(U_19928,U_19924),U_19922))
            & hAPP(U_19928,U_19924) = hAPP(U_19928,U_19922)
            & hBOOL(hAPP(hAPP(U_19928,U_19922),U_19922))
            & hBOOL(hAPP(hAPP(U_19928,U_19924),U_19924)) )
        | ? [U_19923,U_19921] :
            ( ( hAPP(U_19928,U_19923) != hAPP(U_19928,U_19921)
              | ~ hBOOL(hAPP(hAPP(U_19928,U_19921),U_19921))
              | ~ hBOOL(hAPP(hAPP(U_19928,U_19923),U_19923)) )
            & hBOOL(hAPP(hAPP(U_19928,U_19923),U_19921)) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK529]),skolemize(U_19909,sK529(U_19927))],[f_4791_3]) ).

fof(f_4791_5,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ? [U_19924,U_19922] :
            ( ~ hBOOL(hAPP(hAPP(U_19928,U_19924),U_19922))
            & hAPP(U_19928,U_19924) = hAPP(U_19928,U_19922)
            & hBOOL(hAPP(hAPP(U_19928,U_19922),U_19922))
            & hBOOL(hAPP(hAPP(U_19928,U_19924),U_19924)) )
        | ? [U_19921] :
            ( ( hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,U_19921)
              | ~ hBOOL(hAPP(hAPP(U_19928,U_19921),U_19921))
              | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928))) )
            & hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),U_19921)) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK530]),skolemize(U_19923,sK530(U_19928))],[f_4791_4]) ).

fof(f_4791_6,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ? [U_19924,U_19922] :
            ( ~ hBOOL(hAPP(hAPP(U_19928,U_19924),U_19922))
            & hAPP(U_19928,U_19924) = hAPP(U_19928,U_19922)
            & hBOOL(hAPP(hAPP(U_19928,U_19922),U_19922))
            & hBOOL(hAPP(hAPP(U_19928,U_19924),U_19924)) )
        | ( ( hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928))) )
          & hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928))) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK531]),skolemize(U_19921,sK531(U_19928))],[f_4791_5]) ).

fof(f_4791_7,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ? [U_19922] :
            ( ~ hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),U_19922))
            & hAPP(U_19928,sK532(U_19928)) = hAPP(U_19928,U_19922)
            & hBOOL(hAPP(hAPP(U_19928,U_19922),U_19922))
            & hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK532(U_19928))) )
        | ( ( hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928))) )
          & hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928))) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK532]),skolemize(U_19924,sK532(U_19928))],[f_4791_6]) ).

fof(f_4791_8,plain,
    ( ! [U_19928] :
        ( ! [U_19926] : c_Equiv__Relations_Opart__equivp(U_19926,U_19928)
        | ( ~ hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK533(U_19928)))
          & hAPP(U_19928,sK532(U_19928)) = hAPP(U_19928,sK533(U_19928))
          & hBOOL(hAPP(hAPP(U_19928,sK533(U_19928)),sK533(U_19928)))
          & hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK532(U_19928))) )
        | ( ( hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
            | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928))) )
          & hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928))) )
        | ! [U_19912] : ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912)) )
    & ! [U_19927] :
        ( ! [U_19925] : ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927)
        | ( ! [U_19920,U_19918] :
              ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
              | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920)) )
          & ! [U_19919,U_19917] :
              ( ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
                & hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
                & hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919)) )
              | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917)) )
          & hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK533]),skolemize(U_19922,sK533(U_19928))],[f_4791_7]) ).

cnf(f_4791_9,plain,
    ( hBOOL(hAPP(hAPP(U_19927,sK529(U_19927)),sK529(U_19927)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_10,plain,
    ( hBOOL(hAPP(hAPP(U_19927,U_19919),U_19919))
    | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917))
    | ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_11,plain,
    ( hBOOL(hAPP(hAPP(U_19927,U_19917),U_19917))
    | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917))
    | ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_12,plain,
    ( hAPP(U_19927,U_19919) = hAPP(U_19927,U_19917)
    | ~ hBOOL(hAPP(hAPP(U_19927,U_19919),U_19917))
    | ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_13,plain,
    ( hBOOL(hAPP(hAPP(U_19927,U_19920),U_19918))
    | hAPP(U_19927,U_19920) != hAPP(U_19927,U_19918)
    | ~ hBOOL(hAPP(hAPP(U_19927,U_19918),U_19918))
    | ~ hBOOL(hAPP(hAPP(U_19927,U_19920),U_19920))
    | ~ c_Equiv__Relations_Opart__equivp(U_19925,U_19927) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_14,plain,
    ( hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK532(U_19928)))
    | hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_15,plain,
    ( hBOOL(hAPP(hAPP(U_19928,sK533(U_19928)),sK533(U_19928)))
    | hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_16,plain,
    ( hAPP(U_19928,sK532(U_19928)) = hAPP(U_19928,sK533(U_19928))
    | hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_17,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK533(U_19928)))
    | hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_18,plain,
    ( hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK532(U_19928)))
    | hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_19,plain,
    ( hBOOL(hAPP(hAPP(U_19928,sK533(U_19928)),sK533(U_19928)))
    | hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_20,plain,
    ( hAPP(U_19928,sK532(U_19928)) = hAPP(U_19928,sK533(U_19928))
    | hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

cnf(f_4791_21,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19928,sK532(U_19928)),sK533(U_19928)))
    | hAPP(U_19928,sK530(U_19928)) != hAPP(U_19928,sK531(U_19928))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK531(U_19928)),sK531(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,sK530(U_19928)),sK530(U_19928)))
    | ~ hBOOL(hAPP(hAPP(U_19928,U_19912),U_19912))
    | c_Equiv__Relations_Opart__equivp(U_19926,U_19928) ),
    inference(clausify,[status(thm)],[f_4791_8]) ).

fof(f_4792_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_4792_2,plain,
    ! [U_19932,U_19931,U_19930,U_19929] :
      ( hBOOL(hAPP(hAPP(U_19930,U_19932),U_19931))
      | ~ hBOOL(hAPP(hAPP(U_19930,U_19931),U_19932))
      | ~ c_Equiv__Relations_Opart__equivp(U_19929,U_19930) ),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

fof(f_4792_3,plain,
    ! [U_19932,U_19931,U_19930] :
      ( ! [U_19929] : ~ c_Equiv__Relations_Opart__equivp(U_19929,U_19930)
      | hBOOL(hAPP(hAPP(U_19930,U_19932),U_19931))
      | ~ hBOOL(hAPP(hAPP(U_19930,U_19931),U_19932)) ),
    inference(miniscope,[status(thm)],[f_4792_2]) ).

cnf(f_4792_4,plain,
    ( ~ c_Equiv__Relations_Opart__equivp(U_19929,U_19930)
    | hBOOL(hAPP(hAPP(U_19930,U_19932),U_19931))
    | ~ hBOOL(hAPP(hAPP(U_19930,U_19931),U_19932)) ),
    inference(clausify,[status(thm)],[f_4792_3]) ).

fof(f_4793_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_4793_2,plain,
    ! [U_19937,U_19936,U_19935,U_19934,U_19933] :
      ( hBOOL(hAPP(hAPP(U_19934,U_19935),U_19937))
      | ~ hBOOL(hAPP(hAPP(U_19934,U_19936),U_19937))
      | ~ hBOOL(hAPP(hAPP(U_19934,U_19935),U_19936))
      | ~ c_Equiv__Relations_Opart__equivp(U_19933,U_19934) ),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

fof(f_4793_3,plain,
    ! [U_19937,U_19936,U_19935,U_19934] :
      ( ! [U_19933] : ~ c_Equiv__Relations_Opart__equivp(U_19933,U_19934)
      | hBOOL(hAPP(hAPP(U_19934,U_19935),U_19937))
      | ~ hBOOL(hAPP(hAPP(U_19934,U_19936),U_19937))
      | ~ hBOOL(hAPP(hAPP(U_19934,U_19935),U_19936)) ),
    inference(miniscope,[status(thm)],[f_4793_2]) ).

cnf(f_4793_4,plain,
    ( ~ c_Equiv__Relations_Opart__equivp(U_19933,U_19934)
    | hBOOL(hAPP(hAPP(U_19934,U_19935),U_19937))
    | ~ hBOOL(hAPP(hAPP(U_19934,U_19936),U_19937))
    | ~ hBOOL(hAPP(hAPP(U_19934,U_19935),U_19936)) ),
    inference(clausify,[status(thm)],[f_4793_3]) ).

fof(f_4794_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_4794_2,plain,
    ! [U_19939,U_19938] :
      ( c_Relation_Osym(U_19938,c_Transitive__Closure_Otrancl(U_19938,U_19939))
      | ~ c_Relation_Osym(U_19938,U_19939) ),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

cnf(f_4794_3,plain,
    ( c_Relation_Osym(U_19938,c_Transitive__Closure_Otrancl(U_19938,U_19939))
    | ~ c_Relation_Osym(U_19938,U_19939) ),
    inference(clausify,[status(thm)],[f_4794_2]) ).

fof(f_4795_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_4795_2,plain,
    ! [U_19942,U_19941,U_19940] :
      ( c_Relation_Osym(U_19940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19940,U_19940),tc_HOL_Obool)),U_19941),U_19942))
      | ~ c_Relation_Osym(U_19940,U_19942)
      | ~ c_Relation_Osym(U_19940,U_19941) ),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

cnf(f_4795_3,plain,
    ( c_Relation_Osym(U_19940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19940,U_19940),tc_HOL_Obool)),U_19941),U_19942))
    | ~ c_Relation_Osym(U_19940,U_19942)
    | ~ c_Relation_Osym(U_19940,U_19941) ),
    inference(clausify,[status(thm)],[f_4795_2]) ).

fof(f_4796_1,plain,
    ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_sym__Id]) ).

fof(f_4796_2,plain,
    ! [U_19943] : c_Relation_Osym(U_19943,c_Relation_OId(U_19943)),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

cnf(f_4796_3,plain,
    c_Relation_Osym(U_19943,c_Relation_OId(U_19943)),
    inference(clausify,[status(thm)],[f_4796_2]) ).

fof(f_4797_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_4797_2,plain,
    ! [U_19945,U_19944] :
      ( c_Relation_Osym(U_19944,c_Transitive__Closure_Ortrancl(U_19944,U_19945))
      | ~ c_Relation_Osym(U_19944,U_19945) ),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

cnf(f_4797_3,plain,
    ( c_Relation_Osym(U_19944,c_Transitive__Closure_Ortrancl(U_19944,U_19945))
    | ~ c_Relation_Osym(U_19944,U_19945) ),
    inference(clausify,[status(thm)],[f_4797_2]) ).

fof(f_4798_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_4798_2,plain,
    ! [U_19947,U_19946] :
      ( c_Equiv__Relations_Opart__equivp(U_19946,U_19947)
      | ~ c_Equiv__Relations_Oequivp(U_19946,U_19947) ),
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

cnf(f_4798_3,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19946,U_19947)
    | ~ c_Equiv__Relations_Oequivp(U_19946,U_19947) ),
    inference(clausify,[status(thm)],[f_4798_2]) ).

fof(f_4799_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_4799_2,plain,
    ! [U_19950,U_19949,U_19948] :
      ( c_Relation_Osym(U_19948,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19948,U_19948),tc_HOL_Obool)),U_19949),U_19950))
      | ~ c_Relation_Osym(U_19948,U_19950)
      | ~ c_Relation_Osym(U_19948,U_19949) ),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

cnf(f_4799_3,plain,
    ( c_Relation_Osym(U_19948,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19948,U_19948),tc_HOL_Obool)),U_19949),U_19950))
    | ~ c_Relation_Osym(U_19948,U_19950)
    | ~ c_Relation_Osym(U_19948,U_19949) ),
    inference(clausify,[status(thm)],[f_4799_2]) ).

fof(f_4800_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_4800_2,plain,
    ! [U_19952,U_19951] : c_Relation_Osym(U_19951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19951,U_19951),tc_HOL_Obool)),U_19952),hAPP(c_Relation_Oconverse(U_19951,U_19951),U_19952))),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

cnf(f_4800_3,plain,
    c_Relation_Osym(U_19951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19951,U_19951),tc_HOL_Obool)),U_19952),hAPP(c_Relation_Oconverse(U_19951,U_19951),U_19952))),
    inference(clausify,[status(thm)],[f_4800_2]) ).

fof(f_4801_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_4801_2,plain,
    ! [U_19956,U_19955,U_19954,U_19953] :
      ( c_Relation_Osym(U_19955,hAPP(hAPP(c_Relation_Oinv__image(U_19953,U_19955),U_19954),U_19956))
      | ~ c_Relation_Osym(U_19953,U_19954) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

cnf(f_4801_3,plain,
    ( c_Relation_Osym(U_19955,hAPP(hAPP(c_Relation_Oinv__image(U_19953,U_19955),U_19954),U_19956))
    | ~ c_Relation_Osym(U_19953,U_19954) ),
    inference(clausify,[status(thm)],[f_4801_2]) ).

fof(f_4802_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_4802_2,plain,
    ! [U_19958,U_19957] : c_Relation_Osym(U_19957,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19957,U_19957),tc_HOL_Obool)),U_19958),hAPP(c_Relation_Oconverse(U_19957,U_19957),U_19958))),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

cnf(f_4802_3,plain,
    c_Relation_Osym(U_19957,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19957,U_19957),tc_HOL_Obool)),U_19958),hAPP(c_Relation_Oconverse(U_19957,U_19957),U_19958))),
    inference(clausify,[status(thm)],[f_4802_2]) ).

fof(f_4803_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_4803_2,plain,
    ! [U_19961,U_19960,U_19959] :
      ( ( c_Equiv__Relations_Oequiv(U_19959,U_19960,U_19961)
        | ~ c_Relation_Otrans(U_19959,U_19961)
        | ~ c_Relation_Osym(U_19959,U_19961)
        | ~ c_Relation_Orefl__on(U_19959,U_19960,U_19961) )
      & ( ( c_Relation_Otrans(U_19959,U_19961)
          & c_Relation_Osym(U_19959,U_19961)
          & c_Relation_Orefl__on(U_19959,U_19960,U_19961) )
        | ~ c_Equiv__Relations_Oequiv(U_19959,U_19960,U_19961) ) ),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

fof(f_4803_3,plain,
    ( ! [U_19967,U_19965,U_19963] :
        ( c_Equiv__Relations_Oequiv(U_19963,U_19965,U_19967)
        | ~ c_Relation_Otrans(U_19963,U_19967)
        | ~ c_Relation_Osym(U_19963,U_19967)
        | ~ c_Relation_Orefl__on(U_19963,U_19965,U_19967) )
    & ! [U_19966,U_19964,U_19962] :
        ( ( c_Relation_Otrans(U_19962,U_19966)
          & c_Relation_Osym(U_19962,U_19966)
          & c_Relation_Orefl__on(U_19962,U_19964,U_19966) )
        | ~ c_Equiv__Relations_Oequiv(U_19962,U_19964,U_19966) ) ),
    inference(miniscope,[status(thm)],[f_4803_2]) ).

cnf(f_4803_4,plain,
    ( c_Relation_Orefl__on(U_19962,U_19964,U_19966)
    | ~ c_Equiv__Relations_Oequiv(U_19962,U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4803_3]) ).

cnf(f_4803_5,plain,
    ( c_Relation_Osym(U_19962,U_19966)
    | ~ c_Equiv__Relations_Oequiv(U_19962,U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4803_3]) ).

cnf(f_4803_6,plain,
    ( c_Relation_Otrans(U_19962,U_19966)
    | ~ c_Equiv__Relations_Oequiv(U_19962,U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4803_3]) ).

cnf(f_4803_7,plain,
    ( c_Equiv__Relations_Oequiv(U_19963,U_19965,U_19967)
    | ~ c_Relation_Otrans(U_19963,U_19967)
    | ~ c_Relation_Osym(U_19963,U_19967)
    | ~ c_Relation_Orefl__on(U_19963,U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4803_3]) ).

fof(f_4804_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_4804_2,plain,
    ! [U_19970,U_19969,U_19968] :
      ( c_Equiv__Relations_Oequiv(U_19968,U_19969,U_19970)
      | ~ c_Relation_Otrans(U_19968,U_19970)
      | ~ c_Relation_Osym(U_19968,U_19970)
      | ~ c_Relation_Orefl__on(U_19968,U_19969,U_19970) ),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

cnf(f_4804_3,plain,
    ( c_Equiv__Relations_Oequiv(U_19968,U_19969,U_19970)
    | ~ c_Relation_Otrans(U_19968,U_19970)
    | ~ c_Relation_Osym(U_19968,U_19970)
    | ~ c_Relation_Orefl__on(U_19968,U_19969,U_19970) ),
    inference(clausify,[status(thm)],[f_4804_2]) ).

fof(f_4805_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_4805_2,plain,
    ! [U_19973,U_19972,U_19971] :
      ( ( c_Relation_Otrans(U_19971,U_19973)
        & c_Relation_Osym(U_19971,U_19973)
        & c_Relation_Orefl__on(U_19971,U_19972,U_19973) )
      | ~ c_Equiv__Relations_Oequiv(U_19971,U_19972,U_19973) ),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

cnf(f_4805_3,plain,
    ( c_Relation_Orefl__on(U_19971,U_19972,U_19973)
    | ~ c_Equiv__Relations_Oequiv(U_19971,U_19972,U_19973) ),
    inference(clausify,[status(thm)],[f_4805_2]) ).

cnf(f_4805_4,plain,
    ( c_Relation_Osym(U_19971,U_19973)
    | ~ c_Equiv__Relations_Oequiv(U_19971,U_19972,U_19973) ),
    inference(clausify,[status(thm)],[f_4805_2]) ).

cnf(f_4805_5,plain,
    ( c_Relation_Otrans(U_19971,U_19973)
    | ~ c_Equiv__Relations_Oequiv(U_19971,U_19972,U_19973) ),
    inference(clausify,[status(thm)],[f_4805_2]) ).

fof(f_4806_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_4806_2,plain,
    ! [U_19975,U_19974] :
      ( ( c_Predicate_Osymp(U_19974,U_19975)
        | ~ c_Relation_Osym(U_19974,hAPP(c_Set_OCollect(tc_prod(U_19974,U_19974)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19974,U_19974,tc_HOL_Obool),U_19975))) )
      & ( c_Relation_Osym(U_19974,hAPP(c_Set_OCollect(tc_prod(U_19974,U_19974)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19974,U_19974,tc_HOL_Obool),U_19975)))
        | ~ c_Predicate_Osymp(U_19974,U_19975) ) ),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

fof(f_4806_3,plain,
    ( ! [U_19979,U_19977] :
        ( c_Predicate_Osymp(U_19977,U_19979)
        | ~ c_Relation_Osym(U_19977,hAPP(c_Set_OCollect(tc_prod(U_19977,U_19977)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19977,U_19977,tc_HOL_Obool),U_19979))) )
    & ! [U_19978,U_19976] :
        ( c_Relation_Osym(U_19976,hAPP(c_Set_OCollect(tc_prod(U_19976,U_19976)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19976,U_19976,tc_HOL_Obool),U_19978)))
        | ~ c_Predicate_Osymp(U_19976,U_19978) ) ),
    inference(miniscope,[status(thm)],[f_4806_2]) ).

cnf(f_4806_4,plain,
    ( c_Relation_Osym(U_19976,hAPP(c_Set_OCollect(tc_prod(U_19976,U_19976)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19976,U_19976,tc_HOL_Obool),U_19978)))
    | ~ c_Predicate_Osymp(U_19976,U_19978) ),
    inference(clausify,[status(thm)],[f_4806_3]) ).

cnf(f_4806_5,plain,
    ( c_Predicate_Osymp(U_19977,U_19979)
    | ~ c_Relation_Osym(U_19977,hAPP(c_Set_OCollect(tc_prod(U_19977,U_19977)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19977,U_19977,tc_HOL_Obool),U_19979))) ),
    inference(clausify,[status(thm)],[f_4806_3]) ).

fof(f_4807_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_4807_2,plain,
    ! [U_19982,U_19981] :
      ( c_Equiv__Relations_Opart__equivp(U_19982,U_19981)
      | ~ c_Predicate_Otransp(U_19982,U_19981)
      | ~ c_Predicate_Osymp(U_19982,U_19981)
      | ! [U_19980] : ~ hBOOL(hAPP(hAPP(U_19981,U_19980),U_19980)) ),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

cnf(f_4807_3,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19982,U_19981)
    | ~ c_Predicate_Otransp(U_19982,U_19981)
    | ~ c_Predicate_Osymp(U_19982,U_19981)
    | ~ hBOOL(hAPP(hAPP(U_19981,U_19980),U_19980)) ),
    inference(clausify,[status(thm)],[f_4807_2]) ).

fof(f_4808_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_4808_2,plain,
    ! [U_19985,U_19984] :
      ( ( c_Predicate_Otransp(U_19984,U_19985)
        & c_Predicate_Osymp(U_19984,U_19985)
        & ? [U_19983] : hBOOL(hAPP(hAPP(U_19985,U_19983),U_19983)) )
      | ~ c_Equiv__Relations_Opart__equivp(U_19984,U_19985) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

fof(f_4808_3,plain,
    ! [U_19985,U_19984] :
      ( ( c_Predicate_Otransp(U_19984,U_19985)
        & c_Predicate_Osymp(U_19984,U_19985)
        & hBOOL(hAPP(hAPP(U_19985,sK534(U_19985,U_19984)),sK534(U_19985,U_19984))) )
      | ~ c_Equiv__Relations_Opart__equivp(U_19984,U_19985) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK534]),skolemize(U_19983,sK534(U_19985,U_19984))],[f_4808_2]) ).

cnf(f_4808_4,plain,
    ( hBOOL(hAPP(hAPP(U_19985,sK534(U_19985,U_19984)),sK534(U_19985,U_19984)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19984,U_19985) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

cnf(f_4808_5,plain,
    ( c_Predicate_Osymp(U_19984,U_19985)
    | ~ c_Equiv__Relations_Opart__equivp(U_19984,U_19985) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

cnf(f_4808_6,plain,
    ( c_Predicate_Otransp(U_19984,U_19985)
    | ~ c_Equiv__Relations_Opart__equivp(U_19984,U_19985) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

fof(f_4809_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_4809_2,plain,
    ! [U_19988,U_19987] :
      ( ? [U_19986] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_19987,tc_HOL_Obool)),U_19986),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19987,tc_HOL_Obool)),c_HOL_OEx(U_19987)),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool)),hAPP(c_COMBS(U_19987,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19987),c_fconj),hAPP(hAPP(c_COMBS(U_19987,U_19987,tc_HOL_Obool),U_19988),c_COMBI(U_19987))))),hAPP(hAPP(c_COMBC(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,U_19987)),c_fequal)),U_19988)))))
      | ~ c_Equiv__Relations_Opart__equivp(U_19987,U_19988) ),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

fof(f_4809_3,plain,
    ! [U_19988,U_19987] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19987,tc_HOL_Obool)),sK535(U_19988,U_19987)),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19987,tc_HOL_Obool)),c_HOL_OEx(U_19987)),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool)),hAPP(c_COMBS(U_19987,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19987),c_fconj),hAPP(hAPP(c_COMBS(U_19987,U_19987,tc_HOL_Obool),U_19988),c_COMBI(U_19987))))),hAPP(hAPP(c_COMBC(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,U_19987)),c_fequal)),U_19988)))))
      | ~ c_Equiv__Relations_Opart__equivp(U_19987,U_19988) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK535]),skolemize(U_19986,sK535(U_19988,U_19987))],[f_4809_2]) ).

cnf(f_4809_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19987,tc_HOL_Obool)),sK535(U_19988,U_19987)),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19987,tc_HOL_Obool)),c_HOL_OEx(U_19987)),hAPP(hAPP(c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_HOL_Obool)),hAPP(c_COMBS(U_19987,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19987),c_fconj),hAPP(hAPP(c_COMBS(U_19987,U_19987,tc_HOL_Obool),U_19988),c_COMBI(U_19987))))),hAPP(hAPP(c_COMBC(tc_fun(U_19987,tc_HOL_Obool),tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19987,tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),tc_fun(U_19987,tc_HOL_Obool)),c_COMBB(tc_fun(U_19987,tc_HOL_Obool),tc_HOL_Obool,U_19987)),c_fequal)),U_19988)))))
    | ~ c_Equiv__Relations_Opart__equivp(U_19987,U_19988) ),
    inference(clausify,[status(thm)],[f_4809_3]) ).

fof(f_4810_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_4810_2,plain,
    ! [U_19991,U_19990,U_19989] :
      ( ( c_Fun_Oinj__on(U_19989,U_19990,U_19991,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(U_19990,U_19989,U_19989,c_Hilbert__Choice_Oinv__into(U_19989,U_19990,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)),U_19991)),U_19991) != c_Fun_Oid(U_19989) )
      & ( hAPP(c_Fun_Ocomp(U_19990,U_19989,U_19989,c_Hilbert__Choice_Oinv__into(U_19989,U_19990,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)),U_19991)),U_19991) = c_Fun_Oid(U_19989)
        | ~ c_Fun_Oinj__on(U_19989,U_19990,U_19991,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

fof(f_4810_3,plain,
    ( ! [U_19997,U_19995,U_19993] :
        ( c_Fun_Oinj__on(U_19993,U_19995,U_19997,c_Orderings_Otop__class_Otop(tc_fun(U_19993,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(U_19995,U_19993,U_19993,c_Hilbert__Choice_Oinv__into(U_19993,U_19995,c_Orderings_Otop__class_Otop(tc_fun(U_19993,tc_HOL_Obool)),U_19997)),U_19997) != c_Fun_Oid(U_19993) )
    & ! [U_19996,U_19994,U_19992] :
        ( hAPP(c_Fun_Ocomp(U_19994,U_19992,U_19992,c_Hilbert__Choice_Oinv__into(U_19992,U_19994,c_Orderings_Otop__class_Otop(tc_fun(U_19992,tc_HOL_Obool)),U_19996)),U_19996) = c_Fun_Oid(U_19992)
        | ~ c_Fun_Oinj__on(U_19992,U_19994,U_19996,c_Orderings_Otop__class_Otop(tc_fun(U_19992,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4810_2]) ).

cnf(f_4810_4,plain,
    ( hAPP(c_Fun_Ocomp(U_19994,U_19992,U_19992,c_Hilbert__Choice_Oinv__into(U_19992,U_19994,c_Orderings_Otop__class_Otop(tc_fun(U_19992,tc_HOL_Obool)),U_19996)),U_19996) = c_Fun_Oid(U_19992)
    | ~ c_Fun_Oinj__on(U_19992,U_19994,U_19996,c_Orderings_Otop__class_Otop(tc_fun(U_19992,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

cnf(f_4810_5,plain,
    ( c_Fun_Oinj__on(U_19993,U_19995,U_19997,c_Orderings_Otop__class_Otop(tc_fun(U_19993,tc_HOL_Obool)))
    | hAPP(c_Fun_Ocomp(U_19995,U_19993,U_19993,c_Hilbert__Choice_Oinv__into(U_19993,U_19995,c_Orderings_Otop__class_Otop(tc_fun(U_19993,tc_HOL_Obool)),U_19997)),U_19997) != c_Fun_Oid(U_19993) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

fof(f_4811_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_4811_2,plain,
    ! [U_20000,U_19999,U_19998] :
      ( hAPP(c_Fun_Ocomp(U_19999,U_19998,U_19998,c_Hilbert__Choice_Oinv__into(U_19998,U_19999,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool)),U_20000)),U_20000) = c_Fun_Oid(U_19998)
      | ~ 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_4811_1]) ).

cnf(f_4811_3,plain,
    ( hAPP(c_Fun_Ocomp(U_19999,U_19998,U_19998,c_Hilbert__Choice_Oinv__into(U_19998,U_19999,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool)),U_20000)),U_20000) = c_Fun_Oid(U_19998)
    | ~ 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_4811_2]) ).

fof(f_4812_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_4812_2,plain,
    ! [U_20005,U_20004,U_20003,U_20002,U_20001] :
      ( hAPP(c_Fun_Ocomp(U_20002,U_20004,U_20001,hAPP(c_Fun_Ocomp(U_20001,U_20004,U_20002,U_20005),c_Hilbert__Choice_Oinv__into(U_20001,U_20002,c_Orderings_Otop__class_Otop(tc_fun(U_20001,tc_HOL_Obool)),U_20003))),U_20003) = U_20005
      | ~ c_Fun_Oinj__on(U_20001,U_20002,U_20003,c_Orderings_Otop__class_Otop(tc_fun(U_20001,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

cnf(f_4812_3,plain,
    ( hAPP(c_Fun_Ocomp(U_20002,U_20004,U_20001,hAPP(c_Fun_Ocomp(U_20001,U_20004,U_20002,U_20005),c_Hilbert__Choice_Oinv__into(U_20001,U_20002,c_Orderings_Otop__class_Otop(tc_fun(U_20001,tc_HOL_Obool)),U_20003))),U_20003) = U_20005
    | ~ c_Fun_Oinj__on(U_20001,U_20002,U_20003,c_Orderings_Otop__class_Otop(tc_fun(U_20001,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4812_2]) ).

fof(f_4813_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_4813_2,plain,
    ! [U_20010,U_20009,U_20008,U_20007,U_20006] : hAPP(c_Hilbert__Choice_Oinv__into(U_20006,U_20007,U_20008,U_20009),U_20010) = c_Hilbert__Choice_OEps(U_20006,hAPP(hAPP(c_COMBS(U_20006,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20006),c_fconj),hAPP(hAPP(c_COMBC(U_20006,tc_fun(U_20006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20006)),U_20008))),hAPP(hAPP(c_COMBC(U_20006,U_20007,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20007,tc_fun(U_20007,tc_HOL_Obool),U_20006),c_fequal),U_20009)),U_20010))),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

cnf(f_4813_3,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(U_20006,U_20007,U_20008,U_20009),U_20010) = c_Hilbert__Choice_OEps(U_20006,hAPP(hAPP(c_COMBS(U_20006,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20006),c_fconj),hAPP(hAPP(c_COMBC(U_20006,tc_fun(U_20006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20006)),U_20008))),hAPP(hAPP(c_COMBC(U_20006,U_20007,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20007,tc_fun(U_20007,tc_HOL_Obool),U_20006),c_fequal),U_20009)),U_20010))),
    inference(clausify,[status(thm)],[f_4813_2]) ).

fof(f_4814_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_4814_2,plain,
    ! [U_20015,U_20014,U_20013,U_20012,U_20011] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20011,U_20012,c_Orderings_Otop__class_Otop(tc_fun(U_20011,tc_HOL_Obool)),U_20013),U_20015) = U_20014
      | hAPP(U_20013,U_20014) != U_20015
      | ~ c_Fun_Oinj__on(U_20011,U_20012,U_20013,c_Orderings_Otop__class_Otop(tc_fun(U_20011,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

cnf(f_4814_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20011,U_20012,c_Orderings_Otop__class_Otop(tc_fun(U_20011,tc_HOL_Obool)),U_20013),U_20015) = U_20014
    | hAPP(U_20013,U_20014) != U_20015
    | ~ c_Fun_Oinj__on(U_20011,U_20012,U_20013,c_Orderings_Otop__class_Otop(tc_fun(U_20011,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4814_2]) ).

fof(f_4815_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_4815_2,plain,
    ! [U_20019,U_20018,U_20017,U_20016] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20016,U_20017,c_Orderings_Otop__class_Otop(tc_fun(U_20016,tc_HOL_Obool)),U_20018),hAPP(U_20018,U_20019)) = U_20019
      | ~ c_Fun_Oinj__on(U_20016,U_20017,U_20018,c_Orderings_Otop__class_Otop(tc_fun(U_20016,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

cnf(f_4815_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20016,U_20017,c_Orderings_Otop__class_Otop(tc_fun(U_20016,tc_HOL_Obool)),U_20018),hAPP(U_20018,U_20019)) = U_20019
    | ~ c_Fun_Oinj__on(U_20016,U_20017,U_20018,c_Orderings_Otop__class_Otop(tc_fun(U_20016,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4815_2]) ).

fof(f_4816_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_4816_2,plain,
    ! [U_20024,U_20023,U_20022,U_20021,U_20020] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20020,U_20021,U_20023,U_20022),hAPP(U_20022,U_20024)) = U_20024
      | ~ hBOOL(hAPP(hAPP(c_member(U_20020),U_20024),U_20023))
      | ~ c_Fun_Oinj__on(U_20020,U_20021,U_20022,U_20023) ),
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

cnf(f_4816_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20020,U_20021,U_20023,U_20022),hAPP(U_20022,U_20024)) = U_20024
    | ~ hBOOL(hAPP(hAPP(c_member(U_20020),U_20024),U_20023))
    | ~ c_Fun_Oinj__on(U_20020,U_20021,U_20022,U_20023) ),
    inference(clausify,[status(thm)],[f_4816_2]) ).

fof(f_4817_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_4817_2,plain,
    ! [U_20030,U_20029,U_20028,U_20027,U_20026,U_20025] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20025,U_20026,U_20028,U_20027),U_20030) = U_20029
      | hAPP(U_20027,U_20029) != U_20030
      | ~ hBOOL(hAPP(hAPP(c_member(U_20025),U_20029),U_20028))
      | ~ c_Fun_Oinj__on(U_20025,U_20026,U_20027,U_20028) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

cnf(f_4817_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20025,U_20026,U_20028,U_20027),U_20030) = U_20029
    | hAPP(U_20027,U_20029) != U_20030
    | ~ hBOOL(hAPP(hAPP(c_member(U_20025),U_20029),U_20028))
    | ~ c_Fun_Oinj__on(U_20025,U_20026,U_20027,U_20028) ),
    inference(clausify,[status(thm)],[f_4817_2]) ).

fof(f_4818_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_4818_2,plain,
    ! [U_20035,U_20034,U_20033,U_20032,U_20031] :
      ( hAPP(U_20034,hAPP(c_Hilbert__Choice_Oinv__into(U_20033,U_20031,U_20035,U_20034),U_20032)) = U_20032
      | ~ hBOOL(hAPP(hAPP(c_member(U_20031),U_20032),hAPP(c_Set_Oimage(U_20033,U_20031,U_20034),U_20035))) ),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

cnf(f_4818_3,plain,
    ( hAPP(U_20034,hAPP(c_Hilbert__Choice_Oinv__into(U_20033,U_20031,U_20035,U_20034),U_20032)) = U_20032
    | ~ hBOOL(hAPP(hAPP(c_member(U_20031),U_20032),hAPP(c_Set_Oimage(U_20033,U_20031,U_20034),U_20035))) ),
    inference(clausify,[status(thm)],[f_4818_2]) ).

fof(f_4819_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_4819_2,plain,
    ! [U_20040,U_20039,U_20038,U_20037,U_20036] :
      ( hBOOL(hAPP(hAPP(c_member(U_20038),hAPP(c_Hilbert__Choice_Oinv__into(U_20038,U_20036,U_20040,U_20039),U_20037)),U_20040))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20036),U_20037),hAPP(c_Set_Oimage(U_20038,U_20036,U_20039),U_20040))) ),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

cnf(f_4819_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20038),hAPP(c_Hilbert__Choice_Oinv__into(U_20038,U_20036,U_20040,U_20039),U_20037)),U_20040))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20036),U_20037),hAPP(c_Set_Oimage(U_20038,U_20036,U_20039),U_20040))) ),
    inference(clausify,[status(thm)],[f_4819_2]) ).

fof(f_4820_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_4820_2,plain,
    ! [U_20046,U_20045,U_20044,U_20043,U_20042,U_20041] :
      ( U_20045 = U_20046
      | ~ hBOOL(hAPP(hAPP(c_member(U_20042),U_20046),hAPP(c_Set_Oimage(U_20041,U_20042,U_20044),U_20043)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20042),U_20045),hAPP(c_Set_Oimage(U_20041,U_20042,U_20044),U_20043)))
      | hAPP(c_Hilbert__Choice_Oinv__into(U_20041,U_20042,U_20043,U_20044),U_20045) != hAPP(c_Hilbert__Choice_Oinv__into(U_20041,U_20042,U_20043,U_20044),U_20046) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

cnf(f_4820_3,plain,
    ( U_20045 = U_20046
    | ~ hBOOL(hAPP(hAPP(c_member(U_20042),U_20046),hAPP(c_Set_Oimage(U_20041,U_20042,U_20044),U_20043)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20042),U_20045),hAPP(c_Set_Oimage(U_20041,U_20042,U_20044),U_20043)))
    | hAPP(c_Hilbert__Choice_Oinv__into(U_20041,U_20042,U_20043,U_20044),U_20045) != hAPP(c_Hilbert__Choice_Oinv__into(U_20041,U_20042,U_20043,U_20044),U_20046) ),
    inference(clausify,[status(thm)],[f_4820_2]) ).

fof(f_4821_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_4821_2,plain,
    ! [U_20051,U_20050,U_20049] :
      ( ( hAPP(c_Set_Oimage(U_20049,U_20050,U_20051),c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20050,tc_HOL_Obool))
        | ? [U_20048] : hAPP(U_20051,hAPP(c_Hilbert__Choice_Oinv__into(U_20049,U_20050,c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool)),U_20051),U_20048)) != U_20048 )
      & ( ! [U_20047] : hAPP(U_20051,hAPP(c_Hilbert__Choice_Oinv__into(U_20049,U_20050,c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool)),U_20051),U_20047)) = U_20047
        | hAPP(c_Set_Oimage(U_20049,U_20050,U_20051),c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20050,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

fof(f_4821_3,plain,
    ( ! [U_20057,U_20055,U_20053] :
        ( hAPP(c_Set_Oimage(U_20053,U_20055,U_20057),c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20055,tc_HOL_Obool))
        | ? [U_20048] : hAPP(U_20057,hAPP(c_Hilbert__Choice_Oinv__into(U_20053,U_20055,c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool)),U_20057),U_20048)) != U_20048 )
    & ! [U_20056,U_20054,U_20052] :
        ( ! [U_20047] : hAPP(U_20056,hAPP(c_Hilbert__Choice_Oinv__into(U_20052,U_20054,c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool)),U_20056),U_20047)) = U_20047
        | hAPP(c_Set_Oimage(U_20052,U_20054,U_20056),c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20054,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4821_2]) ).

fof(f_4821_4,plain,
    ( ! [U_20057,U_20055,U_20053] :
        ( hAPP(c_Set_Oimage(U_20053,U_20055,U_20057),c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20055,tc_HOL_Obool))
        | hAPP(U_20057,hAPP(c_Hilbert__Choice_Oinv__into(U_20053,U_20055,c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool)),U_20057),sK536(U_20057,U_20055,U_20053))) != sK536(U_20057,U_20055,U_20053) )
    & ! [U_20056,U_20054,U_20052] :
        ( ! [U_20047] : hAPP(U_20056,hAPP(c_Hilbert__Choice_Oinv__into(U_20052,U_20054,c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool)),U_20056),U_20047)) = U_20047
        | hAPP(c_Set_Oimage(U_20052,U_20054,U_20056),c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20054,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK536]),skolemize(U_20048,sK536(U_20057,U_20055,U_20053))],[f_4821_3]) ).

cnf(f_4821_5,plain,
    ( hAPP(U_20056,hAPP(c_Hilbert__Choice_Oinv__into(U_20052,U_20054,c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool)),U_20056),U_20047)) = U_20047
    | hAPP(c_Set_Oimage(U_20052,U_20054,U_20056),c_Orderings_Otop__class_Otop(tc_fun(U_20052,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20054,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4821_4]) ).

cnf(f_4821_6,plain,
    ( hAPP(c_Set_Oimage(U_20053,U_20055,U_20057),c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20055,tc_HOL_Obool))
    | hAPP(U_20057,hAPP(c_Hilbert__Choice_Oinv__into(U_20053,U_20055,c_Orderings_Otop__class_Otop(tc_fun(U_20053,tc_HOL_Obool)),U_20057),sK536(U_20057,U_20055,U_20053))) != sK536(U_20057,U_20055,U_20053) ),
    inference(clausify,[status(thm)],[f_4821_4]) ).

fof(f_4822_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_4822_2,plain,
    ! [U_20061,U_20060,U_20059,U_20058] :
      ( hAPP(U_20060,hAPP(c_Hilbert__Choice_Oinv__into(U_20058,U_20059,c_Orderings_Otop__class_Otop(tc_fun(U_20058,tc_HOL_Obool)),U_20060),U_20061)) = U_20061
      | hAPP(c_Set_Oimage(U_20058,U_20059,U_20060),c_Orderings_Otop__class_Otop(tc_fun(U_20058,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20059,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

cnf(f_4822_3,plain,
    ( hAPP(U_20060,hAPP(c_Hilbert__Choice_Oinv__into(U_20058,U_20059,c_Orderings_Otop__class_Otop(tc_fun(U_20058,tc_HOL_Obool)),U_20060),U_20061)) = U_20061
    | hAPP(c_Set_Oimage(U_20058,U_20059,U_20060),c_Orderings_Otop__class_Otop(tc_fun(U_20058,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20059,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4822_2]) ).

fof(f_4823_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_4823_2,plain,
    ! [U_20065,U_20064,U_20063,U_20062] :
      ( hAPP(c_Set_Oimage(U_20062,U_20063,U_20064),hAPP(c_Set_Oimage(U_20063,U_20062,c_Hilbert__Choice_Oinv__into(U_20062,U_20063,c_Orderings_Otop__class_Otop(tc_fun(U_20062,tc_HOL_Obool)),U_20064)),U_20065)) = U_20065
      | hAPP(c_Set_Oimage(U_20062,U_20063,U_20064),c_Orderings_Otop__class_Otop(tc_fun(U_20062,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20063,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

cnf(f_4823_3,plain,
    ( hAPP(c_Set_Oimage(U_20062,U_20063,U_20064),hAPP(c_Set_Oimage(U_20063,U_20062,c_Hilbert__Choice_Oinv__into(U_20062,U_20063,c_Orderings_Otop__class_Otop(tc_fun(U_20062,tc_HOL_Obool)),U_20064)),U_20065)) = U_20065
    | hAPP(c_Set_Oimage(U_20062,U_20063,U_20064),c_Orderings_Otop__class_Otop(tc_fun(U_20062,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20063,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4823_2]) ).

fof(f_4824_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_4824_2,plain,
    ! [U_20071,U_20070,U_20069,U_20068,U_20067,U_20066] :
      ( hAPP(c_Set_Oimage(U_20066,U_20067,U_20068),hAPP(c_Set_Oimage(U_20067,U_20066,c_Hilbert__Choice_Oinv__into(U_20066,U_20067,U_20069,U_20068)),U_20071)) = U_20071
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20067,tc_HOL_Obool)),U_20071),U_20070))
      | hAPP(c_Set_Oimage(U_20066,U_20067,U_20068),U_20069) != U_20070 ),
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

cnf(f_4824_3,plain,
    ( hAPP(c_Set_Oimage(U_20066,U_20067,U_20068),hAPP(c_Set_Oimage(U_20067,U_20066,c_Hilbert__Choice_Oinv__into(U_20066,U_20067,U_20069,U_20068)),U_20071)) = U_20071
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20067,tc_HOL_Obool)),U_20071),U_20070))
    | hAPP(c_Set_Oimage(U_20066,U_20067,U_20068),U_20069) != U_20070 ),
    inference(clausify,[status(thm)],[f_4824_2]) ).

fof(f_4825_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_4825_2,plain,
    ! [U_20072] : c_Hilbert__Choice_Oinv__into(U_20072,U_20072,c_Orderings_Otop__class_Otop(tc_fun(U_20072,tc_HOL_Obool)),c_Fun_Oid(U_20072)) = c_Fun_Oid(U_20072),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

cnf(f_4825_3,plain,
    c_Hilbert__Choice_Oinv__into(U_20072,U_20072,c_Orderings_Otop__class_Otop(tc_fun(U_20072,tc_HOL_Obool)),c_Fun_Oid(U_20072)) = c_Fun_Oid(U_20072),
    inference(clausify,[status(thm)],[f_4825_2]) ).

fof(f_4826_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_4826_2,plain,
    ! [U_20076,U_20075,U_20074,U_20073] : hAPP(c_Hilbert__Choice_Oinv__into(U_20073,U_20074,c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool)),U_20075),U_20076) = c_Hilbert__Choice_OEps(U_20073,hAPP(hAPP(c_COMBC(U_20073,U_20074,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20074,tc_fun(U_20074,tc_HOL_Obool),U_20073),c_fequal),U_20075)),U_20076)),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

cnf(f_4826_3,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(U_20073,U_20074,c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool)),U_20075),U_20076) = c_Hilbert__Choice_OEps(U_20073,hAPP(hAPP(c_COMBC(U_20073,U_20074,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20074,tc_fun(U_20074,tc_HOL_Obool),U_20073),c_fequal),U_20075)),U_20076)),
    inference(clausify,[status(thm)],[f_4826_2]) ).

fof(f_4827_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_4827_2,plain,
    ! [U_20079,U_20078,U_20077] :
      ( hAPP(c_Set_Oimage(U_20078,U_20077,c_Hilbert__Choice_Oinv__into(U_20077,U_20078,c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool)),U_20079)),c_Orderings_Otop__class_Otop(tc_fun(U_20078,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_20077,U_20078,U_20079,c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

cnf(f_4827_3,plain,
    ( hAPP(c_Set_Oimage(U_20078,U_20077,c_Hilbert__Choice_Oinv__into(U_20077,U_20078,c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool)),U_20079)),c_Orderings_Otop__class_Otop(tc_fun(U_20078,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20077,U_20078,U_20079,c_Orderings_Otop__class_Otop(tc_fun(U_20077,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4827_2]) ).

fof(f_4828_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_4828_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_4828_1]) ).

cnf(f_4828_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_4828_2]) ).

fof(f_4829_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_4829_2,plain,
    ! [U_20087,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)),hAPP(c_Set_Oimage(U_20084,U_20085,U_20086),U_20087)) = U_20087
      | ~ 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_4829_1]) ).

cnf(f_4829_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)),hAPP(c_Set_Oimage(U_20084,U_20085,U_20086),U_20087)) = U_20087
    | ~ 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_4829_2]) ).

fof(f_4830_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_4830_2,plain,
    ! [U_20090,U_20089,U_20088] :
      ( c_Fun_Oinj__on(U_20089,U_20088,c_Hilbert__Choice_Oinv__into(U_20088,U_20089,c_Orderings_Otop__class_Otop(tc_fun(U_20088,tc_HOL_Obool)),U_20090),c_Orderings_Otop__class_Otop(tc_fun(U_20089,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_20088,U_20089,U_20090),c_Orderings_Otop__class_Otop(tc_fun(U_20088,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20089,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

cnf(f_4830_3,plain,
    ( c_Fun_Oinj__on(U_20089,U_20088,c_Hilbert__Choice_Oinv__into(U_20088,U_20089,c_Orderings_Otop__class_Otop(tc_fun(U_20088,tc_HOL_Obool)),U_20090),c_Orderings_Otop__class_Otop(tc_fun(U_20089,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20088,U_20089,U_20090),c_Orderings_Otop__class_Otop(tc_fun(U_20088,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20089,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4830_2]) ).

fof(f_4831_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_4831_2,plain,
    ! [U_20095,U_20094,U_20093,U_20092,U_20091] :
      ( c_Fun_Oinj__on(U_20091,U_20093,c_Hilbert__Choice_Oinv__into(U_20093,U_20091,U_20095,U_20094),U_20092)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20091,tc_HOL_Obool)),U_20092),hAPP(c_Set_Oimage(U_20093,U_20091,U_20094),U_20095))) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

cnf(f_4831_3,plain,
    ( c_Fun_Oinj__on(U_20091,U_20093,c_Hilbert__Choice_Oinv__into(U_20093,U_20091,U_20095,U_20094),U_20092)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20091,tc_HOL_Obool)),U_20092),hAPP(c_Set_Oimage(U_20093,U_20091,U_20094),U_20095))) ),
    inference(clausify,[status(thm)],[f_4831_2]) ).

fof(f_4832_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_4832_2,plain,
    ! [U_20100,U_20099,U_20098,U_20097,U_20096] :
      ( hAPP(c_Set_Oimage(U_20097,U_20096,c_Hilbert__Choice_Oinv__into(U_20096,U_20097,U_20099,U_20098)),hAPP(c_Set_Oimage(U_20096,U_20097,U_20098),U_20100)) = U_20100
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20096,tc_HOL_Obool)),U_20100),U_20099))
      | ~ c_Fun_Oinj__on(U_20096,U_20097,U_20098,U_20099) ),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

cnf(f_4832_3,plain,
    ( hAPP(c_Set_Oimage(U_20097,U_20096,c_Hilbert__Choice_Oinv__into(U_20096,U_20097,U_20099,U_20098)),hAPP(c_Set_Oimage(U_20096,U_20097,U_20098),U_20100)) = U_20100
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20096,tc_HOL_Obool)),U_20100),U_20099))
    | ~ c_Fun_Oinj__on(U_20096,U_20097,U_20098,U_20099) ),
    inference(clausify,[status(thm)],[f_4832_2]) ).

fof(f_4833_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_4833_2,plain,
    ! [U_20107,U_20106,U_20105,U_20104,U_20103,U_20102,U_20101] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20104,U_20102,U_20106,hAPP(c_Fun_Ocomp(U_20101,U_20102,U_20104,U_20103),U_20105)),U_20107) = hAPP(hAPP(c_Fun_Ocomp(U_20101,U_20104,U_20102,c_Hilbert__Choice_Oinv__into(U_20104,U_20101,U_20106,U_20105)),c_Hilbert__Choice_Oinv__into(U_20101,U_20102,hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106),U_20103)),U_20107)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20102),U_20107),hAPP(c_Set_Oimage(U_20101,U_20102,U_20103),hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106))))
      | ~ c_Fun_Oinj__on(U_20104,U_20101,U_20105,U_20106)
      | ~ c_Fun_Oinj__on(U_20101,U_20102,U_20103,hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106)) ),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

cnf(f_4833_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20104,U_20102,U_20106,hAPP(c_Fun_Ocomp(U_20101,U_20102,U_20104,U_20103),U_20105)),U_20107) = hAPP(hAPP(c_Fun_Ocomp(U_20101,U_20104,U_20102,c_Hilbert__Choice_Oinv__into(U_20104,U_20101,U_20106,U_20105)),c_Hilbert__Choice_Oinv__into(U_20101,U_20102,hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106),U_20103)),U_20107)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20102),U_20107),hAPP(c_Set_Oimage(U_20101,U_20102,U_20103),hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106))))
    | ~ c_Fun_Oinj__on(U_20104,U_20101,U_20105,U_20106)
    | ~ c_Fun_Oinj__on(U_20101,U_20102,U_20103,hAPP(c_Set_Oimage(U_20104,U_20101,U_20105),U_20106)) ),
    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))
        | 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_4834_2,plain,
    ! [U_20110,U_20109,U_20108] :
      ( ( hAPP(c_Set_Oimage(U_20108,U_20109,U_20110),c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20109,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(U_20108,U_20109,U_20109,U_20110),c_Hilbert__Choice_Oinv__into(U_20108,U_20109,c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool)),U_20110)) != c_Fun_Oid(U_20109) )
      & ( hAPP(c_Fun_Ocomp(U_20108,U_20109,U_20109,U_20110),c_Hilbert__Choice_Oinv__into(U_20108,U_20109,c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool)),U_20110)) = c_Fun_Oid(U_20109)
        | hAPP(c_Set_Oimage(U_20108,U_20109,U_20110),c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20109,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ( ! [U_20116,U_20114,U_20112] :
        ( hAPP(c_Set_Oimage(U_20112,U_20114,U_20116),c_Orderings_Otop__class_Otop(tc_fun(U_20112,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(U_20112,U_20114,U_20114,U_20116),c_Hilbert__Choice_Oinv__into(U_20112,U_20114,c_Orderings_Otop__class_Otop(tc_fun(U_20112,tc_HOL_Obool)),U_20116)) != c_Fun_Oid(U_20114) )
    & ! [U_20115,U_20113,U_20111] :
        ( hAPP(c_Fun_Ocomp(U_20111,U_20113,U_20113,U_20115),c_Hilbert__Choice_Oinv__into(U_20111,U_20113,c_Orderings_Otop__class_Otop(tc_fun(U_20111,tc_HOL_Obool)),U_20115)) = c_Fun_Oid(U_20113)
        | hAPP(c_Set_Oimage(U_20111,U_20113,U_20115),c_Orderings_Otop__class_Otop(tc_fun(U_20111,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20113,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4834_2]) ).

cnf(f_4834_4,plain,
    ( hAPP(c_Fun_Ocomp(U_20111,U_20113,U_20113,U_20115),c_Hilbert__Choice_Oinv__into(U_20111,U_20113,c_Orderings_Otop__class_Otop(tc_fun(U_20111,tc_HOL_Obool)),U_20115)) = c_Fun_Oid(U_20113)
    | hAPP(c_Set_Oimage(U_20111,U_20113,U_20115),c_Orderings_Otop__class_Otop(tc_fun(U_20111,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20113,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4834_3]) ).

cnf(f_4834_5,plain,
    ( hAPP(c_Set_Oimage(U_20112,U_20114,U_20116),c_Orderings_Otop__class_Otop(tc_fun(U_20112,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))
    | hAPP(c_Fun_Ocomp(U_20112,U_20114,U_20114,U_20116),c_Hilbert__Choice_Oinv__into(U_20112,U_20114,c_Orderings_Otop__class_Otop(tc_fun(U_20112,tc_HOL_Obool)),U_20116)) != c_Fun_Oid(U_20114) ),
    inference(clausify,[status(thm)],[f_4834_3]) ).

fof(f_4835_1,plain,
    ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_Pa_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_4835_2,plain,
    ! [U_20122,U_20121,U_20120,U_20119,U_20118] :
      ( hBOOL(hAPP(U_20121,U_20122))
      | ? [U_20117] :
          ( ~ hBOOL(hAPP(U_20121,hAPP(c_Hilbert__Choice_Oinv__into(U_20118,U_20119,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool)),U_20120),U_20117)))
          & hBOOL(hAPP(hAPP(c_member(U_20119),U_20117),hAPP(c_Set_Oimage(U_20118,U_20119,U_20120),c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))))) )
      | ~ c_Fun_Oinj__on(U_20118,U_20119,U_20120,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

fof(f_4835_3,plain,
    ! [U_20122,U_20121,U_20120,U_20119,U_20118] :
      ( hBOOL(hAPP(U_20121,U_20122))
      | ( ~ hBOOL(hAPP(U_20121,hAPP(c_Hilbert__Choice_Oinv__into(U_20118,U_20119,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool)),U_20120),sK537(U_20122,U_20121,U_20120,U_20119,U_20118))))
        & hBOOL(hAPP(hAPP(c_member(U_20119),sK537(U_20122,U_20121,U_20120,U_20119,U_20118)),hAPP(c_Set_Oimage(U_20118,U_20119,U_20120),c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))))) )
      | ~ c_Fun_Oinj__on(U_20118,U_20119,U_20120,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK537]),skolemize(U_20117,sK537(U_20122,U_20121,U_20120,U_20119,U_20118))],[f_4835_2]) ).

cnf(f_4835_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20119),sK537(U_20122,U_20121,U_20120,U_20119,U_20118)),hAPP(c_Set_Oimage(U_20118,U_20119,U_20120),c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool)))))
    | hBOOL(hAPP(U_20121,U_20122))
    | ~ c_Fun_Oinj__on(U_20118,U_20119,U_20120,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

cnf(f_4835_5,plain,
    ( ~ hBOOL(hAPP(U_20121,hAPP(c_Hilbert__Choice_Oinv__into(U_20118,U_20119,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool)),U_20120),sK537(U_20122,U_20121,U_20120,U_20119,U_20118))))
    | hBOOL(hAPP(U_20121,U_20122))
    | ~ c_Fun_Oinj__on(U_20118,U_20119,U_20120,c_Orderings_Otop__class_Otop(tc_fun(U_20118,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

fof(f_4836_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_4836_2,plain,
    ! [U_20131,U_20130,U_20129,U_20128,U_20127,U_20126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
      | ? [U_20125] :
          ( ? [U_20124] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,U_20125)),hAPP(U_20130,U_20124)) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
              & U_20125 != U_20124
              & hBOOL(hAPP(hAPP(c_member(U_20127),U_20124),U_20128)) )
          & hBOOL(hAPP(hAPP(c_member(U_20127),U_20125),U_20128)) )
      | ? [U_20123] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,U_20123)))
          & hBOOL(hAPP(hAPP(c_member(U_20127),U_20123),U_20128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
      | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

fof(f_4836_3,plain,
    ! [U_20131,U_20130,U_20129,U_20128,U_20127,U_20126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
      | ? [U_20125] :
          ( ? [U_20124] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,U_20125)),hAPP(U_20130,U_20124)) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
              & U_20125 != U_20124
              & hBOOL(hAPP(hAPP(c_member(U_20127),U_20124),U_20128)) )
          & hBOOL(hAPP(hAPP(c_member(U_20127),U_20125),U_20128)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
      | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK538]),skolemize(U_20123,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))],[f_4836_2]) ).

fof(f_4836_4,plain,
    ! [U_20131,U_20130,U_20129,U_20128,U_20127,U_20126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
      | ( ? [U_20124] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))),hAPP(U_20130,U_20124)) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
            & sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126) != U_20124
            & hBOOL(hAPP(hAPP(c_member(U_20127),U_20124),U_20128)) )
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
      | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK539]),skolemize(U_20125,sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))],[f_4836_3]) ).

fof(f_4836_5,plain,
    ! [U_20131,U_20130,U_20129,U_20128,U_20127,U_20126] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))),hAPP(U_20130,sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
        & sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126) != sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
        & hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
      | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK540]),skolemize(U_20124,sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))],[f_4836_4]) ).

cnf(f_4836_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20127),sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20127),sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_8,plain,
    ( sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126) != sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))),hAPP(U_20130,sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | hBOOL(hAPP(hAPP(c_member(U_20127),sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20127),sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20127),sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)),U_20128))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_12,plain,
    ( sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126) != sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

cnf(f_4836_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20129,tc_HOL_Obool)),hAPP(U_20130,sK539(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))),hAPP(U_20130,sK540(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))) != c_Orderings_Obot__class_Obot(tc_fun(U_20129,tc_HOL_Obool))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20127,tc_fun(U_20129,tc_HOL_Obool)),U_20128),U_20130)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20127,c_Groups_Otimes__class_Otimes(U_20126)),hAPP(hAPP(c_COMBB(tc_fun(U_20129,tc_HOL_Obool),U_20126,U_20127),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20126,U_20129,c_Groups_Otimes__class_Otimes(U_20126)),U_20131),c_Groups_Oone__class_Oone(U_20126))),U_20130)),c_Groups_Oone__class_Oone(U_20126)),U_20128)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20129),hAPP(U_20130,sK538(U_20131,U_20130,U_20129,U_20128,U_20127,U_20126))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20127),U_20128))
    | ~ class_Groups_Ocomm__monoid__mult(U_20126) ),
    inference(clausify,[status(thm)],[f_4836_5]) ).

fof(f_4837_1,plain,
    ! [V_Pa_2,V_y_2] :
      ( hBOOL(hAPP(V_Pa_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_Pa_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_4837_2,plain,
    ! [U_20134,U_20133] :
      ( hBOOL(hAPP(U_20134,U_20133))
      | ? [U_20132] : ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Onat__of,U_20132)))
      | ~ 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_4837_1]) ).

fof(f_4837_3,plain,
    ! [U_20134,U_20133] :
      ( hBOOL(hAPP(U_20134,U_20133))
      | ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Onat__of,sK541(U_20134,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(skolemize,[status(esa),new_symbols(skolem,[sK541]),skolemize(U_20132,sK541(U_20134,U_20133))],[f_4837_2]) ).

cnf(f_4837_4,plain,
    ( hBOOL(hAPP(U_20134,U_20133))
    | ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Onat__of,sK541(U_20134,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(clausify,[status(thm)],[f_4837_3]) ).

fof(f_4838_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_4838_2,plain,
    ! [U_20136] :
      ( ? [U_20135] : U_20136 = hAPP(c_Code__Numeral_Onat__of,U_20135)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20136),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

fof(f_4838_3,plain,
    ! [U_20136] :
      ( U_20136 = hAPP(c_Code__Numeral_Onat__of,sK542(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)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK542]),skolemize(U_20135,sK542(U_20136))],[f_4838_2]) ).

cnf(f_4838_4,plain,
    ( U_20136 = hAPP(c_Code__Numeral_Onat__of,sK542(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)))) ),
    inference(clausify,[status(thm)],[f_4838_3]) ).

fof(f_4839_1,plain,
    ! [V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_Pa_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_4839_2,plain,
    ! [U_20139,U_20138] :
      ( hBOOL(hAPP(U_20138,U_20139))
      | ? [U_20137] :
          ( ~ hBOOL(hAPP(U_20138,hAPP(c_Code__Numeral_Oof__nat,U_20137)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20137),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

fof(f_4839_3,plain,
    ! [U_20139,U_20138] :
      ( hBOOL(hAPP(U_20138,U_20139))
      | ( ~ hBOOL(hAPP(U_20138,hAPP(c_Code__Numeral_Oof__nat,sK543(U_20139,U_20138))))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK543(U_20139,U_20138)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK543]),skolemize(U_20137,sK543(U_20139,U_20138))],[f_4839_2]) ).

cnf(f_4839_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK543(U_20139,U_20138)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | hBOOL(hAPP(U_20138,U_20139)) ),
    inference(clausify,[status(thm)],[f_4839_3]) ).

cnf(f_4839_5,plain,
    ( ~ hBOOL(hAPP(U_20138,hAPP(c_Code__Numeral_Oof__nat,sK543(U_20139,U_20138))))
    | hBOOL(hAPP(U_20138,U_20139)) ),
    inference(clausify,[status(thm)],[f_4839_3]) ).

fof(f_4840_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_4840_2,plain,
    ! [U_20141] :
    ? [U_20140] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20140),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      & U_20141 = hAPP(c_Code__Numeral_Oof__nat,U_20140) ),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

fof(f_4840_3,plain,
    ! [U_20141] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK544(U_20141)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      & U_20141 = hAPP(c_Code__Numeral_Oof__nat,sK544(U_20141)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK544]),skolemize(U_20140,sK544(U_20141))],[f_4840_2]) ).

cnf(f_4840_4,plain,
    U_20141 = hAPP(c_Code__Numeral_Oof__nat,sK544(U_20141)),
    inference(clausify,[status(thm)],[f_4840_3]) ).

cnf(f_4840_5,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK544(U_20141)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4840_3]) ).

fof(f_4841_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_4841_2,plain,
    ! [U_20145,U_20144,U_20143,U_20142] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20142,U_20143,U_20144,U_20145,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20143)) = U_20144,
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

cnf(f_4841_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20142,U_20143,U_20144,U_20145,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20143)) = U_20144,
    inference(clausify,[status(thm)],[f_4841_2]) ).

fof(f_4842_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_4842_2,plain,
    ! [U_20147,U_20146] :
      ( ( c_Quickcheck_Obeyond(U_20146,U_20147) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20146),U_20147)) )
      & ( c_Quickcheck_Obeyond(U_20146,U_20147) = U_20147
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20146),U_20147)) ) ),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

fof(f_4842_3,plain,
    ( ! [U_20151,U_20149] :
        ( c_Quickcheck_Obeyond(U_20149,U_20151) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20149),U_20151)) )
    & ! [U_20150,U_20148] :
        ( c_Quickcheck_Obeyond(U_20148,U_20150) = U_20150
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20148),U_20150)) ) ),
    inference(miniscope,[status(thm)],[f_4842_2]) ).

cnf(f_4842_4,plain,
    ( c_Quickcheck_Obeyond(U_20148,U_20150) = U_20150
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20148),U_20150)) ),
    inference(clausify,[status(thm)],[f_4842_3]) ).

cnf(f_4842_5,plain,
    ( c_Quickcheck_Obeyond(U_20149,U_20151) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20149),U_20151)) ),
    inference(clausify,[status(thm)],[f_4842_3]) ).

fof(f_4843_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_4843_2,plain,
    ! [U_20152] : c_Quickcheck_Obeyond(U_20152,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_4843_1]) ).

cnf(f_4843_3,plain,
    c_Quickcheck_Obeyond(U_20152,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_4843_2]) ).

fof(f_4844_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_4844_2,plain,
    ! [U_20158,U_20157,U_20156,U_20155,U_20154,U_20153] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20153,U_20154,U_20155,U_20156,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20154,U_20157,U_20158)) = hAPP(hAPP(hAPP(U_20156,U_20157),U_20158),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20153,U_20154,U_20155,U_20156,U_20158)),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

cnf(f_4844_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20153,U_20154,U_20155,U_20156,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20154,U_20157,U_20158)) = hAPP(hAPP(hAPP(U_20156,U_20157),U_20158),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20153,U_20154,U_20155,U_20156,U_20158)),
    inference(clausify,[status(thm)],[f_4844_2]) ).

fof(f_4845_1,plain,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_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_4845_2,plain,
    ! [U_20162,U_20161,U_20160,U_20159] :
      ( hAPP(c_Set_Oimage(U_20159,U_20160,U_20161),hAPP(c_Set_OCollect(U_20159),U_20162)) = hAPP(c_Set_OCollect(U_20160),hAPP(hAPP(c_COMBB(U_20159,tc_HOL_Obool,U_20160),U_20162),c_Hilbert__Choice_Oinv__into(U_20159,U_20160,c_Orderings_Otop__class_Otop(tc_fun(U_20159,tc_HOL_Obool)),U_20161)))
      | ~ c_Fun_Obij__betw(U_20159,U_20160,U_20161,c_Orderings_Otop__class_Otop(tc_fun(U_20159,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20160,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

cnf(f_4845_3,plain,
    ( hAPP(c_Set_Oimage(U_20159,U_20160,U_20161),hAPP(c_Set_OCollect(U_20159),U_20162)) = hAPP(c_Set_OCollect(U_20160),hAPP(hAPP(c_COMBB(U_20159,tc_HOL_Obool,U_20160),U_20162),c_Hilbert__Choice_Oinv__into(U_20159,U_20160,c_Orderings_Otop__class_Otop(tc_fun(U_20159,tc_HOL_Obool)),U_20161)))
    | ~ c_Fun_Obij__betw(U_20159,U_20160,U_20161,c_Orderings_Otop__class_Otop(tc_fun(U_20159,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20160,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4845_2]) ).

fof(f_4846_1,plain,
    ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_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_4846_2,plain,
    ! [U_20168,U_20167,U_20166,U_20165,U_20164,U_20163] : hAPP(hAPP(c_Product__Type_Ocurry(U_20163,U_20164,U_20165,U_20166),U_20167),U_20168) = hAPP(U_20166,hAPP(hAPP(c_Product__Type_OPair(U_20163,U_20164),U_20167),U_20168)),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

cnf(f_4846_3,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_20163,U_20164,U_20165,U_20166),U_20167),U_20168) = hAPP(U_20166,hAPP(hAPP(c_Product__Type_OPair(U_20163,U_20164),U_20167),U_20168)),
    inference(clausify,[status(thm)],[f_4846_2]) ).

fof(f_4847_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_4847_2,plain,
    ! [U_20173,U_20172,U_20171,U_20170,U_20169] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20170,U_20171,tc_HOL_Obool,U_20169),U_20172),U_20173))
      | ~ hBOOL(hAPP(U_20169,hAPP(hAPP(c_Product__Type_OPair(U_20170,U_20171),U_20172),U_20173))) ),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

cnf(f_4847_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20170,U_20171,tc_HOL_Obool,U_20169),U_20172),U_20173))
    | ~ hBOOL(hAPP(U_20169,hAPP(hAPP(c_Product__Type_OPair(U_20170,U_20171),U_20172),U_20173))) ),
    inference(clausify,[status(thm)],[f_4847_2]) ).

fof(f_4848_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_4848_2,plain,
    ! [U_20175,U_20174] : c_Fun_Obij__betw(U_20174,U_20174,c_Fun_Oid(U_20174),U_20175,U_20175),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

cnf(f_4848_3,plain,
    c_Fun_Obij__betw(U_20174,U_20174,c_Fun_Oid(U_20174),U_20175,U_20175),
    inference(clausify,[status(thm)],[f_4848_2]) ).

fof(f_4849_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_4849_2,plain,
    ! [U_20180,U_20179,U_20178,U_20177,U_20176] :
      ( c_Hilbert__Choice_Oinv__into(U_20179,U_20177,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(U_20176,U_20177,U_20179,U_20178),U_20180)) = hAPP(c_Fun_Ocomp(U_20176,U_20179,U_20177,c_Hilbert__Choice_Oinv__into(U_20179,U_20176,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),U_20180)),c_Hilbert__Choice_Oinv__into(U_20176,U_20177,c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)),U_20178))
      | ~ c_Fun_Obij__betw(U_20179,U_20176,U_20180,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20176,U_20177,U_20178,c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20177,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

cnf(f_4849_3,plain,
    ( c_Hilbert__Choice_Oinv__into(U_20179,U_20177,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(U_20176,U_20177,U_20179,U_20178),U_20180)) = hAPP(c_Fun_Ocomp(U_20176,U_20179,U_20177,c_Hilbert__Choice_Oinv__into(U_20179,U_20176,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),U_20180)),c_Hilbert__Choice_Oinv__into(U_20176,U_20177,c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)),U_20178))
    | ~ c_Fun_Obij__betw(U_20179,U_20176,U_20180,c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20176,U_20177,U_20178,c_Orderings_Otop__class_Otop(tc_fun(U_20176,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20177,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4849_2]) ).

fof(f_4850_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_4850_2,plain,
    ! [U_20185,U_20184,U_20183,U_20182,U_20181] :
      ( c_Fun_Obij__betw(U_20182,U_20181,c_Hilbert__Choice_Oinv__into(U_20181,U_20182,U_20184,U_20183),U_20185,U_20184)
      | ~ c_Fun_Obij__betw(U_20181,U_20182,U_20183,U_20184,U_20185) ),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

cnf(f_4850_3,plain,
    ( c_Fun_Obij__betw(U_20182,U_20181,c_Hilbert__Choice_Oinv__into(U_20181,U_20182,U_20184,U_20183),U_20185,U_20184)
    | ~ c_Fun_Obij__betw(U_20181,U_20182,U_20183,U_20184,U_20185) ),
    inference(clausify,[status(thm)],[f_4850_2]) ).

fof(f_4851_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_4851_2,plain,
    ! [U_20191,U_20190,U_20189,U_20188,U_20187,U_20186] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20187,U_20186,U_20190,c_Hilbert__Choice_Oinv__into(U_20186,U_20187,U_20189,U_20188)),U_20191) = hAPP(U_20188,U_20191)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20186),U_20191),U_20189))
      | ~ c_Fun_Obij__betw(U_20186,U_20187,U_20188,U_20189,U_20190) ),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

cnf(f_4851_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20187,U_20186,U_20190,c_Hilbert__Choice_Oinv__into(U_20186,U_20187,U_20189,U_20188)),U_20191) = hAPP(U_20188,U_20191)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20186),U_20191),U_20189))
    | ~ c_Fun_Obij__betw(U_20186,U_20187,U_20188,U_20189,U_20190) ),
    inference(clausify,[status(thm)],[f_4851_2]) ).

fof(f_4852_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_4852_2,plain,
    ! [U_20194,U_20193,U_20192] :
      ( c_Fun_Obij__betw(U_20193,U_20192,c_Hilbert__Choice_Oinv__into(U_20192,U_20193,c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)),U_20194),c_Orderings_Otop__class_Otop(tc_fun(U_20193,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20192,U_20193,U_20194,c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20193,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

cnf(f_4852_3,plain,
    ( c_Fun_Obij__betw(U_20193,U_20192,c_Hilbert__Choice_Oinv__into(U_20192,U_20193,c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)),U_20194),c_Orderings_Otop__class_Otop(tc_fun(U_20193,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20192,U_20193,U_20194,c_Orderings_Otop__class_Otop(tc_fun(U_20192,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20193,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4852_2]) ).

fof(f_4853_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_4853_2,plain,
    ! [U_20197,U_20196,U_20195] :
      ( c_Hilbert__Choice_Oinv__into(U_20196,U_20195,c_Orderings_Otop__class_Otop(tc_fun(U_20196,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(U_20195,U_20196,c_Orderings_Otop__class_Otop(tc_fun(U_20195,tc_HOL_Obool)),U_20197)) = U_20197
      | ~ c_Fun_Obij__betw(U_20195,U_20196,U_20197,c_Orderings_Otop__class_Otop(tc_fun(U_20195,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20196,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

cnf(f_4853_3,plain,
    ( c_Hilbert__Choice_Oinv__into(U_20196,U_20195,c_Orderings_Otop__class_Otop(tc_fun(U_20196,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(U_20195,U_20196,c_Orderings_Otop__class_Otop(tc_fun(U_20195,tc_HOL_Obool)),U_20197)) = U_20197
    | ~ c_Fun_Obij__betw(U_20195,U_20196,U_20197,c_Orderings_Otop__class_Otop(tc_fun(U_20195,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20196,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4853_2]) ).

fof(f_4854_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_4854_2,plain,
    ! [U_20201,U_20200,U_20199,U_20198] : c_Product__Type_Ocurry(U_20198,U_20199,U_20200,hAPP(c_Product__Type_Oprod_Oprod__case(U_20198,U_20199,U_20200),U_20201)) = U_20201,
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

cnf(f_4854_3,plain,
    c_Product__Type_Ocurry(U_20198,U_20199,U_20200,hAPP(c_Product__Type_Oprod_Oprod__case(U_20198,U_20199,U_20200),U_20201)) = U_20201,
    inference(clausify,[status(thm)],[f_4854_2]) ).

fof(f_4855_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_4855_2,plain,
    ! [U_20205,U_20204,U_20203,U_20202] : hAPP(c_Product__Type_Oprod_Oprod__case(U_20202,U_20203,U_20204),c_Product__Type_Ocurry(U_20202,U_20203,U_20204,U_20205)) = U_20205,
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

cnf(f_4855_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_20202,U_20203,U_20204),c_Product__Type_Ocurry(U_20202,U_20203,U_20204,U_20205)) = U_20205,
    inference(clausify,[status(thm)],[f_4855_2]) ).

fof(f_4856_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_4856_2,plain,
    ! [U_20208,U_20207,U_20206] :
      ( c_Fun_Obij__betw(U_20206,U_20207,U_20208,c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20207,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_20206,U_20207,U_20208),c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20207,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_20206,U_20207,U_20208,c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

cnf(f_4856_3,plain,
    ( c_Fun_Obij__betw(U_20206,U_20207,U_20208,c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20207,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20206,U_20207,U_20208),c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20207,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20206,U_20207,U_20208,c_Orderings_Otop__class_Otop(tc_fun(U_20206,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4856_2]) ).

fof(f_4857_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_4857_2,plain,
    ! [U_20211,U_20210,U_20209] :
      ( ( c_Fun_Obij__betw(U_20209,U_20210,U_20211,c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20210,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(U_20209,U_20210,U_20211),c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20210,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_20209,U_20210,U_20211,c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool))) )
      & ( ( hAPP(c_Set_Oimage(U_20209,U_20210,U_20211),c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20210,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_20209,U_20210,U_20211,c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool))) )
        | ~ c_Fun_Obij__betw(U_20209,U_20210,U_20211,c_Orderings_Otop__class_Otop(tc_fun(U_20209,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20210,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

fof(f_4857_3,plain,
    ( ! [U_20217,U_20215,U_20213] :
        ( c_Fun_Obij__betw(U_20213,U_20215,U_20217,c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20215,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(U_20213,U_20215,U_20217),c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20215,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_20213,U_20215,U_20217,c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool))) )
    & ! [U_20216,U_20214,U_20212] :
        ( ( hAPP(c_Set_Oimage(U_20212,U_20214,U_20216),c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20214,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_20212,U_20214,U_20216,c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool))) )
        | ~ c_Fun_Obij__betw(U_20212,U_20214,U_20216,c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20214,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4857_2]) ).

cnf(f_4857_4,plain,
    ( c_Fun_Oinj__on(U_20212,U_20214,U_20216,c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20212,U_20214,U_20216,c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20214,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4857_3]) ).

cnf(f_4857_5,plain,
    ( hAPP(c_Set_Oimage(U_20212,U_20214,U_20216),c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20214,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20212,U_20214,U_20216,c_Orderings_Otop__class_Otop(tc_fun(U_20212,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20214,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4857_3]) ).

cnf(f_4857_6,plain,
    ( c_Fun_Obij__betw(U_20213,U_20215,U_20217,c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20215,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20213,U_20215,U_20217),c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20215,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20213,U_20215,U_20217,c_Orderings_Otop__class_Otop(tc_fun(U_20213,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4857_3]) ).

fof(f_4858_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_4858_2,plain,
    ! [U_20224,U_20223,U_20222,U_20221,U_20220,U_20219,U_20218] :
      ( c_Fun_Obij__betw(U_20218,U_20221,U_20224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20218,tc_HOL_Obool)),U_20219),U_20220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20221,tc_HOL_Obool)),U_20222),U_20223))
      | ~ c_Fun_Obij__betw(U_20218,U_20221,U_20224,U_20220,U_20223)
      | ~ c_Fun_Obij__betw(U_20218,U_20221,U_20224,U_20219,U_20222)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20221,tc_HOL_Obool)),U_20222),U_20223) != c_Orderings_Obot__class_Obot(tc_fun(U_20221,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20218,tc_HOL_Obool)),U_20219),U_20220) != c_Orderings_Obot__class_Obot(tc_fun(U_20218,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

cnf(f_4858_3,plain,
    ( c_Fun_Obij__betw(U_20218,U_20221,U_20224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20218,tc_HOL_Obool)),U_20219),U_20220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20221,tc_HOL_Obool)),U_20222),U_20223))
    | ~ c_Fun_Obij__betw(U_20218,U_20221,U_20224,U_20220,U_20223)
    | ~ c_Fun_Obij__betw(U_20218,U_20221,U_20224,U_20219,U_20222)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20221,tc_HOL_Obool)),U_20222),U_20223) != c_Orderings_Obot__class_Obot(tc_fun(U_20221,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20218,tc_HOL_Obool)),U_20219),U_20220) != c_Orderings_Obot__class_Obot(tc_fun(U_20218,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4858_2]) ).

fof(f_4859_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_4859_2,plain,
    ! [U_20231,U_20230,U_20229,U_20228,U_20227,U_20226,U_20225] :
      ( c_Fun_Obij__betw(U_20225,U_20226,U_20227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20225,tc_HOL_Obool)),U_20228),U_20230),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20226,tc_HOL_Obool)),U_20229),U_20231))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20226,tc_HOL_Obool)),U_20229),U_20231) != c_Orderings_Obot__class_Obot(tc_fun(U_20226,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20225,U_20226,U_20227,U_20230,U_20231)
      | ~ c_Fun_Obij__betw(U_20225,U_20226,U_20227,U_20228,U_20229) ),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

cnf(f_4859_3,plain,
    ( c_Fun_Obij__betw(U_20225,U_20226,U_20227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20225,tc_HOL_Obool)),U_20228),U_20230),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20226,tc_HOL_Obool)),U_20229),U_20231))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20226,tc_HOL_Obool)),U_20229),U_20231) != c_Orderings_Obot__class_Obot(tc_fun(U_20226,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20225,U_20226,U_20227,U_20230,U_20231)
    | ~ c_Fun_Obij__betw(U_20225,U_20226,U_20227,U_20228,U_20229) ),
    inference(clausify,[status(thm)],[f_4859_2]) ).

fof(f_4860_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_4860_2,plain,
    ! [U_20236,U_20235,U_20234,U_20233,U_20232] :
      ( c_Fun_Obij__betw(U_20233,U_20232,c_Fun_Othe__inv__into(U_20232,U_20233,U_20235,U_20234),U_20236,U_20235)
      | ~ c_Fun_Obij__betw(U_20232,U_20233,U_20234,U_20235,U_20236) ),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

cnf(f_4860_3,plain,
    ( c_Fun_Obij__betw(U_20233,U_20232,c_Fun_Othe__inv__into(U_20232,U_20233,U_20235,U_20234),U_20236,U_20235)
    | ~ c_Fun_Obij__betw(U_20232,U_20233,U_20234,U_20235,U_20236) ),
    inference(clausify,[status(thm)],[f_4860_2]) ).

fof(f_4861_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_4861_2,plain,
    ! [U_20241,U_20240,U_20239,U_20238,U_20237] :
      ( hAPP(c_Finite__Set_Ocard(U_20237),U_20240) = hAPP(c_Finite__Set_Ocard(U_20238),U_20241)
      | ~ c_Fun_Obij__betw(U_20237,U_20238,U_20239,U_20240,U_20241) ),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

cnf(f_4861_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_20237),U_20240) = hAPP(c_Finite__Set_Ocard(U_20238),U_20241)
    | ~ c_Fun_Obij__betw(U_20237,U_20238,U_20239,U_20240,U_20241) ),
    inference(clausify,[status(thm)],[f_4861_2]) ).

fof(f_4862_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_4862_2,plain,
    ! [U_20245,U_20244,U_20243,U_20242] :
      ( U_20245 = c_Orderings_Obot__class_Obot(tc_fun(U_20242,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20242,U_20243,U_20244,U_20245,c_Orderings_Obot__class_Obot(tc_fun(U_20243,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

cnf(f_4862_3,plain,
    ( U_20245 = c_Orderings_Obot__class_Obot(tc_fun(U_20242,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20242,U_20243,U_20244,U_20245,c_Orderings_Obot__class_Obot(tc_fun(U_20243,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4862_2]) ).

fof(f_4863_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_4863_2,plain,
    ! [U_20249,U_20248,U_20247,U_20246] :
      ( U_20249 = c_Orderings_Obot__class_Obot(tc_fun(U_20247,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20246,U_20247,U_20248,c_Orderings_Obot__class_Obot(tc_fun(U_20246,tc_HOL_Obool)),U_20249) ),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

fof(f_4863_3,plain,
    ! [U_20249,U_20248,U_20247] :
      ( ! [U_20246] : ~ c_Fun_Obij__betw(U_20246,U_20247,U_20248,c_Orderings_Obot__class_Obot(tc_fun(U_20246,tc_HOL_Obool)),U_20249)
      | U_20249 = c_Orderings_Obot__class_Obot(tc_fun(U_20247,tc_HOL_Obool)) ),
    inference(miniscope,[status(thm)],[f_4863_2]) ).

cnf(f_4863_4,plain,
    ( ~ c_Fun_Obij__betw(U_20246,U_20247,U_20248,c_Orderings_Obot__class_Obot(tc_fun(U_20246,tc_HOL_Obool)),U_20249)
    | U_20249 = c_Orderings_Obot__class_Obot(tc_fun(U_20247,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4863_3]) ).

fof(f_4864_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_4864_2,plain,
    ! [U_20255,U_20254,U_20253,U_20252] :
      ( ( ( ? [U_20251] : c_Fun_Obij__betw(U_20252,U_20254,U_20251,U_20253,U_20255)
          | hAPP(c_Finite__Set_Ocard(U_20252),U_20253) != hAPP(c_Finite__Set_Ocard(U_20254),U_20255) )
        & ( hAPP(c_Finite__Set_Ocard(U_20252),U_20253) = hAPP(c_Finite__Set_Ocard(U_20254),U_20255)
          | ! [U_20250] : ~ c_Fun_Obij__betw(U_20252,U_20254,U_20250,U_20253,U_20255) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20254),U_20255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20252),U_20253)) ),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

fof(f_4864_3,plain,
    ! [U_20255,U_20254,U_20253,U_20252] :
      ( ( ( c_Fun_Obij__betw(U_20252,U_20254,sK545(U_20255,U_20254,U_20253,U_20252),U_20253,U_20255)
          | hAPP(c_Finite__Set_Ocard(U_20252),U_20253) != hAPP(c_Finite__Set_Ocard(U_20254),U_20255) )
        & ( hAPP(c_Finite__Set_Ocard(U_20252),U_20253) = hAPP(c_Finite__Set_Ocard(U_20254),U_20255)
          | ! [U_20250] : ~ c_Fun_Obij__betw(U_20252,U_20254,U_20250,U_20253,U_20255) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20254),U_20255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20252),U_20253)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK545]),skolemize(U_20251,sK545(U_20255,U_20254,U_20253,U_20252))],[f_4864_2]) ).

cnf(f_4864_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_20252),U_20253) = hAPP(c_Finite__Set_Ocard(U_20254),U_20255)
    | ~ c_Fun_Obij__betw(U_20252,U_20254,U_20250,U_20253,U_20255)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20254),U_20255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20252),U_20253)) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

cnf(f_4864_5,plain,
    ( c_Fun_Obij__betw(U_20252,U_20254,sK545(U_20255,U_20254,U_20253,U_20252),U_20253,U_20255)
    | hAPP(c_Finite__Set_Ocard(U_20252),U_20253) != hAPP(c_Finite__Set_Ocard(U_20254),U_20255)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20254),U_20255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20252),U_20253)) ),
    inference(clausify,[status(thm)],[f_4864_3]) ).

fof(f_4865_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_4865_2,plain,
    ! [U_20260,U_20259,U_20258,U_20257,U_20256] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20256),U_20259))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20257),U_20260)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20257),U_20260))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20256),U_20259)) ) )
      | ~ c_Fun_Obij__betw(U_20256,U_20257,U_20258,U_20259,U_20260) ),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

cnf(f_4865_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20257),U_20260))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20256),U_20259))
    | ~ c_Fun_Obij__betw(U_20256,U_20257,U_20258,U_20259,U_20260) ),
    inference(clausify,[status(thm)],[f_4865_2]) ).

cnf(f_4865_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20256),U_20259))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20257),U_20260))
    | ~ c_Fun_Obij__betw(U_20256,U_20257,U_20258,U_20259,U_20260) ),
    inference(clausify,[status(thm)],[f_4865_2]) ).

fof(f_4866_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_4866_2,plain,
    ! [U_20263,U_20262,U_20261] :
      ( ( c_Fun_Obij__betw(U_20261,U_20261,c_Fun_Oid(U_20261),U_20262,U_20263)
        | U_20262 != U_20263 )
      & ( U_20262 = U_20263
        | ~ c_Fun_Obij__betw(U_20261,U_20261,c_Fun_Oid(U_20261),U_20262,U_20263) ) ),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

fof(f_4866_3,plain,
    ( ! [U_20269,U_20267] :
        ( ! [U_20265] : c_Fun_Obij__betw(U_20265,U_20265,c_Fun_Oid(U_20265),U_20267,U_20269)
        | U_20267 != U_20269 )
    & ! [U_20268,U_20266] :
        ( ! [U_20264] : ~ c_Fun_Obij__betw(U_20264,U_20264,c_Fun_Oid(U_20264),U_20266,U_20268)
        | U_20266 = U_20268 ) ),
    inference(miniscope,[status(thm)],[f_4866_2]) ).

cnf(f_4866_4,plain,
    ( ~ c_Fun_Obij__betw(U_20264,U_20264,c_Fun_Oid(U_20264),U_20266,U_20268)
    | U_20266 = U_20268 ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

cnf(f_4866_5,plain,
    ( c_Fun_Obij__betw(U_20265,U_20265,c_Fun_Oid(U_20265),U_20267,U_20269)
    | U_20267 != U_20269 ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

fof(f_4867_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_4867_2,plain,
    ! [U_20270] : c_Fun_Obij__betw(U_20270,U_20270,c_Fun_Oid(U_20270),c_Orderings_Otop__class_Otop(tc_fun(U_20270,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20270,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

cnf(f_4867_3,plain,
    c_Fun_Obij__betw(U_20270,U_20270,c_Fun_Oid(U_20270),c_Orderings_Otop__class_Otop(tc_fun(U_20270,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20270,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4867_2]) ).

fof(f_4868_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_4868_2,plain,
    ! [U_20277,U_20276,U_20275,U_20274,U_20273,U_20272,U_20271] :
      ( c_Fun_Obij__betw(U_20271,U_20272,U_20273,U_20276,U_20277)
      | hAPP(c_Set_Oimage(U_20271,U_20272,U_20273),U_20276) != U_20277
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20271,tc_HOL_Obool)),U_20276),U_20274))
      | ~ c_Fun_Obij__betw(U_20271,U_20272,U_20273,U_20274,U_20275) ),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

cnf(f_4868_3,plain,
    ( c_Fun_Obij__betw(U_20271,U_20272,U_20273,U_20276,U_20277)
    | hAPP(c_Set_Oimage(U_20271,U_20272,U_20273),U_20276) != U_20277
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20271,tc_HOL_Obool)),U_20276),U_20274))
    | ~ c_Fun_Obij__betw(U_20271,U_20272,U_20273,U_20274,U_20275) ),
    inference(clausify,[status(thm)],[f_4868_2]) ).

fof(f_4869_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_4869_2,plain,
    ! [U_20280,U_20279,U_20278] :
      ( hAPP(c_Set_Oimage(U_20278,U_20279,U_20280),c_Orderings_Otop__class_Otop(tc_fun(U_20278,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20279,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20278,U_20279,U_20280,c_Orderings_Otop__class_Otop(tc_fun(U_20278,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20279,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

cnf(f_4869_3,plain,
    ( hAPP(c_Set_Oimage(U_20278,U_20279,U_20280),c_Orderings_Otop__class_Otop(tc_fun(U_20278,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20279,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20278,U_20279,U_20280,c_Orderings_Otop__class_Otop(tc_fun(U_20278,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20279,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),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_4870_2,plain,
    ! [U_20284,U_20283,U_20282,U_20281] :
      ( hAPP(c_Set_Oimage(U_20281,U_20282,U_20283),c_Orderings_Otop__class_Otop(tc_fun(U_20281,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20282,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20281,U_20282,U_20283,U_20284,c_Orderings_Otop__class_Otop(tc_fun(U_20282,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

cnf(f_4870_3,plain,
    ( hAPP(c_Set_Oimage(U_20281,U_20282,U_20283),c_Orderings_Otop__class_Otop(tc_fun(U_20281,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20282,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20281,U_20282,U_20283,U_20284,c_Orderings_Otop__class_Otop(tc_fun(U_20282,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4870_2]) ).

fof(f_4871_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_4871_2,plain,
    ! [U_20288,U_20287,U_20286,U_20285] :
      ( c_Fun_Obij__betw(U_20285,U_20286,U_20287,U_20288,hAPP(c_Set_Oimage(U_20285,U_20286,U_20287),U_20288))
      | ~ c_Fun_Oinj__on(U_20285,U_20286,U_20287,U_20288) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

cnf(f_4871_3,plain,
    ( c_Fun_Obij__betw(U_20285,U_20286,U_20287,U_20288,hAPP(c_Set_Oimage(U_20285,U_20286,U_20287),U_20288))
    | ~ c_Fun_Oinj__on(U_20285,U_20286,U_20287,U_20288) ),
    inference(clausify,[status(thm)],[f_4871_2]) ).

fof(f_4872_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_4872_2,plain,
    ! [U_20293,U_20292,U_20291,U_20290,U_20289] :
      ( ( c_Fun_Obij__betw(U_20289,U_20290,U_20291,U_20292,U_20293)
        | hAPP(c_Set_Oimage(U_20289,U_20290,U_20291),U_20292) != U_20293
        | ~ c_Fun_Oinj__on(U_20289,U_20290,U_20291,U_20292) )
      & ( ( hAPP(c_Set_Oimage(U_20289,U_20290,U_20291),U_20292) = U_20293
          & c_Fun_Oinj__on(U_20289,U_20290,U_20291,U_20292) )
        | ~ c_Fun_Obij__betw(U_20289,U_20290,U_20291,U_20292,U_20293) ) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

fof(f_4872_3,plain,
    ( ! [U_20303,U_20301,U_20299,U_20297,U_20295] :
        ( c_Fun_Obij__betw(U_20295,U_20297,U_20299,U_20301,U_20303)
        | hAPP(c_Set_Oimage(U_20295,U_20297,U_20299),U_20301) != U_20303
        | ~ c_Fun_Oinj__on(U_20295,U_20297,U_20299,U_20301) )
    & ! [U_20302,U_20300,U_20298,U_20296,U_20294] :
        ( ( hAPP(c_Set_Oimage(U_20294,U_20296,U_20298),U_20300) = U_20302
          & c_Fun_Oinj__on(U_20294,U_20296,U_20298,U_20300) )
        | ~ c_Fun_Obij__betw(U_20294,U_20296,U_20298,U_20300,U_20302) ) ),
    inference(miniscope,[status(thm)],[f_4872_2]) ).

cnf(f_4872_4,plain,
    ( c_Fun_Oinj__on(U_20294,U_20296,U_20298,U_20300)
    | ~ c_Fun_Obij__betw(U_20294,U_20296,U_20298,U_20300,U_20302) ),
    inference(clausify,[status(thm)],[f_4872_3]) ).

cnf(f_4872_5,plain,
    ( hAPP(c_Set_Oimage(U_20294,U_20296,U_20298),U_20300) = U_20302
    | ~ c_Fun_Obij__betw(U_20294,U_20296,U_20298,U_20300,U_20302) ),
    inference(clausify,[status(thm)],[f_4872_3]) ).

cnf(f_4872_6,plain,
    ( c_Fun_Obij__betw(U_20295,U_20297,U_20299,U_20301,U_20303)
    | hAPP(c_Set_Oimage(U_20295,U_20297,U_20299),U_20301) != U_20303
    | ~ c_Fun_Oinj__on(U_20295,U_20297,U_20299,U_20301) ),
    inference(clausify,[status(thm)],[f_4872_3]) ).

fof(f_4873_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_4873_2,plain,
    ! [U_20308,U_20307,U_20306,U_20305,U_20304] :
      ( c_Fun_Oinj__on(U_20304,U_20305,U_20306,U_20307)
      | ~ c_Fun_Obij__betw(U_20304,U_20305,U_20306,U_20307,U_20308) ),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

cnf(f_4873_3,plain,
    ( c_Fun_Oinj__on(U_20304,U_20305,U_20306,U_20307)
    | ~ c_Fun_Obij__betw(U_20304,U_20305,U_20306,U_20307,U_20308) ),
    inference(clausify,[status(thm)],[f_4873_2]) ).

fof(f_4874_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_4874_2,plain,
    ! [U_20311,U_20310,U_20309] :
      ( c_Fun_Oinj__on(U_20309,U_20310,U_20311,c_Orderings_Otop__class_Otop(tc_fun(U_20309,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20309,U_20310,U_20311,c_Orderings_Otop__class_Otop(tc_fun(U_20309,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20310,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

cnf(f_4874_3,plain,
    ( c_Fun_Oinj__on(U_20309,U_20310,U_20311,c_Orderings_Otop__class_Otop(tc_fun(U_20309,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20309,U_20310,U_20311,c_Orderings_Otop__class_Otop(tc_fun(U_20309,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20310,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4874_2]) ).

fof(f_4875_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_4875_2,plain,
    ! [U_20315,U_20314,U_20313,U_20312] :
      ( hAPP(c_Set_Oimage(U_20312,U_20313,U_20314),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20312,tc_HOL_Obool)),U_20315)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20313,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20312,U_20313,U_20314),U_20315))
      | ~ c_Fun_Obij__betw(U_20312,U_20313,U_20314,c_Orderings_Otop__class_Otop(tc_fun(U_20312,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20313,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

cnf(f_4875_3,plain,
    ( hAPP(c_Set_Oimage(U_20312,U_20313,U_20314),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20312,tc_HOL_Obool)),U_20315)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20313,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20312,U_20313,U_20314),U_20315))
    | ~ c_Fun_Obij__betw(U_20312,U_20313,U_20314,c_Orderings_Otop__class_Otop(tc_fun(U_20312,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20313,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4875_2]) ).

fof(f_4876_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_4876_2,plain,
    ! [U_20319,U_20318,U_20317,U_20316] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20316),hAPP(c_Set_Ovimage(U_20316,U_20317,U_20318),U_20319)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20317),U_20319)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20317),U_20319))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20316),hAPP(c_Set_Ovimage(U_20316,U_20317,U_20318),U_20319))) ) )
      | ~ c_Fun_Obij__betw(U_20316,U_20317,U_20318,c_Orderings_Otop__class_Otop(tc_fun(U_20316,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20317,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

cnf(f_4876_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20317),U_20319))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20316),hAPP(c_Set_Ovimage(U_20316,U_20317,U_20318),U_20319)))
    | ~ c_Fun_Obij__betw(U_20316,U_20317,U_20318,c_Orderings_Otop__class_Otop(tc_fun(U_20316,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20317,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4876_2]) ).

cnf(f_4876_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20316),hAPP(c_Set_Ovimage(U_20316,U_20317,U_20318),U_20319)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20317),U_20319))
    | ~ c_Fun_Obij__betw(U_20316,U_20317,U_20318,c_Orderings_Otop__class_Otop(tc_fun(U_20316,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20317,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4876_2]) ).

fof(f_4877_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_4877_2,plain,
    ! [U_20325,U_20324,U_20323,U_20322,U_20321,U_20320] : hAPP(hAPP(c_Product__Type_Ocurry(U_20320,U_20321,U_20322,U_20323),U_20324),U_20325) = hAPP(U_20323,hAPP(hAPP(c_Product__Type_OPair(U_20320,U_20321),U_20324),U_20325)),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

cnf(f_4877_3,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_20320,U_20321,U_20322,U_20323),U_20324),U_20325) = hAPP(U_20323,hAPP(hAPP(c_Product__Type_OPair(U_20320,U_20321),U_20324),U_20325)),
    inference(clausify,[status(thm)],[f_4877_2]) ).

fof(f_4878_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_4878_2,plain,
    ! [U_20330,U_20329,U_20328,U_20327,U_20326] :
      ( hBOOL(hAPP(U_20328,hAPP(hAPP(c_Product__Type_OPair(U_20326,U_20327),U_20329),U_20330)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20326,U_20327,tc_HOL_Obool,U_20328),U_20329),U_20330)) ),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

cnf(f_4878_3,plain,
    ( hBOOL(hAPP(U_20328,hAPP(hAPP(c_Product__Type_OPair(U_20326,U_20327),U_20329),U_20330)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20326,U_20327,tc_HOL_Obool,U_20328),U_20329),U_20330)) ),
    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] :
      ( 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_4879_2,plain,
    ! [U_20335,U_20334,U_20333,U_20332,U_20331] :
      ( hBOOL(hAPP(U_20333,hAPP(hAPP(c_Product__Type_OPair(U_20331,U_20332),U_20334),U_20335)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20331,U_20332,tc_HOL_Obool,U_20333),U_20334),U_20335)) ),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

cnf(f_4879_3,plain,
    ( hBOOL(hAPP(U_20333,hAPP(hAPP(c_Product__Type_OPair(U_20331,U_20332),U_20334),U_20335)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20331,U_20332,tc_HOL_Obool,U_20333),U_20334),U_20335)) ),
    inference(clausify,[status(thm)],[f_4879_2]) ).

fof(f_4880_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_4880_2,plain,
    ! [U_20343,U_20342,U_20341,U_20340,U_20339,U_20338,U_20337,U_20336] :
      ( ( ( c_Fun_Obij__betw(U_20337,U_20341,U_20342,U_20340,U_20343)
          | ~ c_Fun_Obij__betw(U_20336,U_20341,hAPP(c_Fun_Ocomp(U_20337,U_20341,U_20336,U_20342),U_20338),U_20339,U_20343) )
        & ( c_Fun_Obij__betw(U_20336,U_20341,hAPP(c_Fun_Ocomp(U_20337,U_20341,U_20336,U_20342),U_20338),U_20339,U_20343)
          | ~ c_Fun_Obij__betw(U_20337,U_20341,U_20342,U_20340,U_20343) ) )
      | ~ c_Fun_Obij__betw(U_20336,U_20337,U_20338,U_20339,U_20340) ),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

cnf(f_4880_3,plain,
    ( c_Fun_Obij__betw(U_20336,U_20341,hAPP(c_Fun_Ocomp(U_20337,U_20341,U_20336,U_20342),U_20338),U_20339,U_20343)
    | ~ c_Fun_Obij__betw(U_20337,U_20341,U_20342,U_20340,U_20343)
    | ~ c_Fun_Obij__betw(U_20336,U_20337,U_20338,U_20339,U_20340) ),
    inference(clausify,[status(thm)],[f_4880_2]) ).

cnf(f_4880_4,plain,
    ( c_Fun_Obij__betw(U_20337,U_20341,U_20342,U_20340,U_20343)
    | ~ c_Fun_Obij__betw(U_20336,U_20341,hAPP(c_Fun_Ocomp(U_20337,U_20341,U_20336,U_20342),U_20338),U_20339,U_20343)
    | ~ c_Fun_Obij__betw(U_20336,U_20337,U_20338,U_20339,U_20340) ),
    inference(clausify,[status(thm)],[f_4880_2]) ).

fof(f_4881_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_4881_2,plain,
    ! [U_20351,U_20350,U_20349,U_20348,U_20347,U_20346,U_20345,U_20344] :
      ( c_Fun_Obij__betw(U_20344,U_20349,hAPP(c_Fun_Ocomp(U_20345,U_20349,U_20344,U_20350),U_20346),U_20347,U_20351)
      | ~ c_Fun_Obij__betw(U_20345,U_20349,U_20350,U_20348,U_20351)
      | ~ c_Fun_Obij__betw(U_20344,U_20345,U_20346,U_20347,U_20348) ),
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

cnf(f_4881_3,plain,
    ( c_Fun_Obij__betw(U_20344,U_20349,hAPP(c_Fun_Ocomp(U_20345,U_20349,U_20344,U_20350),U_20346),U_20347,U_20351)
    | ~ c_Fun_Obij__betw(U_20345,U_20349,U_20350,U_20348,U_20351)
    | ~ c_Fun_Obij__betw(U_20344,U_20345,U_20346,U_20347,U_20348) ),
    inference(clausify,[status(thm)],[f_4881_2]) ).

fof(f_4882_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_4882_2,plain,
    ! [U_20356,U_20355,U_20354,U_20353,U_20352] :
      ( c_Fun_Obij__betw(U_20352,U_20355,hAPP(c_Fun_Ocomp(U_20353,U_20355,U_20352,U_20356),U_20354),c_Orderings_Otop__class_Otop(tc_fun(U_20352,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20355,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20353,U_20355,U_20356,c_Orderings_Otop__class_Otop(tc_fun(U_20353,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20355,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20352,U_20353,U_20354,c_Orderings_Otop__class_Otop(tc_fun(U_20352,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20353,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

cnf(f_4882_3,plain,
    ( c_Fun_Obij__betw(U_20352,U_20355,hAPP(c_Fun_Ocomp(U_20353,U_20355,U_20352,U_20356),U_20354),c_Orderings_Otop__class_Otop(tc_fun(U_20352,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20355,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20353,U_20355,U_20356,c_Orderings_Otop__class_Otop(tc_fun(U_20353,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20355,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20352,U_20353,U_20354,c_Orderings_Otop__class_Otop(tc_fun(U_20352,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20353,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4882_2]) ).

fof(f_4883_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_4883_2,plain,
    ! [U_20364,U_20363,U_20362,U_20361,U_20360,U_20359,U_20358,U_20357] :
      ( ( ( c_Fun_Obij__betw(U_20362,U_20357,U_20363,U_20364,U_20360)
          | ~ c_Fun_Obij__betw(U_20362,U_20358,hAPP(c_Fun_Ocomp(U_20357,U_20358,U_20362,U_20359),U_20363),U_20364,U_20361) )
        & ( c_Fun_Obij__betw(U_20362,U_20358,hAPP(c_Fun_Ocomp(U_20357,U_20358,U_20362,U_20359),U_20363),U_20364,U_20361)
          | ~ c_Fun_Obij__betw(U_20362,U_20357,U_20363,U_20364,U_20360) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20357,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20362,U_20357,U_20363),U_20364)),U_20360))
      | ~ c_Fun_Obij__betw(U_20357,U_20358,U_20359,U_20360,U_20361) ),
    inference(variable_rename,[status(thm)],[f_4883_1]) ).

cnf(f_4883_3,plain,
    ( c_Fun_Obij__betw(U_20362,U_20358,hAPP(c_Fun_Ocomp(U_20357,U_20358,U_20362,U_20359),U_20363),U_20364,U_20361)
    | ~ c_Fun_Obij__betw(U_20362,U_20357,U_20363,U_20364,U_20360)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20357,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20362,U_20357,U_20363),U_20364)),U_20360))
    | ~ c_Fun_Obij__betw(U_20357,U_20358,U_20359,U_20360,U_20361) ),
    inference(clausify,[status(thm)],[f_4883_2]) ).

cnf(f_4883_4,plain,
    ( c_Fun_Obij__betw(U_20362,U_20357,U_20363,U_20364,U_20360)
    | ~ c_Fun_Obij__betw(U_20362,U_20358,hAPP(c_Fun_Ocomp(U_20357,U_20358,U_20362,U_20359),U_20363),U_20364,U_20361)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20357,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20362,U_20357,U_20363),U_20364)),U_20360))
    | ~ c_Fun_Obij__betw(U_20357,U_20358,U_20359,U_20360,U_20361) ),
    inference(clausify,[status(thm)],[f_4883_2]) ).

fof(f_4884_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_4884_2,plain,
    ! [U_20370,U_20369,U_20368,U_20367,U_20366,U_20365] :
      ( hAPP(c_Set_Oimage(U_20365,U_20366,U_20367),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20368,tc_fun(U_20365,tc_HOL_Obool)),U_20369),U_20370)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20368,tc_fun(U_20366,tc_HOL_Obool)),U_20369),hAPP(hAPP(c_COMBB(tc_fun(U_20365,tc_HOL_Obool),tc_fun(U_20366,tc_HOL_Obool),U_20368),c_Set_Oimage(U_20365,U_20366,U_20367)),U_20370))
      | ~ c_Fun_Obij__betw(U_20365,U_20366,U_20367,c_Orderings_Otop__class_Otop(tc_fun(U_20365,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20366,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

cnf(f_4884_3,plain,
    ( hAPP(c_Set_Oimage(U_20365,U_20366,U_20367),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20368,tc_fun(U_20365,tc_HOL_Obool)),U_20369),U_20370)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20368,tc_fun(U_20366,tc_HOL_Obool)),U_20369),hAPP(hAPP(c_COMBB(tc_fun(U_20365,tc_HOL_Obool),tc_fun(U_20366,tc_HOL_Obool),U_20368),c_Set_Oimage(U_20365,U_20366,U_20367)),U_20370))
    | ~ c_Fun_Obij__betw(U_20365,U_20366,U_20367,c_Orderings_Otop__class_Otop(tc_fun(U_20365,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20366,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4884_2]) ).

fof(f_4885_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_4885_2,plain,
    ! [U_20375,U_20374,U_20373,U_20372,U_20371] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20371,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20371,U_20372,U_20373),U_20374)),U_20375))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20372,tc_HOL_Obool)),U_20374),hAPP(c_Set_Oimage(U_20371,U_20372,U_20373),U_20375))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20372,tc_HOL_Obool)),U_20374),hAPP(c_Set_Oimage(U_20371,U_20372,U_20373),U_20375)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20371,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20371,U_20372,U_20373),U_20374)),U_20375)) ) )
      | ~ c_Fun_Obij__betw(U_20371,U_20372,U_20373,c_Orderings_Otop__class_Otop(tc_fun(U_20371,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20372,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

cnf(f_4885_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20372,tc_HOL_Obool)),U_20374),hAPP(c_Set_Oimage(U_20371,U_20372,U_20373),U_20375)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20371,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20371,U_20372,U_20373),U_20374)),U_20375))
    | ~ c_Fun_Obij__betw(U_20371,U_20372,U_20373,c_Orderings_Otop__class_Otop(tc_fun(U_20371,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20372,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4885_2]) ).

cnf(f_4885_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20371,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20371,U_20372,U_20373),U_20374)),U_20375))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20372,tc_HOL_Obool)),U_20374),hAPP(c_Set_Oimage(U_20371,U_20372,U_20373),U_20375)))
    | ~ c_Fun_Obij__betw(U_20371,U_20372,U_20373,c_Orderings_Otop__class_Otop(tc_fun(U_20371,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20372,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4885_2]) ).

fof(f_4886_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_4886_2,plain,
    ! [U_20379,U_20378,U_20377,U_20376] :
      ( hAPP(c_Set_Ovimage(U_20376,U_20377,U_20378),U_20379) = hAPP(c_Set_Oimage(U_20377,U_20376,c_Hilbert__Choice_Oinv__into(U_20376,U_20377,c_Orderings_Otop__class_Otop(tc_fun(U_20376,tc_HOL_Obool)),U_20378)),U_20379)
      | ~ c_Fun_Obij__betw(U_20376,U_20377,U_20378,c_Orderings_Otop__class_Otop(tc_fun(U_20376,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20377,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

cnf(f_4886_3,plain,
    ( hAPP(c_Set_Ovimage(U_20376,U_20377,U_20378),U_20379) = hAPP(c_Set_Oimage(U_20377,U_20376,c_Hilbert__Choice_Oinv__into(U_20376,U_20377,c_Orderings_Otop__class_Otop(tc_fun(U_20376,tc_HOL_Obool)),U_20378)),U_20379)
    | ~ c_Fun_Obij__betw(U_20376,U_20377,U_20378,c_Orderings_Otop__class_Otop(tc_fun(U_20376,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20377,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4886_2]) ).

fof(f_4887_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_4887_2,plain,
    ! [U_20382,U_20381] :
      ( ? [U_20380] : c_Fun_Obij__betw(tc_Nat_Onat,U_20381,U_20380,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20381),U_20382)),U_20382)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20381),U_20382)) ),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

fof(f_4887_3,plain,
    ! [U_20382,U_20381] :
      ( c_Fun_Obij__betw(tc_Nat_Onat,U_20381,sK546(U_20382,U_20381),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20381),U_20382)),U_20382)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20381),U_20382)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK546]),skolemize(U_20380,sK546(U_20382,U_20381))],[f_4887_2]) ).

cnf(f_4887_4,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,U_20381,sK546(U_20382,U_20381),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20381),U_20382)),U_20382)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20381),U_20382)) ),
    inference(clausify,[status(thm)],[f_4887_3]) ).

fof(f_4888_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_4888_2,plain,
    ! [U_20389,U_20388,U_20387,U_20386,U_20385,U_20384] :
      ( ? [U_20383] : c_Fun_Obij__betw(U_20384,U_20385,U_20383,U_20387,U_20388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20384,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20385,U_20384,U_20389),U_20388)),U_20387))
      | ~ c_Fun_Oinj__on(U_20385,U_20384,U_20389,U_20388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20385,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20384,U_20385,U_20386),U_20387)),U_20388))
      | ~ c_Fun_Oinj__on(U_20384,U_20385,U_20386,U_20387) ),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

fof(f_4888_3,plain,
    ! [U_20389,U_20388,U_20387,U_20386,U_20385,U_20384] :
      ( c_Fun_Obij__betw(U_20384,U_20385,sK547(U_20389,U_20388,U_20387,U_20386,U_20385,U_20384),U_20387,U_20388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20384,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20385,U_20384,U_20389),U_20388)),U_20387))
      | ~ c_Fun_Oinj__on(U_20385,U_20384,U_20389,U_20388)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20385,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20384,U_20385,U_20386),U_20387)),U_20388))
      | ~ c_Fun_Oinj__on(U_20384,U_20385,U_20386,U_20387) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK547]),skolemize(U_20383,sK547(U_20389,U_20388,U_20387,U_20386,U_20385,U_20384))],[f_4888_2]) ).

cnf(f_4888_4,plain,
    ( c_Fun_Obij__betw(U_20384,U_20385,sK547(U_20389,U_20388,U_20387,U_20386,U_20385,U_20384),U_20387,U_20388)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20384,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20385,U_20384,U_20389),U_20388)),U_20387))
    | ~ c_Fun_Oinj__on(U_20385,U_20384,U_20389,U_20388)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20385,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20384,U_20385,U_20386),U_20387)),U_20388))
    | ~ c_Fun_Oinj__on(U_20384,U_20385,U_20386,U_20387) ),
    inference(clausify,[status(thm)],[f_4888_3]) ).

fof(f_4889_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_4889_2,plain,
    ! [U_20392,U_20391] :
      ( ? [U_20390] : c_Fun_Obij__betw(tc_Nat_Onat,U_20391,U_20390,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20391),U_20392)),U_20392)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20391),U_20392)) ),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ! [U_20392,U_20391] :
      ( c_Fun_Obij__betw(tc_Nat_Onat,U_20391,sK548(U_20392,U_20391),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20391),U_20392)),U_20392)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20391),U_20392)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK548]),skolemize(U_20390,sK548(U_20392,U_20391))],[f_4889_2]) ).

cnf(f_4889_4,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,U_20391,sK548(U_20392,U_20391),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20391),U_20392)),U_20392)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20391),U_20392)) ),
    inference(clausify,[status(thm)],[f_4889_3]) ).

fof(f_4890_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_4890_2,plain,
    ! [U_20395,U_20394] :
      ( ? [U_20393] : c_Fun_Obij__betw(U_20394,tc_Nat_Onat,U_20393,U_20395,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20394),U_20395)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20394),U_20395)) ),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

fof(f_4890_3,plain,
    ! [U_20395,U_20394] :
      ( c_Fun_Obij__betw(U_20394,tc_Nat_Onat,sK549(U_20395,U_20394),U_20395,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20394),U_20395)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20394),U_20395)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK549]),skolemize(U_20393,sK549(U_20395,U_20394))],[f_4890_2]) ).

cnf(f_4890_4,plain,
    ( c_Fun_Obij__betw(U_20394,tc_Nat_Onat,sK549(U_20395,U_20394),U_20395,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20394),U_20395)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20394),U_20395)) ),
    inference(clausify,[status(thm)],[f_4890_3]) ).

fof(f_4891_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_4891_2,plain,
    ! [U_20401,U_20400,U_20399,U_20398,U_20397] :
      ( c_Relation_Orefl__on(U_20399,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(U_20399,tc_HOL_Obool)),U_20398),U_20400),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(tc_prod(U_20399,U_20399),tc_HOL_Obool)),U_20398),U_20401))
      | ? [U_20396] :
          ( ~ c_Relation_Orefl__on(U_20399,hAPP(U_20400,U_20396),hAPP(U_20401,U_20396))
          & hBOOL(hAPP(hAPP(c_member(U_20397),U_20396),U_20398)) ) ),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

fof(f_4891_3,plain,
    ! [U_20401,U_20400,U_20399,U_20398,U_20397] :
      ( c_Relation_Orefl__on(U_20399,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(U_20399,tc_HOL_Obool)),U_20398),U_20400),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(tc_prod(U_20399,U_20399),tc_HOL_Obool)),U_20398),U_20401))
      | ( ~ c_Relation_Orefl__on(U_20399,hAPP(U_20400,sK550(U_20401,U_20400,U_20399,U_20398,U_20397)),hAPP(U_20401,sK550(U_20401,U_20400,U_20399,U_20398,U_20397)))
        & hBOOL(hAPP(hAPP(c_member(U_20397),sK550(U_20401,U_20400,U_20399,U_20398,U_20397)),U_20398)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK550]),skolemize(U_20396,sK550(U_20401,U_20400,U_20399,U_20398,U_20397))],[f_4891_2]) ).

cnf(f_4891_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20397),sK550(U_20401,U_20400,U_20399,U_20398,U_20397)),U_20398))
    | c_Relation_Orefl__on(U_20399,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(U_20399,tc_HOL_Obool)),U_20398),U_20400),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(tc_prod(U_20399,U_20399),tc_HOL_Obool)),U_20398),U_20401)) ),
    inference(clausify,[status(thm)],[f_4891_3]) ).

cnf(f_4891_5,plain,
    ( ~ c_Relation_Orefl__on(U_20399,hAPP(U_20400,sK550(U_20401,U_20400,U_20399,U_20398,U_20397)),hAPP(U_20401,sK550(U_20401,U_20400,U_20399,U_20398,U_20397)))
    | c_Relation_Orefl__on(U_20399,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(U_20399,tc_HOL_Obool)),U_20398),U_20400),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20397,tc_fun(tc_prod(U_20399,U_20399),tc_HOL_Obool)),U_20398),U_20401)) ),
    inference(clausify,[status(thm)],[f_4891_3]) ).

fof(f_4892_1,plain,
    ! [V_Pa_2,V_R_2,T_b] :
      ( ( ( ? [B_x] :
              ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x1)) )
        & ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_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_4892_2,plain,
    ! [U_20408,U_20407,U_20406] :
      ( ( ( ? [U_20405] :
              ( hBOOL(hAPP(U_20408,U_20405))
              & hBOOL(hAPP(hAPP(c_member(U_20406),U_20405),c_Quotient_ORespects(U_20406,U_20407))) )
          | ! [U_20404] : ~ hBOOL(hAPP(U_20408,U_20404)) )
        & ( ? [U_20403] : hBOOL(hAPP(U_20408,U_20403))
          | ! [U_20402] :
              ( ~ hBOOL(hAPP(U_20408,U_20402))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20406),U_20402),c_Quotient_ORespects(U_20406,U_20407))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

fof(f_4892_3,plain,
    ! [U_20408,U_20407,U_20406] :
      ( ( ( ? [U_20405] :
              ( hBOOL(hAPP(U_20408,U_20405))
              & hBOOL(hAPP(hAPP(c_member(U_20406),U_20405),c_Quotient_ORespects(U_20406,U_20407))) )
          | ! [U_20404] : ~ hBOOL(hAPP(U_20408,U_20404)) )
        & ( hBOOL(hAPP(U_20408,sK551(U_20408,U_20407,U_20406)))
          | ! [U_20402] :
              ( ~ hBOOL(hAPP(U_20408,U_20402))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20406),U_20402),c_Quotient_ORespects(U_20406,U_20407))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK551]),skolemize(U_20403,sK551(U_20408,U_20407,U_20406))],[f_4892_2]) ).

fof(f_4892_4,plain,
    ! [U_20408,U_20407,U_20406] :
      ( ( ( ( hBOOL(hAPP(U_20408,sK552(U_20408,U_20407,U_20406)))
            & hBOOL(hAPP(hAPP(c_member(U_20406),sK552(U_20408,U_20407,U_20406)),c_Quotient_ORespects(U_20406,U_20407))) )
          | ! [U_20404] : ~ hBOOL(hAPP(U_20408,U_20404)) )
        & ( hBOOL(hAPP(U_20408,sK551(U_20408,U_20407,U_20406)))
          | ! [U_20402] :
              ( ~ hBOOL(hAPP(U_20408,U_20402))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20406),U_20402),c_Quotient_ORespects(U_20406,U_20407))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK552]),skolemize(U_20405,sK552(U_20408,U_20407,U_20406))],[f_4892_3]) ).

cnf(f_4892_5,plain,
    ( hBOOL(hAPP(U_20408,sK551(U_20408,U_20407,U_20406)))
    | ~ hBOOL(hAPP(U_20408,U_20402))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20406),U_20402),c_Quotient_ORespects(U_20406,U_20407)))
    | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(clausify,[status(thm)],[f_4892_4]) ).

cnf(f_4892_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20406),sK552(U_20408,U_20407,U_20406)),c_Quotient_ORespects(U_20406,U_20407)))
    | ~ hBOOL(hAPP(U_20408,U_20404))
    | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(clausify,[status(thm)],[f_4892_4]) ).

cnf(f_4892_7,plain,
    ( hBOOL(hAPP(U_20408,sK552(U_20408,U_20407,U_20406)))
    | ~ hBOOL(hAPP(U_20408,U_20404))
    | ~ c_Equiv__Relations_Oequivp(U_20406,U_20407) ),
    inference(clausify,[status(thm)],[f_4892_4]) ).

fof(f_4893_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_4893_2,plain,
    ! [U_20411,U_20410,U_20409] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20409),U_20410),c_Quotient_ORespects(U_20409,U_20411)))
        | ~ hBOOL(hAPP(hAPP(U_20411,U_20410),U_20410)) )
      & ( hBOOL(hAPP(hAPP(U_20411,U_20410),U_20410))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20409),U_20410),c_Quotient_ORespects(U_20409,U_20411))) ) ),
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

fof(f_4893_3,plain,
    ( ! [U_20417,U_20415] :
        ( ! [U_20413] : hBOOL(hAPP(hAPP(c_member(U_20413),U_20415),c_Quotient_ORespects(U_20413,U_20417)))
        | ~ hBOOL(hAPP(hAPP(U_20417,U_20415),U_20415)) )
    & ! [U_20416,U_20414] :
        ( ! [U_20412] : ~ hBOOL(hAPP(hAPP(c_member(U_20412),U_20414),c_Quotient_ORespects(U_20412,U_20416)))
        | hBOOL(hAPP(hAPP(U_20416,U_20414),U_20414)) ) ),
    inference(miniscope,[status(thm)],[f_4893_2]) ).

cnf(f_4893_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20412),U_20414),c_Quotient_ORespects(U_20412,U_20416)))
    | hBOOL(hAPP(hAPP(U_20416,U_20414),U_20414)) ),
    inference(clausify,[status(thm)],[f_4893_3]) ).

cnf(f_4893_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20413),U_20415),c_Quotient_ORespects(U_20413,U_20417)))
    | ~ hBOOL(hAPP(hAPP(U_20417,U_20415),U_20415)) ),
    inference(clausify,[status(thm)],[f_4893_3]) ).

fof(f_4894_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_4894_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_4894_1]) ).

fof(f_4894_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_4894_2]) ).

cnf(f_4894_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_4894_3]) ).

cnf(f_4894_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_4894_3]) ).

fof(f_4895_1,plain,
    ! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Qa_2,B_x1))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Pa_2,B_x))
          & hBOOL(hAPP(V_Qa_2,B_x)) )
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_bex__reg__right]) ).

fof(f_4895_2,plain,
    ! [U_20433,U_20432,U_20431,U_20430] :
      ( ? [U_20429] :
          ( hBOOL(hAPP(U_20433,U_20429))
          & hBOOL(hAPP(hAPP(c_member(U_20430),U_20429),c_Quotient_ORespects(U_20430,U_20431))) )
      | ! [U_20428] : ~ hBOOL(hAPP(U_20432,U_20428))
      | ? [U_20427] :
          ( ~ hBOOL(hAPP(U_20433,U_20427))
          & hBOOL(hAPP(U_20432,U_20427)) )
      | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

fof(f_4895_3,plain,
    ! [U_20433,U_20432,U_20431,U_20430] :
      ( ? [U_20429] :
          ( hBOOL(hAPP(U_20433,U_20429))
          & hBOOL(hAPP(hAPP(c_member(U_20430),U_20429),c_Quotient_ORespects(U_20430,U_20431))) )
      | ! [U_20428] : ~ hBOOL(hAPP(U_20432,U_20428))
      | ( ~ hBOOL(hAPP(U_20433,sK553(U_20433,U_20432,U_20431,U_20430)))
        & hBOOL(hAPP(U_20432,sK553(U_20433,U_20432,U_20431,U_20430))) )
      | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK553]),skolemize(U_20427,sK553(U_20433,U_20432,U_20431,U_20430))],[f_4895_2]) ).

fof(f_4895_4,plain,
    ! [U_20433,U_20432,U_20431,U_20430] :
      ( ( hBOOL(hAPP(U_20433,sK554(U_20433,U_20432,U_20431,U_20430)))
        & hBOOL(hAPP(hAPP(c_member(U_20430),sK554(U_20433,U_20432,U_20431,U_20430)),c_Quotient_ORespects(U_20430,U_20431))) )
      | ! [U_20428] : ~ hBOOL(hAPP(U_20432,U_20428))
      | ( ~ hBOOL(hAPP(U_20433,sK553(U_20433,U_20432,U_20431,U_20430)))
        & hBOOL(hAPP(U_20432,sK553(U_20433,U_20432,U_20431,U_20430))) )
      | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK554]),skolemize(U_20429,sK554(U_20433,U_20432,U_20431,U_20430))],[f_4895_3]) ).

cnf(f_4895_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20430),sK554(U_20433,U_20432,U_20431,U_20430)),c_Quotient_ORespects(U_20430,U_20431)))
    | ~ hBOOL(hAPP(U_20432,U_20428))
    | hBOOL(hAPP(U_20432,sK553(U_20433,U_20432,U_20431,U_20430)))
    | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(clausify,[status(thm)],[f_4895_4]) ).

cnf(f_4895_6,plain,
    ( hBOOL(hAPP(U_20433,sK554(U_20433,U_20432,U_20431,U_20430)))
    | ~ hBOOL(hAPP(U_20432,U_20428))
    | hBOOL(hAPP(U_20432,sK553(U_20433,U_20432,U_20431,U_20430)))
    | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(clausify,[status(thm)],[f_4895_4]) ).

cnf(f_4895_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20430),sK554(U_20433,U_20432,U_20431,U_20430)),c_Quotient_ORespects(U_20430,U_20431)))
    | ~ hBOOL(hAPP(U_20432,U_20428))
    | ~ hBOOL(hAPP(U_20433,sK553(U_20433,U_20432,U_20431,U_20430)))
    | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(clausify,[status(thm)],[f_4895_4]) ).

cnf(f_4895_8,plain,
    ( hBOOL(hAPP(U_20433,sK554(U_20433,U_20432,U_20431,U_20430)))
    | ~ hBOOL(hAPP(U_20432,U_20428))
    | ~ hBOOL(hAPP(U_20433,sK553(U_20433,U_20432,U_20431,U_20430)))
    | ~ c_Equiv__Relations_Oequivp(U_20430,U_20431) ),
    inference(clausify,[status(thm)],[f_4895_4]) ).

fof(f_4896_1,plain,
    ! [V_Pa_2,T_c,V_R_2,T_b] :
      ( c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_babs__reg__eqv]) ).

fof(f_4896_2,plain,
    ! [U_20437,U_20436,U_20435,U_20434] :
      ( c_Quotient_OBabs(U_20434,U_20436,c_Quotient_ORespects(U_20434,U_20435),U_20437) = U_20437
      | ~ c_Equiv__Relations_Oequivp(U_20434,U_20435) ),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

cnf(f_4896_3,plain,
    ( c_Quotient_OBabs(U_20434,U_20436,c_Quotient_ORespects(U_20434,U_20435),U_20437) = U_20437
    | ~ c_Equiv__Relations_Oequivp(U_20434,U_20435) ),
    inference(clausify,[status(thm)],[f_4896_2]) ).

fof(f_4897_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_4897_2,plain,
    ! [U_20442,U_20441,U_20440,U_20439,U_20438] :
      ( hAPP(c_Quotient_OBabs(U_20438,U_20441,U_20440,U_20442),U_20439) = hAPP(U_20442,U_20439)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20438),U_20439),U_20440)) ),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

cnf(f_4897_3,plain,
    ( hAPP(c_Quotient_OBabs(U_20438,U_20441,U_20440,U_20442),U_20439) = hAPP(U_20442,U_20439)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20438),U_20439),U_20440)) ),
    inference(clausify,[status(thm)],[f_4897_2]) ).

fof(f_4898_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_4898_2,plain,
    ! [U_20448,U_20447,U_20446] :
      ( ? [U_20445] :
        ! [U_20444] : hAPP(U_20447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20445),U_20444)) = hAPP(U_20447,U_20445)
      | ~ c_Wellfounded_Owf(U_20446,c_Transitive__Closure_Otrancl(U_20446,U_20448))
      | ? [U_20443] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20446,U_20446)),hAPP(hAPP(c_Product__Type_OPair(U_20446,U_20446),hAPP(U_20447,hAPP(c_Nat_OSuc,U_20443))),hAPP(U_20447,U_20443))),c_Transitive__Closure_Ortrancl(U_20446,U_20448))) ),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20448,U_20447,U_20446] :
      ( ? [U_20445] :
        ! [U_20444] : hAPP(U_20447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20445),U_20444)) = hAPP(U_20447,U_20445)
      | ~ c_Wellfounded_Owf(U_20446,c_Transitive__Closure_Otrancl(U_20446,U_20448))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20446,U_20446)),hAPP(hAPP(c_Product__Type_OPair(U_20446,U_20446),hAPP(U_20447,hAPP(c_Nat_OSuc,sK555(U_20448,U_20447,U_20446)))),hAPP(U_20447,sK555(U_20448,U_20447,U_20446)))),c_Transitive__Closure_Ortrancl(U_20446,U_20448))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK555]),skolemize(U_20443,sK555(U_20448,U_20447,U_20446))],[f_4898_2]) ).

fof(f_4898_4,plain,
    ! [U_20448,U_20447,U_20446] :
      ( ! [U_20444] : hAPP(U_20447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK556(U_20448,U_20447,U_20446)),U_20444)) = hAPP(U_20447,sK556(U_20448,U_20447,U_20446))
      | ~ c_Wellfounded_Owf(U_20446,c_Transitive__Closure_Otrancl(U_20446,U_20448))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20446,U_20446)),hAPP(hAPP(c_Product__Type_OPair(U_20446,U_20446),hAPP(U_20447,hAPP(c_Nat_OSuc,sK555(U_20448,U_20447,U_20446)))),hAPP(U_20447,sK555(U_20448,U_20447,U_20446)))),c_Transitive__Closure_Ortrancl(U_20446,U_20448))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK556]),skolemize(U_20445,sK556(U_20448,U_20447,U_20446))],[f_4898_3]) ).

cnf(f_4898_5,plain,
    ( hAPP(U_20447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK556(U_20448,U_20447,U_20446)),U_20444)) = hAPP(U_20447,sK556(U_20448,U_20447,U_20446))
    | ~ c_Wellfounded_Owf(U_20446,c_Transitive__Closure_Otrancl(U_20446,U_20448))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20446,U_20446)),hAPP(hAPP(c_Product__Type_OPair(U_20446,U_20446),hAPP(U_20447,hAPP(c_Nat_OSuc,sK555(U_20448,U_20447,U_20446)))),hAPP(U_20447,sK555(U_20448,U_20447,U_20446)))),c_Transitive__Closure_Ortrancl(U_20446,U_20448))) ),
    inference(clausify,[status(thm)],[f_4898_4]) ).

fof(f_4899_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_4899_2,plain,
    ! [U_20455,U_20454,U_20453,U_20452,U_20451,U_20450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20454)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20455)))
      | ? [U_20449] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(U_20454,U_20449)),hAPP(U_20455,U_20449)))
          & hBOOL(hAPP(hAPP(c_member(U_20450),U_20449),U_20452)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20450,tc_HOL_Obool)),U_20451),U_20452)) ),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

fof(f_4899_3,plain,
    ! [U_20455,U_20454,U_20453,U_20452,U_20451,U_20450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20454)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20455)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(U_20454,sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450))),hAPP(U_20455,sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450))))
        & hBOOL(hAPP(hAPP(c_member(U_20450),sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450)),U_20452)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20450,tc_HOL_Obool)),U_20451),U_20452)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK557]),skolemize(U_20449,sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450))],[f_4899_2]) ).

cnf(f_4899_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20450),sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450)),U_20452))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20454)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20455)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20450,tc_HOL_Obool)),U_20451),U_20452)) ),
    inference(clausify,[status(thm)],[f_4899_3]) ).

cnf(f_4899_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(U_20454,sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450))),hAPP(U_20455,sK557(U_20455,U_20454,U_20453,U_20452,U_20451,U_20450))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20454)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20450,tc_fun(U_20453,tc_HOL_Obool)),U_20452),U_20455)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20450,tc_HOL_Obool)),U_20451),U_20452)) ),
    inference(clausify,[status(thm)],[f_4899_3]) ).

fof(f_4900_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_4900_2,plain,
    ! [U_20461,U_20460,U_20459,U_20458,U_20457] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20457,tc_fun(U_20459,tc_HOL_Obool)),U_20458),U_20461)))
      | ? [U_20456] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(U_20461,U_20456)))
          & hBOOL(hAPP(hAPP(c_member(U_20457),U_20456),U_20458)) ) ),
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

fof(f_4900_3,plain,
    ! [U_20461,U_20460,U_20459,U_20458,U_20457] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20457,tc_fun(U_20459,tc_HOL_Obool)),U_20458),U_20461)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(U_20461,sK558(U_20461,U_20460,U_20459,U_20458,U_20457))))
        & hBOOL(hAPP(hAPP(c_member(U_20457),sK558(U_20461,U_20460,U_20459,U_20458,U_20457)),U_20458)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK558]),skolemize(U_20456,sK558(U_20461,U_20460,U_20459,U_20458,U_20457))],[f_4900_2]) ).

cnf(f_4900_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20457),sK558(U_20461,U_20460,U_20459,U_20458,U_20457)),U_20458))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20457,tc_fun(U_20459,tc_HOL_Obool)),U_20458),U_20461))) ),
    inference(clausify,[status(thm)],[f_4900_3]) ).

cnf(f_4900_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(U_20461,sK558(U_20461,U_20460,U_20459,U_20458,U_20457))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20459,tc_HOL_Obool)),U_20460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20457,tc_fun(U_20459,tc_HOL_Obool)),U_20458),U_20461))) ),
    inference(clausify,[status(thm)],[f_4900_3]) ).

fof(f_4901_1,plain,
    ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
      | ? [B_a,B_b] :
          ( ? [B_aa,B_ba] :
              ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
              & hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_4901_2,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466] :
      ( hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
      | ? [U_20465,U_20464] :
          ( ? [U_20463,U_20462] :
              ( ~ hBOOL(hAPP(hAPP(U_20473,U_20463),U_20462))
              & hBOOL(hAPP(hAPP(U_20473,U_20465),U_20464))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20465),U_20464)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20463),U_20462))),U_20472)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20465),U_20464))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) )
      | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

fof(f_4901_3,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466] :
      ( hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
      | ? [U_20464] :
          ( ? [U_20463,U_20462] :
              ( ~ hBOOL(hAPP(hAPP(U_20473,U_20463),U_20462))
              & hBOOL(hAPP(hAPP(U_20473,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),U_20464))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),U_20464)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20463),U_20462))),U_20472)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),U_20464))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) )
      | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK559]),skolemize(U_20465,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))],[f_4901_2]) ).

fof(f_4901_4,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466] :
      ( hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
      | ( ? [U_20463,U_20462] :
            ( ~ hBOOL(hAPP(hAPP(U_20473,U_20463),U_20462))
            & hBOOL(hAPP(hAPP(U_20473,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20463),U_20462))),U_20472)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) )
      | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK560]),skolemize(U_20464,sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))],[f_4901_3]) ).

fof(f_4901_5,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466] :
      ( hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
      | ( ? [U_20462] :
            ( ~ hBOOL(hAPP(hAPP(U_20473,sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),U_20462))
            & hBOOL(hAPP(hAPP(U_20473,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),U_20462))),U_20472)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) )
      | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK561]),skolemize(U_20463,sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))],[f_4901_4]) ).

fof(f_4901_6,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466] :
      ( hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
      | ( ~ hBOOL(hAPP(hAPP(U_20473,sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK562(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
        & hBOOL(hAPP(hAPP(U_20473,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK562(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),U_20472))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) )
      | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK562]),skolemize(U_20462,sK562(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))],[f_4901_5]) ).

cnf(f_4901_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472)))
    | hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
    | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(clausify,[status(thm)],[f_4901_6]) ).

cnf(f_4901_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466))),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK562(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))),U_20472))
    | hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
    | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(clausify,[status(thm)],[f_4901_6]) ).

cnf(f_4901_9,plain,
    ( hBOOL(hAPP(hAPP(U_20473,sK559(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK560(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
    | hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
    | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(clausify,[status(thm)],[f_4901_6]) ).

cnf(f_4901_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_20473,sK561(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)),sK562(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467,U_20466)))
    | hBOOL(hAPP(hAPP(U_20473,U_20470),U_20471))
    | ~ hBOOL(hAPP(hAPP(U_20473,U_20468),U_20469))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20466,U_20467),tc_prod(U_20466,U_20467)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20468),U_20469)),hAPP(hAPP(c_Product__Type_OPair(U_20466,U_20467),U_20470),U_20471))),c_Transitive__Closure_Ortrancl(tc_prod(U_20466,U_20467),U_20472))) ),
    inference(clausify,[status(thm)],[f_4901_6]) ).

fof(f_4902_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_4902_2,plain,
    ! [U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476] :
      ( ? [U_20475,U_20474] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20475),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20475),U_20474))),U_20482)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479) = hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482))) ),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

fof(f_4902_3,plain,
    ! [U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476] :
      ( ? [U_20474] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),U_20474))),U_20482)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479) = hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK563]),skolemize(U_20475,sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476))],[f_4902_2]) ).

fof(f_4902_4,plain,
    ! [U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),sK564(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476))),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),sK564(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)))),U_20482)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479) = hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK564]),skolemize(U_20474,sK564(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476))],[f_4902_3]) ).

cnf(f_4902_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),sK564(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)))),U_20482))
    | hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479) = hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482))) ),
    inference(clausify,[status(thm)],[f_4902_4]) ).

cnf(f_4902_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),sK563(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476)),sK564(U_20482,U_20481,U_20480,U_20479,U_20478,U_20477,U_20476))),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482)))
    | hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479) = hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20476,U_20477),tc_prod(U_20476,U_20477)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20478),U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20476,U_20477),U_20480),U_20481))),c_Transitive__Closure_Ortrancl(tc_prod(U_20476,U_20477),U_20482))) ),
    inference(clausify,[status(thm)],[f_4902_4]) ).

fof(f_4903_1,plain,
    ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
      | ? [B_a,B_b,B_aa,B_ba] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_4903_2,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487] :
      ( hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
      | ? [U_20486,U_20485,U_20484,U_20483] :
          ( ~ hBOOL(hAPP(hAPP(U_20494,U_20486),U_20485))
          & hBOOL(hAPP(hAPP(U_20494,U_20484),U_20483))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20486),U_20485)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483))),U_20493)) )
      | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

fof(f_4903_3,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487] :
      ( hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
      | ? [U_20485,U_20484,U_20483] :
          ( ~ hBOOL(hAPP(hAPP(U_20494,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),U_20485))
          & hBOOL(hAPP(hAPP(U_20494,U_20484),U_20483))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),U_20485)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483))),U_20493)) )
      | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK565]),skolemize(U_20486,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))],[f_4903_2]) ).

fof(f_4903_4,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487] :
      ( hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
      | ? [U_20484,U_20483] :
          ( ~ hBOOL(hAPP(hAPP(U_20494,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
          & hBOOL(hAPP(hAPP(U_20494,U_20484),U_20483))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20484),U_20483))),U_20493)) )
      | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK566]),skolemize(U_20485,sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))],[f_4903_3]) ).

fof(f_4903_5,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487] :
      ( hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
      | ? [U_20483] :
          ( ~ hBOOL(hAPP(hAPP(U_20494,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
          & hBOOL(hAPP(hAPP(U_20494,sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),U_20483))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),U_20483)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),U_20483))),U_20493)) )
      | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK567]),skolemize(U_20484,sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))],[f_4903_4]) ).

fof(f_4903_6,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487] :
      ( hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
      | ( ~ hBOOL(hAPP(hAPP(U_20494,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
        & hBOOL(hAPP(hAPP(U_20494,sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))),U_20493)) )
      | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK568]),skolemize(U_20483,sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))],[f_4903_5]) ).

cnf(f_4903_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))),U_20493))
    | hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
    | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(clausify,[status(thm)],[f_4903_6]) ).

cnf(f_4903_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487))),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493)))
    | hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
    | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(clausify,[status(thm)],[f_4903_6]) ).

cnf(f_4903_9,plain,
    ( hBOOL(hAPP(hAPP(U_20494,sK567(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK568(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
    | hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
    | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(clausify,[status(thm)],[f_4903_6]) ).

cnf(f_4903_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_20494,sK565(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)),sK566(U_20494,U_20493,U_20492,U_20491,U_20490,U_20489,U_20488,U_20487)))
    | hBOOL(hAPP(hAPP(U_20494,U_20489),U_20490))
    | ~ hBOOL(hAPP(hAPP(U_20494,U_20491),U_20492))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20487,U_20488),tc_prod(U_20487,U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20489),U_20490)),hAPP(hAPP(c_Product__Type_OPair(U_20487,U_20488),U_20491),U_20492))),c_Transitive__Closure_Ortrancl(tc_prod(U_20487,U_20488),U_20493))) ),
    inference(clausify,[status(thm)],[f_4903_6]) ).

fof(f_4904_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_4904_2,plain,
    ! [U_20500,U_20499,U_20498,U_20497] :
      ( c_Equiv__Relations_Ocongruent(U_20497,U_20500,U_20498,U_20499)
      | ? [U_20496,U_20495] :
          ( hAPP(U_20499,U_20496) != hAPP(U_20499,U_20495)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20497,U_20497)),hAPP(hAPP(c_Product__Type_OPair(U_20497,U_20497),U_20496),U_20495)),U_20498)) ) ),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

fof(f_4904_3,plain,
    ! [U_20500,U_20499,U_20498,U_20497] :
      ( c_Equiv__Relations_Ocongruent(U_20497,U_20500,U_20498,U_20499)
      | ? [U_20495] :
          ( hAPP(U_20499,sK569(U_20500,U_20499,U_20498,U_20497)) != hAPP(U_20499,U_20495)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20497,U_20497)),hAPP(hAPP(c_Product__Type_OPair(U_20497,U_20497),sK569(U_20500,U_20499,U_20498,U_20497)),U_20495)),U_20498)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK569]),skolemize(U_20496,sK569(U_20500,U_20499,U_20498,U_20497))],[f_4904_2]) ).

fof(f_4904_4,plain,
    ! [U_20500,U_20499,U_20498,U_20497] :
      ( c_Equiv__Relations_Ocongruent(U_20497,U_20500,U_20498,U_20499)
      | ( hAPP(U_20499,sK569(U_20500,U_20499,U_20498,U_20497)) != hAPP(U_20499,sK570(U_20500,U_20499,U_20498,U_20497))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20497,U_20497)),hAPP(hAPP(c_Product__Type_OPair(U_20497,U_20497),sK569(U_20500,U_20499,U_20498,U_20497)),sK570(U_20500,U_20499,U_20498,U_20497))),U_20498)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK570]),skolemize(U_20495,sK570(U_20500,U_20499,U_20498,U_20497))],[f_4904_3]) ).

cnf(f_4904_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20497,U_20497)),hAPP(hAPP(c_Product__Type_OPair(U_20497,U_20497),sK569(U_20500,U_20499,U_20498,U_20497)),sK570(U_20500,U_20499,U_20498,U_20497))),U_20498))
    | c_Equiv__Relations_Ocongruent(U_20497,U_20500,U_20498,U_20499) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

cnf(f_4904_6,plain,
    ( hAPP(U_20499,sK569(U_20500,U_20499,U_20498,U_20497)) != hAPP(U_20499,sK570(U_20500,U_20499,U_20498,U_20497))
    | c_Equiv__Relations_Ocongruent(U_20497,U_20500,U_20498,U_20499) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

fof(f_4905_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_4905_2,plain,
    ! [U_20510,U_20509,U_20508,U_20507,U_20506,U_20505] :
      ( c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509)
      | ? [U_20504,U_20503] :
          ( ? [U_20502,U_20501] :
              ( hAPP(hAPP(U_20509,U_20504),U_20502) != hAPP(hAPP(U_20509,U_20503),U_20501)
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),U_20502),U_20501)),U_20508)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),U_20504),U_20503)),U_20506)) ) ),
    inference(variable_rename,[status(thm)],[f_4905_1]) ).

fof(f_4905_3,plain,
    ! [U_20510,U_20509,U_20508,U_20507,U_20506,U_20505] :
      ( c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509)
      | ? [U_20503] :
          ( ? [U_20502,U_20501] :
              ( hAPP(hAPP(U_20509,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20502) != hAPP(hAPP(U_20509,U_20503),U_20501)
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),U_20502),U_20501)),U_20508)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20503)),U_20506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK571]),skolemize(U_20504,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))],[f_4905_2]) ).

fof(f_4905_4,plain,
    ! [U_20510,U_20509,U_20508,U_20507,U_20506,U_20505] :
      ( c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509)
      | ( ? [U_20502,U_20501] :
            ( hAPP(hAPP(U_20509,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20502) != hAPP(hAPP(U_20509,sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20501)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),U_20502),U_20501)),U_20508)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK572]),skolemize(U_20503,sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))],[f_4905_3]) ).

fof(f_4905_5,plain,
    ! [U_20510,U_20509,U_20508,U_20507,U_20506,U_20505] :
      ( c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509)
      | ( ? [U_20501] :
            ( hAPP(hAPP(U_20509,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)) != hAPP(hAPP(U_20509,sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20501)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),U_20501)),U_20508)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK573]),skolemize(U_20502,sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))],[f_4905_4]) ).

fof(f_4905_6,plain,
    ! [U_20510,U_20509,U_20508,U_20507,U_20506,U_20505] :
      ( c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509)
      | ( hAPP(hAPP(U_20509,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)) != hAPP(hAPP(U_20509,sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK574(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK574(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20508))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK574]),skolemize(U_20501,sK574(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))],[f_4905_5]) ).

cnf(f_4905_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20505,U_20505)),hAPP(hAPP(c_Product__Type_OPair(U_20505,U_20505),sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20506))
    | c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509) ),
    inference(clausify,[status(thm)],[f_4905_6]) ).

cnf(f_4905_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20507,U_20507)),hAPP(hAPP(c_Product__Type_OPair(U_20507,U_20507),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK574(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))),U_20508))
    | c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509) ),
    inference(clausify,[status(thm)],[f_4905_6]) ).

cnf(f_4905_9,plain,
    ( hAPP(hAPP(U_20509,sK571(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK573(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)) != hAPP(hAPP(U_20509,sK572(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505)),sK574(U_20510,U_20509,U_20508,U_20507,U_20506,U_20505))
    | c_Equiv__Relations_Ocongruent2(U_20505,U_20507,U_20510,U_20506,U_20508,U_20509) ),
    inference(clausify,[status(thm)],[f_4905_6]) ).

fof(f_4906_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_4906_2,plain,
    ! [U_20513,U_20512,U_20511] : c_Lazy__Sequence_Oflat(U_20511,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(U_20511),U_20512,U_20513)) = c_Lazy__Sequence_Oappend(U_20511,U_20512,c_Lazy__Sequence_Oflat(U_20511,U_20513)),
    inference(variable_rename,[status(thm)],[f_4906_1]) ).

cnf(f_4906_3,plain,
    c_Lazy__Sequence_Oflat(U_20511,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(U_20511),U_20512,U_20513)) = c_Lazy__Sequence_Oappend(U_20511,U_20512,c_Lazy__Sequence_Oflat(U_20511,U_20513)),
    inference(clausify,[status(thm)],[f_4906_2]) ).

fof(f_4907_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
        | ~ c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) )
      & ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
        | ~ c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__nat]) ).

fof(f_4907_2,plain,
    ! [U_20516,U_20515,U_20514] :
      ( ( c_List_Olist__all(tc_Nat_Onat,U_20514,c_List_Oupt(U_20515,U_20516))
        | ~ c_List_Oall__interval__nat(U_20514,U_20515,U_20516) )
      & ( c_List_Oall__interval__nat(U_20514,U_20515,U_20516)
        | ~ c_List_Olist__all(tc_Nat_Onat,U_20514,c_List_Oupt(U_20515,U_20516)) ) ),
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ( ! [U_20522,U_20520,U_20518] :
        ( c_List_Olist__all(tc_Nat_Onat,U_20518,c_List_Oupt(U_20520,U_20522))
        | ~ c_List_Oall__interval__nat(U_20518,U_20520,U_20522) )
    & ! [U_20521,U_20519,U_20517] :
        ( c_List_Oall__interval__nat(U_20517,U_20519,U_20521)
        | ~ c_List_Olist__all(tc_Nat_Onat,U_20517,c_List_Oupt(U_20519,U_20521)) ) ),
    inference(miniscope,[status(thm)],[f_4907_2]) ).

cnf(f_4907_4,plain,
    ( c_List_Oall__interval__nat(U_20517,U_20519,U_20521)
    | ~ c_List_Olist__all(tc_Nat_Onat,U_20517,c_List_Oupt(U_20519,U_20521)) ),
    inference(clausify,[status(thm)],[f_4907_3]) ).

cnf(f_4907_5,plain,
    ( c_List_Olist__all(tc_Nat_Onat,U_20518,c_List_Oupt(U_20520,U_20522))
    | ~ c_List_Oall__interval__nat(U_20518,U_20520,U_20522) ),
    inference(clausify,[status(thm)],[f_4907_3]) ).

fof(f_4908_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_4908_2,plain,
    ! [U_20523] : c_Lazy__Sequence_Oflat(U_20523,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(U_20523))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20523),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

cnf(f_4908_3,plain,
    c_Lazy__Sequence_Oflat(U_20523,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(U_20523))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20523),
    inference(clausify,[status(thm)],[f_4908_2]) ).

fof(f_4909_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_i_2,V_j_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__interval__nat__def]) ).

fof(f_4909_2,plain,
    ! [U_20528,U_20527,U_20526] :
      ( ( c_List_Oall__interval__nat(U_20526,U_20527,U_20528)
        | ? [U_20525] :
            ( ~ hBOOL(hAPP(U_20526,U_20525))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20525),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20527),U_20528))) ) )
      & ( ! [U_20524] :
            ( hBOOL(hAPP(U_20526,U_20524))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20524),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20527),U_20528))) )
        | ~ c_List_Oall__interval__nat(U_20526,U_20527,U_20528) ) ),
    inference(variable_rename,[status(thm)],[f_4909_1]) ).

fof(f_4909_3,plain,
    ( ! [U_20534,U_20532,U_20530] :
        ( c_List_Oall__interval__nat(U_20530,U_20532,U_20534)
        | ? [U_20525] :
            ( ~ hBOOL(hAPP(U_20530,U_20525))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20525),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20532),U_20534))) ) )
    & ! [U_20533,U_20531,U_20529] :
        ( ! [U_20524] :
            ( hBOOL(hAPP(U_20529,U_20524))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20524),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20531),U_20533))) )
        | ~ c_List_Oall__interval__nat(U_20529,U_20531,U_20533) ) ),
    inference(miniscope,[status(thm)],[f_4909_2]) ).

fof(f_4909_4,plain,
    ( ! [U_20534,U_20532,U_20530] :
        ( c_List_Oall__interval__nat(U_20530,U_20532,U_20534)
        | ( ~ hBOOL(hAPP(U_20530,sK575(U_20534,U_20532,U_20530)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK575(U_20534,U_20532,U_20530)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20532),U_20534))) ) )
    & ! [U_20533,U_20531,U_20529] :
        ( ! [U_20524] :
            ( hBOOL(hAPP(U_20529,U_20524))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20524),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20531),U_20533))) )
        | ~ c_List_Oall__interval__nat(U_20529,U_20531,U_20533) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK575]),skolemize(U_20525,sK575(U_20534,U_20532,U_20530))],[f_4909_3]) ).

cnf(f_4909_5,plain,
    ( hBOOL(hAPP(U_20529,U_20524))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20524),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20531),U_20533)))
    | ~ c_List_Oall__interval__nat(U_20529,U_20531,U_20533) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

cnf(f_4909_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK575(U_20534,U_20532,U_20530)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20532),U_20534)))
    | c_List_Oall__interval__nat(U_20530,U_20532,U_20534) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

cnf(f_4909_7,plain,
    ( ~ hBOOL(hAPP(U_20530,sK575(U_20534,U_20532,U_20530)))
    | c_List_Oall__interval__nat(U_20530,U_20532,U_20534) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

fof(f_4910_1,plain,
    ! [V_j_2,V_i_2,V_Pa_2] :
      ( ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_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_Pa_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_Pa_2),V_i_2,V_j_2)
        | ~ c_List_Olist__ex(tc_Nat_Onat,V_Pa_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_4910_2,plain,
    ! [U_20537,U_20536,U_20535] :
      ( ( c_List_Olist__ex(tc_Nat_Onat,U_20535,c_List_Oupt(U_20536,U_20537))
        | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20535),U_20536,U_20537) )
      & ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20535),U_20536,U_20537)
        | ~ c_List_Olist__ex(tc_Nat_Onat,U_20535,c_List_Oupt(U_20536,U_20537)) ) ),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

fof(f_4910_3,plain,
    ( ! [U_20543,U_20541,U_20539] :
        ( c_List_Olist__ex(tc_Nat_Onat,U_20539,c_List_Oupt(U_20541,U_20543))
        | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20539),U_20541,U_20543) )
    & ! [U_20542,U_20540,U_20538] :
        ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20538),U_20540,U_20542)
        | ~ c_List_Olist__ex(tc_Nat_Onat,U_20538,c_List_Oupt(U_20540,U_20542)) ) ),
    inference(miniscope,[status(thm)],[f_4910_2]) ).

cnf(f_4910_4,plain,
    ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20538),U_20540,U_20542)
    | ~ c_List_Olist__ex(tc_Nat_Onat,U_20538,c_List_Oupt(U_20540,U_20542)) ),
    inference(clausify,[status(thm)],[f_4910_3]) ).

cnf(f_4910_5,plain,
    ( c_List_Olist__ex(tc_Nat_Onat,U_20539,c_List_Oupt(U_20541,U_20543))
    | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20539),U_20541,U_20543) ),
    inference(clausify,[status(thm)],[f_4910_3]) ).

fof(f_4911_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_4911_2,plain,
    ! [U_20547,U_20546,U_20545,U_20544] : hAPP(c_Lazy__Sequence_Obind(U_20544,U_20545,U_20546),U_20547) = c_Lazy__Sequence_Oflat(U_20545,c_Lazy__Sequence_Omap(U_20544,tc_Lazy__Sequence_Olazy__sequence(U_20545),U_20547,U_20546)),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

cnf(f_4911_3,plain,
    hAPP(c_Lazy__Sequence_Obind(U_20544,U_20545,U_20546),U_20547) = c_Lazy__Sequence_Oflat(U_20545,c_Lazy__Sequence_Omap(U_20544,tc_Lazy__Sequence_Olazy__sequence(U_20545),U_20547,U_20546)),
    inference(clausify,[status(thm)],[f_4911_2]) ).

fof(f_4912_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_4912_2,plain,
    ! [U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550,U_20549] :
      ( hAPP(hAPP(U_20553,U_20555),U_20554) = hAPP(hAPP(U_20553,U_20556),U_20554)
      | ? [U_20548] :
          ( hAPP(U_20555,U_20548) != hAPP(U_20556,U_20548)
          & hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),U_20554)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20550),U_20554))
      | ~ c_Finite__Set_Ofolding__image(U_20549,U_20550,U_20551,U_20552,U_20553) ),
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ! [U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550] :
      ( ! [U_20549] : ~ c_Finite__Set_Ofolding__image(U_20549,U_20550,U_20551,U_20552,U_20553)
      | hAPP(hAPP(U_20553,U_20555),U_20554) = hAPP(hAPP(U_20553,U_20556),U_20554)
      | ? [U_20548] :
          ( hAPP(U_20555,U_20548) != hAPP(U_20556,U_20548)
          & hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),U_20554)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20550),U_20554)) ),
    inference(miniscope,[status(thm)],[f_4912_2]) ).

fof(f_4912_4,plain,
    ! [U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550] :
      ( ! [U_20549] : ~ c_Finite__Set_Ofolding__image(U_20549,U_20550,U_20551,U_20552,U_20553)
      | hAPP(hAPP(U_20553,U_20555),U_20554) = hAPP(hAPP(U_20553,U_20556),U_20554)
      | ( hAPP(U_20555,sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550)) != hAPP(U_20556,sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550))
        & hBOOL(hAPP(hAPP(c_member(U_20550),sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550)),U_20554)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20550),U_20554)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK576]),skolemize(U_20548,sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550))],[f_4912_3]) ).

cnf(f_4912_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20550),sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550)),U_20554))
    | hAPP(hAPP(U_20553,U_20555),U_20554) = hAPP(hAPP(U_20553,U_20556),U_20554)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20550),U_20554))
    | ~ c_Finite__Set_Ofolding__image(U_20549,U_20550,U_20551,U_20552,U_20553) ),
    inference(clausify,[status(thm)],[f_4912_4]) ).

cnf(f_4912_6,plain,
    ( hAPP(U_20555,sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550)) != hAPP(U_20556,sK576(U_20556,U_20555,U_20554,U_20553,U_20552,U_20551,U_20550))
    | hAPP(hAPP(U_20553,U_20555),U_20554) = hAPP(hAPP(U_20553,U_20556),U_20554)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20550),U_20554))
    | ~ c_Finite__Set_Ofolding__image(U_20549,U_20550,U_20551,U_20552,U_20553) ),
    inference(clausify,[status(thm)],[f_4912_4]) ).

fof(f_4913_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_4913_2,plain,
    ! [U_20561,U_20560,U_20559,U_20558,U_20557] : c_Lazy__Sequence_Omap(U_20557,U_20558,U_20559,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20557,U_20560,U_20561)) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20558,hAPP(U_20559,U_20560),c_Lazy__Sequence_Omap(U_20557,U_20558,U_20559,U_20561)),
    inference(variable_rename,[status(thm)],[f_4913_1]) ).

cnf(f_4913_3,plain,
    c_Lazy__Sequence_Omap(U_20557,U_20558,U_20559,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20557,U_20560,U_20561)) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20558,hAPP(U_20559,U_20560),c_Lazy__Sequence_Omap(U_20557,U_20558,U_20559,U_20561)),
    inference(clausify,[status(thm)],[f_4913_2]) ).

fof(f_4914_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_4914_2,plain,
    ! [U_20564,U_20563,U_20562] : c_Lazy__Sequence_Omap(U_20562,U_20563,U_20564,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20562)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20563),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

cnf(f_4914_3,plain,
    c_Lazy__Sequence_Omap(U_20562,U_20563,U_20564,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20562)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20563),
    inference(clausify,[status(thm)],[f_4914_2]) ).

fof(f_4915_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_4915_2,plain,
    ! [U_20569,U_20568,U_20567,U_20566,U_20565] : c_New__DSequence_Opos__map(U_20565,U_20566,U_20567,U_20568,U_20569) = c_Lazy__Sequence_Omap(U_20565,U_20566,U_20567,hAPP(U_20568,U_20569)),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

cnf(f_4915_3,plain,
    c_New__DSequence_Opos__map(U_20565,U_20566,U_20567,U_20568,U_20569) = c_Lazy__Sequence_Omap(U_20565,U_20566,U_20567,hAPP(U_20568,U_20569)),
    inference(clausify,[status(thm)],[f_4915_2]) ).

fof(f_4916_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_4916_2,plain,
    ! [U_20572,U_20571,U_20570] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20571),U_20572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20570))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20570),U_20571)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20570),U_20572))) ),
    inference(variable_rename,[status(thm)],[f_4916_1]) ).

cnf(f_4916_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20571),U_20572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20570))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20570),U_20571)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20570),U_20572))) ),
    inference(clausify,[status(thm)],[f_4916_2]) ).

fof(f_4917_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_4917_2,plain,
    ! [U_20573] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20573),U_20573)),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

cnf(f_4917_3,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20573),U_20573)),
    inference(clausify,[status(thm)],[f_4917_2]) ).

fof(f_4918_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_4918_2,plain,
    ! [U_20575,U_20574] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20574),U_20575),c_Groups_Ozero__class_Ozero(U_20574)))
      | ~ class_Rings_Ocomm__semiring__1(U_20574) ),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

cnf(f_4918_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20574),U_20575),c_Groups_Ozero__class_Ozero(U_20574)))
    | ~ class_Rings_Ocomm__semiring__1(U_20574) ),
    inference(clausify,[status(thm)],[f_4918_2]) ).

fof(f_4919_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_4919_2,plain,
    ! [U_20576] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20576)),
    inference(variable_rename,[status(thm)],[f_4919_1]) ).

cnf(f_4919_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_20576)),
    inference(clausify,[status(thm)],[f_4919_2]) ).

fof(f_4920_1,plain,
    ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_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_i_2),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_dvd__setprod]) ).

fof(f_4920_2,plain,
    ! [U_20581,U_20580,U_20579,U_20578,U_20577] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20577),hAPP(U_20581,U_20580)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_20578,U_20577),U_20581),U_20579)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20578),U_20580),U_20579))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20578),U_20579))
      | ~ class_Rings_Ocomm__semiring__1(U_20577) ),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

cnf(f_4920_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20577),hAPP(U_20581,U_20580)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_20578,U_20577),U_20581),U_20579)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20578),U_20580),U_20579))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20578),U_20579))
    | ~ class_Rings_Ocomm__semiring__1(U_20577) ),
    inference(clausify,[status(thm)],[f_4920_2]) ).

fof(f_4921_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_4921_2,plain,
    ! [U_20584,U_20583,U_20582] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20582),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584)))
          | c_Divides_Odiv__class_Omod(U_20582,hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)) != c_Groups_Ozero__class_Ozero(U_20582) )
        & ( c_Divides_Odiv__class_Omod(U_20582,hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)) = c_Groups_Ozero__class_Ozero(U_20582)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20582),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584))) ) )
      | ~ class_Int_Onumber(U_20582)
      | ~ class_Divides_Osemiring__div(U_20582) ),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

cnf(f_4921_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20582,hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)) = c_Groups_Ozero__class_Ozero(U_20582)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20582),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584)))
    | ~ class_Int_Onumber(U_20582)
    | ~ class_Divides_Osemiring__div(U_20582) ),
    inference(clausify,[status(thm)],[f_4921_2]) ).

cnf(f_4921_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20582),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584)))
    | c_Divides_Odiv__class_Omod(U_20582,hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20584),hAPP(c_Int_Onumber__class_Onumber__of(U_20582),U_20583)) != c_Groups_Ozero__class_Ozero(U_20582)
    | ~ class_Int_Onumber(U_20582)
    | ~ class_Divides_Osemiring__div(U_20582) ),
    inference(clausify,[status(thm)],[f_4921_2]) ).

fof(f_4922_1,plain,
    ! [V_ca_2,V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | V_b_2 != V_ca_2
        | V_a_2 != V_b_2 )
      & ( ( V_b_2 = V_ca_2
          & V_a_2 = V_b_2 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff]) ).

fof(f_4922_2,plain,
    ! [U_20587,U_20586,U_20585] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20585,U_20586) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20587),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_20586 != U_20587
        | U_20585 != U_20586 )
      & ( ( U_20586 = U_20587
          & U_20585 = U_20586 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20585,U_20586) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20587),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ( ! [U_20593,U_20591,U_20589] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20589,U_20591) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20593),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_20591 != U_20593
        | U_20589 != U_20591 )
    & ! [U_20592,U_20590,U_20588] :
        ( ( U_20590 = U_20592
          & U_20588 = U_20590 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20588,U_20590) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20592),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4922_2]) ).

cnf(f_4922_4,plain,
    ( U_20588 = U_20590
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20588,U_20590) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20592),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_5,plain,
    ( U_20590 = U_20592
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20588,U_20590) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20592),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20589,U_20591) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20593),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_20591 != U_20593
    | U_20589 != U_20591 ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

fof(f_4923_1,plain,
    ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).

fof(f_4923_2,plain,
    ! [U_20594] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20594,U_20594) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20594),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

cnf(f_4923_3,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20594,U_20594) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20594),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4923_2]) ).

fof(f_4924_1,plain,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H]) ).

fof(f_4924_2,plain,
    ! [U_20596,U_20595] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20595,U_20596) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20595),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_20595 != U_20596 ),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

cnf(f_4924_3,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20595,U_20596) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_20595),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_20595 != U_20596 ),
    inference(clausify,[status(thm)],[f_4924_2]) ).

fof(f_4925_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_Orderings_Obot__class_Obot(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)
        | 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_a_2),V_b_2))
        | c_Orderings_Obot__class_Obot(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) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).

fof(f_4925_2,plain,
    ! [U_20598,U_20597] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20597,U_20598)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20597),U_20598)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20597),U_20598))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20597,U_20598) ) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ( ! [U_20602,U_20600] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20600,U_20602)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20600),U_20602)) )
    & ! [U_20601,U_20599] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20599),U_20601))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20599,U_20601) ) ),
    inference(miniscope,[status(thm)],[f_4925_2]) ).

cnf(f_4925_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20599),U_20601))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20599,U_20601) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

cnf(f_4925_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20600,U_20602)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20600),U_20602)) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

fof(f_4926_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | 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_a_2),V_b_2))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).

fof(f_4926_2,plain,
    ! [U_20604,U_20603] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603,U_20604) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | 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_20603),U_20604))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603,U_20604) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4926_1]) ).

fof(f_4926_3,plain,
    ( ! [U_20608,U_20606] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20606,U_20608) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20606),U_20608)) )
    & ! [U_20607,U_20605] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605),U_20607))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605,U_20607) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4926_2]) ).

cnf(f_4926_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605),U_20607))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605,U_20607) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

cnf(f_4926_5,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20606,U_20608) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20606),U_20608)) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

fof(f_4927_1,plain,
    ! [V_a_2,V_b_2] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | 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_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).

fof(f_4927_2,plain,
    ! [U_20610,U_20609] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610,U_20609) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610),U_20609))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20609),U_20610)) ),
    inference(variable_rename,[status(thm)],[f_4927_1]) ).

cnf(f_4927_3,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610,U_20609) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610),U_20609))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20609),U_20610)) ),
    inference(clausify,[status(thm)],[f_4927_2]) ).

fof(f_4928_1,plain,
    ! [V_k_2,V_l_2] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty]) ).

fof(f_4928_2,plain,
    ! [U_20612,U_20611] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20612,U_20611) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611),U_20612)) ),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

cnf(f_4928_3,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20612,U_20611) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611),U_20612)) ),
    inference(clausify,[status(thm)],[f_4928_2]) ).

fof(f_4929_1,plain,
    ! [V_a_2,V_b_2] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty]) ).

fof(f_4929_2,plain,
    ! [U_20614,U_20613] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20614,U_20613) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20613),U_20614)) ),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

cnf(f_4929_3,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20614,U_20613) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20613),U_20614)) ),
    inference(clausify,[status(thm)],[f_4929_2]) ).

fof(f_4930_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).

fof(f_4930_2,plain,
    ! [U_20616,U_20615] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20615,U_20616) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20616),U_20615))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20616)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20616),U_20615))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20616))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20615,U_20616) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

fof(f_4930_3,plain,
    ( ! [U_20620,U_20618] :
        ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20618,U_20620) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20620),U_20618))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20620)) ) )
    & ! [U_20619,U_20617] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20619),U_20617))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20617),U_20619))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20617,U_20619) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4930_2]) ).

cnf(f_4930_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20619),U_20617))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20617),U_20619))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20617,U_20619) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4930_3]) ).

cnf(f_4930_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20620))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20618,U_20620) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4930_3]) ).

cnf(f_4930_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20620),U_20618))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20618,U_20620) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4930_3]) ).

fof(f_4931_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).

fof(f_4931_2,plain,
    ! [U_20622,U_20621] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20621,U_20622) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ 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))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20621,U_20622) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

fof(f_4931_3,plain,
    ( ! [U_20626,U_20624] :
        ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20624,U_20626) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ( ~ 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))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20623,U_20625) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4931_2]) ).

cnf(f_4931_4,plain,
    ( 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))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20623,U_20625) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

cnf(f_4931_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20624),U_20626))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20624,U_20626) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

cnf(f_4931_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20626),U_20624))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20624,U_20626) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

fof(f_4932_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).

fof(f_4932_2,plain,
    ! [U_20628,U_20627] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_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_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20627),U_20628))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20627,U_20628) ) ),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

fof(f_4932_3,plain,
    ( ! [U_20632,U_20630] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20630,U_20632)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20632),U_20630))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20630),U_20632)) ) )
    & ! [U_20631,U_20629] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20631),U_20629))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20629),U_20631))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20629,U_20631) ) ),
    inference(miniscope,[status(thm)],[f_4932_2]) ).

cnf(f_4932_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20631),U_20629))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20629),U_20631))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20629,U_20631) ),
    inference(clausify,[status(thm)],[f_4932_3]) ).

cnf(f_4932_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20630),U_20632))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20630,U_20632) ),
    inference(clausify,[status(thm)],[f_4932_3]) ).

cnf(f_4932_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20632),U_20630))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20630,U_20632) ),
    inference(clausify,[status(thm)],[f_4932_3]) ).

fof(f_4933_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_a_2,V_b_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).

fof(f_4933_2,plain,
    ! [U_20634,U_20633] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20633,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_20633),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_20633),U_20634))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20633,U_20634) ) ),
    inference(variable_rename,[status(thm)],[f_4933_1]) ).

fof(f_4933_3,plain,
    ( ! [U_20638,U_20636] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20636,U_20638)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638),U_20636))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20636),U_20638)) ) )
    & ! [U_20637,U_20635] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637),U_20635))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20635),U_20637))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20635,U_20637) ) ),
    inference(miniscope,[status(thm)],[f_4933_2]) ).

cnf(f_4933_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637),U_20635))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20635),U_20637))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20635,U_20637) ),
    inference(clausify,[status(thm)],[f_4933_3]) ).

cnf(f_4933_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20636),U_20638))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20636,U_20638) ),
    inference(clausify,[status(thm)],[f_4933_3]) ).

cnf(f_4933_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638),U_20636))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(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_20636,U_20638) ),
    inference(clausify,[status(thm)],[f_4933_3]) ).

fof(f_4934_1,plain,
    ! [V_k_2,V_l_2] :
      ( c_SetInterval_Oord_OgreaterThanLessThan(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,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty]) ).

fof(f_4934_2,plain,
    ! [U_20640,U_20639] :
      ( c_SetInterval_Oord_OgreaterThanLessThan(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_20640,U_20639) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20639),U_20640)) ),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

cnf(f_4934_3,plain,
    ( c_SetInterval_Oord_OgreaterThanLessThan(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_20640,U_20639) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20639),U_20640)) ),
    inference(clausify,[status(thm)],[f_4934_2]) ).

fof(f_4935_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_4935_2,plain,
    ! [U_20641] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20641),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_20641 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_20641 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20641),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

fof(f_4935_3,plain,
    ( ! [U_20643] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20643),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_20643 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_20642] :
        ( U_20642 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20642),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_4935_2]) ).

cnf(f_4935_4,plain,
    ( U_20642 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20642),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_4935_3]) ).

cnf(f_4935_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20643),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_20643 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4935_3]) ).

fof(f_4936_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_4936_2,plain,
    ! [U_20645,U_20644] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20645),U_20644))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20644),U_20645))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20644)) ),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

cnf(f_4936_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20645),U_20644))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20644),U_20645))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20644)) ),
    inference(clausify,[status(thm)],[f_4936_2]) ).

fof(f_4937_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_4937_2,plain,
    ! [U_20649,U_20648,U_20647,U_20646] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_20646),U_20648),U_20649)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),U_20649))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),U_20648))
      | ~ class_Rings_Ocomm__ring__1(U_20646) ),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

cnf(f_4937_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_20646),U_20648),U_20649)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),U_20649))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20646),U_20647),U_20648))
    | ~ class_Rings_Ocomm__ring__1(U_20646) ),
    inference(clausify,[status(thm)],[f_4937_2]) ).

fof(f_4938_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_4938_2,plain,
    ! [U_20652,U_20651,U_20650] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20651),U_20652)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),U_20652))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),U_20651)) ),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

cnf(f_4938_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20651),U_20652)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),U_20652))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20650),U_20651)) ),
    inference(clausify,[status(thm)],[f_4938_2]) ).

fof(f_4939_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_4939_2,plain,
    ! [U_20655,U_20654,U_20653] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20654)),U_20655))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20654)),U_20655)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_20653) ),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

cnf(f_4939_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20654)),U_20655))
    | ~ class_Rings_Ocomm__ring__1(U_20653) ),
    inference(clausify,[status(thm)],[f_4939_2]) ).

cnf(f_4939_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20654)),U_20655))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655))
    | ~ class_Rings_Ocomm__ring__1(U_20653) ),
    inference(clausify,[status(thm)],[f_4939_2]) ).

fof(f_4940_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_4940_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_4940_1]) ).

cnf(f_4940_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_4940_2]) ).

cnf(f_4940_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_4940_2]) ).

fof(f_4941_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_4941_2,plain,
    ! [U_20661,U_20660,U_20659] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20659),U_20661),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20659),U_20661),U_20660))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661))
      | ~ class_Divides_Oring__div(U_20659) ),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

cnf(f_4941_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20659),U_20661),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20659),U_20661),U_20660))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661))
    | ~ class_Divides_Oring__div(U_20659) ),
    inference(clausify,[status(thm)],[f_4941_2]) ).

fof(f_4942_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_4942_2,plain,
    ! [U_20664,U_20663,U_20662] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20662),hAPP(c_Groups_Ouminus__class_Ouminus(U_20662),U_20664)),U_20663) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20662),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20662),U_20664),U_20663))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20662),U_20663),U_20664))
      | ~ class_Divides_Oring__div(U_20662) ),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

cnf(f_4942_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20662),hAPP(c_Groups_Ouminus__class_Ouminus(U_20662),U_20664)),U_20663) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20662),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20662),U_20664),U_20663))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20662),U_20663),U_20664))
    | ~ class_Divides_Oring__div(U_20662) ),
    inference(clausify,[status(thm)],[f_4942_2]) ).

fof(f_4943_1,plain,
    ! [V_n_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),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_dvd__reduce]) ).

fof(f_4943_2,plain,
    ! [U_20666,U_20665] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20666),U_20665)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20665),U_20666)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20665),U_20666))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20666),U_20665))) ) ),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

fof(f_4943_3,plain,
    ( ! [U_20670,U_20668] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20670),U_20668)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20668),U_20670)) )
    & ! [U_20669,U_20667] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20667),U_20669))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20669),U_20667))) ) ),
    inference(miniscope,[status(thm)],[f_4943_2]) ).

cnf(f_4943_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20667),U_20669))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20669),U_20667))) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

cnf(f_4943_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20670),U_20668)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20668),U_20670)) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

fof(f_4944_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ 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_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).

fof(f_4944_2,plain,
    ! [U_20674,U_20673,U_20672,U_20671] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_20671),U_20673),U_20674)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),U_20674))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),U_20673))
      | ~ class_Rings_Ocomm__semiring__1(U_20671) ),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

cnf(f_4944_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_20671),U_20673),U_20674)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),U_20674))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20671),U_20672),U_20673))
    | ~ class_Rings_Ocomm__semiring__1(U_20671) ),
    inference(clausify,[status(thm)],[f_4944_2]) ).

fof(f_4945_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_4945_2,plain,
    ! [U_20678,U_20677,U_20676,U_20675] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20675),hAPP(hAPP(c_Power_Opower__class_Opower(U_20675),U_20676),U_20678)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20675),U_20677),U_20678)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20675),U_20676),U_20677))
      | ~ class_Rings_Ocomm__semiring__1(U_20675) ),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

cnf(f_4945_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20675),hAPP(hAPP(c_Power_Opower__class_Opower(U_20675),U_20676),U_20678)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20675),U_20677),U_20678)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20675),U_20676),U_20677))
    | ~ class_Rings_Ocomm__semiring__1(U_20675) ),
    inference(clausify,[status(thm)],[f_4945_2]) ).

fof(f_4946_1,plain,
    ! [V_ca_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_ca_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_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_ca_2),V_a_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_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_4946_2,plain,
    ! [U_20682,U_20681,U_20680,U_20679] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20681),U_20680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20682),U_20680)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20681),U_20682)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20681),U_20682))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20681),U_20680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20682),U_20680))) ) )
      | ~ 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(variable_rename,[status(thm)],[f_4946_1]) ).

cnf(f_4946_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20681),U_20682))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20681),U_20680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20682),U_20680)))
    | ~ 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_4946_2]) ).

cnf(f_4946_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20681),U_20680)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20679),U_20682),U_20680)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20681),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),U_20681))
    | ~ class_Divides_Osemiring__div(U_20679) ),
    inference(clausify,[status(thm)],[f_4946_2]) ).

fof(f_4947_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_4947_2,plain,
    ! [U_20686,U_20685,U_20684,U_20683] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20686)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20686))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685))) ) )
      | ~ 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_4947_1]) ).

cnf(f_4947_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20686))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685)))
    | ~ 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_4947_2]) ).

cnf(f_4947_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20686))
    | ~ 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_4947_2]) ).

fof(f_4948_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_4948_2,plain,
    ! [U_20690,U_20689,U_20688,U_20687] :
      ( c_Divides_Odiv__class_Omod(U_20687,c_Divides_Odiv__class_Omod(U_20687,U_20690,U_20689),U_20688) = c_Divides_Odiv__class_Omod(U_20687,U_20690,U_20688)
      | ~ 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_4948_1]) ).

cnf(f_4948_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20687,c_Divides_Odiv__class_Omod(U_20687,U_20690,U_20689),U_20688) = c_Divides_Odiv__class_Omod(U_20687,U_20690,U_20688)
    | ~ 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_4948_2]) ).

fof(f_4949_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_4949_2,plain,
    ! [U_20694,U_20693,U_20692,U_20691] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),c_Divides_Odiv__class_Omod(U_20691,U_20693,U_20694)))
      | ~ 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),U_20693))
      | ~ class_Divides_Osemiring__div(U_20691) ),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

cnf(f_4949_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),c_Divides_Odiv__class_Omod(U_20691,U_20693,U_20694)))
    | ~ 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),U_20693))
    | ~ class_Divides_Osemiring__div(U_20691) ),
    inference(clausify,[status(thm)],[f_4949_2]) ).

fof(f_4950_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_4950_2,plain,
    ! [U_20698,U_20697,U_20696,U_20695] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),U_20697))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),U_20698))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),c_Divides_Odiv__class_Omod(U_20695,U_20697,U_20698)))
      | ~ class_Divides_Osemiring__div(U_20695) ),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

cnf(f_4950_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),U_20697))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),U_20698))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),U_20696),c_Divides_Odiv__class_Omod(U_20695,U_20697,U_20698)))
    | ~ class_Divides_Osemiring__div(U_20695) ),
    inference(clausify,[status(thm)],[f_4950_2]) ).

fof(f_4951_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).

fof(f_4951_2,plain,
    ! [U_20699] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20699),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_20699 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( U_20699 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20699),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

fof(f_4951_3,plain,
    ( ! [U_20701] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20701),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_20701 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_20700] :
        ( U_20700 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20700),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_4951_2]) ).

cnf(f_4951_4,plain,
    ( U_20700 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20700),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4951_3]) ).

cnf(f_4951_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20701),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_20701 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4951_3]) ).

fof(f_4952_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_4952_2,plain,
    ! [U_20703,U_20702] :
      ( U_20703 = c_Groups_Ozero__class_Ozero(U_20702)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20702),c_Groups_Ozero__class_Ozero(U_20702)),U_20703))
      | ~ class_Rings_Ocomm__semiring__1(U_20702) ),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

cnf(f_4952_3,plain,
    ( U_20703 = c_Groups_Ozero__class_Ozero(U_20702)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20702),c_Groups_Ozero__class_Ozero(U_20702)),U_20703))
    | ~ class_Rings_Ocomm__semiring__1(U_20702) ),
    inference(clausify,[status(thm)],[f_4952_2]) ).

fof(f_4953_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).

fof(f_4953_2,plain,
    ! [U_20705,U_20704] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20704),c_Groups_Oone__class_Oone(U_20704)),U_20705))
      | ~ class_Rings_Ocomm__semiring__1(U_20704) ),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

cnf(f_4953_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20704),c_Groups_Oone__class_Oone(U_20704)),U_20705))
    | ~ class_Rings_Ocomm__semiring__1(U_20704) ),
    inference(clausify,[status(thm)],[f_4953_2]) ).

fof(f_4954_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | V_x_2 != V_y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).

fof(f_4954_2,plain,
    ! [U_20707,U_20706] :
      ( ( U_20706 = U_20707
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20707),U_20706))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20706),U_20707)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20707),U_20706))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20706),U_20707)) )
        | U_20706 != U_20707 ) ),
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

fof(f_4954_3,plain,
    ( ! [U_20711,U_20709] :
        ( U_20709 = U_20711
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20709))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20709),U_20711)) )
    & ! [U_20710,U_20708] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20710),U_20708))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20708),U_20710)) )
        | U_20708 != U_20710 ) ),
    inference(miniscope,[status(thm)],[f_4954_2]) ).

cnf(f_4954_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20708),U_20710))
    | U_20708 != U_20710 ),
    inference(clausify,[status(thm)],[f_4954_3]) ).

cnf(f_4954_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20710),U_20708))
    | U_20708 != U_20710 ),
    inference(clausify,[status(thm)],[f_4954_3]) ).

cnf(f_4954_6,plain,
    ( U_20709 = U_20711
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20709))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20709),U_20711)) ),
    inference(clausify,[status(thm)],[f_4954_3]) ).

fof(f_4955_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
        | ( V_x_2 != V_y_2
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) )
      & ( V_x_2 = V_y_2
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).

fof(f_4955_2,plain,
    ! [U_20713,U_20712] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20713))
        | ( U_20712 != U_20713
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20712))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20713)) ) ) )
      & ( U_20712 = U_20713
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20712))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20713)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20713)) ) ),
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

fof(f_4955_3,plain,
    ( ! [U_20717,U_20715] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20717))
        | ( U_20715 != U_20717
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20715))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20717)) ) ) )
    & ! [U_20716,U_20714] :
        ( U_20714 = U_20716
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20714))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20716)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20716)) ) ),
    inference(miniscope,[status(thm)],[f_4955_2]) ).

cnf(f_4955_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20716))
    | U_20714 = U_20716
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20716)) ),
    inference(clausify,[status(thm)],[f_4955_3]) ).

cnf(f_4955_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20714))
    | U_20714 = U_20716
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20716)) ),
    inference(clausify,[status(thm)],[f_4955_3]) ).

cnf(f_4955_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20715))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20717))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20717)) ),
    inference(clausify,[status(thm)],[f_4955_3]) ).

cnf(f_4955_7,plain,
    ( U_20715 != U_20717
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20717)) ),
    inference(clausify,[status(thm)],[f_4955_3]) ).

fof(f_4956_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( ( V_x_2 != V_y_2
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).

fof(f_4956_2,plain,
    ! [U_20719,U_20718] :
      ( ( ( ~ 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)) )
        | U_20718 = U_20719
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20719)) )
      & ( ( U_20718 != U_20719
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20719)) )
        | 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_4956_1]) ).

fof(f_4956_3,plain,
    ( ! [U_20723,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_20721 = U_20723
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723)) )
    & ! [U_20722,U_20720] :
        ( ( U_20720 != U_20722
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20722)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20720))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20722)) ) ),
    inference(miniscope,[status(thm)],[f_4956_2]) ).

cnf(f_4956_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20722))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20720))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20722)) ),
    inference(clausify,[status(thm)],[f_4956_3]) ).

cnf(f_4956_5,plain,
    ( U_20720 != U_20722
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20720))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20722)) ),
    inference(clausify,[status(thm)],[f_4956_3]) ).

cnf(f_4956_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723))
    | U_20721 = U_20723
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723)) ),
    inference(clausify,[status(thm)],[f_4956_3]) ).

cnf(f_4956_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20723),U_20721))
    | U_20721 = U_20723
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723)) ),
    inference(clausify,[status(thm)],[f_4956_3]) ).

fof(f_4957_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)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
      | V_a = V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).

fof(f_4957_2,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)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20724),U_20725))
      | U_20724 = U_20725 ),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

cnf(f_4957_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20724),U_20725))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20724),U_20725))
    | U_20724 = U_20725 ),
    inference(clausify,[status(thm)],[f_4957_2]) ).

cnf(f_4957_4,plain,
    ( ~ 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))
    | U_20724 = U_20725 ),
    inference(clausify,[status(thm)],[f_4957_2]) ).

fof(f_4958_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | V_x != V_y ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).

fof(f_4958_2,plain,
    ! [U_20727,U_20726] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20726),U_20727))
      | U_20726 != U_20727 ),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

cnf(f_4958_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20726),U_20727))
    | U_20726 != U_20727 ),
    inference(clausify,[status(thm)],[f_4958_2]) ).

fof(f_4959_1,plain,
    ! [V_x_2,V_y_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).

fof(f_4959_2,plain,
    ! [U_20729,U_20728] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
          | U_20729 != U_20728 )
        & ( 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_4959_1]) ).

cnf(f_4959_3,plain,
    ( 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_4959_2]) ).

cnf(f_4959_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
    | U_20729 != U_20728
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20728),U_20729)) ),
    inference(clausify,[status(thm)],[f_4959_2]) ).

fof(f_4960_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_4960_2,plain,
    ! [U_20731,U_20730] :
      ( 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)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731)) ),
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

cnf(f_4960_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731))
    | U_20730 = U_20731
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731)) ),
    inference(clausify,[status(thm)],[f_4960_2]) ).

cnf(f_4960_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20731),U_20730))
    | U_20730 = U_20731
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731)) ),
    inference(clausify,[status(thm)],[f_4960_2]) ).

fof(f_4961_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_4961_2,plain,
    ! [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)) )
      | U_20732 = U_20733
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733)) ),
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

cnf(f_4961_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733))
    | U_20732 = U_20733
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733)) ),
    inference(clausify,[status(thm)],[f_4961_2]) ).

cnf(f_4961_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20733),U_20732))
    | U_20732 = U_20733
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733)) ),
    inference(clausify,[status(thm)],[f_4961_2]) ).

fof(f_4962_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_4962_2,plain,
    ! [U_20736,U_20735,U_20734] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20734),U_20736))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20735),U_20736))
      | U_20734 != U_20735 ),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

cnf(f_4962_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20734),U_20736))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20735),U_20736))
    | U_20734 != U_20735 ),
    inference(clausify,[status(thm)],[f_4962_2]) ).

fof(f_4963_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_4963_2,plain,
    ! [U_20739,U_20738,U_20737] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20739))
      | U_20738 != U_20739
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20738)) ),
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

cnf(f_4963_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20739))
    | U_20738 != U_20739
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20738)) ),
    inference(clausify,[status(thm)],[f_4963_2]) ).

fof(f_4964_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_4964_2,plain,
    ! [U_20741,U_20740] :
      ( U_20740 = 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)) ),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

cnf(f_4964_3,plain,
    ( U_20740 = 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)) ),
    inference(clausify,[status(thm)],[f_4964_2]) ).

fof(f_4965_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_4965_2,plain,
    ! [U_20743,U_20742] :
      ( U_20742 = U_20743
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20743),U_20742))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20743)) ),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

cnf(f_4965_3,plain,
    ( U_20742 = U_20743
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20743),U_20742))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20743)) ),
    inference(clausify,[status(thm)],[f_4965_2]) ).

fof(f_4966_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_4966_2,plain,
    ! [U_20746,U_20745,U_20744] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20744),U_20746))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20745),U_20746))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20744),U_20745)) ),
    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_20744),U_20746))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20745),U_20746))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20744),U_20745)) ),
    inference(clausify,[status(thm)],[f_4966_2]) ).

fof(f_4967_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_4967_2,plain,
    ! [U_20749,U_20748,U_20747] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20747))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20747),U_20749)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20748))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20748),U_20749))
      | U_20747 != U_20748 ),
    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_20747),U_20749))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20748))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20748),U_20749))
    | U_20747 != U_20748 ),
    inference(clausify,[status(thm)],[f_4967_2]) ).

cnf(f_4967_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20747))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20748))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20748),U_20749))
    | U_20747 != U_20748 ),
    inference(clausify,[status(thm)],[f_4967_2]) ).

fof(f_4968_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_4968_2,plain,
    ! [U_20752,U_20751,U_20750] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20750))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20750),U_20752)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20751))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20751),U_20752))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20750),U_20751)) ),
    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_20750),U_20752))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20751))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20751),U_20752))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20750),U_20751)) ),
    inference(clausify,[status(thm)],[f_4968_2]) ).

cnf(f_4968_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20750))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20751))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20751),U_20752))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20750),U_20751)) ),
    inference(clausify,[status(thm)],[f_4968_2]) ).

fof(f_4969_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_4969_2,plain,
    ! [U_20754,U_20753] :
      ( U_20753 != U_20754
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20754),U_20753))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20753),U_20754)) ),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

cnf(f_4969_3,plain,
    ( U_20753 != U_20754
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20754),U_20753))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20753),U_20754)) ),
    inference(clausify,[status(thm)],[f_4969_2]) ).

fof(f_4970_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_4970_2,plain,
    ! [U_20756,U_20755] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756))
      | ~ 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_20756),U_20755))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) ),
    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_20755),U_20756))
    | ~ 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_20756),U_20755))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) ),
    inference(clausify,[status(thm)],[f_4970_2]) ).

fof(f_4971_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_4971_2,plain,
    ! [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_20758),U_20757))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) ),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

cnf(f_4971_3,plain,
    ( 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_20758),U_20757))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) ),
    inference(clausify,[status(thm)],[f_4971_2]) ).

fof(f_4972_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_4972_2,plain,
    ! [U_20760,U_20759] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20759),U_20760))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20760),U_20759))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20760),U_20759))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20759),U_20760)) ),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

cnf(f_4972_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20759),U_20760))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20760),U_20759))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20760),U_20759))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20759),U_20760)) ),
    inference(clausify,[status(thm)],[f_4972_2]) ).

fof(f_4973_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_4973_2,plain,
    ! [U_20762,U_20761] :
      ( U_20761 != U_20762
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20762),U_20761))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20761),U_20762)) ),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

cnf(f_4973_3,plain,
    ( U_20761 != U_20762
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20762),U_20761))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20761),U_20762)) ),
    inference(clausify,[status(thm)],[f_4973_2]) ).

fof(f_4974_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_4974_2,plain,
    ! [U_20764,U_20763] :
      ( U_20764 != U_20763
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20764),U_20763))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20763),U_20764)) ),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

cnf(f_4974_3,plain,
    ( U_20764 != U_20763
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20764),U_20763))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20763),U_20764)) ),
    inference(clausify,[status(thm)],[f_4974_2]) ).

fof(f_4975_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_4975_2,plain,
    ! [U_20767,U_20766,U_20765] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20767),U_20765))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20765),U_20767)) )
      | U_20766 != U_20767
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20766),U_20765))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20765),U_20766)) ),
    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_20765),U_20767))
    | U_20766 != U_20767
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20766),U_20765))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20765),U_20766)) ),
    inference(clausify,[status(thm)],[f_4975_2]) ).

cnf(f_4975_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20767),U_20765))
    | U_20766 != U_20767
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20766),U_20765))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20765),U_20766)) ),
    inference(clausify,[status(thm)],[f_4975_2]) ).

fof(f_4976_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_4976_2,plain,
    ! [U_20770,U_20769,U_20768] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20770),U_20768))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20768),U_20770)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20770))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20768))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20768),U_20769)) ),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

cnf(f_4976_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20768),U_20770))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20770))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20768))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20768),U_20769)) ),
    inference(clausify,[status(thm)],[f_4976_2]) ).

cnf(f_4976_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20770),U_20768))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20770))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20769),U_20768))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20768),U_20769)) ),
    inference(clausify,[status(thm)],[f_4976_2]) ).

fof(f_4977_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_4977_2,plain,
    ! [U_20772,U_20771] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20771),U_20772))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20772),U_20771))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20772),U_20771))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20771),U_20772)) ),
    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_20771),U_20772))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20772),U_20771))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20772),U_20771))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20771),U_20772)) ),
    inference(clausify,[status(thm)],[f_4977_2]) ).

fof(f_4978_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_4978_2,plain,
    ! [U_20775,U_20774,U_20773] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20775),U_20773))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20773),U_20775)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20775),U_20774))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20775))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20773))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20773),U_20774)) ),
    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_20773),U_20775))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20775),U_20774))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20775))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20773))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20773),U_20774)) ),
    inference(clausify,[status(thm)],[f_4978_2]) ).

cnf(f_4978_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20775),U_20773))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20775),U_20774))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20775))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20774),U_20773))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20773),U_20774)) ),
    inference(clausify,[status(thm)],[f_4978_2]) ).

fof(f_4979_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_4979_2,plain,
    ! [U_20777,U_20776] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20776),U_20777))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20777),U_20776))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20777),U_20776))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20776),U_20777)) ),
    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_20776),U_20777))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20777),U_20776))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20777),U_20776))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20776),U_20777)) ),
    inference(clausify,[status(thm)],[f_4979_2]) ).

fof(f_4980_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_4980_2,plain,
    ! [U_20779,U_20778] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20778),U_20779),U_20779))
      | ~ class_Rings_Ocomm__semiring__1(U_20778) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

cnf(f_4980_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20778),U_20779),U_20779))
    | ~ class_Rings_Ocomm__semiring__1(U_20778) ),
    inference(clausify,[status(thm)],[f_4980_2]) ).

fof(f_4981_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_4981_2,plain,
    ! [U_20783,U_20782,U_20781,U_20780] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20781),U_20783))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20782),U_20783))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20781),U_20782))
      | ~ class_Rings_Ocomm__semiring__1(U_20780) ),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

cnf(f_4981_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20781),U_20783))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20782),U_20783))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20780),U_20781),U_20782))
    | ~ class_Rings_Ocomm__semiring__1(U_20780) ),
    inference(clausify,[status(thm)],[f_4981_2]) ).

fof(f_4982_1,plain,
    ! [V_k,V_l,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k))
      | hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) != hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq]) ).

fof(f_4982_2,plain,
    ! [U_20786,U_20785,U_20784] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20784),U_20785),U_20786))
      | hAPP(c_Groups_Oabs__class_Oabs(U_20784),U_20785) != hAPP(c_Groups_Oabs__class_Oabs(U_20784),U_20786)
      | ~ class_Rings_Olinordered__idom(U_20784) ),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

cnf(f_4982_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20784),U_20785),U_20786))
    | hAPP(c_Groups_Oabs__class_Oabs(U_20784),U_20785) != hAPP(c_Groups_Oabs__class_Oabs(U_20784),U_20786)
    | ~ class_Rings_Olinordered__idom(U_20784) ),
    inference(clausify,[status(thm)],[f_4982_2]) ).

fof(f_4983_1,plain,
    ! [V_k_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff]) ).

fof(f_4983_2,plain,
    ! [U_20789,U_20788,U_20787] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),hAPP(c_Groups_Oabs__class_Oabs(U_20787),U_20788)),U_20789))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),U_20788),U_20789)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),U_20788),U_20789))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),hAPP(c_Groups_Oabs__class_Oabs(U_20787),U_20788)),U_20789)) ) )
      | ~ class_Rings_Olinordered__idom(U_20787) ),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

cnf(f_4983_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),U_20788),U_20789))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),hAPP(c_Groups_Oabs__class_Oabs(U_20787),U_20788)),U_20789))
    | ~ class_Rings_Olinordered__idom(U_20787) ),
    inference(clausify,[status(thm)],[f_4983_2]) ).

cnf(f_4983_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),hAPP(c_Groups_Oabs__class_Oabs(U_20787),U_20788)),U_20789))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20787),U_20788),U_20789))
    | ~ class_Rings_Olinordered__idom(U_20787) ),
    inference(clausify,[status(thm)],[f_4983_2]) ).

fof(f_4984_1,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]) ).

cnf(f_4984_2,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_4984_1]) ).

fof(f_4985_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_4985_2,plain,
    ! [U_20791,U_20790] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20791,U_20790))
      | ~ class_Lattices_Obounded__lattice(U_20790) ),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

cnf(f_4985_3,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20791,U_20790))
    | ~ class_Lattices_Obounded__lattice(U_20790) ),
    inference(clausify,[status(thm)],[f_4985_2]) ).

fof(f_4986_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_4986_2,plain,
    ! [U_20793,U_20792] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20793,U_20792))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20792) ),
    inference(variable_rename,[status(thm)],[f_4986_1]) ).

cnf(f_4986_3,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20793,U_20792))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20792) ),
    inference(clausify,[status(thm)],[f_4986_2]) ).

fof(f_4987_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_4987_2,plain,
    ! [U_20795,U_20794] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20795,U_20794))
      | ~ class_Lattices_Obounded__lattice(U_20794) ),
    inference(variable_rename,[status(thm)],[f_4987_1]) ).

cnf(f_4987_3,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_20795,U_20794))
    | ~ class_Lattices_Obounded__lattice(U_20794) ),
    inference(clausify,[status(thm)],[f_4987_2]) ).

fof(f_4988_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_4988_2,plain,
    ! [U_20797,U_20796] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20797,U_20796))
      | ~ class_Lattices_Obounded__lattice(U_20796) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

cnf(f_4988_3,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20797,U_20796))
    | ~ class_Lattices_Obounded__lattice(U_20796) ),
    inference(clausify,[status(thm)],[f_4988_2]) ).

fof(f_4989_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_4989_2,plain,
    ! [U_20799,U_20798] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20799,U_20798))
      | ~ class_Lattices_Olattice(U_20798) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

cnf(f_4989_3,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_20799,U_20798))
    | ~ class_Lattices_Olattice(U_20798) ),
    inference(clausify,[status(thm)],[f_4989_2]) ).

fof(f_4990_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_4990_2,plain,
    ! [U_20801,U_20800] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20801,U_20800))
      | ~ class_Lattices_Olattice(U_20800) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

cnf(f_4990_3,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_20801,U_20800))
    | ~ class_Lattices_Olattice(U_20800) ),
    inference(clausify,[status(thm)],[f_4990_2]) ).

fof(f_4991_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_4991_2,plain,
    ! [U_20803,U_20802] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20803,U_20802))
      | ~ class_Lattices_Odistrib__lattice(U_20802) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

cnf(f_4991_3,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_20803,U_20802))
    | ~ class_Lattices_Odistrib__lattice(U_20802) ),
    inference(clausify,[status(thm)],[f_4991_2]) ).

fof(f_4992_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_4992_2,plain,
    ! [U_20805,U_20804] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20805,U_20804))
      | ~ class_Lattices_Oboolean__algebra(U_20804) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

cnf(f_4992_3,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_20805,U_20804))
    | ~ class_Lattices_Oboolean__algebra(U_20804) ),
    inference(clausify,[status(thm)],[f_4992_2]) ).

fof(f_4993_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_4993_2,plain,
    ! [U_20807,U_20806] :
      ( class_Orderings_Opreorder(tc_fun(U_20807,U_20806))
      | ~ class_Orderings_Opreorder(U_20806) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

cnf(f_4993_3,plain,
    ( class_Orderings_Opreorder(tc_fun(U_20807,U_20806))
    | ~ class_Orderings_Opreorder(U_20806) ),
    inference(clausify,[status(thm)],[f_4993_2]) ).

fof(f_4994_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_4994_2,plain,
    ! [U_20809,U_20808] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20808,U_20809))
      | ~ class_Finite__Set_Ofinite(U_20809)
      | ~ class_Finite__Set_Ofinite(U_20808) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

cnf(f_4994_3,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_20808,U_20809))
    | ~ class_Finite__Set_Ofinite(U_20809)
    | ~ class_Finite__Set_Ofinite(U_20808) ),
    inference(clausify,[status(thm)],[f_4994_2]) ).

fof(f_4995_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_4995_2,plain,
    ! [U_20811,U_20810] :
      ( class_Lattices_Olattice(tc_fun(U_20811,U_20810))
      | ~ class_Lattices_Olattice(U_20810) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

cnf(f_4995_3,plain,
    ( class_Lattices_Olattice(tc_fun(U_20811,U_20810))
    | ~ class_Lattices_Olattice(U_20810) ),
    inference(clausify,[status(thm)],[f_4995_2]) ).

fof(f_4996_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_4996_2,plain,
    ! [U_20813,U_20812] :
      ( class_Orderings_Oorder(tc_fun(U_20813,U_20812))
      | ~ class_Orderings_Oorder(U_20812) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

cnf(f_4996_3,plain,
    ( class_Orderings_Oorder(tc_fun(U_20813,U_20812))
    | ~ class_Orderings_Oorder(U_20812) ),
    inference(clausify,[status(thm)],[f_4996_2]) ).

fof(f_4997_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_4997_2,plain,
    ! [U_20815,U_20814] :
      ( class_Orderings_Otop(tc_fun(U_20815,U_20814))
      | ~ class_Orderings_Otop(U_20814) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

cnf(f_4997_3,plain,
    ( class_Orderings_Otop(tc_fun(U_20815,U_20814))
    | ~ class_Orderings_Otop(U_20814) ),
    inference(clausify,[status(thm)],[f_4997_2]) ).

fof(f_4998_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_4998_2,plain,
    ! [U_20817,U_20816] :
      ( class_Orderings_Oord(tc_fun(U_20817,U_20816))
      | ~ class_Orderings_Oord(U_20816) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

cnf(f_4998_3,plain,
    ( class_Orderings_Oord(tc_fun(U_20817,U_20816))
    | ~ class_Orderings_Oord(U_20816) ),
    inference(clausify,[status(thm)],[f_4998_2]) ).

fof(f_4999_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_4999_2,plain,
    ! [U_20819,U_20818] :
      ( class_Orderings_Obot(tc_fun(U_20819,U_20818))
      | ~ class_Orderings_Obot(U_20818) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

cnf(f_4999_3,plain,
    ( class_Orderings_Obot(tc_fun(U_20819,U_20818))
    | ~ class_Orderings_Obot(U_20818) ),
    inference(clausify,[status(thm)],[f_4999_2]) ).

fof(f_5000_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_5000_2,plain,
    ! [U_20821,U_20820] :
      ( class_Groups_Ouminus(tc_fun(U_20821,U_20820))
      | ~ class_Groups_Ouminus(U_20820) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

cnf(f_5000_3,plain,
    ( class_Groups_Ouminus(tc_fun(U_20821,U_20820))
    | ~ class_Groups_Ouminus(U_20820) ),
    inference(clausify,[status(thm)],[f_5000_2]) ).

fof(f_5001_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_5001_2,plain,
    ! [U_20823,U_20822] :
      ( class_Groups_Ominus(tc_fun(U_20823,U_20822))
      | ~ class_Groups_Ominus(U_20822) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

cnf(f_5001_3,plain,
    ( class_Groups_Ominus(tc_fun(U_20823,U_20822))
    | ~ class_Groups_Ominus(U_20822) ),
    inference(clausify,[status(thm)],[f_5001_2]) ).

fof(f_5002_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_5002_2,plain,
    ! [U_20825,U_20824] :
      ( class_Enum_Oenum(tc_fun(U_20824,U_20825))
      | ~ class_Enum_Oenum(U_20825)
      | ~ class_Enum_Oenum(U_20824) ),
    inference(variable_rename,[status(thm)],[f_5002_1]) ).

cnf(f_5002_3,plain,
    ( class_Enum_Oenum(tc_fun(U_20824,U_20825))
    | ~ class_Enum_Oenum(U_20825)
    | ~ class_Enum_Oenum(U_20824) ),
    inference(clausify,[status(thm)],[f_5002_2]) ).

fof(f_5003_1,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(fof_nnf,[status(thm)],[arity_Com__Ocom__Nat_Osize]) ).

cnf(f_5003_2,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(clausify,[status(thm)],[f_5003_1]) ).

fof(f_5004_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_5004_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5004_1]) ).

fof(f_5005_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_5005_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5005_1]) ).

fof(f_5006_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_5006_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5006_1]) ).

fof(f_5007_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_5007_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5007_1]) ).

fof(f_5008_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_5008_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5008_1]) ).

fof(f_5009_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_5009_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5009_1]) ).

fof(f_5010_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

cnf(f_5010_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5010_1]) ).

fof(f_5011_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_5011_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5011_1]) ).

fof(f_5012_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_5012_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5012_1]) ).

fof(f_5013_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_5013_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5013_1]) ).

fof(f_5014_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_5014_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5014_1]) ).

fof(f_5015_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_5015_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5015_1]) ).

fof(f_5016_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_5016_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5016_1]) ).

fof(f_5017_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

cnf(f_5017_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5017_1]) ).

fof(f_5018_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

cnf(f_5018_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5018_1]) ).

fof(f_5019_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_5019_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5019_1]) ).

fof(f_5020_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

cnf(f_5020_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5020_1]) ).

fof(f_5021_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

cnf(f_5021_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5021_1]) ).

fof(f_5022_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_5022_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5022_1]) ).

fof(f_5023_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

cnf(f_5023_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5023_1]) ).

fof(f_5024_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

cnf(f_5024_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5024_1]) ).

fof(f_5025_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

cnf(f_5025_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5025_1]) ).

fof(f_5026_1,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]) ).

cnf(f_5026_2,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5026_1]) ).

fof(f_5027_1,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]) ).

cnf(f_5027_2,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5027_1]) ).

fof(f_5028_1,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]) ).

cnf(f_5028_2,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5028_1]) ).

fof(f_5029_1,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]) ).

cnf(f_5029_2,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5029_1]) ).

fof(f_5030_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

cnf(f_5030_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5030_1]) ).

fof(f_5031_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

cnf(f_5031_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5031_1]) ).

fof(f_5032_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

cnf(f_5032_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5032_1]) ).

fof(f_5033_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

cnf(f_5033_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5033_1]) ).

fof(f_5034_1,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).

cnf(f_5034_2,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5034_1]) ).

fof(f_5035_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

cnf(f_5035_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5035_1]) ).

fof(f_5036_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

cnf(f_5036_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5036_1]) ).

fof(f_5037_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

cnf(f_5037_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5037_1]) ).

fof(f_5038_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

cnf(f_5038_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5038_1]) ).

fof(f_5039_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

cnf(f_5039_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5039_1]) ).

fof(f_5040_1,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]) ).

cnf(f_5040_2,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5040_1]) ).

fof(f_5041_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

cnf(f_5041_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5041_1]) ).

fof(f_5042_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

cnf(f_5042_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5042_1]) ).

fof(f_5043_1,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]) ).

cnf(f_5043_2,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5043_1]) ).

fof(f_5044_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

cnf(f_5044_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5044_1]) ).

fof(f_5045_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

cnf(f_5045_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5045_1]) ).

fof(f_5046_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

cnf(f_5046_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5046_1]) ).

fof(f_5047_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

cnf(f_5047_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5047_1]) ).

fof(f_5048_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

cnf(f_5048_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5048_1]) ).

fof(f_5049_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

cnf(f_5049_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5049_1]) ).

fof(f_5050_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

cnf(f_5050_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5050_1]) ).

fof(f_5051_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

cnf(f_5051_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5051_1]) ).

fof(f_5052_1,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).

cnf(f_5052_2,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5052_1]) ).

fof(f_5053_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

cnf(f_5053_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5053_1]) ).

fof(f_5054_1,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Olattice]) ).

cnf(f_5054_2,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5054_1]) ).

fof(f_5055_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

cnf(f_5055_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5055_1]) ).

fof(f_5056_1,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).

cnf(f_5056_2,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5056_1]) ).

fof(f_5057_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

cnf(f_5057_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5057_1]) ).

fof(f_5058_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

cnf(f_5058_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5058_1]) ).

fof(f_5059_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

cnf(f_5059_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5059_1]) ).

fof(f_5060_1,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).

cnf(f_5060_2,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5060_1]) ).

fof(f_5061_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

cnf(f_5061_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5061_1]) ).

fof(f_5062_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

cnf(f_5062_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5062_1]) ).

fof(f_5063_1,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).

cnf(f_5063_2,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5063_1]) ).

fof(f_5064_1,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).

cnf(f_5064_2,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5064_1]) ).

fof(f_5065_1,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).

cnf(f_5065_2,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5065_1]) ).

fof(f_5066_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

cnf(f_5066_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5066_1]) ).

fof(f_5067_1,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).

cnf(f_5067_2,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5067_1]) ).

fof(f_5068_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

cnf(f_5068_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5068_1]) ).

fof(f_5069_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

cnf(f_5069_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5069_1]) ).

fof(f_5070_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

cnf(f_5070_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5070_1]) ).

fof(f_5071_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

cnf(f_5071_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5071_1]) ).

fof(f_5072_1,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).

cnf(f_5072_2,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5072_1]) ).

fof(f_5073_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

cnf(f_5073_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5073_1]) ).

fof(f_5074_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_5074_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5074_1]) ).

fof(f_5075_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_5075_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5075_1]) ).

fof(f_5076_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_5076_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5076_1]) ).

fof(f_5077_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_5077_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5077_1]) ).

fof(f_5078_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_5078_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5078_1]) ).

fof(f_5079_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

cnf(f_5079_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5079_1]) ).

fof(f_5080_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_5080_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5080_1]) ).

fof(f_5081_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_5081_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5081_1]) ).

fof(f_5082_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_5082_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5082_1]) ).

fof(f_5083_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

cnf(f_5083_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5083_1]) ).

fof(f_5084_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

cnf(f_5084_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5084_1]) ).

fof(f_5085_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

cnf(f_5085_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5085_1]) ).

fof(f_5086_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

cnf(f_5086_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5086_1]) ).

fof(f_5087_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

cnf(f_5087_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5087_1]) ).

fof(f_5088_1,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]) ).

cnf(f_5088_2,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5088_1]) ).

fof(f_5089_1,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).

cnf(f_5089_2,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5089_1]) ).

fof(f_5090_1,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]) ).

cnf(f_5090_2,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5090_1]) ).

fof(f_5091_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

cnf(f_5091_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5091_1]) ).

fof(f_5092_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

cnf(f_5092_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5092_1]) ).

fof(f_5093_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

cnf(f_5093_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5093_1]) ).

fof(f_5094_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

cnf(f_5094_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5094_1]) ).

fof(f_5095_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

cnf(f_5095_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5095_1]) ).

fof(f_5096_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

cnf(f_5096_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5096_1]) ).

fof(f_5097_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

cnf(f_5097_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5097_1]) ).

fof(f_5098_1,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]) ).

cnf(f_5098_2,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5098_1]) ).

fof(f_5099_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

cnf(f_5099_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5099_1]) ).

fof(f_5100_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

cnf(f_5100_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5100_1]) ).

fof(f_5101_1,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]) ).

cnf(f_5101_2,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5101_1]) ).

fof(f_5102_1,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]) ).

cnf(f_5102_2,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5102_1]) ).

fof(f_5103_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

cnf(f_5103_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5103_1]) ).

fof(f_5104_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

cnf(f_5104_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5104_1]) ).

fof(f_5105_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

cnf(f_5105_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5105_1]) ).

fof(f_5106_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

cnf(f_5106_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5106_1]) ).

fof(f_5107_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

cnf(f_5107_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5107_1]) ).

fof(f_5108_1,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).

cnf(f_5108_2,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5108_1]) ).

fof(f_5109_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

cnf(f_5109_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5109_1]) ).

fof(f_5110_1,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).

cnf(f_5110_2,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5110_1]) ).

fof(f_5111_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

cnf(f_5111_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5111_1]) ).

fof(f_5112_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

cnf(f_5112_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5112_1]) ).

fof(f_5113_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

cnf(f_5113_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5113_1]) ).

fof(f_5114_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

cnf(f_5114_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5114_1]) ).

fof(f_5115_1,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Obot]) ).

cnf(f_5115_2,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5115_1]) ).

fof(f_5116_1,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).

cnf(f_5116_2,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5116_1]) ).

fof(f_5117_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

cnf(f_5117_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5117_1]) ).

fof(f_5118_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

cnf(f_5118_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5118_1]) ).

fof(f_5119_1,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).

cnf(f_5119_2,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5119_1]) ).

fof(f_5120_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

cnf(f_5120_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5120_1]) ).

fof(f_5121_1,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osize]) ).

cnf(f_5121_2,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5121_1]) ).

fof(f_5122_1,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]) ).

cnf(f_5122_2,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5122_1]) ).

fof(f_5123_1,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).

cnf(f_5123_2,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5123_1]) ).

fof(f_5124_1,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).

cnf(f_5124_2,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5124_1]) ).

fof(f_5125_1,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]) ).

cnf(f_5125_2,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5125_1]) ).

fof(f_5126_1,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).

cnf(f_5126_2,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5126_1]) ).

fof(f_5127_1,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]) ).

cnf(f_5127_2,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5127_1]) ).

fof(f_5128_1,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).

cnf(f_5128_2,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5128_1]) ).

fof(f_5129_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

cnf(f_5129_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5129_1]) ).

fof(f_5130_1,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]) ).

cnf(f_5130_2,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5130_1]) ).

fof(f_5131_1,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).

cnf(f_5131_2,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5131_1]) ).

fof(f_5132_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

cnf(f_5132_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5132_1]) ).

fof(f_5133_1,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).

cnf(f_5133_2,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5133_1]) ).

fof(f_5134_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

cnf(f_5134_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5134_1]) ).

fof(f_5135_1,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).

cnf(f_5135_2,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5135_1]) ).

fof(f_5136_1,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).

cnf(f_5136_2,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5136_1]) ).

fof(f_5137_1,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).

cnf(f_5137_2,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5137_1]) ).

fof(f_5138_1,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Enum_Oenum]) ).

cnf(f_5138_2,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5138_1]) ).

fof(f_5139_1,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Nat_Osize]) ).

cnf(f_5139_2,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5139_1]) ).

fof(f_5140_1,plain,
    class_Nat_Osize(tc_Com_Ostate),
    inference(fof_nnf,[status(thm)],[arity_Com__Ostate__Nat_Osize]) ).

cnf(f_5140_2,plain,
    class_Nat_Osize(tc_Com_Ostate),
    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_20826] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(U_20826))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20826) ),
    inference(variable_rename,[status(thm)],[f_5141_1]) ).

cnf(f_5141_3,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(U_20826))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20826) ),
    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_20827] : class_Nat_Osize(tc_List_Olist(U_20827)),
    inference(variable_rename,[status(thm)],[f_5142_1]) ).

cnf(f_5142_3,plain,
    class_Nat_Osize(tc_List_Olist(U_20827)),
    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_20829,U_20828] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20828,U_20829))
      | ~ class_Finite__Set_Ofinite(U_20829)
      | ~ class_Finite__Set_Ofinite(U_20828) ),
    inference(variable_rename,[status(thm)],[f_5143_1]) ).

cnf(f_5143_3,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_20828,U_20829))
    | ~ class_Finite__Set_Ofinite(U_20829)
    | ~ class_Finite__Set_Ofinite(U_20828) ),
    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_20831,U_20830] :
      ( class_Enum_Oenum(tc_sum(U_20830,U_20831))
      | ~ class_Enum_Oenum(U_20831)
      | ~ class_Enum_Oenum(U_20830) ),
    inference(variable_rename,[status(thm)],[f_5144_1]) ).

cnf(f_5144_3,plain,
    ( class_Enum_Oenum(tc_sum(U_20830,U_20831))
    | ~ class_Enum_Oenum(U_20831)
    | ~ class_Enum_Oenum(U_20830) ),
    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_20833,U_20832] : class_Nat_Osize(tc_sum(U_20832,U_20833)),
    inference(variable_rename,[status(thm)],[f_5145_1]) ).

cnf(f_5145_3,plain,
    class_Nat_Osize(tc_sum(U_20832,U_20833)),
    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_20834] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20834))
      | ~ class_Finite__Set_Ofinite(U_20834) ),
    inference(variable_rename,[status(thm)],[f_5146_1]) ).

cnf(f_5146_3,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20834))
    | ~ class_Finite__Set_Ofinite(U_20834) ),
    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_20835] :
      ( class_Enum_Oenum(tc_Option_Ooption(U_20835))
      | ~ class_Enum_Oenum(U_20835) ),
    inference(variable_rename,[status(thm)],[f_5147_1]) ).

cnf(f_5147_3,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(U_20835))
    | ~ class_Enum_Oenum(U_20835) ),
    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_20836] : class_Nat_Osize(tc_Option_Ooption(U_20836)),
    inference(variable_rename,[status(thm)],[f_5148_1]) ).

cnf(f_5148_3,plain,
    class_Nat_Osize(tc_Option_Ooption(U_20836)),
    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_20838,U_20837] : class_Nat_Osize(tc_Nitpick_Opair__box(U_20837,U_20838)),
    inference(variable_rename,[status(thm)],[f_5149_1]) ).

cnf(f_5149_3,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(U_20837,U_20838)),
    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_20840,U_20839] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_prod(U_20839,U_20840))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20840)
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20839) ),
    inference(variable_rename,[status(thm)],[f_5150_1]) ).

cnf(f_5150_3,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_prod(U_20839,U_20840))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20840)
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20839) ),
    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_20842,U_20841] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20841,U_20842))
      | ~ class_Finite__Set_Ofinite(U_20842)
      | ~ class_Finite__Set_Ofinite(U_20841) ),
    inference(variable_rename,[status(thm)],[f_5151_1]) ).

cnf(f_5151_3,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_20841,U_20842))
    | ~ class_Finite__Set_Ofinite(U_20842)
    | ~ class_Finite__Set_Ofinite(U_20841) ),
    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_20844,U_20843] :
      ( class_Enum_Oenum(tc_prod(U_20843,U_20844))
      | ~ class_Enum_Oenum(U_20844)
      | ~ class_Enum_Oenum(U_20843) ),
    inference(variable_rename,[status(thm)],[f_5152_1]) ).

cnf(f_5152_3,plain,
    ( class_Enum_Oenum(tc_prod(U_20843,U_20844))
    | ~ class_Enum_Oenum(U_20844)
    | ~ class_Enum_Oenum(U_20843) ),
    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_20846,U_20845] : class_Nat_Osize(tc_prod(U_20845,U_20846)),
    inference(variable_rename,[status(thm)],[f_5153_1]) ).

cnf(f_5153_3,plain,
    class_Nat_Osize(tc_prod(U_20845,U_20846)),
    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_20847] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_20847)),
    inference(variable_rename,[status(thm)],[f_5159_1]) ).

cnf(f_5159_3,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_20847)),
    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_20848] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20848)),
    inference(variable_rename,[status(thm)],[f_5201_1]) ).

cnf(f_5201_3,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20848)),
    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_20850,U_20849] : hAPP(c_COMBI(U_20849),U_20850) = U_20850,
    inference(variable_rename,[status(thm)],[f_5202_1]) ).

cnf(f_5202_3,plain,
    hAPP(c_COMBI(U_20849),U_20850) = U_20850,
    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_20854,U_20853,U_20852,U_20851] : hAPP(hAPP(c_COMBK(U_20851,U_20852),U_20853),U_20854) = U_20853,
    inference(variable_rename,[status(thm)],[f_5203_1]) ).

cnf(f_5203_3,plain,
    hAPP(hAPP(c_COMBK(U_20851,U_20852),U_20853),U_20854) = U_20853,
    inference(clausify,[status(thm)],[f_5203_2]) ).

fof(f_5204_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).

fof(f_5204_2,plain,
    ! [U_20860,U_20859,U_20858,U_20857,U_20856,U_20855] : hAPP(hAPP(hAPP(c_COMBB(U_20855,U_20856,U_20857),U_20858),U_20859),U_20860) = hAPP(U_20858,hAPP(U_20859,U_20860)),
    inference(variable_rename,[status(thm)],[f_5204_1]) ).

cnf(f_5204_3,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_20855,U_20856,U_20857),U_20858),U_20859),U_20860) = hAPP(U_20858,hAPP(U_20859,U_20860)),
    inference(clausify,[status(thm)],[f_5204_2]) ).

fof(f_5205_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2),
    inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).

fof(f_5205_2,plain,
    ! [U_20866,U_20865,U_20864,U_20863,U_20862,U_20861] : hAPP(hAPP(hAPP(c_COMBC(U_20861,U_20862,U_20863),U_20864),U_20865),U_20866) = hAPP(hAPP(U_20864,U_20866),U_20865),
    inference(variable_rename,[status(thm)],[f_5205_1]) ).

cnf(f_5205_3,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_20861,U_20862,U_20863),U_20864),U_20865),U_20866) = hAPP(hAPP(U_20864,U_20866),U_20865),
    inference(clausify,[status(thm)],[f_5205_2]) ).

fof(f_5206_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).

fof(f_5206_2,plain,
    ! [U_20872,U_20871,U_20870,U_20869,U_20868,U_20867] : hAPP(hAPP(hAPP(c_COMBS(U_20867,U_20868,U_20869),U_20870),U_20871),U_20872) = hAPP(hAPP(U_20870,U_20872),hAPP(U_20871,U_20872)),
    inference(variable_rename,[status(thm)],[f_5206_1]) ).

cnf(f_5206_3,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_20867,U_20868,U_20869),U_20870),U_20871),U_20872) = hAPP(hAPP(U_20870,U_20872),hAPP(U_20871,U_20872)),
    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_20874,U_20873] :
      ( U_20873 = U_20874
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20873),U_20874)) ),
    inference(variable_rename,[status(thm)],[f_5207_1]) ).

cnf(f_5207_3,plain,
    ( U_20873 = U_20874
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_20873),U_20874)) ),
    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_20876,U_20875] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20875),U_20876))
      | U_20875 != U_20876 ),
    inference(variable_rename,[status(thm)],[f_5208_1]) ).

cnf(f_5208_3,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_20875),U_20876))
    | U_20875 != U_20876 ),
    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_Pa_2] :
      ( ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).

fof(f_5211_2,plain,
    ! [U_20877] :
      ( ~ hBOOL(U_20877)
      | ~ hBOOL(hAPP(c_fNot,U_20877)) ),
    inference(variable_rename,[status(thm)],[f_5211_1]) ).

cnf(f_5211_3,plain,
    ( ~ hBOOL(U_20877)
    | ~ hBOOL(hAPP(c_fNot,U_20877)) ),
    inference(clausify,[status(thm)],[f_5211_2]) ).

fof(f_5212_1,plain,
    ! [V_Pa_2] :
      ( hBOOL(hAPP(c_fNot,V_Pa_2))
      | hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).

fof(f_5212_2,plain,
    ! [U_20878] :
      ( hBOOL(hAPP(c_fNot,U_20878))
      | hBOOL(U_20878) ),
    inference(variable_rename,[status(thm)],[f_5212_1]) ).

cnf(f_5212_3,plain,
    ( hBOOL(hAPP(c_fNot,U_20878))
    | hBOOL(U_20878) ),
    inference(clausify,[status(thm)],[f_5212_2]) ).

fof(f_5213_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).

fof(f_5213_2,plain,
    ! [U_20880,U_20879] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20879),U_20880))
      | ~ hBOOL(U_20880)
      | ~ hBOOL(U_20879) ),
    inference(variable_rename,[status(thm)],[f_5213_1]) ).

fof(f_5213_3,plain,
    ! [U_20880] :
      ( ! [U_20879] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_20879),U_20880))
          | ~ hBOOL(U_20879) )
      | ~ hBOOL(U_20880) ),
    inference(miniscope,[status(thm)],[f_5213_2]) ).

cnf(f_5213_4,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_20879),U_20880))
    | ~ hBOOL(U_20879)
    | ~ hBOOL(U_20880) ),
    inference(clausify,[status(thm)],[f_5213_3]) ).

fof(f_5214_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).

fof(f_5214_2,plain,
    ! [U_20882,U_20881] :
      ( hBOOL(U_20881)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20881),U_20882)) ),
    inference(variable_rename,[status(thm)],[f_5214_1]) ).

cnf(f_5214_3,plain,
    ( hBOOL(U_20881)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_20881),U_20882)) ),
    inference(clausify,[status(thm)],[f_5214_2]) ).

fof(f_5215_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).

fof(f_5215_2,plain,
    ! [U_20884,U_20883] :
      ( hBOOL(U_20884)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20883),U_20884)) ),
    inference(variable_rename,[status(thm)],[f_5215_1]) ).

fof(f_5215_3,plain,
    ! [U_20884] :
      ( ! [U_20883] : ~ hBOOL(hAPP(hAPP(c_fconj,U_20883),U_20884))
      | hBOOL(U_20884) ),
    inference(miniscope,[status(thm)],[f_5215_2]) ).

cnf(f_5215_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20883),U_20884))
    | hBOOL(U_20884) ),
    inference(clausify,[status(thm)],[f_5215_3]) ).

fof(f_5216_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__1]) ).

fof(f_5216_2,plain,
    ! [U_20886,U_20885] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20885),U_20886))
      | ~ hBOOL(U_20885) ),
    inference(variable_rename,[status(thm)],[f_5216_1]) ).

cnf(f_5216_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20885),U_20886))
    | ~ hBOOL(U_20885) ),
    inference(clausify,[status(thm)],[f_5216_2]) ).

fof(f_5217_1,plain,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__2]) ).

fof(f_5217_2,plain,
    ! [U_20888,U_20887] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20888),U_20887))
      | ~ hBOOL(U_20887) ),
    inference(variable_rename,[status(thm)],[f_5217_1]) ).

cnf(f_5217_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20888),U_20887))
    | ~ hBOOL(U_20887) ),
    inference(clausify,[status(thm)],[f_5217_2]) ).

fof(f_5218_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__3]) ).

fof(f_5218_2,plain,
    ! [U_20890,U_20889] :
      ( hBOOL(U_20890)
      | hBOOL(U_20889)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20889),U_20890)) ),
    inference(variable_rename,[status(thm)],[f_5218_1]) ).

fof(f_5218_3,plain,
    ! [U_20890] :
      ( ! [U_20889] :
          ( hBOOL(U_20889)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20889),U_20890)) )
      | hBOOL(U_20890) ),
    inference(miniscope,[status(thm)],[f_5218_2]) ).

cnf(f_5218_4,plain,
    ( hBOOL(U_20889)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20889),U_20890))
    | hBOOL(U_20890) ),
    inference(clausify,[status(thm)],[f_5218_3]) ).

fof(f_5219_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__1]) ).

fof(f_5219_2,plain,
    ! [U_20892,U_20891] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20891),U_20892))
      | hBOOL(U_20891) ),
    inference(variable_rename,[status(thm)],[f_5219_1]) ).

cnf(f_5219_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20891),U_20892))
    | hBOOL(U_20891) ),
    inference(clausify,[status(thm)],[f_5219_2]) ).

fof(f_5220_1,plain,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__2]) ).

fof(f_5220_2,plain,
    ! [U_20894,U_20893] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20894),U_20893))
      | ~ hBOOL(U_20893) ),
    inference(variable_rename,[status(thm)],[f_5220_1]) ).

cnf(f_5220_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20894),U_20893))
    | ~ hBOOL(U_20893) ),
    inference(clausify,[status(thm)],[f_5220_2]) ).

fof(f_5221_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__3]) ).

fof(f_5221_2,plain,
    ! [U_20896,U_20895] :
      ( hBOOL(U_20896)
      | ~ hBOOL(U_20895)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20895),U_20896)) ),
    inference(variable_rename,[status(thm)],[f_5221_1]) ).

fof(f_5221_3,plain,
    ! [U_20896] :
      ( ! [U_20895] :
          ( ~ hBOOL(U_20895)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20895),U_20896)) )
      | hBOOL(U_20896) ),
    inference(miniscope,[status(thm)],[f_5221_2]) ).

cnf(f_5221_4,plain,
    ( ~ hBOOL(U_20895)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20895),U_20896))
    | hBOOL(U_20896) ),
    inference(clausify,[status(thm)],[f_5221_3]) ).

fof(f_5222_1,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

cnf(f_5222_2,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_5222_1]) ).

fof(f_5223_1,plain,
    ! [B_Z,B_s] :
      ( ! [B_s_H] :
          ( v_Q(B_Z,B_s_H)
          | ? [B_Z_H] :
              ( ~ hBOOL(hAPP(hAPP(v_Q_H,B_Z_H),B_s_H))
              & hBOOL(hAPP(hAPP(v_P_H,B_Z_H),B_s)) ) )
      | ~ v_P(B_Z,B_s) ),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

fof(f_5223_2,plain,
    ! [U_20900,U_20899] :
      ( ! [U_20898] :
          ( v_Q(U_20900,U_20898)
          | ? [U_20897] :
              ( ~ hBOOL(hAPP(hAPP(v_Q_H,U_20897),U_20898))
              & hBOOL(hAPP(hAPP(v_P_H,U_20897),U_20899)) ) )
      | ~ v_P(U_20900,U_20899) ),
    inference(variable_rename,[status(thm)],[f_5223_1]) ).

fof(f_5223_3,plain,
    ! [U_20900,U_20899] :
      ( ! [U_20898] :
          ( v_Q(U_20900,U_20898)
          | ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK577(U_20900,U_20899,U_20898)),U_20898))
            & hBOOL(hAPP(hAPP(v_P_H,sK577(U_20900,U_20899,U_20898)),U_20899)) ) )
      | ~ v_P(U_20900,U_20899) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK577]),skolemize(U_20897,sK577(U_20900,U_20899,U_20898))],[f_5223_2]) ).

cnf(f_5223_4,plain,
    ( hBOOL(hAPP(hAPP(v_P_H,sK577(U_20900,U_20899,U_20898)),U_20899))
    | v_Q(U_20900,U_20898)
    | ~ v_P(U_20900,U_20899) ),
    inference(clausify,[status(thm)],[f_5223_3]) ).

cnf(f_5223_5,plain,
    ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK577(U_20900,U_20899,U_20898)),U_20898))
    | v_Q(U_20900,U_20898)
    | ~ v_P(U_20900,U_20899) ),
    inference(clausify,[status(thm)],[f_5223_3]) ).

fof(f_5224_1,negated_conjecture,
    ~ ! [B_Z,B_s] :
        ( v_P(B_Z,B_s)
       => ? [B_P_H,B_Q_H] :
            ( ! [B_s_H] :
                ( ! [B_Z_H] :
                    ( hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s))
                   => hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H)) )
               => v_Q(B_Z,B_s_H) )
            & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,B_P_H,v_c,B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    inference(negate,[status(cth)],[conj_2]) ).

fof(f_5224_2,negated_conjecture,
    ? [B_Z,B_s] :
      ( ! [B_P_H,B_Q_H] :
          ( ? [B_s_H] :
              ( ~ v_Q(B_Z,B_s_H)
              & ! [B_Z_H] :
                  ( hBOOL(hAPP(hAPP(B_Q_H,B_Z_H),B_s_H))
                  | ~ hBOOL(hAPP(hAPP(B_P_H,B_Z_H),B_s)) ) )
          | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,B_P_H,v_c,B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & v_P(B_Z,B_s) ),
    inference(fof_nnf,[status(thm)],[f_5224_1]) ).

fof(f_5224_3,negated_conjecture,
    ? [U_20906,U_20905] :
      ( ! [U_20904,U_20903] :
          ( ? [U_20902] :
              ( ~ v_Q(U_20906,U_20902)
              & ! [U_20901] :
                  ( hBOOL(hAPP(hAPP(U_20903,U_20901),U_20902))
                  | ~ hBOOL(hAPP(hAPP(U_20904,U_20901),U_20905)) ) )
          | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & v_P(U_20906,U_20905) ),
    inference(variable_rename,[status(thm)],[f_5224_2]) ).

fof(f_5224_4,negated_conjecture,
    ? [U_20905] :
      ( ! [U_20904,U_20903] :
          ( ? [U_20902] :
              ( ~ v_Q(sK578,U_20902)
              & ! [U_20901] :
                  ( hBOOL(hAPP(hAPP(U_20903,U_20901),U_20902))
                  | ~ hBOOL(hAPP(hAPP(U_20904,U_20901),U_20905)) ) )
          | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & v_P(sK578,U_20905) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK578]),skolemize(U_20906,sK578)],[f_5224_3]) ).

fof(f_5224_5,negated_conjecture,
    ( ! [U_20904,U_20903] :
        ( ? [U_20902] :
            ( ~ v_Q(sK578,U_20902)
            & ! [U_20901] :
                ( hBOOL(hAPP(hAPP(U_20903,U_20901),U_20902))
                | ~ hBOOL(hAPP(hAPP(U_20904,U_20901),sK579)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
    & v_P(sK578,sK579) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK579]),skolemize(U_20905,sK579)],[f_5224_4]) ).

fof(f_5224_6,negated_conjecture,
    ( ! [U_20904,U_20903] :
        ( ( ~ v_Q(sK578,sK580(U_20904,U_20903))
          & ! [U_20901] :
              ( hBOOL(hAPP(hAPP(U_20903,U_20901),sK580(U_20904,U_20903)))
              | ~ hBOOL(hAPP(hAPP(U_20904,U_20901),sK579)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
    & v_P(sK578,sK579) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK580]),skolemize(U_20902,sK580(U_20904,U_20903))],[f_5224_5]) ).

cnf(f_5224_7,negated_conjecture,
    v_P(sK578,sK579),
    inference(clausify,[status(thm)],[f_5224_6]) ).

cnf(f_5224_8,negated_conjecture,
    ( hBOOL(hAPP(hAPP(U_20903,U_20901),sK580(U_20904,U_20903)))
    | ~ hBOOL(hAPP(hAPP(U_20904,U_20901),sK579))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_5224_6]) ).

cnf(f_5224_9,negated_conjecture,
    ( ~ v_Q(sK578,sK580(U_20904,U_20903))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,U_20904,v_c,U_20903)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_5224_6]) ).

cnf(f_34_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_34_3]) ).

cnf(f_34_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_34_6]) ).

cnf(f_107_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_107_6]) ).

cnf(f_180_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_180_7]) ).

cnf(f_180_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_180_8]) ).

cnf(f_180_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_180_13]) ).

cnf(f_522_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_4]) ).

cnf(f_522_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_5]) ).

cnf(f_522_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_6]) ).

cnf(f_522_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_7]) ).

cnf(f_522_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_8]) ).

cnf(f_522_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_9]) ).

cnf(f_522_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_522_10]) ).

cnf(f_994_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_994_6]) ).

cnf(f_994_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_994_7]) ).

cnf(f_994_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_994_12]) ).

cnf(f_995_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_995_6]) ).

cnf(f_995_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_995_7]) ).

cnf(f_995_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_995_12]) ).

cnf(f_1018_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1018_5]) ).

cnf(f_1019_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1019_5]) ).

cnf(f_1035_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1035_6]) ).

cnf(f_1035_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1035_7]) ).

cnf(f_1035_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1035_12]) ).

cnf(f_1036_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1036_6]) ).

cnf(f_1036_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1036_7]) ).

cnf(f_1036_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1036_12]) ).

cnf(f_1094_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1094_5]) ).

cnf(f_1095_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1095_5]) ).

cnf(f_1096_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1096_5]) ).

cnf(f_1097_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1097_5]) ).

cnf(f_1098_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1098_6]) ).

cnf(f_1098_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1098_7]) ).

cnf(f_1098_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1098_12]) ).

cnf(f_1099_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1099_6]) ).

cnf(f_1099_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1099_7]) ).

cnf(f_1099_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1099_12]) ).

cnf(f_1100_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1100_6]) ).

cnf(f_1100_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1100_7]) ).

cnf(f_1100_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1100_12]) ).

cnf(f_1101_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1101_6]) ).

cnf(f_1101_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1101_7]) ).

cnf(f_1101_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1101_12]) ).

cnf(f_1102_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1102_6]) ).

cnf(f_1102_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1102_7]) ).

cnf(f_1102_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1102_12]) ).

cnf(f_1103_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1103_6]) ).

cnf(f_1103_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1103_7]) ).

cnf(f_1103_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1103_12]) ).

cnf(f_1104_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1104_6]) ).

cnf(f_1104_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1104_7]) ).

cnf(f_1104_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1104_12]) ).

cnf(f_1105_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1105_6]) ).

cnf(f_1105_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1105_7]) ).

cnf(f_1105_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1105_12]) ).

cnf(f_1301_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1301_7]) ).

cnf(f_1301_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1301_8]) ).

cnf(f_1301_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1301_13]) ).

cnf(f_1349_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1349_6]) ).

cnf(f_1491_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1491_3]) ).

cnf(f_1717_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1717_8]) ).

cnf(f_1855_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1855_6]) ).

cnf(f_1856_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1856_6]) ).

cnf(f_1869_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1869_3]) ).

cnf(f_1938_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1938_8]) ).

cnf(f_2390_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2390_3]) ).

cnf(f_2436_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2436_10]) ).

cnf(f_2436_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2436_11]) ).

cnf(f_2436_16_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2436_16]) ).

cnf(f_3642_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3642_3]) ).

cnf(f_3644_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3644_4]) ).

cnf(f_3740_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3740_6]) ).

cnf(f_3740_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3740_7]) ).

cnf(f_4057_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4057_8]) ).

cnf(f_4618_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4618_6]) ).

cnf(f_4955_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4955_4]) ).

cnf(f_4955_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4955_6]) ).

cnf(f_4956_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4956_4]) ).

cnf(f_4956_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4956_6]) ).

cnf(f_4957_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4957_3]) ).

cnf(f_4960_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4960_3]) ).

cnf(f_4961_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4961_3]) ).

cnf(f_4970_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4970_3]) ).

cnf(f_4971_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4971_3]) ).

cnf(f_4972_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4972_3]) ).

cnf(f_4977_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4977_3]) ).

cnf(f_4979_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4979_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_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_8,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hoare__Mirabelle_Otriple_Otriple(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_9,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_10,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hoare__Mirabelle_Otriple_Otriple__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_11,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hoare__Mirabelle_Otriple_Otriple__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_12,axiom,
    ( c_Com_Ocom_OSemi(Eq_x_0,Eq_x_1) = c_Com_Ocom_OSemi(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,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_14,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_15,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,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_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,axiom,
    ( c_Hoare__Mirabelle_Otriple_Otriple__size(Eq_x_0,Eq_x_1,Eq_x_2) = c_Hoare__Mirabelle_Otriple_Otriple__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_40,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_41,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_42,axiom,
    ( c_Com_Ocom_Ocom__size(Eq_x_0) = c_Com_Ocom_Ocom__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,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_44,axiom,
    ( c_Com_Ocom_OCond(Eq_x_0,Eq_x_1,Eq_x_2) = c_Com_Ocom_OCond(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_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_46,axiom,
    ( c_Com_Ocom_OLocal(Eq_x_0,Eq_x_1,Eq_x_2) = c_Com_Ocom_OLocal(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_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_48,axiom,
    ( c_Com_Ocom_OWhile(Eq_x_0,Eq_x_1) = c_Com_Ocom_OWhile(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,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_98,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,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_100,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_101,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,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_103,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_104,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_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,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_113,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_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,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_136,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_137,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_138,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_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_152,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_153,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_154,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_155,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_156,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_157,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_158,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_159,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_160,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_161,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_162,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_163,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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,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_183,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_184,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_185,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_186,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_187,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_188,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_189,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_190,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_191,axiom,
    ( c_Hoare__Mirabelle_Opeek__and(Eq_x_0,Eq_x_1,Eq_x_2) = c_Hoare__Mirabelle_Opeek__and(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_192,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_193,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_194,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_195,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_196,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_197,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_198,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_199,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_200,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_201,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_202,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_203,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_204,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_205,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_206,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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,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_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,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_254,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_255,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_256,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_257,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_258,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_259,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_260,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_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,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_307,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_308,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_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,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_318,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_319,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_320,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_321,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_322,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_323,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_324,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_325,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_326,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_327,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_328,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_329,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_330,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_331,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_332,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_333,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_334,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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(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,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK5(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,
    ( 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_345,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_346,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_347,axiom,
    ( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK13(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_352,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK14(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_353,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK15(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,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK16(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,
    ( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(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_356,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_357,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(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_358,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_359,axiom,
    ( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK23(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,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK24(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,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK25(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,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK26(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_365,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_366,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_367,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_368,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK30(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_369,axiom,
    ( sK31(Eq_x_0,Eq_x_1) = sK31(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,
    ( 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_371,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_372,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK34(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_373,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK35(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_374,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(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,
    ( 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_376,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_377,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(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_378,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(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_379,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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_380,axiom,
    ( sK42(Eq_x_0,Eq_x_1) = sK42(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,
    ( 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_382,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(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_383,axiom,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(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_384,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_385,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK47(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_386,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK48(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_387,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK49(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_388,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK50(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_389,axiom,
    ( sK51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK51(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_390,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(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,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(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,
    ( 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_393,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK55(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_394,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK56(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_395,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK57(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_396,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK58(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,
    ( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK60(Eq_x_0) = sK60(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,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_400,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_401,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_402,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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_403,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_404,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(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,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK67(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_406,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(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,
    ( 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_408,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(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,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK71(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_410,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK72(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,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK73(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_412,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_413,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_414,axiom,
    ( sK76(Eq_x_0,Eq_x_1) = sK76(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,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK77(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_416,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_417,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK79(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_418,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(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_419,axiom,
    ( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(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_420,axiom,
    ( sK82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK82(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_421,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_422,axiom,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK84(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_423,axiom,
    ( sK85(Eq_x_0,Eq_x_1,Eq_x_2) = sK85(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_424,axiom,
    ( sK86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK86(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_425,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK87(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_426,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_427,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_428,axiom,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2) = sK90(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_429,axiom,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(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_430,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(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,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(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_432,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_433,axiom,
    ( sK95(Eq_x_0) = sK95(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_434,axiom,
    ( sK96(Eq_x_0) = sK96(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_435,axiom,
    ( sK97(Eq_x_0) = sK97(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_436,axiom,
    ( sK98(Eq_x_0) = sK98(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_437,axiom,
    ( sK99(Eq_x_0,Eq_x_1) = sK99(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_438,axiom,
    ( sK100(Eq_x_0,Eq_x_1) = sK100(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_439,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_440,axiom,
    ( sK102(Eq_x_0,Eq_x_1) = sK102(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK103(Eq_x_0,Eq_x_1) = sK103(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,
    ( sK104(Eq_x_0,Eq_x_1) = sK104(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,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK105(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_444,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(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_445,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_446,axiom,
    ( sK108(Eq_x_0) = sK108(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK109(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_448,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2) = sK110(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_449,axiom,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(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,
    ( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(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_451,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2) = sK113(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_452,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2) = sK114(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_453,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK115(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_454,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK116(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_455,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_456,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2) = sK118(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_457,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2) = sK119(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_458,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2) = sK120(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_459,axiom,
    ( sK121(Eq_x_0,Eq_x_1) = sK121(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_460,axiom,
    ( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_461,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2) = sK123(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_462,axiom,
    ( sK124(Eq_x_0,Eq_x_1,Eq_x_2) = sK124(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_463,axiom,
    ( sK125(Eq_x_0) = sK125(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_464,axiom,
    ( sK126(Eq_x_0) = sK126(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_465,axiom,
    ( sK127(Eq_x_0) = sK127(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_466,axiom,
    ( sK128(Eq_x_0) = sK128(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_467,axiom,
    ( sK129(Eq_x_0,Eq_x_1) = sK129(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_468,axiom,
    ( sK130(Eq_x_0,Eq_x_1,Eq_x_2) = sK130(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,
    ( 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_470,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2) = sK132(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_471,axiom,
    ( sK133(Eq_x_0,Eq_x_1,Eq_x_2) = sK133(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,
    ( sK134(Eq_x_0,Eq_x_1,Eq_x_2) = sK134(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,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2) = sK135(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,
    ( 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_475,axiom,
    ( sK137(Eq_x_0,Eq_x_1,Eq_x_2) = sK137(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_476,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2) = sK138(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_477,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_478,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_479,axiom,
    ( sK141(Eq_x_0) = sK141(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_480,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2) = sK142(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_481,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2) = sK143(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,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2) = sK144(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_483,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2) = sK145(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_484,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(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,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2) = sK147(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,
    ( sK148(Eq_x_0,Eq_x_1) = sK148(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_487,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_488,axiom,
    ( sK150(Eq_x_0,Eq_x_1,Eq_x_2) = sK150(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_489,axiom,
    ( sK151(Eq_x_0,Eq_x_1,Eq_x_2) = sK151(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_490,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_491,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_492,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2) = sK154(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_493,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2) = sK155(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_494,axiom,
    ( sK156(Eq_x_0,Eq_x_1,Eq_x_2) = sK156(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_495,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2) = sK157(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_496,axiom,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2) = sK158(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_497,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2) = sK159(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_498,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2) = sK160(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_499,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2) = sK161(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_500,axiom,
    ( sK162(Eq_x_0,Eq_x_1,Eq_x_2) = sK162(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,
    ( sK163(Eq_x_0,Eq_x_1,Eq_x_2) = sK163(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,
    ( sK164(Eq_x_0) = sK164(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_503,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_504,axiom,
    ( sK166(Eq_x_0) = sK166(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_505,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_506,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK168(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_507,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK169(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_508,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_509,axiom,
    ( sK171(Eq_x_0,Eq_x_1) = sK171(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_510,axiom,
    ( sK172(Eq_x_0,Eq_x_1) = sK172(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_511,axiom,
    ( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_512,axiom,
    ( sK174(Eq_x_0,Eq_x_1) = sK174(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_513,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_514,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_515,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK177(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_516,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK178(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_517,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK179(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_518,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK180(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_519,axiom,
    ( sK181(Eq_x_0,Eq_x_1) = sK181(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_520,axiom,
    ( sK182(Eq_x_0,Eq_x_1) = sK182(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_521,axiom,
    ( sK183(Eq_x_0,Eq_x_1) = sK183(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_522,axiom,
    ( sK184(Eq_x_0,Eq_x_1) = sK184(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_523,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_524,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK186(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_525,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK187(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_526,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK188(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_527,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK189(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_528,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK190(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_529,axiom,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK191(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_530,axiom,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK192(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_531,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2) = sK193(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_532,axiom,
    ( sK194(Eq_x_0,Eq_x_1,Eq_x_2) = sK194(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_533,axiom,
    ( sK195(Eq_x_0,Eq_x_1,Eq_x_2) = sK195(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_534,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_535,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK197(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_536,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK198(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_537,axiom,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK199(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_538,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK200(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_539,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK201(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_540,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK202(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_541,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK203(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_542,axiom,
    ( sK204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK204(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_543,axiom,
    ( sK205(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK205(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_544,axiom,
    ( sK206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK206(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_545,axiom,
    ( sK207(Eq_x_0,Eq_x_1) = sK207(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_546,axiom,
    ( sK208(Eq_x_0,Eq_x_1) = sK208(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_547,axiom,
    ( sK209(Eq_x_0,Eq_x_1) = sK209(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_548,axiom,
    ( sK210(Eq_x_0,Eq_x_1) = sK210(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,
    ( sK211(Eq_x_0,Eq_x_1) = sK211(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_550,axiom,
    ( sK212(Eq_x_0,Eq_x_1) = sK212(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_551,axiom,
    ( sK213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK213(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_552,axiom,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK214(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_553,axiom,
    ( sK215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK215(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_554,axiom,
    ( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK216(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_555,axiom,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK217(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_556,axiom,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK218(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_557,axiom,
    ( sK219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK219(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_558,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK220(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_559,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK221(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_560,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK222(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_561,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK223(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_562,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK224(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_563,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK225(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_564,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK226(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_565,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK227(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_566,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK228(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_567,axiom,
    ( sK229(Eq_x_0,Eq_x_1) = sK229(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_568,axiom,
    ( sK230(Eq_x_0,Eq_x_1) = sK230(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_569,axiom,
    ( sK231(Eq_x_0,Eq_x_1) = sK231(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_570,axiom,
    ( sK232(Eq_x_0,Eq_x_1) = sK232(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_571,axiom,
    ( sK233(Eq_x_0,Eq_x_1) = sK233(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_572,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_573,axiom,
    ( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK235(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_574,axiom,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2) = sK236(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_575,axiom,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2) = sK237(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_576,axiom,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK238(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_577,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_578,axiom,
    ( sK240(Eq_x_0,Eq_x_1,Eq_x_2) = sK240(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_579,axiom,
    ( sK241(Eq_x_0,Eq_x_1,Eq_x_2) = sK241(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_580,axiom,
    ( sK242(Eq_x_0) = sK242(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_581,axiom,
    ( sK243(Eq_x_0,Eq_x_1,Eq_x_2) = sK243(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,
    ( sK244(Eq_x_0,Eq_x_1,Eq_x_2) = sK244(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,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2) = sK245(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,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2) = sK246(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,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2) = sK247(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,
    ( 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_587,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_588,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_589,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_590,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_591,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_592,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_593,axiom,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK255(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_594,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK256(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_595,axiom,
    ( sK257(Eq_x_0) = sK257(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_596,axiom,
    ( sK258(Eq_x_0) = sK258(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_597,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK259(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_598,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK260(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_599,axiom,
    ( sK261(Eq_x_0) = sK261(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_600,axiom,
    ( sK262(Eq_x_0) = sK262(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_601,axiom,
    ( sK263(Eq_x_0) = sK263(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_602,axiom,
    ( sK264(Eq_x_0) = sK264(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_603,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK265(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_604,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK266(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_605,axiom,
    ( sK267(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) = sK267(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_606,axiom,
    ( sK268(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) = sK268(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_607,axiom,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK269(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_608,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK270(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_609,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK271(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_610,axiom,
    ( sK272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK272(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_611,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK273(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_612,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_613,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK275(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_614,axiom,
    ( sK276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK276(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_615,axiom,
    ( sK277(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK277(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_616,axiom,
    ( sK278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK278(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_617,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_618,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_619,axiom,
    ( sK281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK281(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_620,axiom,
    ( sK282(Eq_x_0,Eq_x_1,Eq_x_2) = sK282(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_621,axiom,
    ( sK283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK283(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_622,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK284(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_623,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK285(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,
    ( sK286(Eq_x_0,Eq_x_1) = sK286(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_625,axiom,
    ( sK287(Eq_x_0) = sK287(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_626,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK288(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_627,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK289(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_628,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK290(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_629,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK291(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_630,axiom,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK292(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,
    ( 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_632,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK294(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_633,axiom,
    ( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK295(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_634,axiom,
    ( sK296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK296(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_635,axiom,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK297(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_636,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2) = sK298(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_637,axiom,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK299(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_638,axiom,
    ( sK300(Eq_x_0,Eq_x_1,Eq_x_2) = sK300(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_639,axiom,
    ( sK301(Eq_x_0) = sK301(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_640,axiom,
    ( sK302(Eq_x_0) = sK302(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_641,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_642,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_643,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK305(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_644,axiom,
    ( sK306(Eq_x_0,Eq_x_1) = sK306(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_645,axiom,
    ( sK307(Eq_x_0,Eq_x_1) = sK307(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_646,axiom,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK308(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,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK309(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_648,axiom,
    ( sK310(Eq_x_0,Eq_x_1) = sK310(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,
    ( sK311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK311(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_650,axiom,
    ( sK312(Eq_x_0,Eq_x_1) = sK312(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_651,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2) = sK313(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_652,axiom,
    ( sK314(Eq_x_0,Eq_x_1) = sK314(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_653,axiom,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK315(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_654,axiom,
    ( sK316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK316(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_655,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_656,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_657,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_658,axiom,
    ( sK320(Eq_x_0,Eq_x_1) = sK320(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_659,axiom,
    ( sK321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK321(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_660,axiom,
    ( sK322(Eq_x_0,Eq_x_1,Eq_x_2) = sK322(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_661,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_662,axiom,
    ( sK324(Eq_x_0,Eq_x_1,Eq_x_2) = sK324(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_663,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_664,axiom,
    ( sK326(Eq_x_0) = sK326(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_665,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_666,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_667,axiom,
    ( sK329(Eq_x_0,Eq_x_1) = sK329(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_668,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2) = sK330(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_669,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2) = sK331(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_670,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_671,axiom,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK333(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_672,axiom,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK334(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_673,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK335(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_674,axiom,
    ( sK336(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK336(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_675,axiom,
    ( sK337(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK337(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,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK338(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,
    ( sK339(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK339(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_678,axiom,
    ( sK340(Eq_x_0,Eq_x_1) = sK340(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_679,axiom,
    ( sK341(Eq_x_0,Eq_x_1) = sK341(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,
    ( sK342(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK342(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_681,axiom,
    ( sK343(Eq_x_0,Eq_x_1,Eq_x_2) = sK343(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_682,axiom,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2) = sK344(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,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK345(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_684,axiom,
    ( sK346(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK346(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_685,axiom,
    ( sK347(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK347(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,
    ( sK348(Eq_x_0,Eq_x_1,Eq_x_2) = sK348(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_687,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2) = sK349(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_688,axiom,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK350(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_689,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK351(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_690,axiom,
    ( sK352(Eq_x_0,Eq_x_1,Eq_x_2) = sK352(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_691,axiom,
    ( sK353(Eq_x_0,Eq_x_1) = sK353(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_692,axiom,
    ( sK354(Eq_x_0,Eq_x_1) = sK354(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_693,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2) = sK355(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_694,axiom,
    ( sK356(Eq_x_0,Eq_x_1) = sK356(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,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK357(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_696,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2) = sK358(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_697,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_698,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_699,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2) = sK361(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,
    ( sK362(Eq_x_0,Eq_x_1,Eq_x_2) = sK362(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,
    ( sK363(Eq_x_0,Eq_x_1) = sK363(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_702,axiom,
    ( sK364(Eq_x_0,Eq_x_1,Eq_x_2) = sK364(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,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2) = sK365(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_704,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK366(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_705,axiom,
    ( sK367(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK367(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_706,axiom,
    ( sK368(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK368(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,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK369(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,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK370(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,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK371(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,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK372(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,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK373(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,
    ( 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_713,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_714,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_715,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK377(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_716,axiom,
    ( sK378(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK378(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_717,axiom,
    ( sK379(Eq_x_0,Eq_x_1) = sK379(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_718,axiom,
    ( sK380(Eq_x_0,Eq_x_1) = sK380(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_719,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_720,axiom,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK382(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_721,axiom,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK383(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_722,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK384(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_723,axiom,
    ( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK385(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_724,axiom,
    ( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK386(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,
    ( 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_726,axiom,
    ( sK388(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK388(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_727,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK389(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_728,axiom,
    ( sK390(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK390(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_729,axiom,
    ( sK391(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK391(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,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK392(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,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK393(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,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK394(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_733,axiom,
    ( sK395(Eq_x_0,Eq_x_1,Eq_x_2) = sK395(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_734,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_735,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK397(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,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2) = sK398(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,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2) = sK399(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_738,axiom,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2) = sK400(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,
    ( sK401(Eq_x_0,Eq_x_1,Eq_x_2) = sK401(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,
    ( 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_741,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2) = sK403(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,
    ( sK404(Eq_x_0) = sK404(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_743,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_744,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK406(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_745,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK407(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,
    ( sK408(Eq_x_0,Eq_x_1) = sK408(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_747,axiom,
    ( sK409(Eq_x_0,Eq_x_1) = sK409(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_748,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_749,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_750,axiom,
    ( sK412(Eq_x_0,Eq_x_1,Eq_x_2) = sK412(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_751,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK413(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_752,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK414(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_753,axiom,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK415(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,
    ( sK416(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK416(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,
    ( sK417(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK417(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_756,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_757,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK419(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,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK420(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,
    ( 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_760,axiom,
    ( sK422(Eq_x_0,Eq_x_1) = sK422(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_761,axiom,
    ( sK423(Eq_x_0,Eq_x_1,Eq_x_2) = sK423(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_762,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2) = sK424(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_763,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2) = sK425(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,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2) = sK426(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,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK427(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_766,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK428(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_767,axiom,
    ( sK429(Eq_x_0,Eq_x_1,Eq_x_2) = sK429(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_768,axiom,
    ( sK430(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK430(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,
    ( sK431(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK431(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_770,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK432(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,
    ( sK433(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK433(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_772,axiom,
    ( sK434(Eq_x_0,Eq_x_1) = sK434(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_773,axiom,
    ( sK435(Eq_x_0,Eq_x_1) = sK435(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_774,axiom,
    ( sK436(Eq_x_0,Eq_x_1,Eq_x_2) = sK436(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_775,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_776,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2) = sK438(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,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2) = sK439(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,
    ( sK440(Eq_x_0,Eq_x_1) = sK440(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_779,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2) = sK441(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,
    ( sK442(Eq_x_0,Eq_x_1,Eq_x_2) = sK442(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_781,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2) = sK443(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,
    ( 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_783,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_784,axiom,
    ( sK446(Eq_x_0,Eq_x_1) = sK446(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_785,axiom,
    ( sK447(Eq_x_0,Eq_x_1) = sK447(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_786,axiom,
    ( sK448(Eq_x_0,Eq_x_1,Eq_x_2) = sK448(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_787,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_788,axiom,
    ( sK450(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK450(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_789,axiom,
    ( sK451(Eq_x_0,Eq_x_1) = sK451(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_790,axiom,
    ( sK452(Eq_x_0,Eq_x_1) = sK452(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_791,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_792,axiom,
    ( sK454(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK454(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_793,axiom,
    ( sK455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK455(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_794,axiom,
    ( sK456(Eq_x_0,Eq_x_1) = sK456(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_795,axiom,
    ( sK457(Eq_x_0,Eq_x_1) = sK457(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_796,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK458(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_797,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_798,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_799,axiom,
    ( sK461(Eq_x_0,Eq_x_1) = sK461(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,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK462(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_801,axiom,
    ( sK463(Eq_x_0,Eq_x_1) = sK463(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,
    ( 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_803,axiom,
    ( sK465(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK465(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_804,axiom,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK466(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_805,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_806,axiom,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK468(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_807,axiom,
    ( sK469(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK469(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_808,axiom,
    ( sK470(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK470(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_809,axiom,
    ( sK471(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK471(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,
    ( sK472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK472(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_811,axiom,
    ( sK473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK473(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,
    ( 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_813,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK475(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_814,axiom,
    ( sK476(Eq_x_0,Eq_x_1) = sK476(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_815,axiom,
    ( sK477(Eq_x_0,Eq_x_1) = sK477(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_816,axiom,
    ( sK478(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK478(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_817,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2) = sK479(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_818,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2) = sK480(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_819,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2) = sK481(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,
    ( sK482(Eq_x_0,Eq_x_1,Eq_x_2) = sK482(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,
    ( sK483(Eq_x_0,Eq_x_1,Eq_x_2) = sK483(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,
    ( sK484(Eq_x_0,Eq_x_1,Eq_x_2) = sK484(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,
    ( sK485(Eq_x_0,Eq_x_1,Eq_x_2) = sK485(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,
    ( sK486(Eq_x_0,Eq_x_1,Eq_x_2) = sK486(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,
    ( 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_826,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_827,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_828,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_829,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_830,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_831,axiom,
    ( sK493(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK493(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_832,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK494(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_833,axiom,
    ( sK495(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK495(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,
    ( 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_835,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_836,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK498(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_837,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_838,axiom,
    ( sK500(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK500(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_839,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_840,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_841,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_842,axiom,
    ( sK504(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK504(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,
    ( sK505(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK505(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,
    ( sK506(Eq_x_0,Eq_x_1,Eq_x_2) = sK506(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_845,axiom,
    ( sK507(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK507(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_846,axiom,
    ( sK508(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK508(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_847,axiom,
    ( sK509(Eq_x_0,Eq_x_1) = sK509(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_848,axiom,
    ( sK510(Eq_x_0,Eq_x_1,Eq_x_2) = sK510(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_849,axiom,
    ( sK511(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK511(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_850,axiom,
    ( sK512(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK512(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_851,axiom,
    ( sK513(Eq_x_0,Eq_x_1,Eq_x_2) = sK513(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_852,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_853,axiom,
    ( sK515(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK515(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_854,axiom,
    ( sK516(Eq_x_0) = sK516(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_855,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_856,axiom,
    ( sK518(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK518(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,
    ( sK519(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK519(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_858,axiom,
    ( sK520(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK520(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_859,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_860,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_861,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_862,axiom,
    ( sK524(Eq_x_0,Eq_x_1) = sK524(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_863,axiom,
    ( sK525(Eq_x_0,Eq_x_1) = sK525(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_864,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_865,axiom,
    ( sK527(Eq_x_0,Eq_x_1) = sK527(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,
    ( sK528(Eq_x_0,Eq_x_1) = sK528(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,
    ( sK529(Eq_x_0) = sK529(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_868,axiom,
    ( sK530(Eq_x_0) = sK530(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_869,axiom,
    ( sK531(Eq_x_0) = sK531(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_870,axiom,
    ( sK532(Eq_x_0) = sK532(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_871,axiom,
    ( sK533(Eq_x_0) = sK533(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_872,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_873,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_874,axiom,
    ( sK536(Eq_x_0,Eq_x_1,Eq_x_2) = sK536(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_875,axiom,
    ( sK537(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK537(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_876,axiom,
    ( sK538(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK538(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_877,axiom,
    ( sK539(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK539(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_878,axiom,
    ( sK540(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK540(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,
    ( sK541(Eq_x_0,Eq_x_1) = sK541(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_880,axiom,
    ( sK542(Eq_x_0) = sK542(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_881,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_882,axiom,
    ( sK544(Eq_x_0) = sK544(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_883,axiom,
    ( sK545(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK545(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_884,axiom,
    ( sK546(Eq_x_0,Eq_x_1) = sK546(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_885,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_886,axiom,
    ( sK548(Eq_x_0,Eq_x_1) = sK548(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_887,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_888,axiom,
    ( sK550(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK550(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_889,axiom,
    ( sK551(Eq_x_0,Eq_x_1,Eq_x_2) = sK551(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_890,axiom,
    ( sK552(Eq_x_0,Eq_x_1,Eq_x_2) = sK552(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_891,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_892,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_893,axiom,
    ( sK555(Eq_x_0,Eq_x_1,Eq_x_2) = sK555(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,
    ( sK556(Eq_x_0,Eq_x_1,Eq_x_2) = sK556(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,
    ( 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_896,axiom,
    ( sK558(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK558(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_897,axiom,
    ( sK559(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK559(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_898,axiom,
    ( sK560(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK560(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_899,axiom,
    ( sK561(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK561(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_900,axiom,
    ( sK562(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK562(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_901,axiom,
    ( sK563(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK563(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,
    ( sK564(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK564(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,
    ( sK565(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK565(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,
    ( sK566(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK566(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,
    ( sK567(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK567(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,
    ( sK568(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK568(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,
    ( sK569(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK569(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_908,axiom,
    ( sK570(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK570(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_909,axiom,
    ( sK571(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK571(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_910,axiom,
    ( sK572(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK572(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_911,axiom,
    ( sK573(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK573(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_912,axiom,
    ( sK574(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK574(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_913,axiom,
    ( sK575(Eq_x_0,Eq_x_1,Eq_x_2) = sK575(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_914,axiom,
    ( sK576(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK576(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_915,axiom,
    ( sK577(Eq_x_0,Eq_x_1,Eq_x_2) = sK577(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_916,axiom,
    ( sK580(Eq_x_0,Eq_x_1) = sK580(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_917,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_918,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_919,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_920,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_921,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_922,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_923,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_924,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_925,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_926,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_927,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_928,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_929,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_930,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_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,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_939,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_940,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_941,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_942,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_943,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_944,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_945,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_946,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_947,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_948,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_949,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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,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_961,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_962,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_963,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_964,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_965,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_966,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_967,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_968,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_969,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_970,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_971,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_972,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_973,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_974,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_975,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_976,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_977,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_978,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_979,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_980,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_981,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_982,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_983,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_984,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_985,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_986,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_987,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_988,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_989,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_990,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_991,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_992,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_993,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_994,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_995,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_996,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_997,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_998,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_999,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_1000,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_1001,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_1002,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_1003,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_1004,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_1005,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_1006,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_1007,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_1008,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_1009,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_1010,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_1011,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_1012,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_1013,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_1014,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_1015,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_1016,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_1017,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_1018,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_1019,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_1020,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_1021,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_1022,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_1023,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_1024,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_1025,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_1026,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_1027,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_1028,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_1029,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_1030,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_1031,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_1032,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_1033,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_1034,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_1035,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_1036,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_1037,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_1038,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_1039,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_1040,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_1041,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_1042,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_1043,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_1044,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_1045,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_1046,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_1047,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_1048,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_1049,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_1050,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_1051,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_1052,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_1053,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_1054,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_1055,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_1056,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_1057,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_1058,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_1059,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_1060,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_1061,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(equality_1062,axiom,
    ( v_P(Eq_y_0,Eq_y_1)
    | ~ v_P(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,
    ( v_Q(Eq_y_0,Eq_y_1)
    | ~ v_Q(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | 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  : SWW299+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03  This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n006.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Sun Sep 20 05:20:43 UTC 2026
% 0.10/0.36  % CPUTime  : 
% 107.35/107.65  % SZS status Theorem for theBenchmark
% 107.35/107.65  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------